A shaft section made of steel (Su = 615 MPa, Se' = 307 MPa) shown in figure is subjected to completely reversed bending and steady torsion. The shaft will be machined with the final dimensions shown in figure. At this location, the loading involves completely reversed bending of 62 N-m, and steady torsion of 45 Nm. To evaluate the factors kt, kts, q and qs, it is recommended to use Excel spreadsheets. Calculate the factor of safety for fatigue using the Goodman criterion. d3 = 27 mm d2 = 20 mm r = 3 mm ძვ T Ground surface
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- What is the maximum power that can be delivered by a hollow propeller shaft (outside diameter 50 mm, inside diameter 40 mm, and shear modulus of elasticity 80 GPa) turning at 600 rpm if the allowable shear stress is 100 MPa and the allowable rate of twist is 3.0°/m?A stepped shaft ACB having solid circular cross sections with two different diameters is held against rotation at the ends (sec figure). If the allowable shear stress in the shaft is 6000 psi, what is the maximum torque (T0) that may be applied at section C? Find (T0)max if the maximum angle of twist is limited to 0.55º. Let G = 10,600 ksi.A tubular shaft being designed for use on a construction site must transmit 120 kW at 1,75 Hz, The inside diameter of the shaft is to be one-half of the outside diameter. If the allowable shear stress in the shaft is 45 MPa, what is the minimum required outside diameter d?
- A long, thin-walled tapered tube AB with a circular cross section (see figure) is subjected to a torque T. The tube has length L and constant wall thickness t. The diameter to the median lines of the cross sections at the ends A and B are dAand dB, respectively. Derive the following formula for the angle of twist of the tube: Hint: If the angle of taper is small, you may obtain approximate results by applying the formulas for a thin-walled prismatic tube to a differential element of the tapered tube and then integrating along the axis of the tube.A hollow steel shaft used in a construction auger has an outer diameter d2= 6.0 in. and inner diameter d1= 4.5 in. (see figure). The steel has a shear modulus of elasticity G = 11.0 × 106 psi. For an applied torque of 150 kip-in., determine the following quantities: shear stress at the outer surface of the shaft, shear stress at the inner surface, and rate of twist (degrees per unit of length). Also, draw a diagram showing how the shear stresses vary in magnitude along a radial line in the cross section.A stepped bar with a hole (see figure) has widths h = 2.4 in. and c = 1.6 in. The fillets have radii equal to 0.2 in. What is the diameter d max of the largest hole that can be drilled through the bar without reducing the load-carrying capacity?
- The stepped shaft shown in the figure is required to transmit 600 kW of power at 400 rpm. The shaft has a full quarter-circular fillet, and the smaller diameter D1= 100 mm. If the allowable shear stress at the stress concentration is 100 MPa, at what diameter will this stress be reached? Is this diameter an upper or a lower limit on the value of D2?A solid copper bar of circular cross section has length L = 1.25 m and shear modulus of elasticity G = 45 GPa. The bar is designed to carry a 250 N · m torque acting at the ends. If the allowable shear stress is 30 M Pa and the allowable angle of twist between the ends is 2.5°, what is the minimum required diameter?A solid circular bar A BCD with fixed supports at ends A and D is acted upon by two equal and oppositely directed torques T0, as shown in the figure. The torques arc applied at points B and C each of which is located at distance x from one end of the bar. (The distance x may vary from zero to L/2.) For what distance x will the angle of twist at points B and C be a maximum? What is the corresponding angle of twist 0max?
- When drilling a hole in a table leg, a furniture maker uses a hand-operated drill (see figure) with a bit of diameter d = 4.0 mm. If the resisting torque supplied by the table leg is equal to 0.3 N · m, what is the maximum shear stress in the drill bit? If the allowable shear stress in the drill bit is 32 MPa, what is the maximum resisting torque before the drill binds up? If the shear modulus of elasticity of the steel is G = 75 GPa, what is the rate of twist of the drill bit (degrees per meter)?Solve the preceding problem for the following data: diameter LO m, thickness 48 mm, pressure 22 MPa, modulus 210 GPa. and Poisson's ratio 0.29Compare the angle of twist 1 for a thin-walled circular tube (see figure) calculated from the approximate theory for thin-walled bars with the angle of twist 2 calculated from the exact theory of torsion for circular bars, Express the ratio 12terms of the non-dimensional ratio ß = r/t. Calculate the ratio of angles of twist for ß = 5, 10, and 20. What conclusion about the accuracy of the approximate theory do you draw from these results?