p1 - cross point

8/19/2019 P1 - Cross Point

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1. BILANGAN KEJUR (kekakuan balok)

A B

A B

K = 3 EI / L

K = 4 EI / L

METOE I!TRIBU!I MOMEN ("RO!)

1


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#. MOMEN $RIMER

q t / m

M ab = 3/16 PL

M ab = 1/8 q l ²

A B

M ab

M ab

2

½L ½L

P


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#. MOMEN $RIMER

q t / m

M ab = Mba = 1/8 PL

M ab = Mba 1/12 q l ²

A B

M ab

M ab

P

3

½L

½L

Mba

Mba


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3 . MOMEN INUK!I % KOE&I!IEN INUK!I

AB

1 tm

0,5 tm

µ = 1/2

µ = Koefisien induksi

4

1 tm


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PM!"K#$%&

% !

P

'

a b

%!

'

Pab/$L

Pb/$

$Momen di ba(a) P*+ = P-b-a/L

%tau M+ = .a a = P-b/L a = Pba/L

Momen .eduksi = Pab

$ - Ladi .a L = Pb-L - 1/3L Pb-b -1/3b

$ - 2 $ -2

= PbL Pb4

$ -6 $ -6

Ra

R

a

Rb

Rb

a = .a = Pb *L b

6 $-L

b = .b = Pa * L a

6.EI.L

5

cF1

F2


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A Buv

X dx qtonm

qdx

d!a " q dx # L $ x % # L & ' # L $ x % &%

6EIL " q # L $ x % # L& ' L&( 2Lx$ x& % dx 6EIL " q # ' x&L ( x ) ( 2 L&x$ 2 Lx& %

6.EI.L " q 6EIL # x) ' 3 Lx& ( 2L&x % dx

" q 6EI L * # x) ' 3 Lx& ( 2 L&x % dx

+

!a " q 24 EI L # x,% $ q 6EI # x) % ( qL6EI #x&%

vu

-

u

-

u

6

L


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ntu/ "+ dan - " L ma/a 0

a " q L, 24 EIL $ q L)6EI ( qL ) 6EI " q L) 24 EI $ 4 qL) 24 EI ( 4qL)24 EI

b " !b "

qL) 24EI


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A BEI

1 tm" M

13L

L

23 L

1EI

!AB "L3EI !BA "

L6EI

AB

!AB L " L 23 L 2EI !AB L " L& 3EI

!AB " L 3EI

BA L " L 13 L 2EI !BA L " L& 6 EI

BA " L

6EI

/a Mom7n " M0Ma/a

!AB " ML

3EI

/a Mom7n " M0 ma/a !BA " ML 6EI

!ba!ab


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10/24

a bP

1+

M

Atau

!AB " ML 3EI

ad Mab " 3EIL !ABa b

a " Pb # L& ' b& %6EIL

ad Mab " 3 EIL !a

" 3EI Pb#L& ' b&% L6EI L " Pb # L& ' b& % 2L&

ntu/ a"b" ½ L0 ma/a

AB

Mab " 3PL 16


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AB

u

v

L

q

a " q24EIL#x,% ' q6EI #x)% (qL6EI #x&%

ntu/ u " + dan v " L0 ma/a

!a " qL) 24EI

v

u u

v v

u

Mab " 3EI !a L " 3EI qL) L 24EI

ad 9

Mab " qL&

11


12/24

12

Mab Mba

A B

Atau

P

P

ab

a " Mab.L ( Mba .L

3EI 6EIb "Mba.L ( Mab. L 3EI 6EI

6

6

2 Mab.L ( Mba .L "

6EI !aMab .L ( 2Mba.L"6EI !b

12

3 Mba.L " EI # 12 !b $6!a %

Mba " EI # 4 !b $2!a % LAtau

Mab " EI# 4!a $2!b % L


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13

P

½L ½ L

AB ntu/ a " b " ½ L ma/a0

!a " !b dan Mab " Mba " EI 2! La " !b " P½ L # L& ' :L& % 6EI.L " PL&

16EI ad Mab " Mba "EIL . 2! " EI x 2

PL&L

16EI

Mab " Mba "

PL


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14

q tm

a " !b " qL) 24EIMab " Mba " EIL . 2! " EI . 2 qL) L 24EI

Mab " Mba "qL&

12

A B


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L

Mab

A BEI

1;ada< BILA=>A= ?ER

B7;a@a mom7nd@7;


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1

6

A B

LMab

Mba

B7;a@a b7a;nGa n


17/24

1

A B1tm

1tm

+05 tm

1tm

+05tm

ab " L $ +05 L 3.EI 6 .EI

" L atau #3L12EI% 4.EIMom7n 1 tm d A m7nmbu


18/24

AB

=


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ontoH Koa< 9

6m 6m 6m 6m

2tm 4t 1tm3

m3m

Ot/ B9 ?ba " 3EIL " 36 " +05

?bc " 4EIL " 46 " +066

A B E

Ot/

9

Nba " +5 9 #+05(+.66% " +0Nbc " +066 9 #+05(+066%"+0

1(

?cb " 4EIL " 46 "+066?cd " 4EIL " 46 "+066

Ncb " +066 9 #+066(+066% " +0Ncd " +066 9 #+066(+066% " +0

18

>7


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2+

Ot/ 9

?dc " 4EIL " 46" +066?d7 " 3EIL " 36" +05

Ndc "+066 9 #+066(+05%" +05Nd7 " +05 9 #+066(+05%" +043

1Mom7n&

@;m7; 9

Mba " 1 q


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+043

+05+05

+05+05 +043

'8 (3

'3 + + (405(205

(3042 (101(+064

(+064

(+032 '

205

'20+

'103

(+032

PHa71

'+014 '+01

'+0+8

(+04

(+04

(+03'+021

'+016'+011

PHa72

(+03

'

+016

'

+021

'+011

(+011

(+011 (+0+5(+0+5 '

+0+3'+0+2

PHa73

'+0+1'+0+2

'+0+3 '+0+1(+0+

1

(+0+

1'605 (605 (+0+1 ' '2025 (202560 '+0+1 (2.25

21


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Bdan Mom7n

'605

(+0+1

'2025

6m 3m 3m 6m 6m

22


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AB

q

L

1qL&

1qL&

L

a " b " 124 qL&

Q " 534

qL&Ra . L " qL . ½L

Ra " qL&2L " ½qL

Mc " ½ qL . ½ L $ q½L . : L " : qL& ' 1 qL& " 2 qL&

' 1 qL& " qL&

Ra

Rb

RaRb

Ra .L " 1 . q.L&.L. 23½.L Ra " 124 . q.L,

L

a " Ra " 124 q.L)Mc " Ra.½ L ' 1 q.L&.½ L.23 .3. ½ L " 124.q.L). ½ L ' 112 .q.L, " 14 q.L, ' 112.q.L,Q" Mc "#32'334% q.L, " 534. qL,

2323


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p1 - cross point

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