1000 Nicm is applied as the shaft re I torque that varies with maximum va ter of shaft required to obtain a safe shaft is steel of S =745 MPa and S, = 18 and a = 16) are in cm.
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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 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 segment of a generator shaft with a hollow circular cross section is subjected to a torque T = 240 kip-in, (see figure). The outer and inner diameters of the shaft arc 8.0 in, and 6.25 in., respectively. What is the maximum permissible compressive load /'that can be applied to the shaft if the allowable in-plane shear stress is rAi(m= 6250 psi
- 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 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 hollow circular tube T of a length L = 15 in. is uniformly compressed by a force P acting through a rigid plate (see figure). The outside and inside diameters of the tube are 3.0 and 2.75 in., respectively. A concentric solid circular bar B of 1.5 in. diameter is mounted inside the lube. When no load is present, there is a clearance c = 0.0I0 in. between the bar B and the rigid plate. Both bar and tube are made of steel having an c[autoplastic stress-strain diagram with E = 29 X LO3 ksi and err= 36 ksi. (a) Determine the yield load Pt- and the corresponding shortening 3yof the lube. (b) Determine the plastic load Ppand the corresponding shortening Spof the tube. (c) Construct a load-displacement diagram showing the load Pas ordinate and the shortening 5 of the tube as abscissa. Hint: The load-displacement diagram is not a single straight line in the region 0 ^ P ^ Pr
- A stepped shaft ACE is held against rotation at ends A and B and subjected to a torque T0acting at section C(see figure). The two segments of the shaft (AC and CB) have diameters dAand dg, respectively, and polar moments of inertia IpAand IpBrespectively. The shaft has length L and segment AC has length a. For what ratio a/L will the maximum shear stresses be the same in both segments of the shaft? For what ratio a/L will the internal torques be the same in both segments of the shaft?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.Solve the preceding problem for the following data: diameter LO m, thickness 48 mm, pressure 22 MPa, modulus 210 GPa. and Poisson's ratio 0.29
- A uniformly tapered aluminum-ally tube AB of circular cross section and length L is fixed against rotation at A and B, as shown in the figure. The outside diameters at the ends are dAand dA.A hollow section of lenth L/2 and constant thickness t = dA/10 is cast into the tube and extends from B half-way toward A. Torque T0is applied at L/2. (a) Find the reactive torques at the supports, TA and TB. Use numerical values as follows: dA = 2.5 in., L = 48., G = 309 × 106 psi, and T0= 40,000 in.-lb. (b) Repeat part (a) if the hollow sections has constant diameter dA.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 copper alloy pipe with a yield stress aY= 290 MPa. is to carry an axial tensile load P = 1500 kN (see figure part a). Use a factor of safety of 1.8 against yielding. (a) If the thickness t of the pipe is one-eighth of its outer diameter, what is the minimum required outer diameter dmin? (b) Repeat part (a) if the tube has a hole of diameter dt 10 drilled through the entire tube, as shown in the figure part b.