2 PROBLEM Compression Member l o 3 126 ft 6 y7 2 2 An axiall

(2) PROBLEM (Compression Member) l o 3\" 1-26 ft 6\" y-7 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)

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