EBK MECHANICS OF MATERIALS
7th Edition
ISBN: 9780100257061
Author: BEER
Publisher: YUZU
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Chapter 3.8, Problem 104P
(a)
To determine
The radius of elastic core of the shaft.
(b)
To determine
The angle of twist at end B of the shaft.
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Students have asked these similar questions
3.38 The aluminum rod AB (G = 27 GPa) is bonded to the brass rod
BD (G = 39 GPa). Knowing that portion CD of the brass rod is
hollow and has an inner diameter of 40 mm, determine the angle
of twist at A.
60 mm
T = 1600 N m
36 mm
TA = S00 N - mn
250 mm
B
375 mm
A
400 mm
Fig. P3.38
The solid circular drill rod AB is made of a
steel that is assumed to be elastoplastic
with TY = 22 ksi and G = 11.2 x 106 psi.
Knowing that a torque T = 73 kip-in. is
applied to the rod and then removed,
determine the permanent angle of twist of
the rod. The permanent angle of twist of
the rod is
5.86 The cast iron inverted T-section supports two concentrated loads of magni-
tude P. The working stresses are 48 MPa in tension, 140 MPa in compression, and
30 MPa in shear. (a) Show that the neutral axis of the cross section is located at
d = 48.75 mm and that the moment of inertia of the cross-sectional area about this
axis is I = 11.918 x 106 mm“. (b) Find the maximum allowable value of P.
1.0 m
1.0 m
15 mm
3 m
150 mm
NA-
d
15 mm
150 mm
FIG. P5.86
Chapter 3 Solutions
EBK MECHANICS OF MATERIALS
Ch. 3.1 - Determine the torque T that causes a maximum...Ch. 3.1 - For the cylindrical shaft shown, determine the...Ch. 3.1 - (a) Determine the torque T that causes a maximum...Ch. 3.1 - (a) Determine the maximum shearing stress caused...Ch. 3.1 - (a) For the 3-in.-diameter solid cylinder and...Ch. 3.1 - Fig. P3.6 3.6 A torque T=3 kN m is applied to the...Ch. 3.1 - The solid spindle AB is made of a steel with an...Ch. 3.1 - The solid spindle AB has a diameter ds = 1.5 in....Ch. 3.1 - Fig. P3.9 and P3.10 3.10 The shafts of the pulley...Ch. 3.1 - Knowing that each of the shafts AB, BC, and CD...
Ch. 3.1 - Fig. P3.11 and P3.12 3.12 Knowing that an...Ch. 3.1 - Under normal operating conditions, the electric...Ch. 3.1 - In order to reduce the total mass of the assembly...Ch. 3.1 - The allowable shearing stress is 15 ksi in the...Ch. 3.1 - The allowable shearing stress is 15 ksi in the...Ch. 3.1 - The solid shaft shown is formed of a brass for...Ch. 3.1 - Solve Prob. 3.17 assuming that the direction of Tc...Ch. 3.1 - The solid rod AB has a diameter dAB= 60 mm and is...Ch. 3.1 - Fig. P3.19 and P3.20 3.20 The solid rod AB has a...Ch. 3.1 - A torque of magnitude T = 1000 N m is applied at D...Ch. 3.1 - Fig. P3.21 and P3.22 3.22 A torque of magnitude T...Ch. 3.1 - Under normal operating conditions a motor exerts a...Ch. 3.1 - Fig P3.23 and P3.24 3.24 Under normal operating...Ch. 3.1 - Prob. 25PCh. 3.1 - Fig. P3.25 and P3.26 3.26 The two solid shafts are...Ch. 3.1 - For the gear train shown, the diameters of the...Ch. 3.1 - Fig. P3.27 and P3.28 3.28 A torque T = 900 N m is...Ch. 3.1 - Fig. P3.29 3.29 While the exact distribution of...Ch. 3.1 - Fig. P3.30 3.30 (a) For a given allowable shearing...Ch. 3.3 - Determine the largest allowable diameter of a...Ch. 3.3 - The ship at A has just started to drill for oil on...Ch. 3.3 - (a) For the solid steel shaft shown, determine the...Ch. 3.3 - (a) For the aluminum pipe shown (G = 27 GPa),...Ch. 3.3 - The electric motor exerts a 500 N m-torque on the...Ch. 3.3 - The torques shown are exerted on pulleys and B....Ch. 3.3 - The aluminum rod BC (G = 26 GPa) is bonded to the...Ch. 3.3 - The aluminum rod AB (G = 27 GPa) is bonded to the...Ch. 3.3 - The solid spindle AB has a diameter ds = 1.75 in....Ch. 3.3 - Fig. p3.39 and p3.40 3.40 The solid spindle AB has...Ch. 3.3 - Two shafts, each of 78in. diameter, are connected...Ch. 3.3 - Two solid steel shafts each of 30-mm diameter, are...Ch. 3.3 - A coder F, used to record in digital form the...Ch. 3.3 - Fig. p3.43 3.44 For the gear train described in...Ch. 3.3 - The design specifications of a 1.2-m-long solid...Ch. 3.3 - 3.46 and 3.47 The solid cylindrical rod BC of...Ch. 3.3 - 3.46 and 3.47 The solid cylindrical rod BC of...Ch. 3.3 - The design of the gear-and-shaft system shown...Ch. 3.3 - The electric motor exerts a torque of 900 Nm on...Ch. 3.3 - A hole is punched at A in a plastic sheet by...Ch. 3.3 - The solid cylinders AB and BC are bonded together...Ch. 3.3 - Solve Prob. 3.51, assuming that cylinder AB is...Ch. 3.3 - The composite shaft shown consists of a...Ch. 3.3 - Fig. p3.53 and p3.54 3.54 The composite shaft...Ch. 3.3 - Two solid steel shafts (G = 77.2 GPa) are...Ch. 3.3 - Solve Prob. 3.55, assuming that the shaft AB is...Ch. 3.3 - 3.57 and 3.58 Two solid steel shafts are fitted...Ch. 3.3 - 3.57 and 3.58 Two solid steel shafts are fitted...Ch. 3.3 - The steel jacket CD has been attached to the...Ch. 3.3 - A torque T is applied as shown to a solid tapered...Ch. 3.3 - Prob. 61PCh. 3.3 - A solid shaft and a hollow shaft are made of the...Ch. 3.3 - An annular plate of thickness t and modulus G is...Ch. 3.5 - Determine the maximum shearing stress in a solid...Ch. 3.5 - Determine the maximum shearing stress in a solid...Ch. 3.5 - Using an allowable shearing stress of 4.5 ksi,...Ch. 3.5 - Using an allowable shearing stress of 50 MPa,...Ch. 3.5 - While a steel shaft of the cross section shown...Ch. 3.5 - Determine the required thickness of the 50-mm...Ch. 3.5 - A steel drive shaft is 6 ft long and its outer and...Ch. 3.5 - The hollow steel shaft shown (G = 77.2 GPa, all =...Ch. 3.5 - A steel pipe of 3.5-in. outer diameter is to be...Ch. 3.5 - 3.73 The design of a machine element calls for a...Ch. 3.5 - Three shafts and four gears are used to form a...Ch. 3.5 - Three shafts and four gears are used to form a...Ch. 3.5 - The two solid shafts and gears shown are used to...Ch. 3.5 - Fig. P3.76 and P3.77 3.77 The two solid shafts and...Ch. 3.5 - The shaft-disk-belt arrangement shown is used to...Ch. 3.5 - A 5-ft-long solid steel shaft of 0.875-in....Ch. 3.5 - A 2.5-m-long steel shaft of 30-mm diameter rotates...Ch. 3.5 - The design specifications of a 1.2-m-long solid...Ch. 3.5 - A 1.5-m-long tubular steel shaft (G = 77.2 GPa) of...Ch. 3.5 - Fig. P3.82 and P3.83 3.83 A 1.5-m-long tubular...Ch. 3.5 - The stepped shaft shown must transmit 40 kW at a...Ch. 3.5 - The stepped shaft shown rotates at 450 rpm....Ch. 3.5 - Knowing that the stepped shaft shown transmits a...Ch. 3.5 - The stepped shaft shown must rotate at a frequency...Ch. 3.5 - Fig. P3.87 and P3.88 3.88 The stepped shaft shown...Ch. 3.5 - A torque of magnitude T = 200 lbin. is applied to...Ch. 3.5 - Fig. P3.89, P3.90 and P3.91 3.90 In the stepped...Ch. 3.5 - In the stepped shaft shown, which has a full...Ch. 3.8 - The solid circular shaft shown is made of a steel...Ch. 3.8 - Prob. 93PCh. 3.8 - Prob. 94PCh. 3.8 - Prob. 95PCh. 3.8 - Fig. P3.95 and P3.96 3.96 The solid shaft shown is...Ch. 3.8 - It is observed that a straightened paper clip can...Ch. 3.8 - The solid shaft shown is made of a mild steel that...Ch. 3.8 - Prob. 99PCh. 3.8 - Prob. 100PCh. 3.8 - Prob. 101PCh. 3.8 - Prob. 102PCh. 3.8 - Prob. 103PCh. 3.8 - Prob. 104PCh. 3.8 - A solid circular rod is made of a material that is...Ch. 3.8 - Prob. 106PCh. 3.8 - Prob. 107PCh. 3.8 - Prob. 108PCh. 3.8 - Prob. 109PCh. 3.8 - Prob. 110PCh. 3.8 - Prob. 111PCh. 3.8 - A 50-mm diameter cylinder is made of a brass for...Ch. 3.8 - Prob. 113PCh. 3.8 - The solid circular drill rod AB is made of a steel...Ch. 3.8 - Prob. 115PCh. 3.8 - Prob. 116PCh. 3.8 - After the solid shaft of Prob. 3.116 has been...Ch. 3.8 - The hollow shaft shown is made of a steel that is...Ch. 3.8 - Prob. 119PCh. 3.8 - Prob. 120PCh. 3.10 - Determine the smallest allowable square cross...Ch. 3.10 - Prob. 122PCh. 3.10 - Using all = 70 MPa and G = 27 GPa, determine for...Ch. 3.10 - Prob. 124PCh. 3.10 - Determine the largest torque T that can be applied...Ch. 3.10 - Each of the two brass bars shown is subjected to a...Ch. 3.10 - Prob. 127PCh. 3.10 - Prob. 128PCh. 3.10 - Prob. 129PCh. 3.10 - Shafts A and B are made of the same material and...Ch. 3.10 - Prob. 131PCh. 3.10 - Shafts A and B are made of the same material and...Ch. 3.10 - Prob. 133PCh. 3.10 - Prob. 134PCh. 3.10 - Prob. 135PCh. 3.10 - A 36-kipin. torque is applied to a 10-ft-long...Ch. 3.10 - A 4-m-long steel member has a W310 60 cross...Ch. 3.10 - Prob. 138PCh. 3.10 - A 5-kipft torque is applied to a hollow aluminum...Ch. 3.10 - A torque T = 750 kNm is applied to the hollow...Ch. 3.10 - A 750-Nm torque is applied to a hollow shaft...Ch. 3.10 - 3.142 and 3.143 A hollow member having the cross...Ch. 3.10 - A hollow member having the cross section shown is...Ch. 3.10 - A 90-Nm torque is applied to a hollow shaft having...Ch. 3.10 - 3.145 and 3.146 A hollow member having the cross...Ch. 3.10 - 3.145 and 3.146 A hollow member having the cross...Ch. 3.10 - A cooling tube having the cross section shown is...Ch. 3.10 - A hollow cylindrical shaft was designed to have a...Ch. 3.10 - Equal torques are applied to thin-walled tubes of...Ch. 3.10 - A hollow cylindrical shaft of length L, mean...Ch. 3 - A steel pipe of 12-in. outer diameter is...Ch. 3 - A torque of magnitude T = 120 Nm is applied to...Ch. 3 - Fig. P3.152 3.153 Two solid shafts are connected...Ch. 3 - Prob. 154RPCh. 3 - Prob. 155RPCh. 3 - A torque of magnitude T = 4 kNm is applied at end...Ch. 3 - Ends A and D of the two solid steel shafts AB and...Ch. 3 - As the hollow steel shaft shown rotates at 180...Ch. 3 - Prob. 159RPCh. 3 - Prob. 160RPCh. 3 - Prob. 161RPCh. 3 - The shaft AB is made of a material that is...
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- 1. The aluminium rod AB is bonded to the brass rod BD. Knowing that portion CD of the brass rod is hollow and has an inner diameter of 40 mm, determine the angle of twist at A. Take GAL = 27 GPa and GBr = 39 GPa respectively. 60 mm T = 1600 N - m 36 mm T = S00 N. m 250 mm 375 mm 400 mm Figure Q4.1: Compound shaftarrow_forwardDeformable bodies.arrow_forward2.14 The aluminum rod ABC (E 10.1 × 106 psi), which consists of two cylindrical portions AB and BC, is to be replaced with a cylin- drical steel rod DE (E = 29 × 106 psi) of the same overall length. Determine the minimum required diameter d of the steel rod if its vertical deformation is not to exceed the deformation of the aluminum rod under the same load and if the allowable stress in the steel rod is not to exceed 24 ksi. Ĵ 12 in. + 18 in. 28 kips -1.5 in. Fig. P2.14 B -2.25 in. 28 kips D E --arrow_forward
- 1) The aluminum rod AB is bonded to the brass rod BD. Knowing that portion CD of the brass rod is hollow and has an inner diameter of 40 mm, determine the angle of twist at A. Take G(aluminum) =27 GPa and G(brass) =39 GPa respectively.arrow_forward3.33 (a) For the solid steel shaft shown, determine the angle of twist at A. Use G = 77 GPa. (b) Solve part a, assuming that the steel shaft is hollow with a 15 mm outer radius and a 10 mm inner radius. 15 mm A 1.8 m T = 250 N. m Fig. P3.33arrow_forward5.86 The cast iron inverted T-section supports two concentrated loads of magnitude P. The working stresses are 48 MPa in tension, 140 MPa in compression, and 30 MPa in shear. (a) Show that the neutral axis of the cross section is located at d ¼ 48:75 mm and that the moment of inertia of the cross-sectional area about this axis is I ¼ 11:918 106 mm4. (b) Find the maximum allowable value of P.arrow_forward
- 3.6 Two forces, each of magnitude P, are applied to the wrench. The diameter of the steel shaft AB is 20 mm. Determine the largest allowable value of P if the shear stress in the shaft is not to exceed 120 MPa and its angle of twist is limited to 7°. Use G= 80 GPa for steel. 300 mm B 500 mm FIG. P3.6arrow_forwardPROBLEM 3.52 A 4 kNm torque T is applied at end A of the composite shaft shown. Knowing that the shear modulus is 77 GPa for the steel and 27 GPa for the aluminium, determine (a) the maximum shear stress in the steel core, (b) the maximum shear stress in the aluminium jacket, and (c) the angle of twist at A. [Ans. (a) 73.6 MPa (b) 34.4 MPa (c) 5.07°] 72 mm 54 mm 2.5 m Steel core Aluminium jackeť Fig. P3.52 and P3.53 22:37 e dx D 14/04/2022 BANG & OLUFSEN 40 delete home end pg up pg dn num backspace lock W ERT U %23 home og up 4.arrow_forwardPROBLEM 3.52 A 4 kNm torque T is applied at end A of the composite shaft shown. Knowing that the shear modulus is 77 GPa for the steel and 27 GPa for the aluminium, determine (a) the maximum shear stress in the steel core, (b) the maximum shear stress in the aluminium jacket, and (c) the angle of twist at A. [Ans. (a) 73.6 MPa (b) 34.4 MPa (c) 5.07°] Hint: angle of twist at 72 mm end A is same for core and jacket 54 mm A 2.5 m Steel core Aluminium jacket Fig. P3.52 and P3.53 22:35 BANG & OLUFSEN delete home end og up pg dn num backspace 4 lock Q WE T U 080 home pg uparrow_forward
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