Explanation Given information: The bar is made up of 2014-T6 aluminum alloy. The length of the bar is 8 ft . The width of the bar is 5 b . The thickness of the bar is b . The both ends of the bar are pinned. The axial load on the bar, P = 600 lb . Calculation: Calculate the area of the cross-section of the bar using the relation: A = Width × Depth (1) Substitute 5 b for width and b for depth in Equation (1). A = 5 b × b = 5 b 2 Show the expression for moment of inertia for the rectangular cross-section as follows: I = b d 3 12 (2) Here, b is the width and d is the depth of the rectangle. Substitute 5 b for b and b for d in Equation (2). I = ( 5 b ) b 3 12 = 5 b 4 12 Calculate the radius of gyration r using the relation: r = I A (3) Substitute 5 b 4 12 for I and 5 b 2 for A in Equation (3). r = ( 5 b 4 12 ) 5 b 2 = 5 b 4 12 × 5 b 2 = 5 b 2 60 = 0.2886 b Calculate the slenderness ratio of the column using the relation: Slenderness Ratio = ( K L r ) (4) The ends of the bar are pinned, thus the value of effective-length factor K = 1 . Substitute 0.2886 b for r , 8 ft for L, 1 for K and 0.2886 b for r in Equation (4). Slenderness Ratio = ( 1 × 8 ft × 12 in . 1 ft 0.2886 b ) = 332.64 b Assume the column as a long column. Show the expression for the allowable stress in 2014-T6 aluminum long column as follows: σ allowable = 54 , 000 ksi ( K L r ) 2 P allowable A = 54 , 000 ksi ( K L r ) 2 (5) Here, P allowable is the allowable load, A is the cross-sectional area, ( K L r ) is the slenderness ratio

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 13.6, Problem 13.91P

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The smallest thickness b of the bar.

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Chapter 13.6, Problem 13.90P

Chapter 13.6, Problem 13.92P

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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...

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