2 PROBLEM Compression Member 12 3 L26 ft 6 y 2 2 An axially

(2) PROBLEM (Compression Member) 12 3 \" 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) 8-Z CI 2018

Solution

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

y\'=(2*6*2*3 + 12*3*7.5)/(2*2*6+12*3)=5.7 in

moment of inertia about minor axis=2*2*6³/12+2*2*6*(5.7-3)²+12*3³/12+12*3*(7.5-5.7)²=390.6 in⁴

area of cross section=2*2*6+12*3=60 in²

radius of gyration=sqrt(390.6/60)=2.55 in

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

slenderness ratio=220.6/2.55=86.5

2) critical buckling stress = pi²*E/(KL/r)²=pi²*29000/86.5² = 38.25 ksi

3)nominal compressive strength = 38.25*60=2295.2 kips

4) design compressive strength=0.9*2295.2=2065.66 kips