Explanation Given information: A wide-flange W12 × 50 of A36 steel acts as a column. The length of the column is L = 10 ft . The column is fixed at the bottom and pinned at the top. The eccentric load applied on the column, P . Show the AISC equation of Sec 13.6 as follows: σ allow = [ 1 − 1 2 ( K L r ( K L r ) c ) 2 ] σ Y [ 5 3 + 3 8 ( K L r ( K L r ) c ) − 1 8 ( K L r ( K L r ) c ) 3 ] Here, σ allow is the allowable stress, σ Y is the yield stress, E is the Young’s modulus, and ( K L r ) is the slenderness ratio. Show the expression for Equation 13-30 as follows: σ max = P A + M c I Here, σ max is the maximum compressive stress, P is the load, A is the area, M is the moment, c is the distance between the centroid of member and outer fibre, and I is the moment of inertia. Calculation: Refer the Appendix B. Show the geometric properties of W12 × 50 section as follows: The area ( A ) of the W12 × 50 section is 14.7 in . 2 The least radius of gyration ( r y ) of the W12 × 50 section is 1.96 in . The moment of inertia, ( I y ) = 56.3 in . 4 . The depth of the section, d = 12.19 in . The thickness of the web of the section, b f = 8.08 in . Show the expression for ( K L r ) c as follows: ( K L r ) c = 2 π 2 E σ Y (1) Here, K is the effective length factor, L is the length of the column, and ( r ) is the radius of gyration, E is the Young’s modulus, and σ Y is the yield stress of the material. Consider the Young’s modulus of the steel is E = 29 × 10 3 ksi . Consider the yield stress of the steel is σ Y = 36 ksi . Substitute 29 × 10 3 ksi for E and 36 ksi for σ Y in Equation (1). ( K L r ) c = 2 π 2 × 29 × 10 3 36 = 58 , 000 π 2 36 = 126 Calculate the value of ( K L r y ) as follows: The value of effective length factor, K = 2 , since one end fixed and another end free. Substitute 2 for K, 10 ft for L, and 1.96 in . for r y . ( K L r y ) = ( 2 × 10 ft × 12 in . 1 ft 1.96 in . ) = 122.44 Show the condition for the column to be a long column as follows: ( K L r ) c ≤ ( K L r y ) ≤ 200 (2) Substitute 42.857 for ( K L r y ) and 126 for ( K L r ) c in Equation (2)

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ISBN: 9781292178202

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 13.7, Problem 13.110P

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To find: the largest eccentric load P that can be applied to the column.

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Chapter 13.7, Problem 13.109P

Chapter 13.7, Problem 13.111P

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Chapter 13 Solutions

MECHANICS OF MATERIAL IN SI UNITS

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 largest eccentric load P that can be applied to the column.

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Chapter 13 Solutions