Mechanics of Materials, 7th Edition
7th Edition
ISBN: 9780073398235
Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek
Publisher: McGraw-Hill Education
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Chapter 3.8, Problem 106P
(a)
To determine
Find the angle of twist which the section first becomes fully plastic.
(b)
To determine
Find the magnitude of the applied torque.
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The steel curved bar shown has rectangular cross-section with a radial height h = 6 mm and thickness b = 4mm. The
radius of the centroidal axis is R = 80 mm. A force P = 10 N is applied as shown. Assume the steel modulus of
207,000 MPa and G = 79.3(103) MPa, repectively.
elasticity and shear modulus E =
Find the vertical deflection at point B. Use Castigliano's method for a curved flexural member and since R/h > 10,
neglect the effect of shear and axial load, thereby assuming that deflection is due to merely the bending moment.
Note the inner and outer radii of the curves bar are:
r = 80 + ½ (6) = 83 mm, r₁ = 80 − ½ (6) = 77 mm
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Sπ/2 sin² 0 d = √π/² cos² 0 d0 =
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Chapter 3 Solutions
Mechanics of Materials, 7th Edition
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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