A solid shaft in a rolling mill transmits 30kW at 100 rpm. Find the diameter in mm of the shaft so as not to exceed a shearing stress of 80 MPa and an angle of twist of more than 10 degrees in a length of 8 meters. G = 83 GPa
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A solid shaft in a rolling mill transmits 30kW at 100 rpm. Find the diameter in mm of the shaft so as not to exceed a shearing stress of 80 MPa and an angle of twist of more than 10 degrees in a length of 8 meters. G = 83 GPa
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- 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 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 thin tubular shaft with a circular cross section (see figure) and with inside diameter 100 mm is subjected to a torque of 5000 N · m. If the allowable shear stress is 42 MPa, determine the required wall thickness t by using (a) the approximate theory for a thin-walled tube and (b) the exact torsion theory for a circular bar.
- 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 propeller shaft for a small yacht is made of a solid steel bar 104 mm in diameter. The allowable stress in shear is 48 MPa, and the allowable rate of twist is 2.0° in 3.5 meters. (a) Assuming that the shear modulus of elasticity is G = 80 GPa, determine the maximum torque that can be applied to the shaft. (b) Repeat part (a) if the shaft is now hollow with an inner diameter of 5d18. Compare values to corresponding values from part (a).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.
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- A stepped shaft ABC consisting of two solid, circular segments is subjected to torques T}and T2acting in opposite directions, as shown in the figure. The larger segment of the shaft has a diameter of dv- 2.25 in. and a length Lt= 30 in.; the smaller segment has a diameter d2— 1.75 in. and a length L, = 20 in. The torques are T, = 21,000 lb-in. and fz=10.000 lb-in. (a) Find reaction torque TAat support A. (b) Find the internal torque T(x) at two locations: x = L1/2 and x = L1+ L2/2. Show these internal torques on properly drawn free-body diagrams (FBDs).A stepped shaft consisting of solid circular segments having diameters D1= 2.0 in, and D2= 2.4 in. (see figure) is subjected to torques T. The radius of the fillet is R = 0,1 in. If the allowable shear stress at the stress concentration is 6000 psi, what is the maximum permissible torque Tmax?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.