A W14 × 90 is used as a column with one (rotation and translation) fixed end, an

Question

A W14 × 90 is used as a column with one (rotation and translation) fixed end, and the other end translation fixed but rotation free. The length is 13 feet. If A992 steel is used.

A.Use formula method to compute the design strength.

B.Use Table 4-1though 4-6 from Part 4 of the AISC Manual (handout 03). Compute the design strength for LRFD.

C.Use Table 4-22 from Part 4 of the AISC Manual (handout03). Compute the design strength for LRFD.

D.If the column must support a service dead load of 180kips and a service live load of 540 kips. Is its available compressive (design) strength enough to support such service loads?

Pay attention on if your answers from a) and b) match.

Explanation / Answer

Given length of column is 13 feet . one end is fixed and other end is pinned

Area of cross section of clumn = 26.5in2

Effective length of column = KL=0.7L=0.7*13=9.1ft

a)Moment of inertia of section about minot axis = 362in4

Euler's Buckling load capapcity of column = pi2EI/(KL)2= (pi2*29000*362)/(9.1*12)2 = 8688.8 kips

From yielding of column cross section point of view,the capacity of column = 0.9*26.5*50=1192.5kips

Axial load capapcity of column=1192.5 kips

b)Per Table 4-1, for effectilve length of 9.1 ft, capacity of W14x90 per LRFD design =1120 kips

c) radius of gyration of column about minor axis = 3.7in

Slenderness ratio =KL/r = (9.1*12)/3.7=29.5

From table 4-22, Fcr corresponding to KL/r of 29.5 and Fy=50ksi is 42.2ksi

Area of cross section of column = 26.5in2

Axial load capacity = 42.2*26.5=1118.3kips

d)Design load on column =(1.2*180)+(1.6*540) = 1080kips

Column demand is lower than capacity. Column has adequate strength

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