Program Listings

$199$

$5\mathrm{.}15.$ For a linearly distributed load for a beam element with end distributed values $p_1$ and $p_2$ as shown in Fig. P$5\mathrm{.}15,$ show that the equivalent nodal loads are given by

$\left[\begin{array}{c}{f}_1\\ f_2\\ f_3\\ f_4\end{array}\right]=\left[\begin{array}{c}\frac{(7p_1+3p_2)l}{20}\\ \frac{(3p_1+2p_2)l^2}{60}\\ \frac{(3p_1+7p_2)l}{20}\\ \frac{-(2p_1+3p_2)l^2}{60}\end{array}\right]$

By setting $p_1=p_2=p,$ check if it is consistent with the values for uniform distributed load case.