Explanation Given information: Proportional limit of the material f e = 40 k s i Proportional limit is the maximum stress where stress is directly proportional to strain. Euler's formulas for the critical stress and critical load f e = π 2 E ( K L r ) 2 And P e = π 2 E I ( K L ) 2 Where K L = Effective length r = radius of gyration E = the modulus of elasticity of the material (psi) (Mpa) I = the least moment of inertia of the cross section (in 4 ) (mm 4 ) The moment of inertia for the rectangular section I = b d 3 12 The modulus of elasticity of steel is about E = 30 , 000 , 000 p s i Calculation: Pinned Substitute f e = 40 k s i in the below formula: f e = π 2 E ( K L r ) 2 40 × 10 3 = π 2 E ( 1 × L r ) 2 L r = π 2 × 30 , 000 , 000 40 × 10 3 L r = 86.036 Fixed Substitute f e = 40 k s i in the below formula: f e = π 2 E ( K L r ) 2 40 × 10 3 = π 2 E ( 0.5 × L r ) 2 L r = π 2 × 30 , 000 , 000 0

Applied Statics and Strength of Materials (6th Edition)

6th Edition

ISBN: 9780133840544

Author: George F. Limbrunner, Craig D'Allaird, Leonard Spiegel

Publisher: PEARSON

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Buckling of columns

The column is described as a vertical member of the structure that carries an axial compressive load, and buckling is a lateral deformation of the column under the application of load.

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Chapter 18, Problem 18.7P

To determine

To Calculate:

The slenderness ratio for each case.

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Chapter 18, Problem 18.6P

Chapter 18, Problem 18.8P

Chapter 18 Solutions

Applied Statics and Strength of Materials (6th Edition)

Ch. 18 - Calculate the Euler buckling load for an axially...Ch. 18 - Calculate the Euler buckling load for a...Ch. 18 - A pin-connected axially loaded compression member...Ch. 18 - Prob. 18.4P Ch. 18 - Plot a curve showing the relationship of feversus...Ch. 18 - A W1222 structural steel wide-flange section is...Ch. 18 - Prob. 18.7P Ch. 18 - Calculate the allowable axial compressive load for...Ch. 18 - A W20059 structural steel wide-flange section is...Ch. 18 - Use Euler’s formula and a factor of safety of 2.5...

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