Explanation Given information: A column is made up of aluminum alloy 2014-T6. The ends of the column are fixed. The length of the column, L = 16 ft . Consider the maximum allowable load acting on the column as P acting at point A. The eccentricity ( e ) of the load is 4.25 in . The allowable bending stress, ( σ b ) allow = 20 ksi . Show the expression of aluminum column (2014-T6 alloy) of Sec 13.6 as follows: σ allow = [ 30.7 − 0.23 ( K L r ) ] , 12 < K L r < 55 Here, σ allow is the allowable stress, and ( K L r ) is the slenderness ratio. Show the expression of interaction formula as follows: ( P A ) ( σ a ) allow + ( ( M ) c I ) ( σ b ) allow = 1 ( P A ) ( σ a ) allow + ( ( P e ) c I ) ( σ b ) allow = 1 Here, P is the axial load, A is the area, e is the eccentricity of load, ( σ a ) allow is the allowable axial stress, ( σ b ) allow is the allowable bending stress, I is the moment of inertia, and c is the distance between the centroid of member and outer fiber. Calculation: Show the cross-section of the column as shown in Figure 1. Refer to Figure 1. The cross-section of the column consists of rectangle PQRS and rectangle 1. The width and depth of the rectangle PQRS are b 2 = 8 in . and d 2 = 9 in . The width and depth of the rectangle 1 are b 1 = 3.75 in . and d 1 = 8 in . Calculate the cross-sectional area ( A ) of the column using the relation: A = b 2 d 2 − 2 b 1 d 1 (1) Substitute 3.75 in . for b 1 , 8 in . for d 1 , 8 in . for b 2 and 9 in . for d 2 in Equation (1): A = ( 8 × 9 ) − ( 2 × 3.75 × 8 ) = 12 in . 2 Calculate the moment of inertia about x- axis using the relation: I x = b 2 d 2 3 12 − 2 × b 1 d 1 3 12 (2) Substitute 8 in . for b 1 , 8 in . for d 1 , 8 in . for b 2 and 9 in . for d 2 in Equation (2): I x = 8 × 9 3 12 − 2 × 3.75 × 8 3 12 = 486 − 320 = 166 in . 4 The width and depth of the flanges are b f = 8 in . and d f = 0.5 in . The width and depth of the web are b w = 0.5 in . and d w = 8 in . Calculate the moment of inertia about y- axis using the relation: I y = { ( Moment of inertia of flanges ) + ( Moment of inertia of web ) } = 2 × d f b f 3 12 + d w b w 3 12 (3) Substitute 8 in . for b f , 0.5 in . for d f , 0.5 in . for b w , and 8 in

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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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 13.118P

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To find: the value of maximum allowableloadP that can be applied to the column.

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Chapter 13.7, Problem 13.117P

Chapter 13.7, Problem 13.119P

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