Question

A continuous beam ABC of span AB = 2m and BC = 4m is having uniformly varying load over span BC is shown in the figure below. If the moment of inertia of cross-section for span AB is half of that of span BC, then the rotation of point B (in radians upto four significant decimals)is ____.

E = 210 GPA
$Take{I}_{AB}=860c{m}^4$

• A. 0.0014
• B. 0.0028
• C. 0.0041
• D. 0.007

Answer 1

The correct option is A 0.0014

Member	FEM (in kN-m)
AB	0
BA	0
BC	-7.2
CD	10.8

$M_{BA}=\frac{2E{I}_{AB}}{2}\left[{\theta }_B\right]=E{I}_{AB}{\theta }_B...\left(1\right)$

$M_{BC}=-7.2+\frac{2E{I}_{BC}}{4}\left[2{\theta }_B\right]=2E{I}_{AB}{\theta }_B...\left(2\right)[2I_{AB}=I_{BC}]$

$Underequilibrium,M_{BA}+M_{BC}=0$

Hence, from (1) and (2), we get

$3I{E}_{AB}{\theta }_B-7.2=0$

$\Rightarrow {\theta }_B=\frac{2.4}{2\times {10}^8\times 860\times {10}^{-8}}=0.0014rad$