1
3.9kviews
Analysis the Continuous beam loaded and supported as shown in fig 1)Using clapeyron's theorem of three moments method Note that support C settles by 8mm during loading Take EI=1600kN/M2

enter image description here

Subject: Structural Analysis II

Topic: Flexibility Method

Difficulty: Medium / High

1 Answer
0
85views

enter image description here

1)Free Bending moment

For AB, BM at E=wl28=24×328=27kN.m

For BC enter image description here    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

enter image description here

3)Three moment theorem

For A1AB

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+61E1x1l1+62E2x2l2=0

A2x2={12×15×2×(23×2)}{12×15×2×(2+13×2)}

=2040

=20

1=BA

=00

=0

2=BC

=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+61E1x1l1+62E2I2l2=0

A1x1={12×15×(23×2)}+{12×2×15×(2+13×2)}

=20+40 =20

int1=cB

=0.0080

1=0.008

int2=intcD

=0.0080

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+300.319.215.36=0 4MB+18Mc+5MD+265.74=0

4MB+18Mc+5MD=265.74_

For, CDD

{l1=5 l2=0}

Mc(l1)+2MD(l1+l2)+MD(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=1623mB

MA=1623MB6

=162636MB

MA=270.5MB_

Putting the value of MA in equation (2)

3(270.5MB)+14MB+4Mc=151.25

811.5mB+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=270.5MB

=270.5(2.67)

25.67kN.m_

Please log in to add an answer.