Question

A portal frame ABCD is subjected to point loads at E & F as shown below.



The horizontal displacement of joint 'D' if $EI=2\times {10}^{6}kN-m^2$ is

• A. $90mm$
• B. $13mm$
• C. $1.3mm$
• D. $9mm$

Answer 1

The correct option is D $9mm$

Member	Range of $x$	$EI$	$M$
$AE$	$0-6$	$EI$	$60x$
$EB$	$0-2$	$EI$	$60(x+6)-60x$
$BF$	$0-4$	$2EI$	$60\times 6+15x$
$DC$	$0-6$	$EI$	$0$
$CF$	$0-4$	$2EI$	$105x$

Member	Range of $x$	$EI$	$M$
$AE$	$0-6$	$EI$	$x$
$EB$	$0-2$	$EI$	$(x+6)$
$BF$	$0-4$	$2EI$	$8-0.25x$
$DC$	$0-6$	$EI$	$x$
$CF$	$0-4$	$2EI$	$6+0.25x$

${\Delta }_D=\int \frac{Mmdx}{EI}=\underset{0}{\overset{6}{\int }}\frac{60x.xdx}{EI}+\underset{0}{\overset{2}{\int }}\frac{(60\times 6)(x+6)dx}{EI}+\underset{0}{\overset{4}{\int }}\frac{(60\times 6+15x)(8-0.25x)}{2EI}+\underset{0}{\overset{6}{\int }}\frac{\left(0\right)\left(x\right)dx}{2EI}+\underset{0}{\overset{4}{\int }}\frac{\left(105x\right)(6+0.25x)}{2EI}=9mm$