Chapter 8, Problem 33P

Consider the buckling of a pinned-pinned column under a compressive axial load P as shown in Fig. P8.33.

The deflection $y\left(x\right)$ of the second buckling mode is given by

$y\left(x\right)=-A\sin \left(\frac{2\pi x}{L}\right)$ where, A is an undetermined constant.

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

(b) Determine the value of the slope at the locations where the deflection is zero.

(c) Determine the value of the deflection at the locations where the slope is zero.

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