Problem 1 Determine the LRFD design strengthcPnfor each of

Problem # 1 Determine the LRFD design strength·@cPn·for each of the compression members shown below. Use the AISC specification and a steel with F, 50 ksi, except when otherwise noted. Use design values for K given in the AISC Construction Manual. a) c) 20 ft 0 in W12 × 65 22 ft 0 in w8 × 31 b) d) HSS 6x6 12 ft 0 in W 10 × 60 18 ft 0 in Fy = 46 ksi AT

Solution

a) the K value for pin-fixed condition is 0.707

Effective length of column = 20*0.707=14.14 ft

Axial compressive strength of W8x31 for effective length of 14.14 ft = 248 kips per Table 4-1 of AISC

b)the K value for pin-pin condition is 1

Effective length of column = 18*1=18 ft

Axial compressive strength of W10x60 for effective length of 18 ft = 475 kips per Table 4-1 of AISC

c)the K value for fixed-fixed condition is 0.5

Effective length of column = 0.5*22=11 ft

Axial compressive strength of W12x65 for effective length of 11 ft = 747 kips per Table 4-1 of AISC

d)the K value for fixed-free condition is 2

Effective length of column=2*12=24 ft=288 in

Given section is HSS6x6x1/4 of grade 46 ksi

radius of gyration=2.34 in

KL/r=288/2.34=123.1

4.71*sqrt(E/fy)=4.71*sqrt(29000/46)=118.26

KL/r>118.26

F_cr=0.877*F_e = 0.877*pi²E/(KL/r)² = 17.95 ksi

Area of cross section of HSS6x6x1/4=5.24 in²

Axial load capapcity = 0.9*5.24*17.95=84.6 kips