Explanation Given information: The A992 steel hollow section acts as a column. The ends of the column are pinned. The length of the column, L = 14 ft . The load on the column is denoted by P . 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. Substitute 29 × 10 3 ksi for E , 10.17 in . 4 for I y , 14 ft for L , and 1 for K in Equation (5). P cr = π 2 ( 29 × 10 3 ksi ) ( 10

10th Edition

ISBN: 9780134319650

Author: Russell C. Hibbeler

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 13.5, Problem 13.57P

To determine

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

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Chapter 13.5, Problem 13.56P

Chapter 13.5, Problem 13.58P

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Chapter 13 Solutions

Mechanics of Materials (10th Edition)

Ch. 13.3 - A 50-in long steel rod has a diameter of 1 in....Ch. 13.3 - A 12-ft wooden rectangular column has the...Ch. 13.3 - The A992 steel column can be considered pinned at...Ch. 13.3 - A steel pipe is fixed supported at its ends. If it...Ch. 13.3 - Determine the maximum force P that can be...Ch. 13.3 - The A992 steel rod BC has a diameter of 50 mm and...Ch. 13.3 - Determine the critical buckling load for the...Ch. 13.3 - The column consists of a rigid member that is...Ch. 13.3 - The aircraft link is made from an A992 steel rod....Ch. 13.3 - Rigid bars AB and BC are pin connected at B. If...

Ch. 13.3 - A 2014-T6 aluminium alloy column has a length of 6...Ch. 13.3 - Solve Prob. 13-5 if the column is pinned at its...Ch. 13.3 - The W12 50 is made of A992 steel and is used as a...Ch. 13.3 - The W12 50 is made of A992 steel and is used as a...Ch. 13.3 - A steel column has a length of 9 m and is fixed at...Ch. 13.3 - A steel column has a length of 9 m and is pinned...Ch. 13.3 - The A992 steel angle has a cross-sectional area of...Ch. 13.3 - The 50-mm-diameter C86100 bronze rod is fixed...Ch. 13.3 - Determine the maximum load P the frame can support...Ch. 13.3 - The W8 67 wide-flange A-36 steel column can be...Ch. 13.3 - Prob. 13.15P Ch. 13.3 - Prob. 13.16P Ch. 13.3 - The 10-ft wooden rectangular column has the...Ch. 13.3 - The 10-fl wooden column has the dimensions shown....Ch. 13.3 - Determine the maximum force P that can be applied...Ch. 13.3 - The A-36 steel pipe has an outer diameter of 2 in....Ch. 13.3 - The A-36 steel pipe has an outer diameter of 2 in....Ch. 13.3 - The deck is supported by the two 40-mm-square...Ch. 13.3 - The deck is supported by the two 40-mm-square...Ch. 13.3 - The beam is supported by the three pin-connected...Ch. 13.3 - The W14 30 A992 steel column is assumed pinned at...Ch. 13.3 - The A992 steel bar AB has a square cross section....Ch. 13.3 - The linkage is made using two A992 steel rods,...Ch. 13.3 - The linkage is made using two A992 steel rods,...Ch. 13.3 - The linkage is made using two A-36 steel rods,...Ch. 13.3 - The linkage is made using two A-36 steel rods,...Ch. 13.3 - The steel bar AB has a rectangular cross section....Ch. 13.3 - Determine if the frame can support a load of P =...Ch. 13.3 - Determine the maximum allowable load P that can be...Ch. 13.3 - Prob. 13.34P Ch. 13.3 - Prob. 13.35P Ch. 13.3 - The members of the truss are assumed to be pin...Ch. 13.3 - Solve Prob. 1336 for member AB, which has a radius...Ch. 13.3 - The truss is made from A992 steel bars, each of...Ch. 13.3 - The truss is made from A992 steel bars, each of...Ch. 13.3 - Prob. 13.40P Ch. 13.3 - The ideal column has a weight w (force/length) and...Ch. 13.3 - The ideal column is subjected to the force F at...Ch. 13.3 - The column with constant El has the end...Ch. 13.3 - Consider an ideal column as in Fig.13-10 c, having...Ch. 13.3 - Consider an ideal column as in Fig. 13-10d, having...Ch. 13.5 - The wood column is fixed at its base and free at...Ch. 13.5 - The W10 12 structural A-36 steel column is used...Ch. 13.5 - The W10 12 structural A-36 steel column is used...Ch. 13.5 - The aluminium column is fixed at the bottom and...Ch. 13.5 - Prob. 13.50P Ch. 13.5 - Prob. 13.51P Ch. 13.5 - The aluminum rod is fixed at its base and free and...Ch. 13.5 - Assume that the wood column is pin connected at...Ch. 13.5 - Prob. 13.54P Ch. 13.5 - The wood column is pinned at its base and top. If...Ch. 13.5 - Prob. 13.56P Ch. 13.5 - Prob. 13.57P Ch. 13.5 - Prob. 13.58P Ch. 13.5 - Prob. 13.59P Ch. 13.5 - The wood column is pinned at its base and top. If...Ch. 13.5 - The brass rod is fixed at one end and free at the...Ch. 13.5 - The brass rod is fixed at one end and free at the...Ch. 13.5 - Prob. 13.63P Ch. 13.5 - A W14 30 structural A-36 steel column is pin...Ch. 13.5 - Prob. 13.65P Ch. 13.5 - The 6061-T6 aluminum alloy solid shaft is fixed at...Ch. 13.5 - The 6061-T6 aluminum alloy solid shaft is fixed at...Ch. 13.5 - The W14 53 structural A992 steel column is fixed...Ch. 13.5 - The W14 53 column is fixed at its base and free...Ch. 13.5 - Prob. 13.70P Ch. 13.5 - The stress-strain diagram for a material can be...Ch. 13.5 - The stress-strain diagram for a material can be...Ch. 13.5 - The stress-strain diagram for the material of a...Ch. 13.5 - Construct the buckling curve, P/A versus L/ r, for...Ch. 13.5 - The stress-strain diagram of the material can be...Ch. 13.5 - The stress-strain diagram of the material can be...Ch. 13.5 - Prob. 13.77P Ch. 13.6 - Determine the largest length of a W10 12...Ch. 13.6 - Using the AISC equations, select from AppendixB...Ch. 13.6 - Take Y = 50 ksi.Ch. 13.6 - Determine the longest length of a W8 31...Ch. 13.6 - Using the AISC equations, select from AppendixB...Ch. 13.6 - Prob. 13.83P Ch. 13.6 - Using the AISC equations, select from AppendixB...Ch. 13.6 - Prob. 13.85P Ch. 13.6 - Prob. 13.86P Ch. 13.6 - Prob. 13.87P Ch. 13.6 - Prob. 13.88P Ch. 13.6 - Using the AISC equations, check if a column having...Ch. 13.6 - The beam and column arrangement is used in a...Ch. 13.6 - Prob. 13.91P Ch. 13.6 - Prob. 13.92P Ch. 13.6 - The 1-in.-diameter rod is used to support an axial...Ch. 13.6 - The 1-in.-diameter rod is used to support an axial...Ch. 13.6 - Prob. 13.95P Ch. 13.6 - Prob. 13.96P Ch. 13.6 - Prob. 13.97P Ch. 13.6 - Prob. 13.98P Ch. 13.6 - The tube is 0.25 in. thick, is made of 2014-T6...Ch. 13.6 - Prob. 13.100P Ch. 13.6 - A rectangular wooden column has the cross section...Ch. 13.6 - Prob. 13.102P Ch. 13.6 - Prob. 13.103P Ch. 13.6 - The bar is made of aluminum alloy 2014-T6....Ch. 13.6 - Prob. 13.105P Ch. 13.6 - Prob. 13.106P Ch. 13.7 - The W8 15 wide-flange A-36 steel column is...Ch. 13.7 - Solve Prob.13-107 if the column is fixed at its...Ch. 13.7 - Prob. 13.109P Ch. 13.7 - Prob. 13.110P Ch. 13.7 - The W8 15 wide-flange A992 steel column is fixed...Ch. 13.7 - The W8 15 wide-flange A992 steel column is fixed...Ch. 13.7 - The W12 22 wide-flange A-36 steel column is fixed...Ch. 13.7 - Prob. 13.114P Ch. 13.7 - Prob. 13.115P Ch. 13.7 - Prob. 13.116P Ch. 13.7 - A 20-ft-long column is made of aluminum alloy...Ch. 13.7 - A 20-ft-long column is made of aluminum alloy...Ch. 13.7 - The 2014-T6 aluminum hollow column is fixed at its...Ch. 13.7 - The 2014-T6 aluminum hollow column is fixed at its...Ch. 13.7 - Prob. 13.121P Ch. 13.7 - Prob. 13.122P Ch. 13.7 - Prob. 13.123P Ch. 13.7 - Prob. 13.124P Ch. 13.7 - The 10-in.-diameter utility pole supports the...Ch. 13.7 - Using the NFPA equations of Sec 13.6. and Eq....Ch. 13.7 - Prob. 13.127P Ch. 13 - The wood column has a thickness of 4 in. and a...Ch. 13 - The wood column has a thickness of 4 in. and a...Ch. 13 - A steel column has a length of 5 m and is free at...Ch. 13 - The square structural A992 steel tubing has outer...Ch. 13 - If the A-36 steel solid circular rod BD has a...Ch. 13 - If P = 15 kip, determine the required minimum...Ch. 13 - The steel pipe is fixed supported at its ends. 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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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Chapter 13 Solutions