Answer to Question #162295 in Mechanical Engineering for Zawad

Question #162295

A hollow circular column is made of AISI C1015, as rolled and its Outer and inner diameter is 4.5 in and 4.021 in.

I = 7.2 in^4, k= 1.5 in, L= 15 ft, effective length= 0.65*L, N=2.5.

Single column area= 3.174 in^2

total load,F= 200 kips

Determine minimum number of column and equivalent stress.


1
Expert's answer
2021-02-15T05:40:11-0500

Outer diameter d0 = 4.5 in

Inner diamer di = 4.021 in

I = 7.2 in4

k = 1.5 in

L = 15 ft

Effective Length = 0.65 L

N = 2.5

Single column area = 3.174 in2

Total load F = 200 kips

section modulus Z = "\\frac{I}{y}= \\frac{7.2}{2.25}=3.2 in^3"

Critical load for one coloumn

P="\\frac{\\pi^2EI}{L^2}=\\frac{3.14^2\\times 27557\\times 7.2}{180^2}=60.377 kips"

Number of column = 60.377 ​= 3.31

number of column will be 4

Value of equivalnt stress = 

"\\frac{60.377}{3.174}=19.022 ksi"

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