Chapter 8, Problem 34P

Consider the buckling of a pinned-fixed column under a compressive load P as shown in Fig. P8.34.

The deflection $y\left(x\right)$ of the buckled configuration is given by

$y\left(x\right)=-A\left[\sin \left(\frac{4.4934}{L}x\right)+\frac{0.97616}{L}x\right]$ where A is an undetermined constant.

1. Determine the equation for the slope $\theta =\frac{dy}{dx}$.

1. Evaluate both the deflection and slope at the points $x=0$ and $x=L$.
2. Determine the location and magnitude of the maximum deflection.
3. Use the results of parts (b) and (c) to sketch the buckled deflection $y\left(x\right)$.