A circular steel shaft with length, L (m) has an outer diameter, d2 (mm) and inner diameter, d1 (mm). The modulus of rigidity G = 75 Gpa. Analyze the shaft due to an applied torque, T (kN-m) at both ends. (1) T Given: d1= 100 mm, d2 = 150 mm, L = 1.0 m and T = 16 kN-m. What is the torsional shear stress at the inner surface in Mpa? (2 decimals)
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- 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, JoA 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 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
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- A makeshift compact torsional spring is made of steel (Gst = 11,000,000 psi) and is composed of a solid inner shaft from C to B and a hollow shaft from A to B. The solid and hollow shafts are connected through an unyielding ring at B. The necessary radiuses are shown below. Assume the ring attached to the hollow shaft at A is rigid with no rotation. If the torque applied T at point C is 2 kip-in, find the: - Maximum shear stress in the solid inner shaft, ksi b. Maximum shear stress in the hollow outer shaft, ksi c Angle of twist at point C, degrees 12 in. 12 in. B 0.75 in. T 1 in. 0.6 in.A solid constant-diameter circular shaft is subjected to the torques of TA = 480 lb-ft, TB = 1060 lb-ft, Tc= 860 lb-ft, and Tp = 280 lb-ft, acting in the directions shown. The bearings shown allow the shaft to turn freely. (a) Plot a torque diagram showing the internal torque in segments (1), (2), and (3) of the shaft. Use the sign convention presented in %D Section 6.6. (b) If the allowable shear stress in the shaft is 5800 psi, what is the minimum acceptable diameter for the shaft? TB TA Tc (1) Tp (3) В C D Answer: (a) T1 = Ib-ft T2 = Ib-ft T3 = Ib-ft (b) d = in.A solid constant-diameter circular shaft is subjected to torques TA = 420 lb- ft, TB = 1,040 lb- ft, TC = 850 lb-ft, andTD = 230 lb-ft, acting in the directions shown in the figure. The bearings shown allow the shaft to turn freely. (a) Plot a torque diagram showing the internal torque in segments (1), (2), and (3) of the shaft. Use the right-hand rule. (b) If the allowable shear stress in the shaft is 6,000 psi, what is the minimum acceptable diameter for the shaft?
- The shaft shown has two pulleys, where pulley C is the input and pulley A is the output. The shaft is supported by frictionless bearings at points O and B. The pulley diameters are dA = 361 mm and dc = 224 mm. The input tensions on pulley Care T3 = 267 N and T4 = 0.10*T3. The shaft diameter, ds = 25 mm. T₁ da ХОА 1₂ oo ds B dc T3 XAB XBC T₁ • What is the tension T₁ on the output pulley (in N)? Assume the lower tension is 10% of the higher tension.A makeshift compact torsional spring is made of steel (Gst = 11,000,000 psi) and is composed of a solid inner shaft from C to B and a hollow shaft from A to B. The solid and hollow shafts are connected through an unyielding ring at B. The necessary radiuses are shown below. Assume the ring attached to the hollow shaft at A is rigid with no rotation. If the torque applied Tat point C is 2 kip-in, find the: a Maximum shear stress in the solid inner shaft, ksi a. Maximum shear stress in the hollow outer shaft, ksi c Angle of twist at point C, degrees 12 in. 12 in. B 0.75 in. T 1 in. 0.6 in.Gear shaft ABCDE is subjected to the torques shown in the figure. Find the internal torque in each seg- ment, and then plot the torsional moment diagram. Assume that the spacing between gears is constant, i.e., 10 in. T1 = T2 = 1000 lb-in. 500 lb-in. A B T3 = 800 Ib-in. C Ta = 500 lb-in. d = 1.0 in. D T; = 800 lb-in. E