EBK MECHANICS OF MATERIALS
7th Edition
ISBN: 9780100257061
Author: BEER
Publisher: YUZU
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Chapter 11.3, Problem 25P
To determine
Find the strain energy for the prismatic beam AB.
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12. A single strain gage is cemented to
solid 96-mm-diameter aluminum
shaft at an angle B = 20° with a line
parallel to the axis of the shaft.
Knowing that G = 27 GPa, determine
the torque T corresponding to a gage
reading of 400u.
48 mm
Figure P12
Show by integration that the strain energy of the tapered rod AB is U = 1/4 P^2L/EA min
Now solve the problem again but add a torque at point B, which acts together with P as shown in the figure.
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)
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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- 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 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_forward2. A steel wire 30 ft long, hanging vertically, supports a load of 500 lbf. Neglecting the weight of the wire, determine the required diameter if the stress is not to exceed 20,000 psi and the total elongation is not to exceed 0. in. Assume E = 29 × 106 psi.arrow_forward9.59 In many situations it is known that the normal stress in a given direction is zero. For example, o; = 0 in the case of the thin plate shown. For this case, which is known as plane stress, show that if the strains e, and e, have been determined experimentally, we can express o, o, and e̟ as follows: €x + v€y 0, = E 1 - v2 + νε, Fig. P9.59 = E 1 v² (e, + €„)arrow_forward
- 9.38 The assembly shown consists of an aluminum shell (E. = 70 GPa, a, = 23.6 X 10°C) fully bonded to a steel core (E, = 200 GPa, a, = 11.7 × 10-ºC) and is unstressed at a temperature of 20°C. Considering only axial deformations, determine the stress in the aluminum shell when the temperature reaches 180°C. 200 mm 20 mm Aluminum shell Steel 50 mm core Fig. P9.38arrow_forwardA steel wire 30 ft long, hanging vertically, supports a load of 500 lb. Neglecting the weight of the wire, determine the required diameter if the stress is not to exceed 20 ksi and the total elongation is not to exceed 0.10 in. Assume E = 29 × 10° psi. 0.22 in 0.30 in 0.28 in. 0.20 in.arrow_forwardProblem 20.1 A thin plate made of steel with E = 29000 ksi and G = 11000 ksi has strains at a particular point represented as Ex = 600μ, y = 100µ, Yxy = 1500µ, as determined by strain gages. Determine the principal strains and the maximum shearing strain at the point. Determine the principal strain directions. Draw a sketch showing the principal strain distortions and the maximum shearing strain distortion.arrow_forward
- A solid 20-mm-diameter shaft is subjected to an axial load P. The shaft is made of aluminum [E = 70 GPa; v=0.33]. A strain gage is mounted on the shaft at the orientation shown in Fig. P13.77. (a) If P= 18.5 kN, determine the strain reading that would be expected from the gage. (b) If the gage indicates a strain value of ε = 950 ue, determine the axial force P applied to the shaft.arrow_forwardA bracket is supported by means of 4 rivets of same size, as shown in Fig. 9.37. Determine the diameter of the rivet if the maximum shear stress is 140 MPa. [Ans. 16 mm]arrow_forwardQuestion-2: A solid 20-mm-diameter shaft is subjected to an axial load P. The shaft is made of aluminum [E = 70 GPa; v= 0.33]. A strain gage is mounted on the shaft at the orientation shown in Fig. P13.77. (a) If P = 18.5 kN, determine the strain reading that would be expected from the gage. (b) If the gage indicates a strain value of e= 950 uE, determine the axial force P applied to the shaft.arrow_forward
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