x 12 A 572 Grade 50 14 W 1272 A 992 20 ft 412 A 672 Grade 50

\'x 12. A 572 Grade 50- 14 W 12×72 A 992 20 ft 4.12. A 672 Grade 50 Problem 3 (30 points) A W 12x65 A992 section is used as a column as shown. The column has a span length of 24 ft and is pinned at the top and fixed at the bottom. On the weak axis, a pinned support is provided at 9 ft from the top to strengthen the column. Determine the column load carrying capacity 24 Pt 5 ft CORE Strong Axis Weak Axis ONOR CODE H

Solution

Effective length of section about strong axis = 24*0.707=16.97 ft

radius of gyration of section about major axis = 5.28 in

KL/r = 16.97*12/5.28=38.57

effective length about minor axis = 15*0.707=10.61 ft

radius of gyration about minor axis = 3.02 in

KL/r = 10.61*12/3.02=42.16

The slenderness ratio that governs the design is KL/r=42.16

4.71*sqrt(E/fy)=4.71*sqrt(29000/50)=113.4

42.16<113.4

therefore,. F_cr=0.658^(Fy/Fe)F_y

F_e=pi²E/(KL/r)²=pi²*29000/42.16²=161 ksi

F_cr=0.658^(50/161)*50 = 43.9 ksi

Area of cross section=19.1 in²

Axial load capacity = 0.9*43.9*19.1=754.64 kips