Chapter 8, Problem 28P

A simply supported beam is subjected to a load P at $x=\frac{L}{4}$ shown in Fig.P8.28. The deflection of the beam is given by $y\left(x\right)=-\frac{P}{128EI}\left(7L^{2}x-16x^3\right),0\le x\le \frac{L}{4}$ where EI is the flexural rigidity of the beam. Find the following:

(a) The equation for the slope $\theta =\frac{dy\left(x\right)}{dx}$.

(b) The location and magnitude of maximum deflection $y_{\max }$.

(c) Evaluate both the deflection and slope at $x=0$ and $x=\frac{L}{4}$.

(d) Use the results of parts (b) and (c) to sketch the deflection $y\left(x\right)$ from $0\le x\le \frac{L}{4}$ .