EBK MECHANICS OF MATERIALS
7th Edition
ISBN: 8220100257063
Author: BEER
Publisher: YUZU
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Chapter 8.2, Problem 21P
To determine
Show that the maximum shearing stress at point K as
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Problem 3.4 not problem 3.3 thanks, problem 3.4 thanks
A composite shaft shown, composed of a steel (G = 77 GPa) core inside an aluminum (G = 25 GPa) jacket, carries a torque, T = 10 kN-m. The shaft is designed such that the aluminum jacket will fail first upon the application of the torque.
1) If the allowable shear strength of aluminum is 45 MPa, determine the minimum thickness, t, of the aluminum jacket, that can carry the torque.2) What must be the minimum shear strength of steel such that the aluminum jacket will fail first?3) Determine the maximum angle of twist that can be applied to the shaft.
A torque of T= 40 kip-in. acts on
gear C of the assembly shown in Fig.
P6.91. Shafts (1) and (2) are solid
2.00-in.-diameter stainless steel shafts
and shaft (3) is a solid 1.75-in.-
diameter stainless steel shaft. Assume
L=8 in. and G= 12,500 ksi.
Determine:
21
54 secth
(1)
(2)
(3).
(a) the maximum shear stress
magnitude in shaft (1).
42 leeth
(b) the maximum shear stress
magnitude in shaft segment (3).
(c) the rotation angle of gear E.
Figure E6.9-5
(d) the rotation angle of gear C.
Chapter 8 Solutions
EBK MECHANICS OF MATERIALS
Ch. 8.2 - A W10 = 39 rolled-steel beam supports a load P as...Ch. 8.2 - Solve Prob. 8.1, assuming that P = 22.5 kips and a...Ch. 8.2 - An overhanging W920 449 rolled-steel beam...Ch. 8.2 - Solve Prob. 8.3, assuming that P = 850 kN and a =...Ch. 8.2 - 8.5 and 8.6 (a) Knowing that all = 160 MPa and all...Ch. 8.2 - 8.5 and 8.6 (a) Knowing that all = 160 MPa and all...Ch. 8.2 - 8.7 and 8.8 (a) Knowing that all = 24 ksi and all...Ch. 8.2 - 8.7 and 8.8 (a) Knowing that all = 24 ksi and all...Ch. 8.2 - 8.9 through 8.14 Each of the following problems...Ch. 8.2 - 8.9 through 8.14 Each of the following problems...
Ch. 8.2 - 8.9 through 8.14 Each of the following problems...Ch. 8.2 - Prob. 12PCh. 8.2 - 8.9 through 8.14 Each of the following problems...Ch. 8.2 - 8.9 through 8.14 Each of the following problems...Ch. 8.2 - Determine the smallest allowable diameter of the...Ch. 8.2 - Determine the smallest allowable diameter of the...Ch. 8.2 - Using the notation of Sec. 8.2 and neglecting the...Ch. 8.2 - The 4-kN force is parallel to the x axis, and the...Ch. 8.2 - The vertical force P1 and the horizontal force P2...Ch. 8.2 - The two 500-lb forces are vertical and the force P...Ch. 8.2 - Prob. 21PCh. 8.2 - Prob. 22PCh. 8.2 - The solid shaft AB rotates at 600 rpm and...Ch. 8.2 - The solid shaft AB rotates at 600 rpm and...Ch. 8.2 - The solid shafts ABC and DEF and the gears shown...Ch. 8.2 - Prob. 26PCh. 8.2 - Prob. 27PCh. 8.2 - Prob. 28PCh. 8.2 - The solid shaft AE rotates at 600 rpm and...Ch. 8.2 - The solid shaft AE rotates at 600 rpm and...Ch. 8.3 - Two 1.2-kip forces are applied to an L-shaped...Ch. 8.3 - Two 1.2-kip forces are applied to an L-shaped...Ch. 8.3 - The cantilever beam AB has a rectangular cross...Ch. 8.3 - 8.34 through 8.36 Member AB has a uniform...Ch. 8.3 - 8.34 through 8.36 Member AB has a uniform...Ch. 8.3 - 8.34 through 8.36 Member AB has a uniform...Ch. 8.3 - Prob. 37PCh. 8.3 - Two forces are applied to the pipe AB as shown....Ch. 8.3 - Several forces are applied to the pipe assembly...Ch. 8.3 - The steel pile AB has a 100-mm outer diameter and...Ch. 8.3 - Three forces are applied to a 4-in.-diameter plate...Ch. 8.3 - The steel pipe AB has a 72-mm outer diameter and a...Ch. 8.3 - A 13-kN force is applied as shown to the...Ch. 8.3 - A vertical force P of magnitude 60 lb is applied...Ch. 8.3 - Three forces are applied to the bar shown....Ch. 8.3 - Prob. 46PCh. 8.3 - Three forces are applied to the bar shown....Ch. 8.3 - Three forces are applied to the bar shown....Ch. 8.3 - Two forces are applied to the small post BD as...Ch. 8.3 - Two forces are applied to the small post BD as...Ch. 8.3 - Three forces are applied to the machine component...Ch. 8.3 - Prob. 52PCh. 8.3 - Three steel plates, each 13 mm thick, are welded...Ch. 8.3 - Three steel plates, each 13 mm thick, are welded...Ch. 8.3 - Two forces P1 and P2 are applied as shown in...Ch. 8.3 - Two forces P1 and P2 are applied as shown in...Ch. 8.3 - Prob. 57PCh. 8.3 - Four forces are applied to a W8 28 rolled-steel...Ch. 8.3 - A force P is applied to a cantilever beam by means...Ch. 8.3 - Prob. 60PCh. 8.3 - A 5-kN force P is applied to a wire that is...Ch. 8.3 - Knowing that the structural tube shown has a...Ch. 8.3 - The structural tube shown has a uniform wall...Ch. 8.3 - The structural tube shown has a uniform wall...Ch. 8 - (a) Knowing that all = 24 ksi and all = 14.5 ksi,...Ch. 8 - Neglecting the effect of fillets and of stress...Ch. 8 - Knowing that rods BC and CD are of diameter 24 mm...Ch. 8 - The solid shaft AB rotates at 450 rpm and...Ch. 8 - A 6-kip force is applied to the machine element AB...Ch. 8 - A thin strap is wrapped around a solid rod of...Ch. 8 - A close-coiled spring is made of a circular wire...Ch. 8 - Forces are applied at points A and B of the solid...Ch. 8 - Knowing that the bracket AB has a uniform...Ch. 8 - For the post and loading shown, determine the...Ch. 8 - Knowing that the structural tube shown has a...Ch. 8 - The cantilever beam AB will be installed so that...
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- Problem 3.1 not 3.2, I’m not asking about 3.2 even though it’s in the picturearrow_forwardProb.10: [3.17] Shaft AB is made of a steel with an allowable shearing stress of 90 MPa and shaft BC is made of an aluminum with allowable shearing stress of 60 MPa. Knowing that the diameter of shaft BC is 50 mm and neglecting the effect of stress concentrations, determine (a) the largest torque T that can be applied at A if the allowable stress is not to exceeded in the shaft BC, (b) the corresponding required diameter of shaft AB. Aluminum Steel- C T' В Aarrow_forward6 ft The composite shaft shown consists of a 0.2-in.-thick brass jacket (G = 5.6 × 10° psi) bonded to a 1.2-in.-diameter steel core (Gsteel = 11.2 x 10° psi). Knowing that the shaft is subjected to 5-kip · in. torques, determine (a) the maximum shearing stress in the brass jacket, (b) the maximum shearing stress in the steel core, (c) the angle of twist of end B relative to end A. T B Brass jacket 1.2 in. - Steel core 0.2 in.arrow_forward
- Q.2 (a) A hollow steel shaft of length 1.75 m transmits 2000 kW of power at a speed of 150 rev/min. The inside diameter is to be 0.75 times the outside diameter. The maximum allowable torsional shear stress for the steel is 130 MN/m and the modulus of rigidity (G) for the steel is 83 GN/m?. Given that a factor of safety of 2 is required for the shaft, determine: i) the torque acting on the shaft; ii) the required external and internal diameters for the shaft; ii) the torsional shear stress set-up in the shaft material at the inside surface of the hollow shaft, and sketch the stress distribution through the shaft wall; iv) the angle of twist (in degrees) due to the torque.arrow_forward(c) A torque T = 5600 Nm is applied to a hollow shaft having the cross section shown in Fig. Q2(c). Neglecting the effect of stress concentrations, determine the shearing stress at points a and b. Hint: q T 2A 90 mm 50 mm 75 mm with common notations. Fig. Q2(c) 5 mm -5 mmarrow_forwardA compound shaft consists of two pipe segments. Segment (1) has an outside diameter of 220 mm and a wall thickness of 10 mm. Segment (2) has an outside diameter of 140 mm and a wall thickness of 15 mm. The shaft is subjected to torques TB = 40 kN-m and TC = 12 kN-m, which act in the directions shown in Fig. P6.4. Determine the maximum shear stress magnitude in each shaft segment. only HANDWRITTEN answer needed ( NOT TYPED)arrow_forward
- Prob.9: [3.8] The solid spindle AB is made of steel with an allowable shearing stress of 84 MPa, and sleeve CD is made of a brass with an allowable shearing stress of 50 MPa. Determine (a) the largest torque T that can be applied at A if the allowable shearing stress is not to be exceeded in sleeve CD, (b) the corresponding required value of the diameter ds of spindle AB. T 100 mm D 200 mm t = 6 mm B C 75 mmarrow_forward(a.) Determine the maximum length of the flexible shaft consists of a 5mm -diameter steel wire encased in a stationary tube that fits closely enough to impose a frictional torque of 0.20 kg-mm/mm. (b.) Determine the maximum length of the shaft if the shearing stress is not to exceed 140MP.. What will be the angular deformation of one end relative to the other end? G = 83 GPa. Steel Wire 5mm Stationary Tubearrow_forwardThe solid shaft shown is formed of a brass for which the allowable shearing stress is 55 MPa. Neglecting the effect of stress concentra-tions, determine the smallest diameters dAB and dBC for which the allowable shearing stress is not exceededarrow_forward
- 1. A drive shaft to the blades of a helicopter transmits 800 kW at 200 rev/min. Neglecting transmission losses; determine the minimum external and internal diameters of the hollow circular section aluminum alloy shaft, when the maximum permissible shear stress in the shaft is limited to 30 MPa. It may be assumed that the external diameter of this shaft is twice its internal diameter. What will be the resulting angle of twist of this shaft over a length of 2 m, given that the modulus of rigidity, C 26900MPA.arrow_forward3. A solid circular shaft is 1.8 m and is made of steel with G = 70 GPa. When rotating at w = 70 rad/s, it transmits 28 kW of power from engine A to generator B. As the design engineer, you are asked to: (a) Determine the shaft's smallest allowable radius if the allowable shear stress is T allow = 80 MPa. (b) Determine the shaft's smallest allowable radius If the allowable angle of twist is allow = 0.1 rad (in other words, the shaft is restricted not to twist more than 0.1 rad). (c) If both conditions (a) and (b) are required simultaneously, which radius will you select as the allowable radius. (In other words which condition controls the situation)? Briefly explain your answer. (1 kW = 1000 Watts) Barrow_forwardThe composite shaft shown consists of a 0.2-in.-thick brass jacket (G = 5.6 × 106 psi) bonded to a 1.2-in.-diameter steel core (Gsteel = 11.2 × 106 psi). Knowing that the shaft is subjected to 5 kip-in. torques, determine: The torques in steel and brass. The maximum shearing stress in the brass jacket. The maximum shearing stress in the steel core. The angle of twist in the shaft.arrow_forward
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