written 6.6 years ago by | • modified 6.6 years ago |
Subject: Structural Analysis II
Topic: Flexibility Method
Difficulty: Medium / High
written 6.6 years ago by | • modified 6.6 years ago |
Subject: Structural Analysis II
Topic: Flexibility Method
Difficulty: Medium / High
written 6.6 years ago by | • modified 6.6 years ago |
1)Free Bending moment
For AB, BM at E=wl28=24×328=27kN.m
For BC ML=−7.5×2=−15kN
MR=7.5×2
=15kN.M
For CD BM at G=wabl=15×2×35=30kN.m
2) Free Bending moment diagram
3)Three moment theorem
For A1−A−B
MA1(l1)+2MA(l1+l2)+MB(l2)+6A1x1l1+6A2x2l2=0
0+2MA(0+3)+MB(3)+6×0×006×54×1.53=0
6MA+3MB=−162_
For A-B-C
MA(l1)+2MB(l1+l2)+Mc(l2)+5A1x1l1+6A2x2l2+6∫1E1x1l1+6∫2E2x2l2=0
A2x2={12×15×2×(23×2)}−{12×15×2×(2+13×2)}
=20−40
=−20
∫1=∫B−∫A
=0−0
=0
∫2=∫B−∫C
=0−(−0.08)
=0.008
3(MA)+2MB(3+4)+Mc(4)=6×54×1.53+6×(−20)4+0+6×0.008×16004=0
3MA+14MB+4Mc+162+(−30)+0+19.2=0
3MA+14MB+4Mc=−151.2_
For , B-C-D
MB(l1)+2Mc(l1+l2)+MD(l2)+6A1¯x1l1+6A2x2l2+6∫1E1x1l1+6∫2E2I2l2=0
A1x1=−{12×15×(23×2)}+{12×2×15×(2+13×2)}
=−20+40 =20
int1=∫c−∫B
=−0.008−0
∫1=−0.008
int2=intc−∫D
=−0.008−0
∫2=−0.008
4MB+18Mc+5M0+6×204+6×75×2.675+6×(−0.008)16004+6×(−0.008)×16005=0
4MB+18Mc+5MD+60+240.3+(−19.2)+(−15.36)=0 4MB+18Mc+5MD+300.3−19.2−15.36=0 4MB+18Mc+5MD+265.74=0
4MB+18Mc+5MD=−265.74_
For, C−D−D′
{l1=5 l2=0}
Mc(l1)+2MD(l1+l2)+M′D(l2)+gA1x1+6A2x2+6×0.008×16005+0
5Mc+10mD+209.7+15.36=0
5mc+10mD=−225.0_
From equation (1) we get
6mA+3MB=−162
6MA=−162−3mB
MA=−162−3MB6
=−1626−36MB
MA=−27−0.5MB_
Putting the value of MA in equation (2)
3(−27−0.5MB)+14MB+4Mc=−151.25
−81−1.5mB+14MB+4MC=−151.2
−81+12.5MB+4Mc=−151.2
12.5MB+4Mc=−151.2+81
12.5MB+4Mc=−70.2_
Solving 3,4 & 6 we get
MB=−26.7kN.m_
Mc=−9.19kN.m_
MD=17.90kN.m_
MA=−27−0.5MB
=−27−0.5(−2.67)
25.67kN.m_