Explanation Given information: The column is made up of W12 × 26 structural A992 steel. The ends of the column are pinned. The length of the column is denoted by L . The eccentricity of loading ( e ) is 6 in . The length ( L ) on the column is denoted by 11.5 ft . The load on the column is denoted by P . Calculation: Show the section properties of W12 × 26 as follows: The cross-sectional area ( A ) is 7.65 in . 2 . The moment of inertia ( I x ) is 204 in . 4 The moment of inertia ( I y ) is 17.3 in . 4 The radius of gyration ( r x ) is 5.17 in . The overall depth of cross-section ( d ) is 12.22 in . Consider the buckling of column about y-y axis: The column is pinned, thus the value of effective length factor ( K ) is 1. The Young’s modulus ( E ) of the steel column 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 (1) 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 11.5 ft for L , 29 × 10 3 ksi for E , 17.3 in . 4 for I , and 1 for K in Equation (1). P c r = π 2 ( 29 × 10 3 ) ( 17.3 ) ( 1 × 11.5 ft × 12 in . 1 ft ) 2 = 4951.58 × 10 3 19 , 044 = 260 kip Thus, the load on the column based on the buckling criteria is 260 kip _ . Check the validity of Euler’s formula: Consider the yielding stress of the steel, σ Y = 50 ksi . Calculate the critical stress using the relation; σ cr = P cr A (2) Substitute 260 kip for P cr and 7.65 in . 2 for A in Equation (2). σ cr = 260 kip 7.65 in . 2 = 33.986 ksi < ( σ Y = 50 ksi ) Thus, the Euler’s formula is valid. Consider the yielding of column about x-x axis. Show the expression for secant formula as follows: σ Y = P A [ 1 + e c r 2 sec ( K L 2 r P E A ) ] (3) Here, P is the vertical load, σ max is the maximum elastic stress, e is the eccentricity of the load P , c is the distance of centroidal axis to the outer fiber of the column, A is the cross-sectional area of the column, K is the effective length factor, L is the length of the column, E is modulus of elasticity of the material, and r is the radius of gyration

10th Edition

ISBN: 2818440034374

Author: 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 13.63P

To determine

The load supported by the column without buckling or yielding.

To compare: The obtained eccentric load with the axial critical load P′ .

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Chapter 13.5, Problem 13.62P

Chapter 13.5, Problem 13.64P

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Chapter 13 Solutions

MECHANICS OF MATERIALS

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. If...Ch. 13 - The W200 46 wide-flange A992-steel column can be...Ch. 13 - The wide-flange A992 steel column has the cross...Ch. 13 - The wide-flange A992 steel column has the cross...

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The load supported by the column without buckling or yielding. To compare: The obtained eccentric load with the axial critical load P ′ .

Solution Summary: The author analyzes the load supported by the column without buckling or yielding. The maximum axial load is higher than the maximum eccentric load.

Concept explainers

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The load supported by the column without buckling or yielding.

To compare: The obtained eccentric load with the axial critical load P′ .

Want to see the full answer?

Chapter 13 Solutions

The load supported by the column without buckling or yielding. To compare: The obtained eccentric load with the axial critical load P ′ .

Solution Summary: The author analyzes the load supported by the column without buckling or yielding. The maximum axial load is higher than the maximum eccentric load.

Concept explainers

Videos

The load supported by the column without buckling or yielding. To compare: The obtained eccentric load with the axial critical load P′ .

Want to see the full answer?

Chapter 13 Solutions

The load supported by the column without buckling or yielding.

To compare: The obtained eccentric load with the axial critical load P′ .