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- 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.A propeller shaft of solid circular cross section and diameter d is spliced by a collar of the same material (see figure). The collar is securely bonded to both parts of the shaft. What should be the minimum outer diameter dyof the collar in order that the splice can transmit the same power as the solid shaft?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.
- Solve the preceding problem for a welded Tank with a = 62°,r = 19 irM = 0.65 in.,p = 240 psu E = 30 X 106 psi, and v = 0.30Two sections of steel drill pipe, joined by bolted flange plates at B, arc subjected to a concentrated torque 4000 kip-in. at x = 3 ft, and a uniformly distributed torque t0= 50 kip-ft/ft is applied on pipe BC. Let G = 11,800 ksi and assume that pipes AB and BC have the same inner diameter, d = 12 in. Pipe AB has a thickness tAB= 3/4 in., and pipe BC has a thickness tBC= 5/8 in. Find the reactive torques at A and C and the maximum shear stresses in each segment.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 stepped shaft (see figure) has diameter D2= 1.5 in, and a full quarter-circular fillet. The allowable shear stress is 15,000 psi and the load T = 4800 1b-in. What is the smallest permissible diameter D1?A thin-walled steel tube having an elliptical cross section with constant thickness t (see figure) is subjected to a torque T = 18 kip-in. Determine the shear stress and the rate of twist in degrees per inch) if G = 12 × 106 psi, t = 0.2 in., a = 3 in., and b = 2 in. Note: See Appendix E, Case 16, for the properties of an ellipse.A stepped shaft ACB having solid circular cross sections with two different diameters is held against rotation at the ends (see figure), (a) If the allowable shear stress in the shaft is 43 MPa, what is the maximum torque (T0)max that may be applied at section C? (b) Find (ï^),^ if the maximum angle of twist is limited to 1.85', Let G = 28 GPa.
- A full quarter-circular fillet is used at the shoulder of a stepped shaft having diameter D2= 1.0 in. (see figure), A torque T = 500 lb-in. acts on the shaft. Determine the shear stress at the stress concentration for values as follows: D1= 0.7,0.8, and 0.9 in. Plot a graph showing versus 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 torque T is applied to a thin-walled tube having a cross section in the shape of a regular hexagon with constant wall thickness t and side length b (see figure). Obtain formulas for the shear stress rand the rate of twist