Explanation Given information: The shear force ( V ) applied in the box girder is 5 kip . Calculation: Show the cross-section of the beam as shown in Figure 1. Refer to Figure 1. The width and depth of the rectangles 1 are b 1 = 11 in . and d 1 = 0.5 in . The width and depth of the rectangles 2 are b 2 = 8 in . and d 2 = 0.5 in . The width and depth of the rectangle 3 are b 3 = 10 in . and d 3 = 0.5 in . Consider the area of the rectangle 1, 2, and 3 as A 1 , A 2 and A 3 . Refer to Figure 1. Calculate the area of the rectangle 1, 2, and 3 as follows: A 1 = b 1 d 1 = 11 × 0.5 = 5.5 in . 2 A 2 = b 2 d 2 = 2 ( 8 × 0.5 ) = 8 in . 2 A 3 = b 3 d 3 = 10 × 0.5 = 5 in . 2 Consider the distance between the bottom of the strut and the centroid of rectangles 1,2 and 3 are denoted by y 1 , y 2 and y 3 . Calculate the distance ( y ¯ ) of neutral axis from the bottom of strut using the relation: y ¯ = ( A 1 y 1 + A 2 y 2 + 2 A 3 y 3 A 1 + A 2 + 2 A 3 ) (1) Substitute 5.5 in . 2 for A 1 , 0.25 in . for y 1 , 8 in . 2 for A 2 , 4.5 in . for y 2 , 5 in . 2 for A 3 , and 6.25 in . for y 3 in Equation (1). y ¯ = [ ( 5.5 × 0.25 ) + ( 8 × 4.5 ) + ( 5 × 6.25 ) 5.5 + 8 + 5 ] = [ ( 1.375 ) + ( 36 ) + ( 31.25 ) 18.5 ] = 3.70945 in . Calculate the moment of inertia ( I ) as follows: I = I 1 + 2 I 2 + I 3 (2) Find the value of I 1 as follows: I 1 = b 1 d 1 3 12 + a 1 ( y ¯ − y 1 ) 2 (3) Substitute 11 in. for b 1 , 0.5 in . for d 1 , 5.5 in . for a 1 , 3.70945 in . for y ¯ , and 0.25 in . for y 1 in Equation (3). I 1 = 11 × 0.5 3 12 + ( 11 × 0.5 ) ( 3.70946 − 0.25 ) 2 = 0.11458 + 65.8232 = 65.9377 in 4 Find the value of I 2 as follows: I 2 = b 2 d 2 3 12 + a 2 ( y 2 − y ¯ ) 2 (4) Substitute 8 in. for b 2 , 0.5 in . for d 2 , 8 in 2 for a 2 , 3.70945 in . for y ¯ , and 4.5 in . for y 2 in Equation (4). I 2 = 2 [ 0.5 × 8 3 12 + ( 0.5 × 8 ) ( 4.5 − 3.70946 ) 2 ] = 2 ( 21.3333 + 2.4998 ) = 2 ( 23.83 ) = 47.6656 in 4 Find the value of I 3 as follows: I 3 = b 3 d 3 3 12 + a 3 ( y 3 − y ¯ ) 2 (5) Substitute 10 in. for b 3 , 0.5 in . for d 3 , 5 in 2 for a 3 , 3

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Chapter 7.5, Problem 7.56P

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Chapter 7 Solutions

Mechanics of Materials

Ch. 7.2 - In each case, calculate the value of Q and t that...Ch. 7.2 - If the beam is subjected to a shear force of V =...Ch. 7.2 - Determine the shear stress at points A and B if...Ch. 7.2 - Determine the absolute maximum shear stress in the...Ch. 7.2 - If the beam is subjected to a shear force of V =20...Ch. 7.2 - If the beam is made from four plates and subjected...Ch. 7.2 - If the wide-flange beam is subjected to a shear of...Ch. 7.2 - If the wide-flange beam is subjected to a shear of...Ch. 7.2 - If the wide-flange beam is subjected to a shear of...Ch. 7.2 - Prob. 7.4P

Ch. 7.2 - Prob. 7.5P Ch. 7.2 - The wood beam has an allowable shear stress of...Ch. 7.2 - The shaft is supported by a thrust bearing at A...Ch. 7.2 - The shaft is supported by a thrust bearing at A...Ch. 7.2 - Determine the largest shear force V that the...Ch. 7.2 - If the applied shear force V = 18 kip, determine...Ch. 7.2 - The overhang beam is subjected to the uniform...Ch. 7.2 - *7-12. The beam has a rectangular cross section...Ch. 7.2 - Determine the maximum shear stress in the strut if...Ch. 7.2 - Determine the maximum shear force V that the strut...Ch. 7.2 - 7-15. The strut is subjected to a vertical shear...Ch. 7.2 - Prob. 7.16P Ch. 7.2 - If the beam is subjected to a shear of V=15 kN,...Ch. 7.2 - If the wide-flange beam is subjected to a shear of...Ch. 7.2 - If the wide-flange beam is subjected to a shear of...Ch. 7.2 - Prob. 7.20P Ch. 7.2 - If the beam is made from wood having an allowable...Ch. 7.2 - Determine the shear stress at point B on the web...Ch. 7.2 - Determine the maximum shear stress acting at...Ch. 7.2 - Prob. 7.24P Ch. 7.2 - 7-25. Determine the maximum shear stress in the...Ch. 7.2 - 7-26. The beam has a square cross section and is...Ch. 7.2 - The beam is slit longitudinally along both sides....Ch. 7.2 - The beam is to be cut longitudinally along both...Ch. 7.2 - The beam has a rectangular cross section and is...Ch. 7.2 - The beam in Fig.6-48f is subjected to a fully...Ch. 7.3 - The two identical boards are bolted together to...Ch. 7.3 - Two identical 20-mm-thick plates are bolted to the...Ch. 7.3 - The boards are bolted together to form the...Ch. 7.3 - The boards are bolted together to form the...Ch. 7.3 - Prob. 7.32P Ch. 7.3 - Prob. 7.33P Ch. 7.3 - Prob. 7.34P Ch. 7.3 - Prob. 7.35P Ch. 7.3 - Prob. 7.36P Ch. 7.3 - Prob. 7.37P Ch. 7.3 - Prob. 7.38P Ch. 7.3 - A beam is constructed from three boards bolted...Ch. 7.3 - The simply supported beam is built up from three...Ch. 7.3 - The simply supported beam is built up from three...Ch. 7.3 - The T-beam is constructed as shown. If each nail...Ch. 7.3 - Prob. 7.43P Ch. 7.3 - Prob. 7.44P Ch. 7.3 - Prob. 7.45P Ch. 7.3 - 7–46. The beam is subjected to a shear of V = 800...Ch. 7.3 - The beam is made from four boards nailed together...Ch. 7.3 - The beam is made from three polystyrene strips...Ch. 7.5 - A shear force of V=300 kN is applied to the box...Ch. 7.5 - A shear force of V=450 kN is applied to the box...Ch. 7.5 - A shear force of V = 18 kN is applied to the box...Ch. 7.5 - A shear force of V = 18 kN is applied to the box...Ch. 7.5 - The aluminum strut is 10 mm thick and has the...Ch. 7.5 - The aluminum strut is 10 mm thick and has the...Ch. 7.5 - Prob. 7.56P Ch. 7.5 - Prob. 7.57P Ch. 7.5 - Prob. 7.58P Ch. 7.5 - Prob. 7.59P Ch. 7.5 - The built-up beam is formed by welding together...Ch. 7.5 - The assembly is subjected to a vertical shear of V...Ch. 7.5 - 7–62. Determine the shear-stress variation over...Ch. 7.5 - 7–63. Determine the location e of the shear...Ch. 7.5 - Determine the location e of the shear center,...Ch. 7.5 - The beam supports a vertical shear of V=7 kip....Ch. 7.5 - The stiffened beam is constructed from plates...Ch. 7.5 - The pipe is subjected to a shear force of V=8 kip....Ch. 7.5 - *7–68. A thin plate of thickness t is bent to form...Ch. 7.5 - A thin plate of thickness t is bent to form the...Ch. 7.5 - 7–70. Determine the location e of the shear...Ch. 7 - The beam is fabricated from four boards nailed...Ch. 7 - The T-beam is subjected to a shear of V = 150 kN....Ch. 7 - The member is subject to a shear force of V = 2...Ch. 7 - Determine the shear stress at points B and C on...Ch. 7 - Determine the maximum shear stress acting at...

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