MEKANIKA REKAYASA - YuLiana Margaretha · PDF file– Statika : obyek yang dikenai gaya...

MEKANIKA REKAYASA

llmu Rekayasa Klasik Sebagai Sarana Menguasai Program Aplikasi Rekayasa

Masih perlukah mempelajari Mekanika Teknik Klasik dalam Era Serba Komputer

Studi kasus Mekanika Teknik Klasik dan Program Rekayasa

Mekanika Teknik (MT) cong Mekanika Rekaya congAnalisa Struktur cong Structural Analysis

bull10487081048708 MT Mata kuliah wajib di S1 teknik sipilbull10487081048708 Isi MT mayoritas metoda klasik manualbull10487081048708 Pemahaman tentang MTsangat membantu profesi bidang

rekayasa konstruksibull10487081048708 MT cara manual jarang dipakai di dunia kerja karena

digantikan dengan program komputer (kecuali struktur yang lsquosederhanarsquo)

bull10487081048708 MT melatih mahasiswa memahami perilaku gaya gaya aksi reaksi pada struktur bangunan

Program Aplikasi Komputer untukRekayasa (Analisa Struktur)

Sangat canggih mudah pengoperasiannya menu yg user-friendly seperti Windows

Relatif mudah didapat dari yang mahal atau murah bahkan ada yang gratis di internet (di down-load)

Andalan insinyur untuk perencanaan struktur yang sebenarnya

Perkembangan dunia komputer sangat pesat dan berimbas juga ke dunia rekayasa konstruksi

Dampak ke profesi engineer

Apakah profesi insinyur (sipil) yang hampir selalu berkecimpung dengan pekerjaan hitung-menghitung juga dapat diganti komputer

Hardware semakin murah software ada kecenderungan ope source (gratis)

Apakah jika telah membeli atau mempunyai piranti yang dimaksud maka penyelesaian mekanika teknik secara otomatis dapat diperoleh

PEMODELAN STRUKTUR

October 6 2009

Relly Andayani

Structural Types

Continous Beam

Structural Types

Cable Stayed

Structural TypesChimney

TrussStructural Types

Suspension BridgeStructural Types

Retaining Wall

Structural Types

Structural TypesDamm

STRUCTURAL TYPES Truss

LOADSConcentrate Load

LOADSSpread Load

LOADS

Howhellip

helliphelliphelliphellip

Structural ModelsContinous Beam


Structural ModelsCable Stayed

Cable Stayed

Structural Models

Chimney

Structural Models

ChimneyStructural Models

Truss

Structural Models

Truss

Structural Models

Suspension Bridge

Structural Models

Suspension Bridge

Structural Models

Retaining Wall

Structural Models

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models

Structural Models Truss

Truss

Structural Models


Concentrate LoadLOADS

LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed

BEARINGLink SupportPendel




bull Gaya adalah interaksi antara benda-benda yang berpengaruh terhadap bentuk atau gerak atau keduanya pada benda yang terlibat

bull Gaya adalah besaran vektor ndash Besar (magnitude) ndash Arah (direction and sense) ndash Titik tangkap (point of application)

bull Satuan gaya SI units N (Newton) kN (kilo Newton = 1000 Newton)

US units pound (lb ) kip (k) = 1000 pound

GAYA

bull Bagaimana beban mempengaruhi struktur

ndash Statika obyek yang dikenai gaya berada dalam keseimbangan (tidak bergerak tidak ada percepatan) bull Gaya-gaya bull Tumpuan dan hubungan bull Keseimbangan ndash Mekanika obyek yang dikenai gaya dapat berubah bentuk bull Tegangan dan regangan bull Defleksi bull Tekuk

Mekanika dan Statika

bull Presentasi gaya ndash Secara matematis ndash Secara grafis bull Secara grafis ndash sebagai garis bull panjang garis AElig besar gaya bull arah garis AElig arah gaya bull garis kerja AElig garis yang panjangnya tak tertentu yang terdapat pada vektor gaya tersebut

Besar gaya L Newton misal jika 1 Newton digambarkan dengan panjang garis 1 cm maka 4 Newton asymp 4 cm Arah gaya dinyatakan dalam tg atau besar sudut α (deg) x y

GAYA

bull Garis kerja gaya ndash garis yang panjangnya tak tertentu yang terdapat pada vektor gaya tersebut bull Titik tangkap suatu gaya dapat dipindahkan ke titik lain yang terletak pada garis kerjanya tanpa mengubah efek translational dan rotasional dari gaya terhadap benda yang dibebani bull Gaya yang bekerja pada benda tegar dapat dipandang bekerja di MANA SAJA di sepanjang garis kerjanya

GAYA

SISTEM GAYA

bull Macam sistem gaya ndash collinear ndash coplanar

bull Concurrent bull Parallel bull Non-concurrent non-paralel

ndash space bull Noncoplanar parallel bull Noncoplanar concurrent bull Noncoplanar nonconcurrent

SISTEM GAYA

SISTEM GAYA

SISTEM GAYA

bull Resultan gayandash Dua atau lebih gaya yang taksejajardapat dijadikan sederhana menjadi saturesultan gaya tanpa mengubah efektranslasional maupun rotasional ygditimbulkannyapada benda dimanagaya-gaya tsb bekerja AElig pengaruh kombinasi gaya-gaya tsbsetara dgn pengaruh satu gaya yang disebut sebagai resultan gaya-gaya tsb

bull Cara mencari besar dan arahresultan gaya ndash Paralellogramjajaran genjang gaya

atau segitiga gayandash Polygon gayandash aljabar

RESULTAN GAYA

F1

F2

R

φ

Find Resultante of two forces

Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B

bull Metoda paralellogramjajaran genjang gaya

ndash Resultan gaya dinyatakan dgn diagonal jajaran genjang yg dibentuk oleh kedua vektorgaya

RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA

Mencari resultan gaya-gayaMetoda paralellogram jajaran genjang gaya

R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1

Tiga gaya Resultan gaya final

Mencari resultan gaya-gaya Metoda polygon gayaMasing-masing vektor gaya digambar berskala dan salingmenyambung (ujung disambung dengan pangkal urutan tidakpenting) Garis penutup yaitu garis yang berawal dari titik awalvektor pertama ke titik akhir vektor terakhir merupakan gayaresultan dari semua vektor tsb gaya resultan tersebut menutuppoligon gaya

RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R

Dua Gaya ldquoTIP TO TAILrdquo TECHNIQUE

Mencari resultan gaya-gaya Cara aljabar

RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α

Resolusi gaya Adalah penguraian gaya menjadi komponen-komponennya

KOMPONEN GAYA

Gaya F Komponen gaya-gaya F1 dan F2

Komponen gaya-gaya F1 dan F2

φ

F

F1

F2 F2

F11

2

Mencari komponen gaya Cara grafis

KOMPONEN GAYA

F1 dan F2 adalah komponen gaya dari gaya FSebuah gaya dapat diuraikan menjadi sistem komponen gaya yang berbeda-beda

Force FForce F Force F

F1

F1F1

F2 F2F2

Mencari komponen gaya Cara aljabar

KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT

Equilibrant Gaya penyeimbang sama besar tetapi berlawanan arah denganresultan

Equilibrant menyeimbangkan sejumlah gaya-gaya denganmenutup poligon gaya sbquotip-to-taillsquo atau sbquohead-to-taillsquo

Force B

Forc

e A Equilibriant

Resultan

Equilibriant

KESEIMBANGAN STATIS Jika struktur tidak dikenai gaya struktur tersebut dapat dikatakandalam keadaan diam

KESEIMBANGAN

Struktur tidak dikenai gaya Struktur diam

Jika struktur dikenaisebuah atau sekelompokgaya yang mempunyairesultan struktur akanbergerak (mengalamipercepatan) yang disebabkan oleh gaya-gaya tersebut Arah darigerakannya sama dengandengan garis kerja sebuahgaya atau resultan darisekelompok gaya tsb Besarnya percepatantegantung dari hubunganantara massa strukturdengan besarnya gaya

KESEIMBANGAN

Struktur dikenai ndua gaya yang mempunyai resultan

RotasiOverturning tergulingTranslasisliding

F1

F2 R

R

F1

F2

Jika struktur dikenai sekumpulan gaya yang tidak mempunyairesultan yaitu sekumpulan gaya yang membentuk segitigagaya atau poligon gaya yang tertutup struktur tersebut dapattetap diam dalam keadaan kesetimbangan statis

KESEIMBANGAN STATIS

1 Struktur dikenai 3 gaya

F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3

2 R adalah resultan dari gaya F1 dan F2 R dan F3 saling meniadakan (F3 adalah equilibriant dari gaya resultan R)

3 F1 F3 dan F3 membentuk segitiga gaya (poligon gaya) tertutup

Secara grafis

Resultan = 0 dengan metode sbquotail-to-tiplsquo sistem gaya-gaya merupakan poligon tertutup

KESEIMBANGAN

KESEIMBANGAN BENDA TEGAR

Kondisi keseimbangan Semua gaya eksternal yang bekerja pada benda tegar membentuksistem gaya-gaya yang ekuivalen dengan 0 (zero) Tidak terjaditranslasi maupun rotasi

Secara analitis

KESEIMBANGAN

Keseimbangan translasionalbull Total dari seluruh komponen vertikal seluruh gaya = 0

ΣFv = 0

bull Total dari seluruh komponen gaya horisontal dari seluruh gaya = 0ΣFH = 0

Keseimbangan rotasionalbull Total dari seluruh momen dari seluruh gaya = 0

ΣM = 0

KESEIMBANGAN

Keseimbangan sistem gaya collinear

Keseimbangan sistem gaya concurrent

Gaya-gaya berada pada satu garis kerjaSeimbang jika

R = ΣF = 0

Gaya-gaya berada melalui satu titik yang samaSeimbang jika

Rx = ΣFx = 0Ry = ΣFy = 0

KESEIMBANGANSistem dua gayaDua gaya bekerja pada suatu benda berada dalam keseimbangan jikabull kedua gaya collinearbull Besar dua gaya sama tapi berlawanan arah

Sistem tiga gayaTiga gaya bekerja pada suatu benda berada dalam keseimbangan jikabull ketiga gaya concurrent (garis kerja ketiga gaya bertemu pada satu titikbull satu gaya merupakan equilibriant dari dua gaya yang lain (berarti bahwa gaya resultan dari ketiga gaya = 0bull Secara grafis (tail-to-tiprdquo) sistem tiga gaya tersebut merupakan poligon tertutup

KESEIMBANGANJika gaya-gaya pada benda bebas lebih dari tigabull Uraikan semua gaya dalam komponen-komponen gaya arah V atau arah (x) dan arah H atau arah (y)bull Tuliskan persamaan keseimbangan (ΣFv = 0 dan ΣFH = 0)bull Selesaikan persamaan secara simulta

Contoh

Tentukan gaya tarik pada kabel BA BC CD dan CE jika W = 10 kN

W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB

JawabTinjau keseimbangan pada titik BGaya pada kabel BA BC dan beban W merupakan sistem 3 gaya concurrent

Syarat keseimbanganDengan metoda ldquoTip-to-Tailrdquo ketiga gaya merupakan poligon tertutup

AB = CB cos 3010 = CB sin 30CB = 20 kNAB = 173 kN

Dengan metoda analitisΣ FH = -10 + CB sin 30 = 0CB = 20 kNΣFv = -AB + CB cos 30 = 0AB = 173 kN

KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5

Tinjau keseimbangan di titik C

Dengan metoda analitisΣFv = -20 sin 30 + CE x 45 = 0CE = 125 kNΣFH = -20 cos 30 ndash CE x 35 + CD = 0 CD = 248 kN

KESEIMBANGAN

Sistem multi gaya

Sistem multi gaya disederhanakan menjadi satu gaya resultan dan dua gaya reaksi tumpuan

Gaya-gaya eksternal yang bekerja pada struktur harus digantikan oleh satu gaya yaitu gata resultannya

Sehingga sistem multi gaya bisa disederhanakan menjadi sistem tiga gaya Resultan

Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV

STRUKTUR RANGKA BATANG

Asumsi Terdiri dari batang-batang struktur yang dihubungkan

satu sama lain dengan sendi tanpa ada pergesekan Gaya-gaya bekerja pada titik-titik simpul Gaya yang bekerja pada titik simpul didistribusikan ke

anggota rangka batang menurut sumbu batang Jika gaya batang menyebabkan batang bertambah

panjang batang tersebut menahan gaya tarik (positif) dan sebaliknya jika gaya batang menyebabkan batang bertambah pendek batang tersebut menahan gaya tekan (negatif)

Perubahan panjang akibat gaya yang bekerja diabaikan

Ciri-ciri rangka batang yang stabil

Tidak Stabil

Stabil

Ketentuan untuk Rangka Batang

Jika ditambahkan titik simpul sebanyak = s

Dibutuhkan tambahan batang (n) = 2 x s

Jika jumlah titik simpul = j maka tambahan titik yang baru = j - 3

Banyaknya batang tambahan = 2 x ( j ndash 3 )

Jumlah batang total (m) = 3 + 2 x ( j ndash 3 ) = 2j - 3

Pada contoh di atas m = 2 x 7 ndash 3 = 11

Cara Perhitungan Rangka Batang

Keseimbangan titik simpul analitis (method of joint) dan grafis (Cremona)

Metode potongan analitis (Ritter) dan grafis (Culman)

Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4

No No Batang Gaya Batang

1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y

0)()()( 2 =timesminustimesminustimes yBxPxRA

A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

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PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

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Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

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Slide Number 110

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Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

Masih perlukah mempelajari Mekanika Teknik Klasik dalam Era Serba Komputer
















PEMODELAN STRUKTUR

October 6 2009

Relly Andayani

Structural Types

Continous Beam

Structural Types

Cable Stayed




Retaining Wall

Structural Types




LOADSSpread Load

LOADS

Howhellip





Cable Stayed

Structural Models

Chimney

Structural Models


Truss

Structural Models

Truss

Structural Models

Suspension Bridge

Structural Models

Suspension Bridge

Structural Models

Retaining Wall

Structural Models

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135
















PEMODELAN STRUKTUR

October 6 2009

Relly Andayani

Structural Types

Continous Beam

Structural Types

Cable Stayed




Retaining Wall

Structural Types




LOADSSpread Load

LOADS

Howhellip





Cable Stayed

Structural Models

Chimney

Structural Models


Truss

Structural Models

Truss

Structural Models

Suspension Bridge

Structural Models

Suspension Bridge

Structural Models

Retaining Wall

Structural Models

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

Structural Types

Continous Beam

Structural Types

Cable Stayed




Retaining Wall

Structural Types




LOADSSpread Load

LOADS

Howhellip





Cable Stayed

Structural Models

Chimney

Structural Models


Truss

Structural Models

Truss

Structural Models

Suspension Bridge

Structural Models

Suspension Bridge

Structural Models

Retaining Wall

Structural Models

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

Structural Types

Cable Stayed




Retaining Wall

Structural Types




LOADSSpread Load

LOADS

Howhellip





Cable Stayed

Structural Models

Chimney

Structural Models


Truss

Structural Models

Truss

Structural Models

Suspension Bridge

Structural Models

Suspension Bridge

Structural Models

Retaining Wall

Structural Models

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135




Retaining Wall

Structural Types




LOADSSpread Load

LOADS

Howhellip





Cable Stayed

Structural Models

Chimney

Structural Models


Truss

Structural Models

Truss

Structural Models

Suspension Bridge

Structural Models

Suspension Bridge

Structural Models

Retaining Wall

Structural Models

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135




LOADSSpread Load

LOADS

Howhellip





Cable Stayed

Structural Models

Chimney

Structural Models


Truss

Structural Models

Truss

Structural Models

Suspension Bridge

Structural Models

Suspension Bridge

Structural Models

Retaining Wall

Structural Models

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

LOADS

Howhellip





Cable Stayed

Structural Models

Chimney

Structural Models


Truss

Structural Models

Truss

Structural Models

Suspension Bridge

Structural Models

Suspension Bridge

Structural Models

Retaining Wall

Structural Models

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

Howhellip





Cable Stayed

Structural Models

Chimney

Structural Models


Truss

Structural Models

Truss

Structural Models

Suspension Bridge

Structural Models

Suspension Bridge

Structural Models

Retaining Wall

Structural Models

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135




Cable Stayed

Structural Models

Chimney

Structural Models


Truss

Structural Models

Truss

Structural Models

Suspension Bridge

Structural Models

Suspension Bridge

Structural Models

Retaining Wall

Structural Models

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

Chimney

Structural Models


Truss

Structural Models

Truss

Structural Models

Suspension Bridge

Structural Models

Suspension Bridge

Structural Models

Retaining Wall

Structural Models

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135


Truss

Structural Models

Truss

Structural Models

Suspension Bridge

Structural Models

Suspension Bridge

Structural Models

Retaining Wall

Structural Models

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

Truss

Structural Models

Suspension Bridge

Structural Models

Suspension Bridge

Structural Models

Retaining Wall

Structural Models

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

Suspension Bridge

Structural Models

Suspension Bridge

Structural Models

Retaining Wall

Structural Models

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

Suspension Bridge

Structural Models

Retaining Wall

Structural Models

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

Retaining Wall

Structural Models

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

Retaining Wall

Structural Models

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

Damm

Structural Models

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

Damm

Structural Models


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135


Truss

Structural Models



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135



LOADSSpread Load

LOADS

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

LOADSSpread Load

LOADS

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

LOADS

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

LOADS

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

BEARINGRolled

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

BEARINGRolled

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

BEARINGRolled

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

BEARING

Symbol

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

BEARINGPinned

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

BEARINGPinned

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

BEARINGPinned

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

BEARINGFixed

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

BEARINGFixed

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

BEARINGFixed









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135









GAYA






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135






GAYA


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135


GAYA

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

SISTEM GAYA




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135




SISTEM GAYA

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

SISTEM GAYA

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

SISTEM GAYA




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135




RESULTAN GAYA

F1

F2

R

φ


Resultante

Resultante

Forc

e A

Force B

F

Forc

e A

Force B

Forc

e A

Force B



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135



RESULTAN GAYA

F2

F1

R R

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

RESULTAN GAYA


R

R

R

F1 F1 F1 F1F2 F2

F3 F3 R1 R1 R1



RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135


RESULTAN GAYA

RF1F1

F2

F2

R F1

F2

R



RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135


RESULTAN GAYA

F1 F1 F1

F2F2 F2R R R

φφ

α


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135


KOMPONEN GAYA



φ

F

F1

F2 F2

F11

2


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135


KOMPONEN GAYA



F1

F1F1

F2 F2F2


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135


KOMPONEN GAYA

F cos α

F si

n α F

α

F

α φ

γ

F1

F2

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

GAYA EQUILIBRANT



Force B

Forc

e A Equilibriant

Resultan

Equilibriant


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135


KESEIMBANGAN



KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135


KESEIMBANGAN



F1

F2 R

R

F1

F2


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135


KESEIMBANGAN STATIS


F1

F2 R

F1

F2F3

F3

F1

F2

F3

1 2 3



Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

Secara grafis


KESEIMBANGAN



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135



Secara analitis

KESEIMBANGAN


ΣFv = 0



ΣM = 0

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

KESEIMBANGAN




R = ΣF = 0






Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135




Contoh


W

A

4

B

C D

E

30o

3

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

KESEIMBANGAN

W

AB B 30o

BC

x

y

30oW = 10 kNBC

AB





KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

KESEIMBANGAN

4

20 kN

C D

E

30o

3

y

x

20 kN

C D

Ey

x

20 sin 30

CE x 45

CE x 3520 cos 30

4

3

5



KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

KESEIMBANGAN

Sistem multi gaya




Reaksi tumpuan

Reaksi tumpuan

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

INTERNAL FORCES

Axial Forces

Compression ( - )

Tension ( + )

P P

P P

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

INTERNAL FORCES

Shear Force P

R R

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

INTERNAL FORCES

Moment P

+++

RAV RBV








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135








Tidak Stabil

Stabil











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135











Cremona

1

23

P1

P3

P2

P1

13

P2

1

2

23

P3

P1

P2

P3

P1

P2

P3

13

2

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

1

A1

B1

2

B1

B2

3

A1

A2

D1

4

A2

A3T2

5

B2

D1T2

D2

B3

6

B3

B4

7

D2

A3

A4


1 A1

2 A2

3 A3

4 A4

5 B1

6 B2

7 B3

8 B4

9 T1

10 T2

11 T3

12 D1

13 D2

RA RB

-( )-( )-( )-( )+( )+( )+( )+( )-( )+( )-( )-( )-( )

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

12

3

4

5 6

7

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A2 A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

RA

B2

D1

A2

1

sum = 01M

x x x x

x

y


A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

A2

RA

B2

D1

A2

1

A2

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

A1

A3

A4

B1 B2 B3B4

T1

T2T3D1

D2

RA RB

x x x x

x

y

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

FORCES RESULTANTE

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

FORCES RESULTANTE

P1 P2 P3 P4 P5

P1

P2

P3

P4

P5

R

O

S1

S1

S2S2

S3S3

S4

S4

S5

S5

S6

S6

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

FORCES COMPONENT

P1 P2

RAv RBv

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

FORCES COMPONENT

P1 P2

RAv RBv

P1R

S1O

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

FORCES COMPONENT

RBv S2S3

P1 P2

RAv

P1

P2R

S1O

S1

S2

S3

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

Slide Number 89

Slide Number 90

Slide Number 91

Slide Number 92

Slide Number 93

Slide Number 94

Slide Number 95

Slide Number 96

Slide Number 97

Slide Number 98

Slide Number 99

Slide Number 100

Slide Number 101

Slide Number 102

Slide Number 103

Slide Number 104

Slide Number 105

Slide Number 106

Slide Number 107

Slide Number 108

Slide Number 109

Slide Number 110

Slide Number 111

Slide Number 112

Slide Number 113

Slide Number 114

Slide Number 115

Slide Number 116

INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

Slide Number 125

Slide Number 126

Slide Number 127

FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

Slide Number 134

Slide Number 135

FORCES COMPONENT

P1 P2

RAv

P1

P2R

S1O

RBv S2S3

S1

S2

S3

C

S1

S3

C

S1

C

RAV

S3

C

RBV

ab

cd

e

e

d

c

b

a

RS

s1

s1

s2

s2

s3

s3

s4s4

s5

s5

s6

s6

RESULTAN GAYA

ab

cd

e

e

d

c

b

a

RS

MEKANIKA REKAYASA

Slide Number 2

Slide Number 3

Slide Number 4


Slide Number 6

Slide Number 7

Slide Number 8

Slide Number 9

Slide Number 10

Slide Number 11

Slide Number 12

Slide Number 13

Slide Number 14

Slide Number 15

Slide Number 16

Slide Number 17

Slide Number 18

Slide Number 19

Slide Number 20

Slide Number 21

Slide Number 22

Slide Number 23

Slide Number 24

Slide Number 25

Slide Number 26

Slide Number 27

Slide Number 28

Slide Number 29

Slide Number 30

Slide Number 31

Slide Number 32

Slide Number 33

Slide Number 34

Slide Number 35

Slide Number 36

Slide Number 37

PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

Slide Number 43

Slide Number 44

Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

Slide Number 54

Slide Number 55

Slide Number 56

Slide Number 57

Slide Number 58

Slide Number 59

Slide Number 60

Slide Number 61

Slide Number 62

Slide Number 63

Slide Number 64

Slide Number 65

Slide Number 66

LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

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INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

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FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

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RESULTAN GAYA

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MEKANIKA REKAYASA

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PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

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Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

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INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

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FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

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MEKANIKA REKAYASA

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PEMODELAN STRUKTUR

Structural Types

Structural Types

Structural Types

Slide Number 42

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Structural Types

STRUCTURAL TYPES

LOADS

LOADS

LOADS

Howhellip

Structural Models

Structural Models

Structural Models

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LOADS

Slide Number 68

LOADS

LOADS

LOADS

Slide Number 72

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

BEARING

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INTERNAL FORCES

INTERNAL FORCES

INTERNAL FORCES





Cremona

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FORCES RESULTANTE

FORCES RESULTANTE

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

FORCES COMPONENT

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MEKANIKA REKAYASA - YuLiana Margaretha · PDF file– Statika : obyek yang dikenai gaya...

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