Mechanics of Materials-Access
9th Edition
ISBN: 9780133402735
Author: HIBBELER
Publisher: PEARSON
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Chapter 10.7, Problem 10.66P
To determine
To derive: An expression for an equivalent torque
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Maximum shear stress developed on the surface of a solid circular shaft under pure torsion is 240 MPa. If the shaft diameter is doubled, then what is the maximum shear stress developed corresponding to the torque?
A thin-walled tube having a semi circular shape has an outside diameter of 50 mm and a wall thickness of 2mm. If the stress concentration at the corners is neglected,What torque will cause a shearing stress of 40 MPa in N-m?
A motor drives 50 hp to a shafting 1 1/2 in. diameter and 3 ft. long. If the maximum shearing stress produced by torsion is 39,628 psi and the total angle of twist in the shaft is 9.080, calculate the torque (based on angle of twist and shearing) and angular speed in rpm. G = 12 x 106 psi.
Chapter 10 Solutions
Mechanics of Materials-Access
Ch. 10.3 - Prove that the sum of the normal strains in...Ch. 10.3 - The state of strain at the point on the arm has...Ch. 10.3 - Prob. 10.3PCh. 10.3 - Prob. 10.4PCh. 10.3 - 10-5. The state of strain at the point on the gear...Ch. 10.3 - Use the strain transformation equations and...Ch. 10.3 - Use the strain transformation equations and...Ch. 10.3 - Prob. 10.8PCh. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Use the strain- transformation equations to...
Ch. 10.3 - 10–11. The state of strain on an element has...Ch. 10.3 - Determine the equivalent state of strain on an...Ch. 10.3 - Determine the equivalent state of strain which...Ch. 10.3 - Use the strain transformation equations to...Ch. 10.3 - Determine the equivalent state of strain, which...Ch. 10.3 - Prob. 10.17PCh. 10.3 - Prob. 10.18PCh. 10.3 - 10–19. Solve part (a) of Prob. 10–4 using Mohr’s...Ch. 10.3 - *10–20. Solve part (a) of Prob. 10–5 using Mohr’s...Ch. 10.3 - using Mohrs circle. 106. The state of strain at a...Ch. 10.5 - The strain at point A on the bracket has...Ch. 10.5 - Determine (a) the principal strains at A, (b) the...Ch. 10.5 - Prob. 10.24PCh. 10.5 - Prob. 10.25PCh. 10.5 - 10–26. The 60° strain rosette is attached to point...Ch. 10.5 - 10–27. The strain rosette is attached at the point...Ch. 10.5 - Prob. 10.28PCh. 10.6 - For the case of plane stress, show that Hookes law...Ch. 10.6 - to develop the strain tranformation equations....Ch. 10.6 - Determine the modulus of elasticity and Polssons...Ch. 10.6 - If it is subjected to an axial load of 15 N such...Ch. 10.6 - If it has the original dimensions shown, determine...Ch. 10.6 - If it has the original dimensions shown, determine...Ch. 10.6 - A strain gage having a length of 20 mm Is attached...Ch. 10.6 - Determine the bulk modulus for each of the...Ch. 10.6 - The strain gage is placed on the surface of the...Ch. 10.6 - 10–39. The strain in the x direction at point A on...Ch. 10.6 - Determine the applied load P. What is the shear...Ch. 10.6 - If a load of P = 3 kip is applied to the A-36...Ch. 10.6 - The cube of aluminum is subjected to the three...Ch. 10.6 - Prob. 10.43PCh. 10.6 - *10–44. Strain gauge b is attached to the surface...Ch. 10.6 - Prob. 10.45PCh. 10.6 - 10?46. The principal strains in a plane, measured...Ch. 10.6 - 10–47. The principal stresses at a point are shown...Ch. 10.6 - *10–48. The 6061-T6 aluminum alloy plate fits...Ch. 10.6 - Determine the normal stresses x and y in the plate...Ch. 10.6 - The steel shaft has a radius of 15 mm. Determine...Ch. 10.6 - Prob. 10.51PCh. 10.6 - Prob. 10.52PCh. 10.6 - Air is pumped into the steel thin-walled pressure...Ch. 10.6 - Air is pumped into the steel thin-walled pressure...Ch. 10.6 - Prob. 10.55PCh. 10.6 - The thin-walled cylindrical pressure vessel of...Ch. 10.6 - The thin-walled cylindrical pressure vessel of...Ch. 10.6 - Prob. 10.58PCh. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - A material is subjected to plane stress. Express...Ch. 10.7 - The yield stress for a zirconium-magnesium alloy...Ch. 10.7 - Solve Prob. 1061 using the maximum distortion...Ch. 10.7 - Prob. 10.63PCh. 10.7 - Prob. 10.64PCh. 10.7 - Prob. 10.65PCh. 10.7 - Prob. 10.66PCh. 10.7 - Prob. 10.67PCh. 10.7 - If the material is machine steel having a yield...Ch. 10.7 - The short concrete cylinder having a diameter of...Ch. 10.7 - 10–70. Derive an expression for an equivalent...Ch. 10.7 - Prob. 10.71PCh. 10.7 - Prob. 10.72PCh. 10.7 - If the 2-in diameter shaft is made from brittle...Ch. 10.7 - If the 2-in diameter shaft is made from cast iron...Ch. 10.7 - 10–75. The components of plane stress at a...Ch. 10.7 - Prob. 10.76PCh. 10.7 - 10–77. If the A-36 steel pipe has outer and inner...Ch. 10.7 - Prob. 10.78PCh. 10.7 - Prob. 10.79PCh. 10.7 - Prob. 10.80PCh. 10.7 - Prob. 10.81PCh. 10.7 - Prob. 10.82PCh. 10.7 - Prob. 10.83PCh. 10.7 - Prob. 10.84PCh. 10.7 - 10–85. The state of stress acting at a critical...Ch. 10.7 - The shaft consists of a solid segment AB and a...Ch. 10.7 - Prob. 10.87PCh. 10.7 - Prob. 10.88PCh. 10.7 - 10–89. The gas tank has an inner diameter of 1.50...Ch. 10.7 - The gas tank is made from A-36 steel and has an...Ch. 10.7 - The internal loadings at a critical section along...Ch. 10.7 - *10–92. The shaft consists of a solid segment AB...Ch. 10.7 - Prob. 10.93PCh. 10 - In the case of plane stress, where the in-plane...Ch. 10 - The plate is made of material having a modulus of...Ch. 10 - If the material is machine steel having a yield...Ch. 10 - Determine if yielding has occurred on the basis of...Ch. 10 - The 60 strain rosette is mounted on a beam. The...Ch. 10 - Use the strain transformation equations to...Ch. 10 - If the strain gages a and b at points give...Ch. 10 - Use the strain-transformation equations and...Ch. 10 - Use the strain transformation equations to...Ch. 10 - Specify the orientation of the corresponding...
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- A high strength steel band saw, 30 mm wide by 0.80 mm thick, runs over pulleys 500 mm in diameter. What maximum flexural stress is developed? What minimum diameter pulleys can be used without exceeding a flexural stress of 500 MPa? Assume E = 300 GPa.arrow_forwardA solid and a hollow shaft are made of same material. The diameter of the solid shaft is 300 mm and has the same cross-sectional area as a hollow shaft with inside diameter of 250 mm. Find the ratio of the Angles of twist in equal lengths of these shafts, when stressed to the same intensityarrow_forwardA shaft with a hollow cross section is subjected to torque of magnitude T = 5.5 kN-m. If the outer diameter of the shaft is 0.1 m and its wall thickness is 10 mm, what would be the minimum diameter of a solid steel shaft needed if it would be subjected to the maximum shear stress of the hollow shaft?arrow_forward
- A shaft is used to transmit 55 kW power at 500 rpm is subjected to a bending moment of 450 Nm. Calculate the diameter of the shaft if the shear strength of the shaft is 180 MPa.arrow_forwardA high-strength steel band saw, 25 mm wide, runs over pulleys 900 mm in diameter. What minimum thickness of the steel band can be used without exceeding a flexural stress of 300? Assume E = 230 GPa. Answer must be in mm.arrow_forwardAn SAE 1040 Cold Drawn Steel shaft is subjected to a Torque of 1,200 lb-ft. If the design factor N=2 and there is no bending moment (M=0). What should be the minimum diameter of the shaft?arrow_forward
- In drilling a deep oil well the drill shaft, consisting of sections of “drill rod”, is powered from the top, while the load or counter torque is taken off at the bottom. The drill hole is 3 1/2 miles deep. Assuming a solid drill rod of circular cross section and 1 in. diameter, designed to a working shear stress of 5,000 psi, turning at 700 rpm, calculate (a) The wind-up, i.e. the twist angle between the top and bottom. (b) The horsepower of the driving motor. (c) State all assumptions, and comment on the results. What other considerations may have to be taken into account in using this drill? NOTE: The shear modulus of steel may be taken as 12 x 106 psi. Also 1 mile = 5,280 ft.arrow_forwardA single solid circular shaft 400 mm diameter running at 250 RPM, is to be replaced by two hollow circular shafts of equal size running at 150 RPM and developing 50% additional power. The internal diameter of hollow shaft may be taken as one third of their external diameters. If the working stress of the new shaft is 30% greater than that of the former, find the external and internal diameter of hollow shafts.arrow_forwardA flanged bolt coupling consists of eight 10 mm diameter steel bolts on a bolt circle 400 mm in diameter, and six 10 mm diameter steel bolts on a concentric bolt circle 300 mm in diameter. What torque can be applied without exceeding a shearing stress of 60 MPa in the bolts?arrow_forward
- A drill rod with a diameter of 12 mm is made of high-strength steel alloy with a shear modulus of 80 GPa. The rod is to be subjected to a torque T. What is the minimum required length L of the rod so that the cross section at one end can be rotated 90⁰ with respect to the other end without exceeding an allowable shear stress of 300 MPa?arrow_forwardTwo solid shafts, 50 mm in diameter, are connected by a flange coupling with six bolts and a pitch circle diameter of 95 mm. If the maximum shear stress in the shaft due to a torque is to be the same as the shear stress in the bolts, calculate a suitable bolt diameter. If the maximum working shear stress is limited to 55 MPa, what maximum power will be transmitted by the coupling at 700 r/min?arrow_forwardA hollow steel shaft 2304mm long is to be designed to transmit a torque of 28350 kJ. The shear modulus of elasticity, G = 82,740 GPa for steel. The total angle of twist of the length of the shaft is must not exceed 6 degrees. And the shear stress in the shaft must not exceed 110.32 MPa. What would be the ratio of the outside diameter to inside diameter?arrow_forward
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