5. A car is driving down the road and goes over a speed bump. The car has a solid circular drive shaft that is subjected to a tensile axial force of F = 400 kN, a bending moment of M = 10.0 kN·m, and a torque of T = 18.0 kN·m as a result of the bump. The shaft has a diameter d = 10.0 cm and mechanical 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? F M T M
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- A shaft having length equal to 10 m and diameter equal to (50+ 01) mm is simply supported at both ends. The shaft carries four masses (150 + 01) kg, (200 + 01) kg, (250 + 01) kg and (300 + 01) kg. These masses are located at a distance of 1.5 m, 2.5 m, 5.5 m and 7.5 m from the left hand side support, respectively. The modulus of elasticity, E, for the material of the shaft is 200 GN/m2 and mass density for the shaft material is 7500 kg/m3. Determine critical speed of the shaft in revolutions per minute for the following two cases: Effect of the mass of the shaft is neglected. 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 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, JoThe length of the smooth circular shaft with a solid cross-sectional area of 315nm2 is 1 meter. Instead of this shaft, it is desired to use an evacuated circular-section shaft with a wall thickness of 3 mm with the same length and weight. For these two cases, compare the angles of rotation that would occur if a moment M = 600 (N.m) was applied to the end of the shaft made of material G-80 GPa.
- A shaft is supported by two bearings placed1.2 m apart. A pulley of diameter Dc=0. 675 meter is mounted at a distance of 300 mm to the right of left hand bearing and this drives a pulley directly below it with the help of belt having maximum tension of 2.25 kN. Another pulley of diameter Dd= 0.575 meteris placed 200 mm to the left of right hand bearing and is driven with the help of electric motor and belt, which is placed horizontally to the right. The angle of contact for both the pulleys is 180° and u = 0.24. Determine the suitable diameter for a solid shaft, allowing working stress of 63 MPa in tension and 42 MPa in shearfor the material of shaft. Assume that the torque on one pulley is equal to that on the other pulley C A De m B Da m 0.3 m 0.2 m 1.2 m.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 HowA 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 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, JoA vertical shaft is supported by two deep groove ball bearings as shown below. The shaft will be driven by vee belts through a pulley. The combined tensions of the belt apply and the weight of the pulley assembly applies a force of 5.4kN and 900N respectively. The shaft has a diameter of 32mm. Bearing A at the top supports the shaft radially whereas bearing B at the bottom supports the shaft axially and radially. Two deep groove ball bearings have been selected for this application. The models of the bearings are SKF 6305 and SKF 6205 for bearing A and B respectively. a) What are the forces at bearing A and B? b) Paste a screenshot of the graph showing the distribution of the forces in the shaft. c) From the report, find the static load capacity for: Bearing A Bearing B
- 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: FeA shaft having length equal to 10 m and diameter equal to 70mm is simply supported at both ends. The shaft carries four masses 170 kg, 220 kg, 270kg and 320 kg. These masses are located at a distance of 1.5 m, 2.5 m, 5.5 m and 7.5 m from the left hand side support, respectively. The modulus of elasticity, E, for the material of the shaft is 200 GN/m2 and mass density for the shaft material is 7500 kg/m3. Determine critical speed of the shaft in revolutions per minute for the following two cases: Effect of the mass of the shaft is neglected. Effect of the mass of the shaft is considered. What is the usefulness of the answers determined in this problem?A counterweight of mass m= 4.10 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 = 6.00 cm and mass M = 2.30 kg. The spokes have negligible mass. What is the net torque on the system about the axle of the pulley? When the counterweight has a speed v, the pulley has an angular speed ? = v/R. Determine the magnitude of the total angular momentum of the system about the axle of the pulley. Using your result from (b) and τ = (dL) / (dt), calculate the acceleration of the counterweight. (Enter the magnitude of the acceleration.)