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Question

A portal frame ABCD is shown in figure. If the support 'D' sinks by an amount of 15 mm and EI = 48000 kN-m2, the moment developed at joint 'D' (in kN-m, upto two decimal places) is____.

  1. 196.32

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Solution

The correct option is A 196.32
Given EI = 48000 kN-m2

No external load is applied on the frame, the fixed end moments of all members will be zero.

Slope deflection equations are ;

MBA=3EI3[θB]

MBC=2EI2[2θB+θc3×152000]

MCB=2EI2[2θc+θB3×152000]

MCD=2EI2[2θC]

Under equilibrium

MBA+MBC=0

48000θB+96000θB+48000θC1080=0

144000θB+48000C=1080...(1)

MCB+MCD=0

96000θC+48000θB1080+96000θc=0

48000θB+192000θC=1080..(2)

From (1) and (2) , we get

θB=0.00613 rad θC=0.00409 rad

MDC=2EI2[θC]=48000×0.00409

MDC=196.32kNm



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