Question 6.EP.5: For the column of Example Problem 6-4, compute the maximum s...

Objective         Compute the stress and the deflection for the eccentrically loaded column.

Given        Data from Example Problem 6_4 , but eccentricity = e = 0.75 in. Solid circular cross section: D = 0.75 in; L = 32 in; Initially straight Both ends are pinned; KL = 32 in; r = 0.188 in; c = DI2 = 0.375 in. Material: AISI 1040 hot-rolled steel; E =30×10^{6} psi.

Analysis        Use Equation (6_12) \sigma_{L / 2}=\frac{P}{A}\left[1+\frac{e c}{r^{2}} \sec \left(\frac{K L}{2 r} \sqrt{\frac{P}{A E}}\right)\right] to compute maximum stress. Then use Equation (6_14) y_{\max }=e\left[\sec \left(\frac{K L}{2 r} \sqrt{\frac{P}{A E}}\right)-1\right] to compute maximum deflection.

Results          All terms have been evaluated before. Then the maximum stress is found from Equation (6_12): \sigma_{L / 2}=\frac{P}{A}\left[1+\frac{e c}{r^{2}} \sec \left(\frac{K L}{2 r} \sqrt{\frac{P}{A E}}\right)\right]

\sigma_{L / 2}=29300 \mathrm{psi} The maximum deflection is found from Equation (6_14): y_{\max }=e\left[\sec \left(\frac{K L}{2 r} \sqrt{\frac{P}{A E}}\right)-1\right]

Comments        The maximum stress is 29 300 psi at the midlength of the column. The deflection there is 0.293 in from the original straight central axis of the column.