Strength Of Materials -

: [ P_cr = \frac\pi^2 EI(KL)^2 ] where (K) = effective length factor (1 pinned-pinned, 0.5 fixed-fixed, 2 fixed-free, 0.7 fixed-pinned).

: [ \tau_max = \sqrt\left( \frac\sigma_x - \sigma_y2 \right)^2 + \tau_xy^2 ] Occurs at ( \theta_p \pm 45^\circ ). Strength of materials