Question

The mid-span deflection simply supported beam $AB$ with loading as shown in figure is given by

• A. $\frac{2520}{EI}$
• B. $\frac{5276}{EI}$
• C. $\frac{5400}{EI}$
• D. $\frac{8613}{EI}$

Answer 1

The correct option is C $\frac{5400}{EI}$

Let us apply unit load method:

Segment	Origin	Range of $x$	$EI$	$M$	$m$
$AC$	$A$	$0-6$	$EI$	$32.5x+150$	$\frac{x}{2}$
$BC$	$B$	$0-6$	$EI$	$147.5x-\frac{30x^2}{2}$	$\frac{x}{2}$

${\Delta }_C={\int }_0^l\frac{Mmdx}{EI}$

$\Rightarrow {\Delta }_C={\int }_0^6\frac{(32.5x+150)\left(\frac{x}{2}\right)dx}{EI}+{\int }_o^6\frac{(147.5x-15x^2)\left(\frac{x}{2}\right)dx}{EI}$

$\Rightarrow {\Delta }_C=\frac{2520}{EI}+\frac{2880}{EI}=\frac{5400}{EI}$