5. A car is driving down the road and goes over a speed bump. The car has a solid circular drive shaft thatis subjected to a tensile axial force of F = 400 kN, a bending moment of M = 10.0 kN·m, and atorque of T = 18.0 kN·m as a result of the bump. The shaft has a diameter d = 10.0 cm andmechanical properties of E = 200 GPa, v = 0.35 and σ = 200 MPa.a. What and where is the maximum stress? Hint: use the principle of superposition.b. What are the principal stresses and their directions?c. If it is a ductile steel, will the shaft yield?d. If it is a brittle steel, will the shaft fail?FMTM

Step 1: Step 2: Step 3: Step 4:

Answered: 5. A car is driving down the road and…

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.3.18P: A stepped shaft ABC consisting of two solid, circular segments is subjected to uniformly distributed...

See similar textbooks

Similar questions

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, Jo
Mechanics of deformable bodies
A solid bar of circular cross section has a diameter of 40mm and length of 1300mm. G=80GPa and torque applied at both ends is 340 N.m. Determine the angle of rotation in radians.
A hamster wheel of radius 25 cm has a rung that is travelling at a constant speed. The rung makes one complete revolution in 3 s. The axle of the hamster wheel is 27 cm above the ground. Write the equation that models this situation, beginning when the rung is at the very top of the wheel. AID A rung Axle Oh(t) = 25 cos(6лt) + 27 Oh(t) = 52 cos(6лt) + 2 Oh(t) = 25 cos (t) + 27 Oh(t) = 52 cos (t) + 2 wiki How
A shaft having length equal to 10 m and diameter equal to (50+ 01) mm is simply supported at both ends. The shatt carries four masses (150 + 01) kg, (200 + 01) kg, (250 +01) kg and (300 + 01) kg. These masses are located at a distance of 1.5m, 2.5 m, 5.5 mand 7.5 m from the left hand side support, respectively. The modulus of elasticity, E, for the material of the shaft is 200 GN/m? and mass density for the shaft material is 7500 kg/m?3. Determine critical speed of the shaft in revolutions per minute for the following two cases: 1. Effect of the mass of the shaft is neglected. 2. Effect of the mass of the shaft is considered. What is the usefulness of the answers determined in this problem?
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
A constant couple C = 200i + 300j + 350k N · m acts on a rigid body. The unit vector associated with the fixed axis of rotation of the body for an infinitesimal angular displacement dO is e0 = 0.250i + 0.350j - 0.903k. Determine the work done on the body by the couple during an angular displacement of 1.5 rad.
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 hamonic torque given by M(1) = Mo cos ot about the shaft axis with Mg = 200 N-m and as = 500 rad/s. The mass moment of inertia of the rotor about the shaft axis is h = 0.05 kg-m. Assuming the equivalent tosional damping constant of the system as e, = 2.5 N-m-s/rad, determine the steady-state response of the rotor, 6(1). ka M() = Ma cos e Turbine rotor, Jo A 50-kg turbine is mounted on four parallel springs, each of stiffness of 3 x 10° N/m When the machine operates at 40 Hz. its steady-state amplitude is observed as 1.8 mm What is the magnitude of the excitation? Given m = 50 kg. k = 3x 10 Nm. e = 40 Hz. X= 1.8 mm Find: Fe
A shaft is composed of elements made of S355 with a modulus of elasticity of 2.1×1052.1×105 N/mm² and a Poisson's ratio of 0.3. As shown in the picture, on the right side, there are two forces of 10,000 N each, acting at an angle of 15° upwards, creating a moment that is statically compensated by the force F2 on the left side. The shaft is supported at positions A and B. In the same position (for simplicity), there are two critical cross-sections leading to stress concentrations. The sleeve near F2 is shrink-fitted. The dimensions there are d=50 mm, D=120 mm, and the length of the sleeve is 50 mm. Ha=1 µm and Hn=1 µm. The fit is H7/s6. Determine breell.
Given: The wheel has a motor which can apply a moment M=26 N•m The wheel rolls without slipping and has a radius r= 0.2 m v= 1.5 m/s F= 15N 0= 30° Find M Determine the power of the hub motor Determine the efficiency of the motor if a total of 375 W is applied.
Figure 1 shows a composite shaft ABCD acted upon horizontal forces. The moduli of elasticity and the cross-section areas of the segments of the shaft are also provided. Eal 70 GPa E = 126 GPa E = 200 GPa AAR=58 mm² ABC 77 mm2 Acp = 39 mm² Сopper 20KN 8 kN Aluminum Steel 7 kN B 20KN A 8 kN 450 mm -300 mm -- 400 mm Figure 1: Axially loaded composite shaft 2.1. Construct the diagram of internal normal forces for each cross-section of the (6) shaft (3) 2.2. Calculate the displacement of the point C with respect to the fixed-point A 2.3. If the shaft must have one uniform diameter determine the required minimum diameter of the shaft if the normal yield stress in the composite shaft must not (11) exceed 450 MPa with a factor of safety equal to 1.8.
A counterweight of mass m = 4.30 kg is attached to a light cord that is wound around a pulley as shown in the figure below. The pulley is a thin hoop of radius R = 7.00 cm and mass M = 2.80 kg. The spokes have negligible mass. m (a) What is the net torque on the system about the axle of the pulley? magnitude N. m direction Select-- (b) When the counterweight has a speed v, the pulley has an angular speed w = v/R. Determine the magnitude of the total angular momentum of the system about the axle of the pulley. kg • m)v (c) Using your result from (b) and 7 = dL/dt, calculate the acceleration of the counterweight. (Enter the magnitude of the acceleration.) m/s2

SEE MORE QUESTIONS

Recommended textbooks for you

Mechanics of Materials (MindTap Course List)

Mechanical Engineering

ISBN:

9781337093347

Author:

Barry J. Goodno, James M. Gere

Publisher:

Cengage Learning

Mechanics of Materials (MindTap Course List)

Mechanical Engineering

ISBN:

9781337093347

Author:

Barry J. Goodno, James M. Gere

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS