Chapter 8, Problem 31P

Consider a beam under a linear distributed load and supported as shown in Fig. P8.31. The deflection of the beam is given by

$y\left(x\right)=\frac{W_0}{120EIL}\left(-x^5+2L^2{x}^3-L^{4}x\right)$ Where L is the length and EI is the flexural rigidity of the beam. Find the following:

(a) The location and value of the maximum deflection $y_{\max }$.

(b) The value of the slope $\theta =\frac{dy\left(x\right)}{dx}$ at the ends $x=0$ and $x=L$.

(e) Use your results in (a) and (b) to sketch the deflection $y\left(x\right)$.