Question

A cantilever beam of span L is subjected to a load W at a distance 'a' from support. It is desired to obtain the vertical displacement at the free end by unit load method. The expression for deflection is

• A. $y={\int }_0^a\frac{W(a-x)(a-x)}{EI}dx$
• B. $y={\int }_0^a\frac{W(a-x)(L-x)}{EI}dx$
• C. $y={\int }_0^a\frac{W(x-a)(L-x)}{EI}dx$
• D. $y={\int }_0^a\frac{W(L-x)(L-x)}{EI}dx$

Answer 1

The correct option is B $y={\int }_0^a\frac{W(a-x)(L-x)}{EI}dx$

The expression is of unit load method integrated from $0$ to $a$.

	$M$	$m$	limit of $x$
$AB$	$-w(a-x)$	$-(L-x)$	$0$ to $a$
$BC$	$0$	$-(L-x)$	$0$ to $L$

$y=\int \frac{Mmdx}{EI}={\int }_0^a\frac{w(a-x)(L-x)dx}{EI}+0$