The tubular rotor shaft of a wind turbine shown in Figure 3(a) is of 50 mm and 40 mm outer and inner diameters respectively, and it is expected to be subjected to the following extreme loading conditions which act simultaneously: A torque of 2.5kNm about the axis. A bending moment of 3.6kNm acting on the vertical plane containing the shaft axis. A 73.6kNm 2-5m Figure 3(a)

The tubular rotor shaft of a wind turbine shown in Figure 3(a) is of 50 mm and 40 mm outer and inner diameters respectively, and it is expected to be subjected to the following extreme loading conditions which act simultaneously: A torque of 2.5kNm about the axis. A bending moment of 3.6kNm acting on the vertical plane containing the shaft axis. A 73.6kNm 2-5m Figure 3(a)

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 1.3.17P: A stepped shaft ABC consisting of two solid, circular segments is subjected to torques T}and...

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A stepped shaft ABC consisting of two solid, circular segments is subjected to uniformly distributed torque t1acting aver segment 1 and concentrated torque t2applied at C, as shown in the figure. Segment 1 of the shaft has a diameter of d1= 57 mm and length of L1= 0.75 m; segment 2 has a diameter d2— 44 mm and length L2= 0.5 m. Torque intensity /,"= 3100 N . m/m and T2= 1100 N. m. (a) Find reaction torque TAat support A. (b) Find the internal torque T(x) at two locations: .x = L1/2 and at .x = L1+ L2/2. Show these internal torques on properly drawn free-body diagrams.
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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 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 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
Calculate
The tubular rotor shaft of a wind turbine shown in Figure 3(a) is of 50 mm and 40 mm outer and inner diameters respectively, and it is expected to be subjected to the following extreme loading conditions which act simultaneously: A torque of 2.5kNm about the axis. A bending moment of 3.6kNm acting on the vertical plane containing the shaft axis. A ) 3.6ENm 2-5 m Figure 3(a)
3. (a) The tubular rotor shaft of a wind turbine shown in Figure 3(a) is of 50 mm and 40 mm outer and inner diameters respectively, and it is expected to be subjected to the following extreme loading conditions which act simultaneously: A torque of 2.5kNm about the axis. • A bending moment of 3.6kNm acting on the vertical plane containing the shaft axis. 3.6 ENm 25m Figure 3(a) Calculate the following: i. The polar second moment of area, J ii. The shear stress at point A on the outer surface of the shaft (where the vertical plane containing the shaft axis intersects the outer periphery of the shaft). i. The second moment of area I about a diametric axis (i.e., an axis across a diameter of the cross-section). iv. The bending stress at point A. (b) The spherical LPG storage tank shown in Figure 3(b) has the following design specifications: Tank diameter of 22 m, shell plate thickness of 24 mm, yield stress of steel plates 550 MPa, a factor of safety of 2. Calculate the design pressure,…
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The tubular rotor shaft of a wind turbine shown in Figure 3(a) is of 50 mm and 40 mm outer and inner diameters respectively, and it is expected to be subjected to the following extreme loading conditions which act simultaneously: (a) A torque of 2.5kNm about the axis. A bending moment of 3.6kNm acting on the vertical plane containing the shaft axis. A 3.6 ENm 2-5m Figure 3(a) Calculate the following: i. The polar second moment of area, J
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 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.