Mechanics of Materials
9th Edition
ISBN: 9780133254426
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Chapter 11.4, Problem 11.40P
To determine
The minimum diameter (d) of the solid shaft.
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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
A turbine rotor is mounted on a stepped shaft that is fixed at both ends as shown in
The torsional stiffnesses of the two segments of the shaft are given by ka = 3,000 N-m/rad
and k2 = 4,000 N-m/rad. The turbine generates a harmonic torque given by M(t) = Mo cos
wt about the shaft axis with M, = 200 N-m and w = 500 rads. The mass moment of inertia
of the rotor about the shaft axis is Jo = 0.05 kg-m. Assuming the equivalent torsional
damping constant of the system as c, = 2.5 N-m-s/rad, determine the steady-state response
of the rotor, 6(1).
O(1)
ke
M(1) = M, cos ot
Turbine rotor, Jo
The following shaft, having a diameter of 20 mm, is made of steel (Sut = 520 MPa, Se = 260 MPa) and is subjected to a fully reversed transverse force F = 120 N and a fully reversed torque T = 60 N.m. The shaft is fixed at its left end. Find the factor of safety at A for infinite lifetime using the modified Goodman diagram.
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 its dimensions if it is to be...Ch. 11.2 - Determine the minimum width of the beam to the...Ch. 11.2 - if P=10 kip.Ch. 11.2 - If the allowable bending stress is allow = 22 ksi...
Ch. 11.2 - The allowable bending stress is allow = 24 ksi and...Ch. 11.2 - The allowable bending stress is allow = 22 ksi and...Ch. 11.2 - 11–7. Draw the shear and moment diagrams for the...Ch. 11.2 - *11–8. The simply supported beam is made of timber...Ch. 11.2 - The beam has an allowable normal stress of allow =...Ch. 11.2 - The beam has an allowable normal stress of allow...Ch. 11.2 - 11–11. The timber beam is to be loaded as shown....Ch. 11.2 - If each beam is to be designed to carry 90 lb/ft...Ch. 11.2 - 11–13. Select the lightest steel wide-flange beam...Ch. 11.2 - 11–14. Select the lightest-weight steel...Ch. 11.2 - Prob. 11.15PCh. 11.2 - The beam has an allowable normal stress of allow....Ch. 11.2 - Determine the maximum cable force P that can...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 - Prob. 11.20PCh. 11.2 - Prob. 11.21PCh. 11.2 - Prob. 11.22PCh. 11.2 - 11–23. The beam is constructed from three boards...Ch. 11.2 - Prob. 11.24PCh. 11.2 - Prob. 11.25PCh. 11.2 - Select the lightest-weight wide-flange beam from...Ch. 11.2 - Prob. 11.27PCh. 11.2 - * 11–28. The joist AB used in housing construction...Ch. 11.2 - If the maximum bending stress is not to exceed...Ch. 11.2 - 11–30. The simply supported beam supports a load...Ch. 11.4 - Determine the variation in the width was a...Ch. 11.4 - Prob. 11.32PCh. 11.4 - Prob. 11.33PCh. 11.4 - The beam is made from a plate that has a constant...Ch. 11.4 - Determine the variation in the depth d of a...Ch. 11.4 - Determine the variation of the radius r of the...Ch. 11.4 - Prob. 11.37PCh. 11.4 - Determine the variation in the width b as a...Ch. 11.4 - The tubular shaft has an inner diameter of 15 mm....Ch. 11.4 - Prob. 11.40PCh. 11.4 - Prob. 11.41PCh. 11.4 - Prob. 11.42PCh. 11.4 - Prob. 11.43PCh. 11.4 - Prob. 11.44PCh. 11.4 - Prob. 11.45PCh. 11.4 - Prob. 11.46PCh. 11 - The cantilevered beam has a circular cross...Ch. 11 - Select the lightest-weight wide-flange overhanging...Ch. 11 - Prob. 11.49RPCh. 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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- The end gear (closest to the journal bearing at A) is subjected to the loading shown in the figure. The journal bearings A and B exert on the shaft only the y and z components of the 100 mm 250 mm 50 mm support reactions. Dětermine the equilibrium torque T at gear C. Using the "Maximum 75 mm 150 mm Distortion Energy Theory" with Jallowable the together 80 MPa, smallest calculate possible diameter of the shaft millimeter that will support the loading. to the nearest 100 mm F.= 15 kNarrow_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_forward4. The shaft shown below, is made of ASTM-A-36 steel with Sy = 250 MPa and p = 7.86 g/cm³. The bearings at A and B only carry vertical loads. A 6m W X -ØD T As shown in the figure, the shaft is carrying a torque T = 400 Nm and its own weight per unit length w. a. Determine the location of maximum stress. b. Using the distortion energy theory, find the diameter of the shaft, D, if the desired safety factor is 2.1. C. Using the result from b. what would be the safety factor if the max shear theory is used?arrow_forward
- A turbine rotor is mounted on a stepped shaft that is fixed at both ends as shown in The torsional stiffnesses of the two segments of the shaft are given by k = 3,000 N-m/rad and k2 = 4,000 N-m/rad. The turbine generates a harmonic torque given by M(1) = Mo cos wt about the shaft axis with M, = 200 N-m and w = 500 rad/s. The mass moment of inertia of the rotor about the shaft axis is J, = 0.05 kg-m?. Assuming the equivalent torsional damping constant of the system as e, = 2.5 N-m-s/rad, determine the steady-state response of the rotor, 0(1). O(1) M(1) = Mg cos etr %3! Turbine rotor, Joarrow_forwardDetermine the resisting torque at support A and B , of the shaft shown in the figure.arrow_forwardDetermine to the nearest millimeter the minimum diameter of the solid shaft if it is subjected to the gear loading. The bearings at A and B exert force components only in the y and z directions on the shaft. Base the design on the maximum distortion energy theory of failure with sallow = 150 MPa.arrow_forward
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