Explanation Given information: The joint is subjected to an axial force of P = 9 kN . The diameter of the bolt is 6 mm. Calculation: The cross sectional dimension of the shaded shear plane is 100 mm × 100 mm . Find the cross sectional area of the shaded shear plane as shown below. A P = 100 × 100 = 10 , 000 mm 2 Find the cross sectional area of the bolt as shown below. A b = π d b 2 4 Here, d b is the diameter of the bolt. Substitute 6 mm for d b . A b = π × 6 2 4 = 28.274 mm 2 Sketch the Free Body Diagram of the shear plane of the bolt as shown in Figure 1. Refer to Figure 1. Find the internal loadings as shown below. Apply the Equations of Equilibrium as shown below. Summation of forces along y direction is Equal to zero. ∑ F y = 0 4 V b − 9 = 0 4 V b = 9 V b = 2.25 kN Find the average shear stress developed in each shear plane of the bolt ( τ avg ) a − a as shown below. ( τ avg ) a − a = V b A b Here, V b is the shear force and A b is the cross sectional area of the bolt. Substitute 2.25 kN for V b and 28.274 mm 2 for A b . ( τ avg ) a − a = 2.25 kN × 1 , 000 N 1 kN 28.274 = 79.6 N / mm 2 Convert the unit from N / mm 2 to MPa

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Chapter 1.5, Problem 1.52P

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The average shear stress developed in each shear plane of the bolt and the member.

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Chapter 1.5, Problem 1.51P

Chapter 1.5, Problem 1.53P

Chapter 1 Solutions

Mechanics of Materials

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Ch. 1.2 - The shaft is supported by a smooth thrust bearing...Ch. 1.2 - 1-5. Determine the resultant internal loadings in...Ch. 1.2 - 1-6. Determine the normal force, shear force, and...Ch. 1.2 - 1-7. The cable will fail when subjected to a...Ch. 1.2 - *1-8. Determine the resultant internal loadings on...Ch. 1.2 - 1-9. Determine the resultant internal loadings on...Ch. 1.2 - The boom DF of the jib crane and the column DE...Ch. 1.2 - 1-11. The forearm and biceps support the 2-kg load...Ch. 1.2 - *1-12. The serving tray T used on an airplane is...Ch. 1.2 - The blade of the hacksaw is subjected to a...Ch. 1.2 - The blade of the hacksaw is subjected to a...Ch. 1.2 - 1-15. A 150-lb bucket is suspended from a cable on...Ch. 1.2 - *1-16. A 150-lb bucket is suspended from a cable...Ch. 1.2 - 1-17. 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The built-up shaft consists of a pipe AB and...Ch. 1.5 - Prob. 1.35P Ch. 1.5 - Prob. 1.36P Ch. 1.5 - The plate has a width of 0.5 m. If the stress...Ch. 1.5 - The two members used in the construction of an...Ch. 1.5 - Prob. 1.39P Ch. 1.5 - Determine the average normal stress in each of the...Ch. 1.5 - If the average normal stress in each of the...Ch. 1.5 - Determine the maximum average shear stress in pin...Ch. 1.5 - 1-43. The 150-kg bucket is suspended from end E of...Ch. 1.5 - *1-44. The 150-kg bucket is suspended from end E...Ch. 1.5 - Prob. 1.45P Ch. 1.5 - 1-46. The 20-kg chandelier is suspended from the...Ch. 1.5 - Prob. 1.47P Ch. 1.5 - If P = 15 kN, determine the average shear stress...Ch. 1.5 - 1-49. The joint is subjected to the axial member...Ch. 1.5 - Prob. 1.50P Ch. 1.5 - Prob. 1.51P Ch. 1.5 - Prob. 1.52P Ch. 1.5 - Prob. 1.53P Ch. 1.5 - Prob. 1.54P Ch. 1.5 - The 2-Mg concrete pipe has a center of mass at...Ch. 1.5 - The 2-Mg concrete pipe has a center of mass at...Ch. 1.5 - Prob. 1.57P Ch. 1.5 - Prob. 1.58P Ch. 1.5 - 1-59. The jib crane is pinned at A and supports a...Ch. 1.5 - *1-60. If the shaft is subjected to an axial force...Ch. 1.5 - Prob. 1.61P Ch. 1.5 - Prob. 1.62P Ch. 1.5 - Prob. 1.63P Ch. 1.5 - *1-64. A vertical force of P = 1500 N is applied...Ch. 1.5 - Prob. 1.65P Ch. 1.5 - Determine the largest load P that can be applied...Ch. 1.5 - Prob. 1.67P Ch. 1.5 - Prob. 1.68P Ch. 1.7 - Rods AC and BC are used to suspend the 200-kg...Ch. 1.7 - If it is subjected to double shear, determine the...Ch. 1.7 - Determine the maximum average shear stress...Ch. 1.7 - If each of the three nails has a diameter of 4 mm...Ch. 1.7 - The strut is glued to the horizontal member at...Ch. 1.7 - Determine the maximum average shear stress...Ch. 1.7 - If the eyebolt is made of a material having a...Ch. 1.7 - If the bar assembly is made of a material having a...Ch. 1.7 - Determine the maximum force P that can be applied...Ch. 1.7 - The pin is made of a material having a failure...Ch. 1.7 - If the bolt head and the supporting bracket are...Ch. 1.7 - Six nails are used to hold the hanger at A against...Ch. 1.7 - If A and B are both made of wood and are 38 in....Ch. 1.7 - Prob. 1.70P Ch. 1.7 - Prob. 1.71P Ch. 1.7 - Prob. 1.72P Ch. 1.7 - The steel swivel bushing in the elevator control...Ch. 1.7 - 1-74. Member B is subjected to a compressive force...Ch. 1.7 - Prob. 1.75P Ch. 1.7 - Prob. 1.76P Ch. 1.7 - The tension member is fastened together using two...Ch. 1.7 - 1-78. The 50-kg flowerpot is suspended from wires...Ch. 1.7 - 1-79. The 50-kg flowerpot is suspended from wires...Ch. 1.7 - *1–80. The thrust bearing consists of a circular...Ch. 1.7 - 1-81. The steel pipe is supported on the circular...Ch. 1.7 - The steel pipe is supported on the circular base...Ch. 1.7 - 1-83. The 60 mm × 60 mm oak post is supported on...Ch. 1.7 - *1-84. The frame is subjected to the load of 4 kN...Ch. 1.7 - Prob. 1.85P Ch. 1.7 - The two aluminum rods support the vertical force...Ch. 1.7 - The two aluminum rods AB and AC have diameters of...Ch. 1.7 - The compound wooden beam is connected together by...Ch. 1.7 - Determine the required minimum thickness t of...Ch. 1.7 - Determine the maximum allowable load P that can be...Ch. 1.7 - Prob. 1.91P Ch. 1.7 - *1-92. If the allowable hearing stress for the...Ch. 1.7 - The rods AB and CD are made of steel. Determine...Ch. 1.7 - The aluminum bracket A is used to support the...Ch. 1.7 - Prob. 1.95P Ch. 1.7 - *1-96. The pin support A and roller support B of...Ch. 1 - The beam AB is pin supported at A and supported by...Ch. 1 - The long bolt passes through the 30-mm-thick...Ch. 1 - Determine the required thickness of member BC to...Ch. 1 - The circular punch B exerts a force of 2 kN on the...Ch. 1 - Determine the average punching shear stress the...Ch. 1 - The 150 mm by 150 mm block of aluminum supports a...Ch. 1 - The yoke-and-rod connection is subjected to a...Ch. 1 - The cable has a specific weight (weight/volume)...

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