Explanation Given information: The magnitude of the load P is 100 kN . Calculation: Show the cross-section of the beam as shown in Figure 1. Refer to Figure 1. Calculate the total area ( A ) of the cross-section as follows: A = A 1 + A 2 = ( 100 × 20 ) + ( 60 × 20 ) = 2000 mm 2 Show the expression for centroid distance ( Y ¯ ) of the cross-section of the beam as follows: Y ¯ = ∑ A y ¯ ∑ A = ( A 1 y ¯ 1 + A 1 y ¯ 2 A 1 + A 2 ) Consider the distance of centroid of the rectangle 1, 2 from the base is denoted by y ¯ 1 = 10 mm and y ¯ 2 = − 10 mm . Y ¯ = ( A 1 y ¯ 1 + A 1 y ¯ 2 A 1 + A 2 ) Refer Figure 1. Calculate the distance ( Y ¯ ) as follows: Y ¯ = ( 100 × 20 × 10 + 60 × 20 × ( − 10 ) 100 × 20 + 60 × 20 ) = 8 , 000 3 , 200 = 2.5 mm The coordinates of the load point are X p = a and Y p = − 2.5 mm . Show the bending couples M x and M y as follows: M x = P Y p = 100 × ( − 2.5 ) = − 250 kN ⋅ mm M y = − P a = − 100 a Calculate the moment of inertia ( I x ) using the relation: I x = 1 12 b 1 h 1 3 + ( b 1 h 1 ) d 1 2 + 1 12 b 2 h 2 3 + ( b 2 h 2 ) d 2 2 (1) Here, b and h are the width and depth of the section, d is the distance between the neutral axis and centroid of rectangle. Substitute 100 mm for b 1 , 20 mm for h 1 , 7.5 mm for d 1 , 60 mm for b 2 , 20 mm for h 2 , and 12.5 mm for d 2 . I x = [ ( 1 12 × 100 × 20 3 ) + 100 × 20 × ( 7

7th Edition

ISBN: 9780073398235

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

Publisher: McGraw-Hill Education

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Chapter 4.9, Problem 145P

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Find the largest distance a for which the maximum tensile stress in the beam not exceed 75 MPa.

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Chapter 4.9, Problem 144P

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Chapter 4 Solutions

Mechanics of Materials, 7th Edition

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Find the largest distance a for which the maximum tensile stress in the beam not exceed 75 MPa .

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Find the largest distance a for which the maximum tensile stress in the beam not exceed 75 MPa.

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