Explanation Given information: The effective length of the compression member is l e = 5 ft . Calculation: Show the cross section of the compression member as in Figure 1. Find the cross sectional area ( A ) of the cross section using the equation. A = b 1 d 1 + b 2 d 2 + b 3 d 3 Here, the width of the section 1 is b 1 , the depth of the section 1 is d 1 , the width of the section 2 is b 2 , the depth of the section 2 is d 2 , the width of the section 3 is b 3 , the depth of the section 3 is d 3 . Substitute 4 in. for b 1 , 0.6 in. for d 1 , 0.4 in. for b 2 , 2.8 in. for d 2 , 4 in. for b 3 , and 0.6 in. for d 3 . A = ( 4 × 0.6 ) + ( 0.4 × 2.8 ) + ( 4 × 0.6 ) = 5.92 in . 2 Find the moment of inertia in x -axis ( I x ) using the relation. I x = b 1 d 1 3 12 + A 1 ( y ¯ − y 1 ) 2 + b 2 d 2 3 12 + b 3 d 3 3 12 + A 3 ( y ¯ − y 3 ) 2 Here, the area of the section 1 is A 1 , the distance between the neutral axis and the bottom fibre is y ¯ , the distance of the section 1 from bottom of the member is y 1 , and the distance of the section 2 from bottom of the member is y 2 . Due to symmetry of the member, y ¯ = 2 in . . A 1 = ( 4 × 0.6 ) in . 2 ; y 1 = 3.7 in . A 3 = ( 4 × 0.6 ) in . 2 ; y 3 = 0.3 in . Substitute 4 in. for b 1 , 0.6 in. for d 1 , 0.4 in. for b 2 , 2.8 in. for d 2 , 4 in. for b 3 , 0.6 in. for d 3 , ( 4 × 0.6 ) in . 2 for A 1 , 3.7 in. for y 1 , ( 4 × 0.6 ) in . 2 for A 3 ,2 in. for y ¯ , and 0.3 in. for y 3 . I x = 4 × 0.6 3 12 + ( 4 × 0.6 ) ( 2 − 3.7 ) 2 + 0.4 × 2.8 3 12 + 4 × 0

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Author: BEER

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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 10.3, Problem 64P

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Find the allowable centric load P of the aluminum alloy.

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Chapter 10.3, Problem 63P

Chapter 10.3, Problem 65P

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Chapter 10 Solutions

EBK MECHANICS OF MATERIALS

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Find the allowable centric load P of the aluminum alloy.

Solution Summary: The author calculates the cross sectional area of the compression member using the equation.

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