Mechanics of Materials
11th Edition
ISBN: 9780137605460
Author: Russell C. Hibbeler
Publisher: Pearson Education (US)
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Chapter 5.3, Problem 3P
To determine
Amount of Torque.
ii.
To determine
Amount of Torque
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The copper pipe has an outer diameter of 2.5 in. and an inner
diameter of 2.25 in. It is tightly secured to the wall at C and a
uniformly distributed torque is applied to it as shown.(Figure 1) Points
A and B lie on the pipe's outer surface.
Figure
C
B
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2 ft
V
150 lb-ft/ft.
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A
2 ft
V
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Determine the shear stress at point A.
Express your answer to three significant figures and include appropriate units.
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Determine the shear stress at point B.
Express your answer to three significant figures and include appropriate units.
Value
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The halves of the coupling are held together by four 5/8-in.-diameter bolts. The working stresses are 12 ksi for
shear in the bolts and 15 ksi for bearing in the coupling. Find the largest torque T that can be safely transmitted by
the coupling. Assume that the forces in the bolts have equal magnitudes.
0.5 in.
3.5 in.
The solid shaft has a linear taper from rA at one end to rB at the other. Derive an equation that gives the maximum shear stress in the shaft at a location x along the shaft’s axis.
Chapter 5 Solutions
Mechanics of Materials
Ch. 5.3 - The solid circular shaft is subjected to an...Ch. 5.3 - The hollow circular shaft is subjected to an...Ch. 5.3 - The shaft is hollow from A to B and solid from B...Ch. 5.3 - Determine the maximum shear stress in the...Ch. 5.3 - Determine the maximum shear stress in the shaft at...Ch. 5.3 - Determine the shear stress a: point A on the...Ch. 5.3 - The solid 50-mm-diameter shaft is subjected to the...Ch. 5.3 - The gear motor can develop 3 hp when it turns at...Ch. 5.3 - The solid shaft of radius r is subjected to a...Ch. 5.3 - The solid shaft of radius r is subjected to a...
Ch. 5.3 - Prob. 3PCh. 5.3 - The copper pipe has an outer diameter of 40 mm and...Ch. 5.3 - The copper pipe has an outer diameter of 2.50 in....Ch. 5.3 - The link acts as part of the elevator control for...Ch. 5.3 - The assembly consists of two sections of...Ch. 5.3 - A steel tube having an outer diameter of 2.5 in....Ch. 5.3 - The rod has a diameter of 1 in. and a weight of 10...Ch. 5.3 - The rod has a diameter of 1 in. and a weight of 15...Ch. 5.3 - Prob. 20PCh. 5.3 - The 60-mm-diameter solid shaft is subjected to the...Ch. 5.3 - The 60-mm-diameter solid shaft is subjected to the...Ch. 5.3 - The solid shaft is subjected to the distributed...Ch. 5.3 - If the tube is made from a material having an...Ch. 5.3 - Prob. 29PCh. 5.3 - The motor delivers 50 hp while turning at a...Ch. 5.3 - The solid steel shaft AC has a diameter of 25 mm...Ch. 5.3 - Prob. 35PCh. 5.4 - The 60 mm-diameter steel shaft is subjected to the...Ch. 5.4 - Prob. 10FPCh. 5.4 - The hollow 6061-T6 aluminum shaft has an outer and...Ch. 5.4 - A series of gears are mounted on the...Ch. 5.4 - The 80-mm-diameter shaft is made of steel. If it...Ch. 5.4 - The 80-mm-diameter shaft is made of steel. If it...Ch. 5.4 - The propellers of a ship are connected to an A-36...Ch. 5.4 - Show that the maximum shear strain in the shaft is...Ch. 5.4 - Determine the angle of twist of end B with respect...Ch. 5.4 - Determine the maximum allowable torque T. Also,...Ch. 5.4 - If the allowable shear stress is allow = 80 MPa,...Ch. 5.4 - Determine the angle of twist of the end A.Ch. 5.4 - The hydrofoil boat has an A992 steel propeller...Ch. 5.4 - Also, calculate the absolute maximum shear stress...Ch. 5.4 - If a torque of T = 50 N m is applied to the bolt...Ch. 5.4 - If a torque of T= 50N m is applied to the bolt...Ch. 5.4 - If the motor delivers 4 MW of power to the shaft...Ch. 5.4 - Determine the angle of twist at the free end A of...Ch. 5.5 - Gst = 75 GPa.Ch. 5.5 - The shaft is made of L2 tool steel, has a diameter...Ch. 5.5 - Each has a diameter of 25 mm and they are...Ch. 5.5 - Each has a diameter of 25 mm and they are...Ch. 5.5 - It is fixed at its ends and subjected to a torque...Ch. 5.5 - 5–89. Determine the absolute maximum shear stress...Ch. 5.7 - If the yield stress for brass is Y = 205 MPa,...Ch. 5.7 - By what percentage is the shaft of circular cross...Ch. 5.7 - Prob. 97PCh. 5.7 - Also, find the angle of twist of end B. The shaft...Ch. 5.7 - Also, find the corresponding angle of twist at end...Ch. 5.7 - Prob. 110PCh. 5.7 - Determine the average shear stress in the tube if...Ch. 5.7 - By what percentage is the torsional strength...Ch. 5.7 - Prob. 114PCh. 5.7 - Prob. 115PCh. 5.7 - Prob. 119PCh. 5.10 - Prob. 121PCh. 5.10 - If the radius of the fillet weld connecting the...Ch. 5.10 - Prob. 125PCh. 5.10 - Determine the radius of the elastic core produced...Ch. 5.10 - Prob. 128PCh. 5.10 - Determine the torque T needed to form an elastic...Ch. 5.10 - Determine the torque applied to the shaft.Ch. 5.10 - Prob. 131PCh. 5.10 - Determine the ratio of the plastic torque Tp to...Ch. 5.10 - Determine the applied torque T, which subjects the...Ch. 5.10 - Determine the radius of its elastic core if it is...Ch. 5.10 - Plot the shear-stress distribution acting along a...Ch. 5.10 - If the material obeys a shear stress-strain...Ch. 5.10 - It is made of an elastic perfectly plastic...Ch. 5.10 - Prob. 139PCh. 5.10 - Prob. 140PCh. 5.10 - Prob. 142PCh. 5.10 - Prob. 143PCh. 5 - The shaft is made of A992 steel and has an...Ch. 5 - The shaft is made of A992 steel and has an...Ch. 5 - Determine the shear stress at the mean radius p =...Ch. 5 - If the thickness of its 2014-T6-aluminum skin is...Ch. 5 - Determine which shaft geometry will resist the...Ch. 5 - If couple forces P = 3 kip are applied to the...Ch. 5 - If the allowable shear stress for the aluminum is...Ch. 5 - Determine the angle of twist of its end A if it is...Ch. 5 - This motion is caused by the unequal belt tensions...
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- One-half length of 50 mm diameter steel rod is solid while the remaining half is hollow having a bore of 5 mm. The rod is subjected to equal and opposite torque at its ends. If the maximum shear stress in solid portion is T, the maximum shear stress in the hollow portion isarrow_forwardThe shaft is made from a solid steel section AB and a tubular portion made of steel and having a brass core. If it is fixed to a rigid support at A, and a torque of T = 50 lb.ft is applied to it at C, determine the rotation angle that occurs at C relative to A and compute the maximum shear stress and maximum shear strain in the brass and steel. Take Gst = 11500 ksi, Gbr = 5600 Ksi. 3 ft 0.5 in. B 1 in. T = 50 lb•ftarrow_forwardThe tool shown is made up of an oak wood part. The tool works in torsion and the allowable shear stress for the wood is 213 psi. If the wooden handle has as a minimum section a circular area of diameter 1.4, find the maximum allowable torque T. Express the result in Ib-in with a decimal approximation T D Tarrow_forward
- The aluminum shaft, composed of three segments, is fastened to rigid supports at A and D. Calculate the maximum shear stress in each segment when the two torques are appliedarrow_forwardThe spring ABC has a stiffness of 500N/m and an unstretched length of 6m. Calculate the horizontal force, F applied to the cord which is attached at B so that the displacement of the pulley from the wall is d= 1.5m. A k = 500 N/m 6 m F k = 500 N/m Fig. Q3 Force equation: Force equation 3D Moment 3D Cosine rule R - 4 +B-2AB cos e F- Fi+Fj+Fk Ff = F +F +F moment about a point M-rxF Sine rule F| di+dj+dk F F3 Fc sin 4 sin B sinC moment about an axis M=rF Force resultant R-R R +R R. 8= tan Rarrow_forwardThe horizontal force P is subjected on the slit open circular ring beam. Determine the horizontal and vertical displacements at point A. You are given a circular ring that is not entirely closed; it is open with a small gap so that theta goes from 0 to 2*Pi. The force P acts horizontally at the point where the ring is split, point A. Then you need to add a fictitious vertical load and a fictitious moment at point A.arrow_forward
- The copper pipe has an outer diameter of 3 in. and an inner diameter of 2.50 in. If it is tightly secured to the wall at C and it is subjected to the uniformly distributed torque along its entire length, determine the absolute maximum shear stress in the pipe. Discuss the validity of this result.arrow_forwardYA 37 N-m The braket shown in figure is subjected to three forces and one couple as Shown in figure. Find the result ant R of the force System and the of it's line of action with the lines AB and BC. 120N 600N 9. 30 200 mm 50 mm V1OON points of intersedion R = 446.86 NoO =26:58s %3D d=0.0447m =44.7 mm « a = 0. ol m = lomm 6 %3D b=0.05 m = 50 mm · loommarrow_forwardThe shaft has an outer diameter of 100 mm and an inner diameter of 80 mm. If it is subjected to the three torques, plot the shear stress distribution along a radial line for the cross section within region CD of the shaft. The smooth bearings at A and B do not resist torque. E 10 kN m B 15 kN m 5 kN-marrow_forward
- The solid-circular member AC, having a diameter D and a shear modulus of 69 GPa, is subjected to the torques 2T and 3T at points A and B, respectively. If Tallow = 35 MPa and (OA/c)allow =2°. detemine the maximum pemissible value of the torque T. Use the table given below and your student ID to find the values of L1, L2, and D. B A 3T 2T Student L1 (m) L2 (m) D ID (mm) 1131731 1 0.6 78arrow_forwardCompute the work done by the indicated force when the disk undergoes the specified displacement S=3m. (assume the unstressed position is at X = 1.2 m) X 2.5m S = 3m K = 120 N/m Farrow_forwardThe solid-circular member AC, having a diameter D and a shear modulus of 69 GPa, is subjected to the torques 2T and 3T at points A and B, respectively. If tallow = 35 MPa and (fA/C)allow =2o, determine the maximum permissible value of the torque T. Use the table given below and your student ID to find the values of L1, L2, and D. Student ID L1 (m) L2 (m) D (mm) 1131731 1 0.6 78arrow_forward
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