Explanation Given information: The beam made up of four boards nailed together. The nailing is done on both sides of the beam. The shear resisted by each nail is 3 kN . The spacing ( s ) between the nail is 100 mm . Convert the unit of spacing as follows: s = 100 mm × 1 m 1 , 000 mm = 0.1 m Consider the maximum load applied on the end of the beam is denoted by P . Calculation: Show the free body diagram of the beam as shown in Figure 1: Refer to Figure 1. Consider the moment at the support A is denoted by M . Consider the vertical reaction at the support A is denoted by R . Consider the shear force at the support is denoted by V . Take the moment of all the forces about the support A as follows: M = ( 3 × 2 ) + ( P × 4 ) = 6 + 4 P Calculate the value of R as follows: R = 3 + P Show the shear force diagram of the beam as shown in Figure 2: Refer to Figure 2. The shear force V at the support is 3 + P . Show the cross-section of the beam as in Figure 3: Refer Figure 3. The cross-section dimension of the outer rectangle , width b 1 = 310 mm and depth d 1 = 150 mm The cross-section dimension of the inner rectangle, width b 2 = 250 mm and depth d 2 = 90 mm Calculate the moment of inertia of the beam using the relation: I = I 1 − I 2 = b 1 d 1 3 12 − b 2 d 2 3 12 (1) Substitute 310 mm for b 1 , 150 mm for d 1 , 250 mm for b 2 , and 90 mm for d 2 , in Equation (1). I = 310 × 150 3 12 − 250 × 90 3 12 = 1046.25 × 10 6 − 182.25 × 10 6 12 = 864 × 10 6 12 = 72 × 10 6 mm 4 × 1 m 4 10 12 mm 4 I = 72 × 10 − 6 m 4 Calculate the first moment of area ( Q ) using the relation: Q = A ′ y ¯ ′ Here, A ′ is the area of the shaded area, and y ¯ ′ is the distance between the centroid of the shaded area and the neutral axis

9th Edition

ISBN: 2810014920922

Author: HIBBELER

Publisher: PEARSON

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Chapter 7.3, Problem 7.45P

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The maximum value of the load P that can be applied at the end of the beam.

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Chapter 7.3, Problem 7.44P

Chapter 7.3, Problem 7.46P

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MECHANICS OF MATERIALS-TEXT

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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