Chapter 8, Problem 24P

A simply supported beam is loaded as shown in Fig. P8.24. Using singularity functions, the shear along the beam can be expressed by the equation:

$V\left(x\right)=20\left[{\langle x-0\rangle }^1-{\langle x-5\rangle }^1\right]-15{\langle x-8\rangle }^0-57$

By definition, the singularity function can be expressed as follows:

${\langle x-a\rangle }^n=\left\{\begin{array}{cc}{\left(x-a\right)}^n& \text{when }x>a\\ 0& \text{when }x\le a\end{array}\right\}$

Use a numerical method to find the point(s) where the shear equals zero.

FIGURE P8.24