Question 18.P.11: The beam AB shown in Figure P18.11 is subjected to a distrib...
The beam AB shown in Figure P18.11 is subjected to a distributed load that varies from p_{1} per unit length at \mathrm{A} to p_{2} per unit length at \mathrm{B}. Obtain the equivalent consistent loads at the two ends of the beam using (a) interpolation functions given in Equation 18.26,
\begin{aligned}&N_1(x)=x\left(1-\frac{x}{L}\right)^2 \\&N_2(x)=1-3\left(\frac{x}{L}\right)^2+2\left(\frac{x}{L}\right)^3 \\&N_3(x)=\frac{x^2}{L}\left(\frac{x}{L}-1\right) \\&N_4(x)=3\left(\frac{x}{L}\right)^2-2\left(\frac{x}{L}\right)^3\end{aligned} (18.26)
(b) interpolation functions given in Problem 18.7.
\begin{aligned}&\text { (a) and (b) } \\&\mathbf{f}=\left[\begin{array}{c}\frac{1}{20} p_{1} L^{2}+\frac{1}{30} p_{2} L^{2} \\\frac{7}{20} p_{1} L+\frac{3}{20} p_{2} L \\-\frac{1}{30} p_{1} L^{2}-\frac{1}{20} p_{2} L^{2} \\\frac{3}{20} p_{1} L+\frac{7}{20} p_{2} L\end{array}\right]\end{aligned}
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