Explanation Given information: The rectangular column is made up of wood. The length of the bar is 12 ft . The width of the rectangular wooden cross-section is a The depth of the rectangular wooden cross-section is 2 a . The column is pinned at top and fixed at base. The allowable axial load on the column is 15 kip . Calculation: Show the expression for the cross-sectional area of the rectangular wooden column as follows: A = b d (1) Here, b is the width and d is the depth of the rectangle. Substitute a for b and 2 a for d in Equation (1). A = a × 2 a = 2 a 2 Substitute 3 in . for a. A = 2 ( 3 ) 2 = 18 in 2 Calculate the slenderness ratio of the column using the relation: Slenderness Ratio = ( K L d ) (2) Here K is the effective length factor, L is the length of column and d is the depth of cross-section area. The column is fixed at one end and pinned at another end, thus the value of K = 0.7 . Substitute 3 in . for d and0.7 for K in Equation (2). Slenderness Ratio = ( 0.7 × L 3 in . ) = 0.2333 L (3) Assume the column as intermediate column. Show the expression for NFPA Timber column formula for intermediate column as follows: σ allow = 1.20 [ 1 − 1 3 ( K L / d 26 ) 2 ] ksi P allowable A = 1.20 [ 1 − 1 3 ( K L / d 26 ) 2 ] ksi (4) Substitute 0.2333 L for ( K L d ) , 15 kip for P allowable , and 18 in

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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 13.6, Problem 102P

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the maximum length of the column.

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Chapter 13.6, Problem 101P

Chapter 13.6, Problem 103P

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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 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 - Prob. 34P Ch. 13.3 - Prob. 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 - Prob. 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 aluminium column is fixed at the bottom and...Ch. 13.5 - Prob. 50P Ch. 13.5 - Prob. 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. 54P Ch. 13.5 - Prob. 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. 65P 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 - 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. 13.6 - Using the AISC equations, select from AppendixB...Ch. 13.6 - Take Y = 50 ksi.Ch. 13.6 - Using the AISC equations, select from AppendixB...Ch. 13.6 - Prob. 83P Ch. 13.6 - Using the AISC equations, select from AppendixB...Ch. 13.6 - Prob. 97P Ch. 13.6 - Prob. 98P Ch. 13.6 - The tube is 0.25 in. thick, is made of 2014-T6...Ch. 13.6 - Prob. 100P Ch. 13.6 - A rectangular wooden column has the cross section...Ch. 13.6 - Prob. 102P Ch. 13.7 - The W8 15 wide-flange A-36 steel column is...Ch. 13.7 - Prob. 110P 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 - 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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