Question

The horizontal deflection at C for the frame loaded and supported as shown in the following figure is

• A. $\frac{M{l}^2}{4EI}$
• B. $\frac{M{l}^2}{2EI}$
• C. $\frac{M{l}^2}{EI}$
• D. $\frac{M{l}^2}{3EI}$

Answer 1

The correct option is B $\frac{M{l}^2}{2EI}$

$\delta H_c=\int \frac{M_x{m}_x}{EI}dx$

Member	$M_x$	$m_x$	$\delta H_c=\int \frac{M_x{m}_x}{EI}dx$
BC	(-) M	0	0
BA	(-) M	$-1\times x$	$={\int }_0^l\frac{-M(-x)dx}{EI}=\frac{M{l}^2}{2EI}$

$\delta H_c=\frac{+M{l}^2}{2EI}$