Old spec Statics Session 19 Example 1 (ENGR5004)

Old spec Statics Session 19 Example 1TutorialOld spec ENGR2162:210 min

ENGR216 (old spec) Statics session 19 worked example 1 (slides 8-10) official answers

A 2 m long steel column of solid circular cross section with radius $r = 40$ mm has $E = 200$ GPa and allowable normal stress $\sigma_{all} = 100$ MPa. Using a factor of safety $k = 2.5$ on Euler's critical load for buckling, determine the maximum compressive axial load the column can carry if:

Formulas you may need

Euler critical stress $\sigma_{cr} = \dfrac{\pi^2 E}{(L_e/\rho)^2}$ , $\rho = \sqrt{I/A}$ (on the formula sheet)
Effective lengths: pinned-pinned $L_e = L$ , fixed-fixed $L_e = 0.5L$ (on the formula sheet)
Solid circle $\rho = r/2$ (on the formula sheet: $I = \pi r^4/4$ , $A = \pi r^2$ )
Allowable load $P_{max} = \min(\sigma_{cr}/k,\ \sigma_{all})\,A$ (learn this)

(a)
the column is pinned at both ends;
P_max =kN
(b)
the column is fixed at both ends.
P_max =kN