Explanation Given information: The shear force in the beam is V = 2 kN . Convert the unit of the shear force as follows: V = 2 kN × 1 , 000 N 1 kN = 2 , 000 N The spacing between the nails is s = 75 mm . Convert the unit of the spacing as follows: s = 75 mm × 1 m 1 , 000 mm = 0.075 m The diameter ( d ) of the nail is 4 mm . Convert the unit of the diameter of the nail as follows: d = 4 mm × 1 m 1 , 000 mm = 0.004 m Calculation: Sketch the cross section of the beam as shown in Figure 1. Refer to Figure 1. The width and depth of rectangle 1 are b 1 = 200 mm and d 1 = 50 mm . The width and depth of rectangle 2 are b 2 = 25 mm and d 2 = 200 mm . Consider the distance between the bottom of beam and centroid of rectangle 1 and 2 are denoted by y 1 = 175 mm and y 2 = 100 mm . Consider the area of the rectangle 1 and 2 are denoted by A 1 and A 2 . Calculate the value of A 1 and A 2 as follows: A 1 = b 1 d 1 = 200 × 50 = 10 , 000 mm 2 A 2 = b 2 d 2 = 25 × 200 = 5 , 000 mm 2 Find the location of neutral axis as shown below. y ¯ = ∑ A y ∑ A Here, A is the area of the section and y is the Centroid of the section. Calculate the location of neutral axis from the bottom of the beam. y ¯ = A 1 y 1 + 2 A 2 y 2 A 1 + 2 A 2 = ( 10 , 000 × 175 ) + 2 × ( 5 , 000 × 100 ) 10 , 000 + 2 × 5 , 000 = 2 , 750 , 000 20000 = 137.5 mm Find the moment of inertia as shown below. I = b 1 d 1 3 12 + A 1 ( y ¯ − y 1 ) 2 + b 2 d 2 3 12 + A 2 ( y ¯ − y 2 ) 2 Refer Figure 1. Calculate the moment of inertia for the beam. I = [ ( 1 12 × 200 × 50 3 + 10 , 000 × ( 175 − 137.5 ) 2 ) + 2 ( 1 12 × 25 × 200 3 + 5 , 000 × ( 137.5 − 100 ) 2 ) ] = ( 208.33 × 10 4 + 1406

9th Edition

ISBN: 9789810694364

Author: Russell C Hibbeler

Publisher: Pearson Education

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Question

Chapter 7.3, Problem 7.38P

To determine

the average shear stress developed in each nail.

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Chapter 7.3, Problem 7.37P

Chapter 7.3, Problem 7.39P

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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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