Explanation Given information: The allowable shear stress of the wood is τ allow = 450 psi . Shear strength of each bolt is 1.5 kip. Spacing between the bolts is 6 in. Calculation: Sketch the cross section of the boards as shown in Figure 1. Refer to Figure 1. Find the location of the neutral axis as shown below. y ¯ = ∑ A y ∑ A Here, A is the cross sectional area and y is the centroid of the section. y ¯ = 2 × [ 4 × 1 × 4 2 ] + [ 4 × 1 × ( 2 + 4 2 ) ] 2 × [ 4 × 1 ] + [ 4 × 1 ] = 32 12 = 2.6667 in . Find the moment of inertia as shown below. I = b d 3 12 + A h 2 Here, b is the width of the cross section d is the depth of the cross section, and h is the difference between the centroid and the location of the neutral axis. I = 2 × [ 1 12 × 1 × 4 3 + 1 × 4 ( 2.6667 − 2 ) 2 ] + 1 12 × 1 × 4 3 + 1 × 4 ( 4 − 2.6667 ) 2 = 2 × 7.11129 + 12.44409 = 26.6667 in . 4 Sketch the shear diagram at point B as shown in Figure 2. Refer to Figure 2. Find the first moment of area at B as shown below. Q B = y ¯ 1 A 1 Here, y ¯ 1 is the distance between the neutral axis and the centroid of the area under consideration and A 1 is the area of cross section at B . Substitute 1.3333 in. for y ¯ 1 and ( 4 × 1 ) in 2 for A B . Q B = 1.3333 × ( 4 × 1 ) = 5.333 in 3 Sketch the shear diagram at point D as shown in Figure 3. Refer to Figure 3. Find the first moment of area at D as shown below. Q D = y ¯ 3 A 3 Here, y ¯ 3 is the distance between the neutral axis and the centroid of the area under consideration and A 3 is the area of cross section at D . Substitute 2.3333 in. for y ¯ 3 and ( 2 × 1 ) in 2 for A 3 . Q D = 2.3333 × ( 2 × 1 ) = 4.6667 in 3 Find the maximum first moment of area as shown below. Q max = y ¯ 2 A 2 + Q D Here, y ¯ 2 is the distance between the neutral axis and the centroid of the area under consideration and A 2 is the area of cross section, and Q D is the first moment of area at D

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ISBN: 9789810694364

Author: Russell C Hibbeler

Publisher: Pearson Education

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Chapter 7.3, Problem 7.36P

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The maximum allowable internal shear V that can act on the beam.

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Chapter 7.3, Problem 7.35P

Chapter 7.3, Problem 7.37P

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Chapter 7 Solutions

Mechanics Of Materials, Si Edition

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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