Explanation Given information: The length of the 2014-T6 aluminum alloy column is L = 3 m . Show the unit conversion of the load as follows: L = 3 m × 1 , 000 mm 1 m = 3 , 000 mm The column is pinned at both the end. The column is braced against the weak axis at its mid height. Calculation: Show the cross-section of the column as shown below: Refer to Figure 1. The dimensions of the top flange, width b 1 = 100 mm and depth d 1 = 15 mm . The dimensions of the web, width b 2 = 15 mm and depth d 2 = 170 mm . The dimensions of the bottom flange, width b 3 = 100 mm and depth d 3 = 15 mm . Consider the area of the top flange, web, and bottom flange is denoted by A 1 , A 2 , and A 3 respectively. Calculate the area A 1 , A 2 and A 3 as follows: A 1 = b 1 d 1 = 100 × 15 = 1500 mm 2 A 2 = b 2 d 2 = 15 × 170 = 2550 mm 2 A 3 = b 3 d 3 = 100 × 15 = 1 , 500 mm 2 Calculate the cross-sectional area A of the column using relation. A = A 1 + A 2 + A 3 = 1 , 500 mm 2 + 2 , 550 mm 2 + 1 , 500 mm 2 = 5550 mm 2 Calculate the moment of inertia I x of the cross-section of the column along the x -axis using the relation: I x = b 2 d 2 3 12 + ( b 1 d 1 3 12 + A 1 ( d y ) 1 2 ) + ( b 3 d 3 3 12 + A 3 ( d y ) 3 2 ) (1) Substitute 100 mm for b 1 , 15 mm for d 1 , 15 mm for b 2 , 170 mm for d 2 , 100 mm for b 3 , 15 mm for d 3 , 1500 mm 2 for A 1 , 1500 mm 2 for A 3 , 92.5 mm for ( d y ) 1 , 92.5 mm for ( d y ) 3 in Equation (1). I x = 15 × 170 3 12 + ( 100 × 15 3 12 + 1 , 500 × ( 92.5 ) 2 ) + ( 100 × 15 3 12 + 1 , 500 × ( 92.5 ) 2 ) = 15 × 170 3 12 + 2 ( 100 × 15 3 12 + 1 , 500 × ( 92.5 ) 2 ) = 6.1412 × 10 6 + 25.725 × 10 6 = 31.86 × 10 6 mm 4 Calculate the moment of inertia I y of the cross-section of the column along the y -axis using the relation: I y = d 1 b 1 3 12 + d 2 b 2 3 12 + d 3 b 3 3 12 (2) Substitute 100 mm for b 1 , 15 mm for d 1 , 15 mm for b 2 , 170 mm for d 2 , 100 mm for b 3 , and 15 mm for d 3 in Equation (2)

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 13.6, Problem 13.93P

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The allowable axial force for the column.

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Chapter 13.6, Problem 13.92P

Chapter 13.6, Problem 13.94P

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