Question
Download Solution PDFFor a fixed beam loaded as shown below, if the support, B rotates + θB radian anticlockwise, the fixed end moment at ‘B’ is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
For the given fixed beams:
Fixed end moments can be thought of as the superposition of moments induced due to uniformly distributed load and due to rotational slip of end B calculated separately.
Thus net fixed end moment at B –
MBA = MBA1 – MBA2 {Taking clockwise as positive}
Calculation for moment uniformly distributed load:-
By using standard result,
Calculation for moment due to rotational slip:-
Compatibility Equation:
θB = -θ0
⇒ On conjugate Beam - S.F at B = - θ0
δB = 0
⇒ On conjugate Beam - B.M at B = 0
From BMD
&
⇒ M1 = 2M2
From (1)
&
Thus MBA2 = M1 as explained above
Hence
∵ Our assumed direction is not similar to those given in the option hence the adopted sign convention must be opposite to that given. Adopting proper sign convention.
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