Chapter 8, Problem 29P

A simply supported beam is subjected to an applied moment $M_0$, at its center z = 4 as shown in Fig. P.29. The deflection of the beam is given by

$y\left(x\right)=\frac{M_0}{6EIL}\left(L^{2}x-\frac{3L{x}^2}{4}-x^3\right),$ $0\le x\le \frac{L}{2}$ where EI is the flexural rigidity of the beam. Find the following:

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

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

(c) Evaluate both the deflection and slope at the points A and B ( $x=0$ and $x=\frac{L}{2}$ ).

(d) Use the results of parts (a)-(c) to sketch the deflection $y\left(x\right)$ from ( $x=0$ and $x=\frac{L}{2}$ ).