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

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

See similar textbooks

Videos

Question

Chapter 7.3, Problem 7.36P

To determine

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.3, Problem 7.35P

Chapter 7.3, Problem 7.37P

Students have asked these similar questions

Please answer Oxygen at 300 kPa and 90°C flowing at an average velocity of 3 m/s is expanded in an adiabatic nozzle. What is the maximum velocity of the oxygen at the outlet of this nozzle when the outlet pressure is 60 kPa? Use the table containing the ideal gas specific heats of various common gases. The maximum velocity of the oxygen at the outlet of this nozzle is 532.5 Numeric ResponseEdit Unavailable. 532.5 incorrect.m/s.

A container filled with 70 kg of liquid water at 95°C is placed in a 90-m3 room that is initially at 12°C. Thermal equilibrium is established after a while as a result of heat transfer between the water and the air in the room. Assume the room is at the sea level, well sealed, and heavily insulated. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine the amount of heat transfer between the water and the air in the room. The amount of heat transfer between the water and the air in the room is kJ.

A strain gauge rosette that is attached to the surface of a stressed component gives 3 readings (ɛa = A, b = B, &c = C). If the strain gauge rosette is of the D° type (indicating the angle between each of the gauges), construct a Mohr's Strain Circle overleaf. You should assume that gauge A is aligned along the x-axis. Using the Mohr's Strain Circle calculate the: (i) principal strains (ε1, 2)? (ii) principal angles (1, 2)? You should measure these anticlockwise from the y-axis. (iii) maximum shear strain in the plane (ymax)?

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...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.