MECHANICS OF MATERIALS
11th Edition
ISBN: 9780137605521
Author: HIBBELER
Publisher: RENT PEARS
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Chapter 11.2, Problem 43P
To determine
The required diameter (d) of the shaft using maximum distortion energy theory.
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The journal bearings at A and B exert only x and z components of force on the shaft. Determine the shaft’s diameter to the nearest millimeter so that it can resist the loadings. Use the maximum distortion energy theory of failure with sallow = 200 MPa.
1-
The bearings at A and B exert only y and z components of force on the shaft. If Sy =
150 MPa for the selected ductile material, determine the factor of safety if the shaft diameter
is 40 mm. Use the maximum distortion-energy theory of failure.
Show the following procedures through the calculation
steps (Free Body diagram (FBD), Reaction at A and D,
Bending moment diagram, point of max. moment,
Torque diagram, draw the element showing general
stress (x, Txy), the factor of safety using the MDE.
500 N
100 mm
150 mm
200 mm
150 mm
100 mm.
500 N
The rod is pinned at its end A and attached to a torsional spring having a stiffness k, which measures the torque per radian of rotation of the spring. If a force P is always applied perpendicular to the end of the rod, determine the displacement of the force. EI is constant.
Chapter 11 Solutions
MECHANICS OF MATERIALS
Ch. 11.2 - Determine the minimum dimension a to the nearest...Ch. 11.2 - of the rod to safely support the load. The rod is...Ch. 11.2 - The wood has an allowable normal stress of allow =...Ch. 11.2 - of the beam's cross section to safely support the...Ch. 11.2 - Determine the minimum dimension b to the nearest...Ch. 11.2 - The beam is made of steel having an allowable...Ch. 11.2 - Determine the minimum width of the beam to the...Ch. 11.2 - if P=10 kip.Ch. 11.2 - The beam has an allowable normal stress of allow...Ch. 11.2 - If each beam is to be designed to carry 90 lb/ft...
Ch. 11.2 - Determine its height h so that it simultaneously...Ch. 11.2 - to safely support the load. The wood has an...Ch. 11.2 - and the wood has an allowable normal stress of...Ch. 11.2 - if allow = 30 ksi and allow = 15 ksi. The journal...Ch. 11.2 - if allow = 30 ksi and allow = 15 ksi. The journal...Ch. 11.2 - The tapered beam supports a uniform distributed...Ch. 11.2 - Determine the variation in the depth d of a...Ch. 11.2 - Prob. 41PCh. 11.2 - The pulleys fixed to the shaft are loaded as...Ch. 11.2 - Prob. 43PCh. 11.2 - Prob. 44PCh. 11 - The cantilevered beam has a circular cross...Ch. 11 - Select the lightest-weight wide-flange overhanging...Ch. 11 - Prob. 3RPCh. 11 - Determine the shaft's diameter to the nearest...Ch. 11 - Select the lightest-weight wide-flange beam from...Ch. 11 - The simply supported joist is used in the...Ch. 11 - The simply supported joist is used in the...Ch. 11 - by 4-in. pieces of wood braced as shown. If the...
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- If a shaft is made of a material for which sY = 75 ksi, determine the maximum torsional shear stress required to cause yielding using the maximum distortion energy theory.arrow_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_forwardDetermine the maximum shear stress in the solid shaft. The diameter of the shaft is 1 in. Assume the bearings between A and B and between C and D have no friction. 20 ft'lb 45 ft'lb 55 ft'lb D 30 ft'lb B Aarrow_forward
- The bearings at A and B exert only x and z components of force on the steel shaft. Determine the shaft’s diameter to the nearest millimeter so that it can resist the loadings of the gears without exceeding an allowable shear stress of 82 MPa. Use the maximum-shear-stress theory of failure.arrow_forwardpleasearrow_forwardIf the solid shaft AB to which the valve handle is attached is made of C83400 red brass and has a diameter of 10 mm, determine the maximum couple forces F that can be applied to the handle just before the material starts to fail. Take 7allow = 40 MPa. What is the angle of twist of the handle? The shaft is fixed at A. 150 mm 150 mm 150 mmarrow_forward
- The solid steel shaft DF has a diameter of 25 mm and is supported by smooth bearings at D and E. It is coupled to a motor at F, which delivers 12 kW of power to the shaft while it is turning at 50 rev>s. If gears A, B, and C remove3 kW, 4 kW, and 5 kW respectively, determine the maximum shear stress in the shaft within regions CF and BC. The shaft is free to turn in its support bearings D and E.arrow_forwardThe crank is loaded by a single force F, = 200 lb which causes twisting and bending of the 1-in diameter shaft AB fixed to the support. The 2 in shaft is made of hot-rolled AISI 1035 steel. Identify the point with the maximum von Mises stress at end A and find the factor of safety using the distortion-energy theory of 1-in dia. t in in B failure. 5 in 6 in SOLUTION:arrow_forwardThe propellers of a ship are connected to an A-36 steel shaft that is 60 m long and has an outer diameter of 340 mm and inner diameter of 260 mm. If the power output is 4.5 MW when the shaft rotates at 20 rad>s, determine the maximum torsional stress in the shaft and its angle of twist.arrow_forward
- The 304-stainless-steel cylinder has an inner diameter of 4 in. and a wall thickness of 0.1 in. If it is subjected to an internal pressure of p = 80 psi, axial load of 500 lb, and a torque of 70 lb · ft, determine if yielding occurs according to the maximum distortion energy theory.arrow_forwardThe solid steel shaft AC has a diameter of 25 mm and is supported by smooth bearings at D and E. It is coupled to a motor at C, which delivers 3 kW of power to the shaft while it is turning at 50 rev>s. If gears A and B remove1 kW and 2 kW, respectively, determine the maximum shear stress in the shaft within regions AB and BC. The shaft is free to turn in its support bearings D and E.arrow_forwardIf the 2-in.-diameter shaft is made from brittle material having an ultimate stress of sult = 50 ksi, for both tension and compression, determine if the shaft fails according to the maximum normal stress theory. Use a factor of safety of 1.5 against rupture.arrow_forward
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