Chapter 5, Problem 36P

A simply supported beam is subjected to distributed loads w₁and w₂as shown. The bending moment as a function of x is given by the following equations:

$M\left(x\right)=R_{A}x-\frac{w_1{x}^2}{2}$ for $0\le x\le a$

$M\left(x\right)=R_{A}x-\frac{w_{1}a}{2}\left(2x-a\right)$ for $a\le x\le \left(a+b\right)$

$M\left(x\right)=R_B\left(L-x\right)-\frac{w_2{\left(L-x\right)}^2}{2}$ for $\left(a+b\right)\le x\le L$

where $R_A=\left[w_{1}a\left(2L-a\right)+w_2{c}^2\right]/\left(2L\right)$ and $R_B=\left[w_{2}c\left(2L-a\right)+w_1{a}^2\right]/\left(2L\right)$ are the reactions at the supports. Make a plot of the bending moment M as a function of x (one plot that shows the moment for $0\le x\le L$ ).Take L = 16 ft, a = b = 6 ft, w₁= 400 lb/ft, and w₂= 200 lb/ft.