Chapter 8, Problem 35P

Consider a beam under a uniform distributed load and supported as shown in Fig. P8.35. The deflection of the beam is given by

$y\left(x\right)=\frac{-w}{48EI}\left(2x^4-5x^{3}L+3x^2{L}^2\right)$ when L is the length and El 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 $y\left(x\right)$.