Kuliah2-Penurunan Rms Dasar

7/21/2019 Kuliah2-Penurunan Rms Dasar

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BALOK TERJEPIT (JEPIT - JEPIT)

(II)penurunan rms asar

2

1 2

α=0 β=0

M!

M2H

S"#a$ $umpuan %ep"$ &a'a(!) $"a* memun+*"n*an $er%a"n,a

r$as"pu$aran suu$(2) mampu mener"ma +a,a en+an ara'

sem&aran+



/A0A /A0A PD BLK TERJEPIT


3

1

M

H

α=0

1

MH3

1

M

Hα=0

1

M

Hβ3

STRUKTUR STATIS TAK TENTU LUARTIN/KAT 4



HUB /RS ELASTIS DAN MOMEN


4

! 2α

β

α=β=0(%ep"$)

α

ο

β

ο! 2

De#rmas" paa s"asar a*"&a$ +a,a P

α

β

M!!De#rmas" paas"s$em asar a*"&a

&e&an M!1

α

2

β

2

M2! De#rmas" paa s"s

asar a*"&a$ &e&anM2!

(a)

(&)

(6)

()



HUB /RS ELASTIS DAN MOMEN (2)


5

Den+an superps"s" "p$ pers. /rs e5as$"s

2221o

2211o

MM

MM

β β β β

α α α α

Pers

A$as sr pers. /rs e5as$"s $erse&u$ ma*a M! an

M2

1221

2o2o

1 βα βα

)α β(β )βα -(α M

=

1221

1o1o

2 βα βα

)βα (α )α β(β

M =

Pers (

Pers (



HUB /RS ELASTIS DAN MOMEN (4)


6

Karena $umpuan %ep"$ ma*a α=β=0 se'"n+a M! anmen%a"

1 β

2α

2 β

1α

2 βoα 2

α o β

1M

=

2121

1o1o

2 α β βα

α β βα M

= Pers (4&)

Nampa* &a'a M! an M2 $er+an$un+ paa su

pu$aran r$as" $umpuan (ter-dpt hub. Momen dan Srotasi α)

Pers (4a)



MEN/ITUN/ α an β


7

/una*an 7Mmen area me$'e8 (en+mem&e&an" s"s$em asar en+an "a+ra&"an+ M a*"&a$ &e&an 5uar se&a+a" &e&an)

α o=βos$ r$as" a*"&a$ &e&an 5uar p s"s$e

&a5* asar seer'anaα 1=β1s$ r$as" a*"&a$ &e&an M!! p &a5

asar seer'ana

α 2=β2s$ r$as" a*"&a$ &e&an M2! p &a5

asar seer'ana Lebih jelas; Lihat kembali slide II-4 utk defnisi α dan



MEN/HITUN/ α! an β! a*"&a$ M!!


8

α

!β

AB

De#rmas" pas"s$em asar

M!!

!D"a+ram M

a*"&a$M!!

!(EI)B"an+ M(EI) s&e&an p s"s$easar

β

L(2EI)

(6!)

(62)

(64

)



MEN/HITUN/ α! an β! (5an%u$an)


9

Den+an &erpeman *p +am&ar ,+ $a" (s5"e Ima*a:0;M

B =

3E

!

!

1!

3

2

E

1!

2

1 )( "

1 # =

×

=

α

$E

!

!

1!

3

1

E

1.!.

2

1 ) β( "

1b =

=

Pers(;)

Pers(<)

Ra an R& aa5a' mas"n+ mas"n+ r$as" α! an

"se$"ap $umpuan a*"&a$ &" M s&+ &e&an p s"s$&5* seer'ana



MEN/HITUN/ α2 an β2


10

Un$u* men+'"$un+ α

2

an β

2

a*"&a$ M2

! +una*an 6ar

,+ sama sp$ men+'"$un+ α! an β!:

α

2

β

2

A B

De#rmas" ps"s$em asa

M2!

1 D"a+ram Ma*"&a$ M2!

!(EI)

B"an+ M(Es&+ &e&an p

s"s$em asa2

β

2

L/(2EI)

(!)

(2)

(4)



MEN/HITUN/ α2 an β2 (5an%u$an)


11

Se5an%u$n,a: +n su&s$"$us" α an β "a$as *e persa$au (4) ma*a "per5e':

0;MB =

$E

!

!

1!

3

1

E

1!

2

1 )(α "

2 # =

×

=

3E

!

!

1!

3

2

E

1!

2

1 )(β"

2B =

=

2121

2o2o

1 α β βα

βα α βM

=

Per'a$"*an=> $ern,a$a α

1=β

2= an α

2=β

1 ; an $er-p$ an$ara M an s$ r$as"

D+n em"*Pers(?)



HUB. M= SDT ROTASI DAN EI


12

2121

2o2o

1 α β βα

)α β(β )βα (α

M

=

2211

2o1o

α α α α

)α β(β )α α (α

=

22

21

oo

α α

$E

! β β

3E

!α α

=

2$E!2

3E!

$E!

o3E!

o

)( )(

) β(β )α (α

2$E!2

3E!

$E!

o$E!

o

)( )(

) β(β )2α (2α

2$E!

23E!

$E!

oo

)( )(

)% β(β )α &2(α

2$E!23E!

$E!

oo )% β(2α β)&(2α



HUB. M= SDT ROTASI DAN EI (5an%u$an!


13

}

22''

$E

!

3E

!

$E

!

β2α β2α }

$E

! β2α β2α

2''

}

$E3!

! β2α β2α

2''

}

'' 3

$

β2α β2α

}

!

2E β2α β2α M''1

D+n 6arasama

"per5e' M2

}

!

2E

α 2βα 2βM ''2 Pers(@)

Pers(?)



HUB. M= SDT ROTASI DAN EI (5an%u$an2


14

Karena α=β=0 men+"n+a$ $umpuan %ep"$ ma*a :

!

2E β2α M oo1

Pers(9)

Pers

()

!

2Eα 2βM oo2

Tern,a$a M! an M2 #un+s" ar" αo= βo an *e*a*ua

E:

Ja" *"$a 'an,a per5u men6ar" αo an βoDeCn"s" α an β 5"'a$ *em&a5" s5"e n (@)

Kuliah2-Penurunan Rms Dasar

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