P1 - Cross Point
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Transcript of 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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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&
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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
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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
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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
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Bdan Mom7n
'605
(+0+1
'2025
6m 3m 3m 6m 6m
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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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