Explanation Given Information: The length of the column, L = 20 ft The allowable load, P = 25k The value of the young modulus, E = 29000 ksi The value of maximum stress, s y = 36 ksi The thickness of the steel pipe, t = d/20 here d is the outside diameter of the steel pipe. Concept Used: d i = d − 2 ( t ) A = π 4 ( d o 2 − d i 2 ) I = π 64 ( d o 4 − d i 4 ) r = I A L c = critical length of column in ft. Then we choose different diameters d and calculate till the value of P a l l o w =P i = 1 , 2...4 n 1 i = N A i if K L i r > K L c r & n 1 i = 5 3 + 3 ( K L i r ) 8 ( K L c r ) − ( K L i r ) 3 8 ( K L c r ) 3 i f K L i r ≤ K L c r n 2 i = 23 12 if K L i r > K L c r & n 2 i = N A if K L i r ≤ K L c r σ a l l o w = σ y [ 1 n 1 i ( 1 − ( K L i r ) 2 2 ( K L c r ) 2 ) ] i f K L i r ≤ K L c r σ a l l o w = σ y [ ( K L c r ) 2 2 n 2 i ( K L i r ) 2 ] i f K L i r > K L c r P a l l o w = σ a l l o w × A Calculation: d i = d − 2 ( t ) A = π 4 ( d 2 − ( d − 2 t ) 2 ) h e r e t = d / 20 A = .14923 d 2 I = π 64 ( d 4 − ( ( d − 2 ( d / 20 ) ) 4 ) = π 64 ( d 4 − ( .9 d ) 4 ) = 0.016881 d 4 r = 0.016881 d 4 0.14932 d 2 = .33623 d ( K L r ) max = 200 , h e r e K = 1 L max = 200 × .33623 d = 67.246 d K L c / r = 2 π 2 29000 36 = 126.1 L c = ( 126

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN: 9781337093347

Author: Barry J. Goodno, James M. Gere

Publisher: Cengage Learning

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Chapter 11, Problem 11.9.17P

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The value of the outside diameter d for a steel pipe.

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Mechanics of Materials (MindTap Course List)

Ch. 11 - A rigid bar of length L is supported by a linear...Ch. 11 - The figure shows an idealized structure consisting...Ch. 11 - -2-3. Two rigid bars are connected with a...Ch. 11 - Repeat Problem 11.2-3 assuming that R= 10 kN ·...Ch. 11 - The figure shows an idealized structure consisting...Ch. 11 - An idealized column consists of rigid bar ABCD...Ch. 11 - An idealized column is made up of rigid segments...Ch. 11 - The figure shows an idealized structure consisting...Ch. 11 - The figure shows an idealized structure consisting...Ch. 11 - The figure shows an idealized structure consisting...

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