Chapter 8, Problem 30P

A simply supported beam is subjected to a sinusoidal distributed load, as shown in the Fig. P8.30. The deflection y(x) of the beam is given by

$y\left(x\right)=\frac{w_0{L}^4}{16{\pi }^{4}EI}\sin \left(\frac{2\pi x}{L}\right)$ where EI is the flexural rigidity of the beam. Find the following:

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

(b) The value of the slope where the deflection is zero.

(c) The value of the deflection at the location where the slope is zero.

(d) Use the results of parts (b) and (c) to sketch the deflection $y\left(x\right)$.