Question 11.5: Compute the allowable compressive strength, Pa , for the col...
Compute the allowable compressive strength, P_{a} , for the column described in Example Problem 11–4 except it will be installed with both ends fixed instead of pinned.
Actual slenderness ratio = SR = KL/r = (0.65)(3050 mm/20.4 mm) = 97.2 From Example Problem 11–4,
Transition slenderness ratio = SR_{t} = 123.7
Elastic critical buckling stresss = s_{e} = π² E/(SR)² = π² (200 000 MPa)/(97.2)²
s_{e} = = 209.0 MPa
Then the column is short and Equation (11–10) is applied next.
The exponent d = = s_{y}/s_{e} = 290 MPa/209.4MPa = 1.388
and
s_{cr} = [ 0.658^{d}]s_{y} = [0.658^{1.388}] (290 MPa) = 162.8 MPa
Nominal buckling strength P_{n} = s_{cr} A_{g} = (162.2 N/mm²)(1136 mm²) = 184.3 kN
Using Equation (11–13),
Allowable compressive strength = P_{a} = P_{n} /1.67 = 184.3 kN/1.67 = 110.4 kN
Comment The resulting allowable compressive strength for the fixed-end column is 2.11 times greater than the column design having pinned ends.