EBK MECHANICS OF MATERIALS
7th Edition
ISBN: 9780100257061
Author: BEER
Publisher: YUZU
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Textbook Question
Chapter 11.3, Problem 16P
Show by integration that the strain energy of the tapered rod AB is
where Amin is the cross-sectional area at end B.
Fig. P11.16
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Prove that the sum of the normal strains in perpendicular directions is constant, i.e., Px + Py = Px′ + Py′
H.W.7 A rigid steel bar ABC is supported by three rods.
There is no strain in the rods before load P is applied. After
load P is applied, the axial strain in rod (1) is 1,200 µɛ.
(1)
2,000 mm
(a) Determine the axial strain in rods (2).
(b) Determine the axial strain in rods (2) if there is a 0.5 mm
gap in the connections between rods (2) and the rigid
bar before the load is applied.
520 mm
400 mm
1,250 mm
(2)
A thin wire, lying along the x axis, is strained such that each point on the wire is displaced Δx = kx2 along the x axis. If k is constant, what is the normal strain at any point P along the wire?
Chapter 11 Solutions
EBK MECHANICS OF MATERIALS
Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - Determine the modulus of resilience for each of...Ch. 11.3 - The stress-strain diagram shown has been drawn...Ch. 11.3 - The stress-strain diagram shown has been drawn...Ch. 11.3 - Prob. 7PCh. 11.3 - Prob. 8PCh. 11.3 - Using E = 29 106 psi, determine (a) the strain...Ch. 11.3 - Using E = 200 GPa, determine (a) the strain energy...
Ch. 11.3 - A 30-in. length of aluminum pipe of...Ch. 11.3 - A single 6-mm-diameter steel pin B is used to...Ch. 11.3 - Prob. 13PCh. 11.3 - Prob. 14PCh. 11.3 - The assembly ABC is made of a steel for which E =...Ch. 11.3 - Show by integration that the strain energy of the...Ch. 11.3 - Prob. 17PCh. 11.3 - Prob. 18PCh. 11.3 - Prob. 19PCh. 11.3 - 11.18 through 11.21 In the truss shown, all...Ch. 11.3 - Prob. 21PCh. 11.3 - Each member of the truss shown is made of aluminum...Ch. 11.3 - Each member of the truss shown is made of aluminum...Ch. 11.3 - 11.24 through 11.27 Taking into account only the...Ch. 11.3 - Prob. 25PCh. 11.3 - 11.24 through 11.27 Taking into account only the...Ch. 11.3 - 11.24 through 11.27 Taking into account only the...Ch. 11.3 - Prob. 28PCh. 11.3 - Prob. 29PCh. 11.3 - Prob. 30PCh. 11.3 - 11.30 and 11.31 Using E = 200 GPa, determine the...Ch. 11.3 - Assuming that the prismatic beam AB has a...Ch. 11.3 - Prob. 33PCh. 11.3 - The design specifications for the steel shaft AB...Ch. 11.3 - Show by integration that the strain energy in the...Ch. 11.3 - The state of stress shown occurs in a machine...Ch. 11.3 - Prob. 37PCh. 11.3 - The state of stress shown occurs in a machine...Ch. 11.3 - Prob. 39PCh. 11.3 - Prob. 40PCh. 11.3 - Prob. 41PCh. 11.5 - A 5-kg collar D moves along the uniform rod AB and...Ch. 11.5 - The 18-lb cylindrical block E has a horizontal...Ch. 11.5 - The cylindrical block E has a speed v0 =16 ft/s...Ch. 11.5 - Prob. 45PCh. 11.5 - Prob. 46PCh. 11.5 - The 48-kg collar G is released from rest in the...Ch. 11.5 - Prob. 48PCh. 11.5 - Prob. 49PCh. 11.5 - Prob. 50PCh. 11.5 - Prob. 51PCh. 11.5 - The 2-kg block D is dropped from the position...Ch. 11.5 - The 10-kg block D is dropped from a height h = 450...Ch. 11.5 - Prob. 54PCh. 11.5 - A 160-lb diver jumps from a height of 20 in. onto...Ch. 11.5 - Prob. 56PCh. 11.5 - A block of weight W is dropped from a height h...Ch. 11.5 - 11.58 and 11.59 Using the method of work and...Ch. 11.5 - 11.58 and 11.59 Using the method of work and...Ch. 11.5 - 11.60 and 11.61 Using the method of work and...Ch. 11.5 - 11.60 and 11.61 Using the method of work and...Ch. 11.5 - 11.62 and 11.63 Using the method of work and...Ch. 11.5 - 11.62 and 11.63 Using the method of work and...Ch. 11.5 - Using the method of work and energy, determine the...Ch. 11.5 - Using the method of work and energy, determine the...Ch. 11.5 - The 20-mm diameter steel rod BC is attached to the...Ch. 11.5 - Torques of the same magnitude T are applied to the...Ch. 11.5 - Prob. 68PCh. 11.5 - The 20-mm-diameter steel rod CD is welded to the...Ch. 11.5 - The thin-walled hollow cylindrical member AB has a...Ch. 11.5 - 11.71 and 11.72 Each member of the truss shown has...Ch. 11.5 - 11.71 and 11.72 Each member of the truss shown has...Ch. 11.5 - Each member of the truss shown is made of steel...Ch. 11.5 - Each member of the truss shown is made of steel....Ch. 11.5 - Each member of the truss shown is made of steel...Ch. 11.5 - The steel rod BC has a 24-mm diameter and the...Ch. 11.9 - 11.77 and 11.78 Using the information in Appendix...Ch. 11.9 - 11.77 and 11.78 Using the information in Appendix...Ch. 11.9 - 11.79 through 11.82 For the beam and loading...Ch. 11.9 - 11.79 through 11.82 For the beam and loading...Ch. 11.9 - 11.79 through 11.82 For the beam and loading...Ch. 11.9 - 11.79 through 11.82 For the beam and loading...Ch. 11.9 - 11.83 through 11.85 For the prismatic beam shown,...Ch. 11.9 - 11.83 through 11.85 For the prismatic beam shown,...Ch. 11.9 - 11.83 through 11.85 For the prismatic beam shown,...Ch. 11.9 - 11.86 through 11.88 For the prismatic beam shown,...Ch. 11.9 - 11.86 through 11.88 For the prismatic beam shown,...Ch. 11.9 - 11.86 through 11.88 For the prismatic beam shown,...Ch. 11.9 - For the prismatic beam shown, determine the slope...Ch. 11.9 - For the prismatic beam shown, determine the slope...Ch. 11.9 - For the beam and loading shown, determine the...Ch. 11.9 - For the beam and loading shown, determine the...Ch. 11.9 - 11.93 and 11.94 For the beam and loading shown,...Ch. 11.9 - 11.93 and 11.94 For the beam and loading shown,...Ch. 11.9 - For the beam and loading shown, determine the...Ch. 11.9 - For the beam and loading shown, determine the...Ch. 11.9 - Prob. 97PCh. 11.9 - For the beam and loading shown, determine the...Ch. 11.9 - 11.99 and 11.100 For the truss and loading shown,...Ch. 11.9 - 11.99 and 11.100 For the truss and loading shown,...Ch. 11.9 - 11.101 and 11.102 Each member of the truss shown...Ch. 11.9 - 11.101 and 11.102 Each member of the truss shown...Ch. 11.9 - 11.103 and 11.104 Each member of the truss shown...Ch. 11.9 - 11.103 and 11 104 Each member of the truss shown...Ch. 11.9 - A uniform rod of flexural rigidity EI is bent and...Ch. 11.9 - For the uniform rod and loading shown and using...Ch. 11.9 - For the beam and loading shown and using...Ch. 11.9 - Two rods AB and BC of the same flexural rigidity...Ch. 11.9 - Three rods, each of the same flexural rigidity EI,...Ch. 11.9 - Three rods, each of the same flexural rigidity EI,...Ch. 11.9 - 11.111 through 11.115 Determine the reaction at...Ch. 11.9 - 11.111 through 11.115 Determine the reaction at...Ch. 11.9 - 11.111 through 11.115 Determine the reaction at...Ch. 11.9 - 11.111 through 11.115 Determine the reaction at...Ch. 11.9 - 11.111 through 11.115 Determine the reaction at...Ch. 11.9 - For the uniform beam and loading shown, determine...Ch. 11.9 - 11.117 through 11.120 Three members of the same...Ch. 11.9 - 11.117 through 11.120 Three members of the same...Ch. 11.9 - 11.117 through 11.120 Three members of the same...Ch. 11.9 - 11.117 through 11.120 Three members of the same...Ch. 11.9 - 11.121 and 11.122 Knowing that the eight members...Ch. 11.9 - 11.121 and 11.122 Knowing that the eight members...Ch. 11 - Rod AB is made of a steel for which the yield...Ch. 11 - Each member of the truss shown is made of steel...Ch. 11 - The ship at A has just started to drill for oil on...Ch. 11 - Collar D is released from rest in the position...Ch. 11 - Each member of the truss shown is made of steel...Ch. 11 - A block of weight W is placed in contact with a...Ch. 11 - Two solid steel shafts are connected by the gears...Ch. 11 - A 160-lb diver jumps from a height of 20 in. onto...Ch. 11 - For the prismatic beam shown, determine the slope...Ch. 11 - A disk of radius a has been welded to end B of the...Ch. 11 - A uniform rod of flexural rigidity EI is bent and...Ch. 11 - The steel bar ABC has a square cross section of...
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- Prove that the sum of the normal strains in perpendicular directions is constant, i.e., P x+ P y = P x + P y .arrow_forwardA steel cable is used to support an elevator cage at the bottom of a 2100-ft-deep mineshaft. A uniform normal strain of 240 μin./in. is produced in the cable by the weight of the cage. At each point, the weight of the cable produces an additional normal strain that is proportional to the length of the cable below the point. Assume D = 2100 ft and d = 500 ft. If the total normal strain in the cable at the cable drum (upper end of the cable) is 790 μin./in., determine (a) the strain in the cable at a depth of 500 ft. (b) the total elongation of the cable. Drum Cable Answers: (a) ε = (b) 8 = i i d D Elevator cage X uin./in. in.arrow_forwardH.W.7 A rigid steel bar ABC is supported by three rods. There is no strain in the rods before load P is applied. After load P is applied, the axial strain in rod (1) is 1,200 µue. (1) 2,000 mm (a) Determine the axial strain in rods (2). (b) Determine the axial strain in rods (2) if there is a 0.5 mm gap in the connections between rods (2) and the rigid bar before the load is applied. 520 mm 400 mm 1,250 mm (2)arrow_forward
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