Explanation Given information: The A992 steel hollow section acts as a column. The ends of the column are pinned. The length of the column is denoted by L . The load on the column is 45 kip . The outer width ( b 1 ) of the hollow rectangular section is 3 in . The outer depth ( d 1 ) of the hollow rectangular section is 6 in . The inner width ( b 2 ) of the hollow rectangular section is 2 in . The inner depth ( d 2 ) of the hollow rectangular section is 5 in . The eccentricity ( e ) of the loading is 6 in . The ends of the column are pinned. Calculation: Calculate the cross-sectional area ( A ) of the rectangular hollowcolumn using the relation: A = b 1 d 1 − b 2 d 2 (1) Substitute 3 in . for b 1 , 6 in . for d 1 , 2 in . for b 2 , and 5 in . for d 2 in Equation (1): A = 3 × 6 − 2 × 5 = 18 − 10 = 8 in . 2 Calculate the moment of inertia ( I y ) using the relation: I y = 1 12 d 1 b 1 3 − 1 12 d 2 b 2 3 (2) Substitute 3 in . for b 1 , 6 in . for d 1 , 2 in . for b 2 , and 5 in . for d 2 in Equation (2): I y = 1 12 × 6 × 3 3 − 1 12 × 5 × 2 3 = 13.5 − 3.33 = 10.17 in . 4 Calculate the moment of inertia ( I x ) using the relation: I x = 1 12 b 1 d 1 3 − 1 12 b 2 d 2 3 (3) Substitute 3 in . for b 1 , 6 in . for d 1 , 2 in . for b 2 , and 5 in . for d 2 in Equation (3): I x = ( 1 12 × 3 × 6 3 ) − ( 1 12 × 2 × 5 3 ) = 54 − 20.83 = 33.17 in . 4 Calculate the value of radius of gyration ( r x ) using a relation: r x = I x A (4) Substitute 33.17 in . 4 for I x and 8 in . 2 for A in Equation (4). r x = 33.17 in . 4 8 in . 2 = 4 .146 in . 2 = 2.036 in . Consider the buckling of column about y-y axis: Thesteelcolumn is pinned, thus the value of effective length factor ( K ) is 1. Consider the Young’s modulus ( E ) of the steel is 29 × 10 3 ksi . Show the expression for Euler’s formula as follows: P cr = π 2 E I y ( K L ) y 2 (5) Here, E is the Young’s modulus, I is the moment of inertia, K is the effective length factor, L is the length of the member. The load on the column is 45 kip . Substitute 45 kip for P cr , 29 × 10 3 ksi for E , 10.17 in . 4 for I y , and 1 for K in Equation (5)

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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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 13.5, Problem 13.62P

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The maximum allowable load on the column without yielding or buckling.

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Chapter 13.5, Problem 13.61P

Chapter 13.5, Problem 13.63P

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The maximum allowable load on the column without yielding or buckling.

Solution Summary: The author calculates the maximum allowable load on the column without yielding or buckling. The cross-sectional area of the rectangular hollowcolumn is (A).

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