Explanation Given information: Consider the applied moment is denoted by M . The maximum allowable stress in the component is 45 MPa . Calculation: Show the cross-section of the curved beam as shown in Figure 1. Refer Figure 1. Consider the cross-section of the beam consists of rectangle 1 and 2. Consider the distance between the center C and the centroid of the rectangle 1, 2 are denoted by r ¯ 1 and r ¯ 2 . Show the value of r ¯ 1 and r ¯ 2 as follows: r ¯ 1 = 150 mm+ 135 2 mm =217 .5 mm r ¯ 2 = 150 mm+135 mm+ 45 2 mm = 307.5 mm Consider Rectangle 2. Consider the width and depth of the rectangle 1 are b = 108 mm and d = 45 mm Calculate the area A of the rectangle 1 as follows: A = b h = 108 × 45 = 4860 mm 2 Calculate the value of the expression b ln r i + 1 r i as follows: For Rectangle 2, i is 2. Then, b ln r i + 1 r i = b ln r 2 + 1 r 1 = b ln r 3 r 2 Substitute 330 mm for r 3 , 285 mm for r 2 , and 108 mm for b . b ln r i + 1 r i = 108 ln ( 330 285 ) = 15.8332 Calculate the value of product A r ¯ 2 as follows: Substitute 4860 mm 2 for A and 307.5 mm for r ¯ 2 . A r ¯ 2 = 4860 mm 2 × 172 .5 mm = 1 , 494 , 450 mm 3 Similarly calculate the remaining values for rectangle 2 and 3 as shown in Table 1. Rectangle b h A b ln r i + 1 r i r ¯ A r ¯ 2 108 45 4860 15.8332 172.5 1,494,550 1 36 135 4860 23.1067 262.5 1,057,050 ∑ 9,720 38.9399 25,516,00 Calculate the mean radius of the cross-section ( r ¯ ) using the relation: r ¯ = ∑ A r ¯ i ∑ A Substitute 25,516,00 for ∑ A r ¯ i and 9,720 for ∑ A . r ¯ = 25 , 516 , 00 9 , 720 = 262.5 mm Calculate the radius of the neutral surface R using the relation: R = ∑ A ∑ b i ( ln r i + 1 r i ) (1) Substitute 38

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Chapter 4.10, Problem 174P

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Find the magnitude of the largest moment M applied to the component.

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Chapter 4.10, Problem 173P

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Find the magnitude of the largest moment M applied to the component.

Solution Summary: The author calculates the magnitude of the largest moment M applied to the component. The maximum allowable stress is 45MPa.

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Find the magnitude of the largest moment M applied to the component.

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