Question

A cable is supported at both ends at the same level and is subjected to U.D.L over the entire span. If $y_c$ is the central dip and ${}^{\prime }{l}^{\prime }$ is the span of a cable, then horizontal thrust developed at the support is

• A. $w{l}^2/3y_c$
• B. $w{l}^2/8y_c$
• C. $w{l}^3/8y_c$
• D. $w{l}^2/2y_c$

Answer 1

The correct option is B $w{l}^2/8y_c$



$V_a+V_b=wl$
$V_a=V_b=\frac{wl}{2}$

Taking moment about 'C'

$\sum M_C=0$

$V_b\times \frac{l}{2}+H_b\times y_c-w\times \frac{l}{2}\times \frac{l}{4}=0$

$\frac{wl}{2}\times \frac{l}{2}+H_b\times y_c=\frac{w{l}^2}{8}$
$H_b\times y_c=\frac{w{l}^2}{8}-\frac{w{l}^2}{4}=-\frac{w{l}^2}{8}$

$H_b=\frac{w{l}^2}{8y_c}(\leftarrow )$