2 PROBLEM Compression Member L26 ft 6 y 2 2 An axially loade

(2) PROBLEM (Compression Member) L-26 ft 6\" y=? 2\" 2 An axially loaded column is given as shown in the figure. Using the listed data determine the following: (1) The slenderness ratio (2) The critical buckling stress (ksi) (3) The nominal compressive stregth (kips) (4) The design strength of the column (kips) STL-528-Z ZEYTINCI SPRING 2018

Solution

a)let the centroid be at y\' as shown in the figure in question

y\'=(2*6*2*3 + 10*3*7.5)/(2*2*6+10*3)=5.5 in

moment of inertia about minor axis=2*2*6³/12+2*2*6*(5.5-3)²+10*3³/12+10*3*(7.5-5.5)²=364.5 in⁴

area of cross section=2*2*6+10*3=54 in²

radius of gyration=sqrt(364.5/54)=2.6 in

Effective length=26*0.707=18.38 ft=220.6 in

slenderness ratio=220.6/2.6=84.85

2) critical buckling stress = pi²*E/(KL/r)²=pi²*29000/84.85² = 39.76 ksi

3)nominal compressive strength = 39.76*54=2146.78 kips

4) design compressive strength=0.9*2146.78=1932.1 kips