Rizkya j Maharani J_metode Matriks Dan Engilab Mekrek V

LAPORAN TUGAS BESAR

MEKANIKA REKAYASA V

Nama

Nim

DI SUSUN OLEH:

: RIZKYA J. MAHARANI J.

z 09222010064

PROGRAM STUDI TEKNIK SIPPIL

FAKULTAS TEKNIK UNTVERSITAS ANTAKUSUMA

PANGKALAN BUN

2012

r!!*{ {uf{tAMA)

r rlanln nrnflrj.nrlrrrllutuLtLUl U\ t Ll\U!

' VJ Va la

LAPOF.AN TTJGAS BESAR MEKANIKIA REILA,YASA V

Dikerjakan Sebagai Syarat mengrkuti Ujian Akl^'ir Scmests dan sebagar

Persyaratan Mengikuti Yudisium.

}.IAI,{A . DTTIZVA I il,AAITAP ANI I-it,. ai-r--tr-.-l . iuzr\ t t t J. Lru uu uv uat J-

NI]\4 :09222810064

Asisten

D^*^t-^t--* D.,* ,--,,--,2 nnl /)-r {l! rEl\(ll.rr t I-, l.lll. .} {ll I Ll(li I !U I !

Dosen Pengampu,

\TTT-I.I\T_t I \-IJ,Lr .

r\l

ill^-* +^L.,1 .rrrvrrBvl'orrr'rt .

Ketua hodi Teknik Sipil

NIDN.

SOALTUGAS : MEKAIIKAREKAYASAVJurusan/Semester : Teknik SiPil / VDosen : JUNI GULTOM ST.,MTPDiberikan kepada mahasi swaNam a -'-.8,3Fys....{:..Ygbw.r.i. J

l

NTM

:

struktur portal seperti gambar :

: og2ZZoloo 64

lH=.rco -EG

D

Kekakuan Balok:

DE:EF= 2.5E1GH=HI= 2.0EI

Kekrkuan Kolom:AI)=BE=CF= 3.0EIDG : EH = FI: 2.5 EI

Bentang Balok:

LI :..... ...... cm

L2= ....6......... ".Tinggi Kolom :

Hl =......V....... cm

H2 =....... ,... cm

Beban:

ql =!' m'

q2-. .. kglm'

H2

iui=:oo1

I

H1

kg

Juni Gultom., ST.MTP

- Sebagai syarat pelaksanaan ujian semester MK ini.

CA

Diminta

Hitung dan Garnbar Bidang M, Q dan N dengan Metode Matrix Kekakuan DAN Engilab serta SAP 2fi)0

P.Bun" I Oktober 2010Dosen pengasuh,

Catatan

SOAL TUGAS - BALOKANALISIS STRUKTUR METODE MATRIKS

Ketentuan soal : Nilai X dan YContoh: NIM

Nonna- fr-{4haSFU-. d- l

berdasarkan NIM : LOl 070XYL0107054, maka nilai X:5 dan nilaiY:4.

Soal no. I : Ilitung gaya ddam dan momen pada titik A, B, C, D, E dan F dengan carametriks.

1,5 m 1,5 m

Diketahui konstnrksi balok (bidang) :

Pt :2000 + (50 * X) N. P2: 1000 + (50 * Y) N.

Ql = (200 ' Y) N.

p3 = (200 * X) N.

Batang: A{ dan E-F = EI E = 200000 MPa.C-E = ZEI

Batang balok persegi panjang dengan lebar 20 cm.

Soal no. 2 : Hitung gaya dalam dan momen pada titik A, B, C, D dan E dengan caramatriks.

1,5 m 3.0 m 2,0 m 2,0 m

Diketahui konstruksi balok (bidang) :

Pl :4000 + (50 * X) N. Ml :200 Nm.

Ql : (300 * Y) N.Batang : A-C dan C-E : EI E = 200000 MPa.

Batang balok persegi panjang dengan lebar 20 x 40 cm.

PROGRAM STUDI TEKNIK SIPIL

FAKULTAS TEKNIK

V

ki r+on p ,_ S-l, 3uo, -6_itlor. n yrf

17 Cr.t Etr

a/, f *,n6f , lno

A",kL b*L Ns

/

/

%

rucAs BEsAR /+R*KHKITAA , Y,rlln1ka _ ReLaxgsa

NAMA : ant TNrM .

NAMAASISTEN

NAMA DOSEN

HARUS SELESAI TANGGAT

Tugas Besar Mekanika Rekayasa V

clrsoiqn Seal Ne

Dh,1 kurrin kgi bcrio k

Pi =tsc,P H = 2,3 FU

?o= l2CL1 N : tt2 F-U

Yz= ldoc N . 1,2 kH

[*,= ]ce M -' c,B kt{

, A *t F-I = LlAun

C"V = 2El

f : ZcDooo Mlc,

t. Mtn.qnfqhol, elzrr,rett

facla shr,tfuc ini

cc E

2 - Ma.ne,rtutoil [<tite nrrtfis gir.rFh-rr ( p )

_ s. f4atnFs___rh!F__[_4_i=31 Ytt ct'{rr Fl d,tpor wr^ t i

Universitas Antakusuma Prodi Teknik Sipil


4' Morvre v'r Pnv, nr

Vloec

Ylo cn

ffi

' lrgn ,,shr

Yt'cE --

= C,6 i- €t45 + O

= ltOS n|\im

= 4v' ?v

-

{ >t_iit

M'E"=-qL" -PL\78

,-e.S_3: -ttL ? + (-a 1-t) 7 o)Ll

=-C,L -8'15 *z= -3,AV [.|.{rn

G.= C,8ro - ltzS = -0,,1q

Universitas Antakusurna Prodi Teknik Sipil


: . Maki tr kekakuun f s

s 4v\/z LEt/z e a u,6/, *,/, c c H,

o C Or,/, ZEy', \sa C Ler7, Orr/, 11"

(d, A" du dq

T [4eircr[rifur",11 _!q1r4 K

lF)"= t6 r l.! A itJ 4vYL "'/, c o8,1" 4Eh 0 O I

c o lvls %/t

c c 'u/, avlt) Lt

ip j , [EJ-' IGl = o,t/Et x (-t,os) = o,rof /yr

v I -- | aet /" ','/,Y, A-dl D D

0 D aE /.t Avt/s



bE\i2 it5b6v,

- 0 tl)l _c, 2>lg

Lu\ /"/) Ft -0, :i0LVt /./t '-0,'LlD

X lr'lor'nern S4lqlyl__Ej[qh clarr

X Mcmcrr [ritgrl !ili,,r r,1a'. cf rtel(r ,Iulrr,^ ( H )L;----=-

luletakun clan o folan.

E Me=O

Vr..r -P t {W4=eVro.z -1,].1 ti,l8 =0

E Mn =o Vnc =;)!=< KN (t){.0 r + P, \ r f!1s6 =e .Bg$hot ,

- V<n z l2a i + t,l8 :oVna )- : 9,48

Vac t Vcn - Pi =oofiL I tr14 - I,t =O


2tZ -7,3 =O'cl+

= tr74. kN tt)


AB @-t) nn'

IgMx= -x)(= I -> Y1b=O,56.1

= 0,56 kNm

x Lx =VoLn . Le = 0"Y,6 kM

t( ftx =o

bLx) -?, x

Mo = o,Tb (r rD) -2,) o

= 0,'j % kNt'nx=f --+Vl" --a,i'b (rht).-a,').t

= b'lL-, - 2,3

=-[,,t6 KN vn

x Lx = \lA -?Lg = Lc= D,Vb - 2,2 = -[,?d{

x F{x =o

*Mcr * t4Fc =o

VAe" 3 - 7,4' lr5 - t,l 'lr9 -lr2-(o I 3,7L =o

Vce -: -- 2,8"E lv'16 = o V"Y = 1,2 kH cl)

-Vr..Z l?2.3 + ?" ,t,9-F A1.1,9 *l4cr *Msc=D

-Vf.C.3t l,L-Z * 1,7-lt5'r 2r4-1,9 - l,L6+3)LL=O

-Vg. 3 t 3 ,C * t,8 + 3, (, -: i,26 1 3,26 -'oVWZ'':i

VOc=2,5,.H (t') kon,tol

Var +Vrc -\, -?a-&,=or <-\' -4Lte \ 2rV ltz- - iL-)r4 =O

0r=o,8rH +{* =l/:l Ik--l'2L

zME =o


4,s -4,8 :D ol'.


Benla CD ( o ^r,q)*x Mx' e .< -Y Q^' : l4ru

t=Ox:tr9 -> Mo = itL.ltg -'/r - o,t It,5)" a,9b kM m

*,/i,

7=t,9 -, Lp =[tL'(o,e'i,Y) -- grll kN

* filx =o

/=c -b Vlp= l,L tr,9.o)-i,r- -0,?s - l,L.e * a -1,26= i.r$ -O,9O:lrLL= f);71-r., kHm

x =1,5 -> Me = :,2 ittF 1r,5)*l,e [0,] hr,t ) - 1.,r.1,9 --,/r.,i,B -rrg L- r,26

= J A - 2,6+l,B = o,!- t,e.Lktt m.

4Lx=dtx" --VL-&-?' -Q,jx

x = C -> Lp = l),1-. - t,2- -1,) - (0,& O )

= -1,'-t- KH

K: lr5-) LE = t , L -t,I _1,,L - Lo,e t,i)= *t-1kU

( Nt<'O



?a = ),zEH

Pr = 2,3kH

Si?dfl

in'ta

- 1,?4F$



t\t\ai arr fral l'{e , :

: Drl FHrrl

\--(_zcc y4 )U = t:oD ff .: i,, krt

bc.tc.i'n . A-c ( -F = ft.latrE = :|c ct c l4?"

. Lu4.,'r i;oi*' r "rs

i' i'4lirenti;Fat olzvltcn at 4etnoLan

{o sfruptr,u^ r'/1, 'lirCr,'na I t Pltntiil rti /u

A_

^t. f4ir,otl tu Lcrr \r, tt c'*, ^ lt, l'irufh,r ( P )

63,

Universitas Antakusuma Prodi Telmik Sipil


i l,tatr.f r-- {+N-W, a4^,

MoAc =qd ru"+b +(b4A"\ + I'lu (eo*b)---lt-- L,

= i,z 3 F O,L,g ('t.l,Z *3

' l,i8 +c-l-l1'c -- r, t& {.Mnr-r%ft -: qn-Gtr +

'-\,1V - croL' -ltTg KMv*'



?

L 'iv

VlucE = j ?c = z.4,e.4ri = 2,63 kMr"

t-EL = t-)

G = Vl'ca '> V|oce€ t'75 3,5ts

I'q lalcrrr

'n'/<,s At'/q,, o ;



btrnClr:ttr kesph',rbrnr, tAr qnlrrr rt lctltr /.nrt cr1Lcr clqlc,rn

0ltiJl&Yq6 In'/q,s

0 0 4t,/ri,S ,U/q,f

telq,s .lr,/4,5

I L?'/<,t

3,r,5 f,t

A, tflt7'g1

t''ie .r, ir ifu n6i C\(.+t) a

!l - lK1-' io.

fur:r= '/) C,c</ )/ / / /

LI rr fur.t rl (lctLl q tLtll Ah.l

!h . L(1 IA-1 [{, 4$,9 "'/'l,t c o c\''/q,s AL',/q,t c c l- ofrt -f

C O 4Eln,s ,tt/q,t i €rA' e k/o,s 4t'A,5



ktbaliFon



?tr|r'r &ofti ?"rlotaFan Dqtan

4,, !,7WnaMo= O

e'1,9 ^ At l,g - l4.rn * Plt t MCn

Vn".A,f - 3,L.ifi - lref tlrt i [,23 =o

VRc-4,e -+63 =O

Vnc - l, ag kH (r)>.lV\6 = o

-(.lc+.4,r+ 0.r.3 -fYr.+M, +Nlcp =D

-Vc*. 4,9+ 3,6.2-lto,f'to,p! Ifii =o kontro I ,

- Vca. 4,9 + =Q

Vcr+ . &, gi k+ (t*2 tia. "r U

i,$!' r 21€11

3,L-3,6 =Q'- oF!

(=O K* = - l{nc = -1,0W KNrvr

X"r,9 -) \9g ' \fi.9 .lr5 - (0,oe )

= A, FE l.t-tm

V - lv = i,',J\j kN

x Nx=c345.7/4,q: \Qb tsN

V n)an4 V C (o -a)m( Mr= Vr (r,s t * ) -Hac t I4i -'/" qn,

x=o --+ Mg t l,g4 (t,9to) ' ,.,0g {- 0,2 -O" D, ?9 KNM.

X=5 --> M. = i.,O) (t,%.3\ -tfiF 'f o,L - Vr.lD.3z= -1,cJe - trOg) +0,2 -€,4; r.Ir1a:i FNm

Universitas Ariiakusuma Prodi Teknik Sipit


Lr = 494 = V* - 4*

X=O

= i,c9 FNI

x. 3 + Vc-- :Ll-Z - (t..2'a)=-i.ji l"N

Nr = 0,7!,'l a /q,v o,bb kh{ -

2 [4r =o

Vcv.4,q - P, . ?19 ' MuE =oVcs , 4. s '4,9 - 2tD - 2rgg =Q

Vee .4,1

,* 1'gt kNm

2Ac = o

-Vf. 4,s+ ?, -2,L5 Mcr.-O. VcE lVuc -7,:e-Vsc 4 v + 4,5 - 2(LV - ), Q9 =o J,8'l + \,49 -1,9=0^ Vec'4,Q + b,?a =Q

\E1 -- i.'<u t'Nm

x =Vve

bentan CD (o- z,cq)Vn

Vcv.< -V[cv*=o -+ Ma = 2,gi o - 2,99

= -?,0, kNr,l

|40 = 2,8\ 2t Zg - z,qg

= 3,V? ?4nx tr = dmx = VcV x N^ -- Vce- = o,tr1q kt{

x,af Fx

ii i - !r l r_t ,- _ n-__ l! F_t_--!t- F!--!tunlveNlfEls flnfaKusuma rf(J{Il reKnrK Jrplr E


Brl',\ ( a - !.25 ) m.

xVlx= Vev '(t,te f x) -Pt x -V1cVy=o lYp

= b,32 - 2, gE

= Z, kNrn

x--1,75 -b Mg = R,8[ ( z,ls 'l1]g) - 1,7 "2129 - 2tgF

= O,OA [zNm.

x L* =@ = Vvv - P'

&*

LO=Ls=3,S1 '1,2- -t ,49. \.,s

* tJ* = Vrs"

uniuk ben\

L*=o(o -9 ) rvr

lm" Vr - Q.* :l,O$ -ltL.a =()d* l,og : l,tX

ti . l' - l--r -l ---- -. - h-.. lr h I -rt Fr -rtuntvers;tcls ftnfzlKusuma rruqr r eKnlK Jrpll

x = o,9l l?1

Mv.v.r = f o.gi ) l0,L vft.l,z- te,9l )

'-),63 -tto' lo,L-0r$o? t,?8 \.-f-tm


't,'b47Y\-l

Mevx'n

lr09FH

i-.- -.-rr , l -.-l- - - h l!h !, !l n! rluntveft;tfuts AnGrKusuma rrour reKRlK Jtpl(

Tugas Besar Mekanika Rekayasa V\

Soal no . 3

rhthtnqan clan

ke ksPur^biolq M,D,H notode. rna{ril.-s

Dg -Er = 2,5 Vt6* = hl = lv €

Kekakuan ko le*AD=bE=Cf=3,CElDc -- Eh -- Fr = 2t9 Et

4' : tOOo

4z '- t1o

Asumii kens+ruh i rtu I btrlo

Universitas Antakusuma Prodi Teknik

At a\arPandtPetrv',o s i oxictl


?tnqelesatan :

nenfuFan demn uqn

kBnstruksi ini ,ler to elemen c[ctn 6 kincnah"sentuLan klnmak's

Universitas Antakusuma Prodi Telsrik


M? 6H , \V'/tz . ot7.L'/o = 2,ZEYV ga = *qL/t, - -t'n47,, = -1rL5IAD Lrr -- 4L" t,.- - 0ft9. bL/,. -^

-MPHI: /fz - ot+r. bT lL -_ tizglvlP il+ = -qf/,L > _o'1e'6h = -2tLq

MP Dt = 4v'/r, - l.t;L /- ttz = 3

VtP E0 . '41"/it - -t'" /r.,Vf -- qv'lu , AL"/rt

v1?a0. 0

MPW.= @

M? wv

M?Fl=ol\4f 0A = D

MP

0

l'tl? tc 'Y1? bf =

D

0

G,=Ut 2,tlg :2129.S1 : *)r25 I 1,25 ., O

-1,19 ; 6

= o t3 =b+3

So -- o +-3| = o,2-

Ue = 0,9 o'V



Q1 = 2r)f

S-7 =o,2-

(9s = -3

beban Ekiw l'n


llus"trasi Derormasi


Diasums', kor, Di = I ealuan.

Universitas Antakusuma Prodi Te}rrik

Diaturnsi[.an


DibarrFan Ds = Saif,an

= I (d{uan

= I (afuqn

Di bentarl 0a



Ben fu{. Pu ^ouo

A:l a[ ibolEonu1ara4 ^/v

h = i Sqfuan, me

lt 6 lz

\ \ \

do r\ dt'z \ II dp ,ldrt hr

tI r/

t/( &,," f a,t I

LO


;t=6diLi,-oo*do<6

iNo+n@r€9P:S9:S95S9Rr!!!!!!!!I--II--I--I

o o o o o o o o o o o o o o o o o ooooq

oooqoN!

o!

€!

NE

@

E

n!

E

o o o o o o o o o o o o o o o o o ooooqo

oooul

o o o o o o o o o o o o o o o ooIul

oooodi

o o

o o o o o o o o o o o o o o o ooooq

oooe o o

o o o o o o o o o o o o oooo4

oooqo

o o o o

o o o o o o o o o o o o o ooooId

oooll o o o o

o o o o o o o o o o o oF@@I

omodto

o o o o o

o o o o o o o o o o o oood!o

F@oq o o o o o o

o o o o o o o O o oF€@q

oGod!o

o o o o o o o o

o o o o o o o o o odd

4oo5I o o o o o o o o

o o o o o o o oFE5q

6o6qd

o o o o o o o o o o

o o o o o o f o64od!F

FEEq o o o o o o o o o o

o o o o o om{h<i

oo! o o o o o o o o o o o o

o o o o o oo!q

oq\o o o o o o o o o o o o o

o o o o *Fct

€6a o o o o o o o o o o o o o o

o o o o€@

a6t:o

o o o o o o o o o o o o o o

o ostFoct

o!tj

o o o o o o o o o o o o o o o o

o oo{n

{tsu!o

o o o o o o o o o o o o o o o o

aFnci

6+.i

o o o o o o o o o o o o o o o o o o

o

.j

{Fu3

o o o o o o o o o o o o oio o o o o

e

d

o

oo

o!

6

o@

d

o

d

o

o

q

o

d

o

q{

o@

o@

oNo

Ilo o o o: c o

l

o oiooPoo

o o o Ots o oo

o o o o

o o o o o o

o o o o o o o

I Io o o o o

D oo o o o o

f 9o o o o o

3 9o o o o o

I 9o o o o o

I ou o o o o

!t33

o o o o o o

3,cc

o o o o o o o

c

33o o o o o

!

3o o o o o o o

INuoo

o o o o o

9N

ooo o o o o o

0

o

0

0o

o!

0@

o o o o o o o o olooPFooooo

o o o o o o o o oFooooooo

o o o o o o9 I P P

@

@@

I Io

9Noo

PNooo

IN

oo

IN

oo

INuoo

IN

oo

9 9 I P I Io o oooooc

dooodooooooeooedddoa3 6 6 i 5 G E d i 5 6 - o n o= q E @ - =

E6EiHGEdFEB-@!oqFaNts

- n @ r> O - - mT g 6l T m mO = I I Onom@o>r--m6)omrc'mf=oT

DDDODDPP@{ouF@Nts

o3of!:.3on

eI

o o o ooI

o o o o o o o boIo& o

@

Io@ oo o bo o

@NPoo

o@ oo

obo

00009990O!OUAUNP

-lE

il

o o o o o o o

o o o o o

oo

oo

oo

o

o

a

o

o

o

o

o

o

o

a

o

o

o

o

oo o o o o

oo oPo o o o

oo Foo o o o

90o oo o o

F! o o o o o

o Io o o o

o po o o

o oo o o

9 oo o o o o

9a

I

o

o o o o o o

o o o o o a o

o

ooo o o o o

f,

)l

o a o o o o o

)))

o o o o o o

l

)l

o o o o o o o

oa999OOO@!6U50NP

6re{ij!,r-_b!!!6

I I

g e,s t H. ;. E E s. 3- [ a * r _- .. E e $.s

{

&8 gt* H E f; E E^ E E.'s s s.'E c E

a

0

a

o

DDDDADPA

*+uH==*9

86655Gi6tr:5

!-==;;=-==:=;-=;=;-=

B' B E- g 6' f; E A E E E c a 5 s -' ts s s *'

=I

3

tsG;iHfiFE5356E{ou5oNPEBEiddE;s=6aEJe

I

BEdi.-di;3=i€E!'

xrHAlomWrEArAlE(mlLul

MOMEIT AKIflR(MOMEN rrfl$ ffo|I.fsl

@

.i

-3Lffi

Iol

ts@qo

6.i

3 1606

@@qo

F@

c;

35343 -32271

ANALISTSENGIW

Isi E, A,l Element GroupE = Elastisitas; A= LuasPenampang; I = Inersia Batang

a. Element Grcup #1 Kolom balokE = 200000 kpaA = 350mmx600 rTrrTr = 210000 mm2 = 0,2! m2

I =Lln*350x6003mm = 6300000000 mma = 0,0063 ma

rsu lNewl

Youngs Modulus E -Section dtea A =

Section mom. of inertia | =

Delete Applv fancel

2. Gambar Model Struktur

3. Buat Pembebanan

4. Analisis (F = K.A)

5. Perlihatkan Gambar Momen, Lintang dan Normal

Gambar bidang momen

t:

Gambar bidang lintang

Gambar bidang normal

{

I

E

F

I

I

ft

I

L \--

Lendutan

6. Data Output

Data j l'/ede displacemenis I

Con straintiSpring reactions

Node Fcrce Fx

Element tsrces ConslraifftlSpririg reactions ,

'|{, tP*li* v**es: GSd axesJ

Eiement folres Podivevahm: .EJ-4

-6,3r461939i??iiE-ilt

E ,J-;JE iSJS i ll4lE-UJ

-l.$8-68591893;

t.tigjE8i93Bs35

:,?frfi:il3r553lf!;235$lg$r34?3fl

,l ii52i2l306jjEIl-i 1:11:233i5rjti.2

- - e;l;?lFolFlFcc

- ir -- i 9H. h .LHU- -eJ'JJ:evrJ:\rpj

3 :62i55i82cgi3rnAtrl...a!6antar rJ;lsir:llBE

I 2r32IE:66tS869

-i ?r3!i6?6$t9869

D,3ItE8g8r$23[695

-il,3176898$$n69E

?,?rl3?358 332i 5?E-i]?

-[,316?r82l,.,]2irlj

-1.&16Bl328jil$61

-3 E?9392r96:.6iS5

3,82939:r96:6i85a . a-t!ta-t^a-. I'; *f4iU.:fi:i;l-r.

i 2{js8i29?33irr:

il LJ?687:C12!3r383

il l!C39,:ij38?6186

,1.:216tjEr:8s369

3,?3611i3itilgi38

-?.$98B388j1j3jt

2,?i98ffi8815?331

i ,i69l9r9trD2:?r

s.8i3t15fE?ELt?93

B E98Eir32?1t099?

6, 31136 lg 39 t- ??i5E-tJ2-0 tB5?53?eSfl6f6BS-ff,3Tf689BrE?38696

i.88;f !f 1993??g II D ,_q90DB:.r3j'183?i. i2?lgt36s33l33

f . :4?3?3S833:D5f E-'lp0, 12?62500 8...r^:.389

E ,698'l rr322 t t[S9?

Flodedisplacerftents [min] [max] t fm.vd.esEhbdua*J

7. Selesai

i,a Q.t

9,9133955151 0085E-0.,r

1. Bfi89781826325 1 E-03

1,874903t40tl1$88-03

l"tl0811546lS37iE-fl3

t "197289.{87907$BE-03

1,23446?trlEi59t3E-03

-r.6#96i76!4ffiE-ts

-6.629?6S160772tr-jj

.i',sovztzr41zEZgE-i3

' -r, Tr?oEorTigE-lj

-6, 97311'Pgf'a+E+it

-4,81828$i58i16#E-or

4,32ffir98fi119i39E-fi4

-: l?7i9101540672E-03

i 8211228ffi

Rizkya j Maharani J_metode Matriks Dan Engilab Mekrek V

Documents

Transcript of Rizkya j Maharani J_metode Matriks Dan Engilab Mekrek V