Explanation Given information: A rectangular bar made up of aluminum alloy 2014-T6. The width of cross-sectional area of the bar, b = 4 in . The depth of cross-sectional area of the bar, d = 6 in . The bottom end of the bar is fixed and top end is pinned. The length of the bar, L = 10 ft . Consider the maximum allowable load acting on the column as P. The allowable bending stress ( σ b ) allow is 18 ksi . Show the expression of aluminum column (2014-T6 alloy) of Sec 13.6 as follows: ( σ a ) allow = [ 54 , 000 ( K L r ) 2 ] ksi, K L r > 55 Here, σ allow is the allowable stress, E is the Young’s modulus, and ( K L r ) is the slenderness ratio. Show the expression of interaction formula as follows: ( P A ) ( σ a ) allow + ( M c A r 2 ) ( σ b ) allow = 1 Here, ( σ a ) allow is the allowable axial stress, ( σ b ) allow is the allowable bending stress, P is the load, A is the cross-sectional area, M is the moment, c is the distance between the centroid of member and outer fiber, r is the radius of gyration, and I is the moment of inertia. Calculation: Calculate the cross-sectional area ( A ) of the rectangular bar using the relation: A = b d (1) Substitute 4 in . for b and 6 in . for d in Equation (1): A = 4 × 6 = 24 in . 2 Calculate the moment of inertia about x- axis using the relation: I x = b d 3 12 (2) Substitute 4 in . for b and 6 in . for d in Equation (2): I x = 4 × 6 3 12 = 72 in . 4 Calculate the least radius of gyration ( r x ) using relation: r x = I x A (3) Substitute 72 in . 4 for I x and 24 in . 2 for A in Equation (3): r x = 72 24 = 1.732 in . Calculate the moment of inertia about y- axis using the relation: I y = d b 3 12 (4) Substitute 4 in . for b and 6 in . for d in Equation (4): I y = 6 × 4 3 12 = 32 in . 4 Calculate the least radius of gyration ( r y ) using relation: r y = I y A (5) Substitute 32 in . 4 for I y and 24 in . 2 for A in Equation (5): r y = 32 24 = 1.155 in . Calculate the slenderness ratio of column about y-y axis using the relation: Slenderness ratio = ( K L r ) y (6) The column is fixed at one end and pinned at another end. Thus, the value of K = 0

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 13.7, Problem 13.122P

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To find: the maximum allowable eccentric load P that can be applied to the bar.

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Chapter 13.7, Problem 13.121P

Chapter 13.7, Problem 13.123P

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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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the maximum allowable eccentric load P that can be applied to the bar.

Solution Summary: The author explains the maximum allowable eccentric load P that can be applied to a rectangular bar made of aluminum alloy 2014-T6.

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Chapter 13 Solutions