Euler Equation Determine the critical buckling load for each of the columns, usi

Question

Euler Equation

Determine the critical buckling load for each of the columns, using the Euler equation. E= 29000 ksi. Porportional limit= 36000psi. Assume simple ends and maximum permissible L/r=200.

A solid round bar of 1.25 in. diameter:

a. L= 4ft. 0in.

Answer is 14.89 kips

I tried getting the radius of the diameter and then using the equation but I'm not getting the answer. Any help will be greatly appreciated. Thanks.

Euler Equation Fe = pi^2 E/(L/r)^2 Determine the critical buckling load for each of the columns, using the Euler equation. E= 29000 ksi. Porportional limit= 36000psi. Assume simple ends and maximum permissible L/r=200. A solid round bar of 1.25 in. diameter: a. L= 4ft. 0in. Answer is 14.89 kips I tried getting the radius of the diameter and then using the equation but I'm not getting the answer. Any help will be greatly appreciated. Thanks.

Explanation / Answer

given r in the formula is not the radius of the bar. It is radius of gyration of the cylindrical bar which is given by

r = actual radius / 2 for solid cylinder

=> r = d/(22) =0.442 inch

L = 4 ft = 48 inch

L/r =48/0.442 =108.6

Fe = 2*29000/(108.6)2 =24268 ksi

d is the diameter

also Fe calculted from gives critical stress not the critical load.

critical load = Fe x r2 = 24268**0.4422 =14894 ips =14.894 kips

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