Chapter 8, Problem 36P

A cantilever beam is pinned at the end $x=L$, and subjected to an applied moment $x=L$ as shown in Fig. P8.36. The deflection $y\left(x\right)$ of the beam is given by

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

1. The equation of the slope $\theta =\frac{dy\left(x\right)}{dx}$.
2. The location and magnitude of the maximum deflection $y_{\max }$.
3. Evaluate both the deflection and slope at the points A and B ( $x=0$ and $x=L$
4. ).
5. Use the results in parts (b) and (c) to sketch the deflection $y\left(x\right)$ and clearly indicate the location of the maximum deflection on the sketch.