shaft along BC is twice as that of along AB. The torsional rigidity of AB is GJ. The torque required for unit twist at B is
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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 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 solid circular shaft AB of diameter d is fixed against rotation at both ends (sec figure), A circular disk is attached to the shaft at the location shown. What is the largest permissible angle of rotation 0max of the disk if the allowable shear stress in the shaft is Tallow? [Assume that a >b. Also, use Eqs. (3-50a and b) of Example 3-9 to obtain the reactive torques.]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 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 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 uniformly tapered aluminum-alloy tube AB with a circular cross section and length L is shown in the figure. The outside diameters at the ends arc dAand dB= 2dA. A hollow section of length LB and constant thickness t = dA/10 is cast into the tube and extends from B halfway toward A. (a) Find the angle of twist é of the tube when it is subjected to torques T acting at the ends. Use numerical values: dA= 2.5 in., L = 48 in., G = 3.9 × 106 psi, and T =40,000 in.-lb. (b) Repeat part (a) if the hollow section has con stant diameter rfj (see figure part b)
- A hollow tube ABCDE constructed of monel metal is subjected to five torques acting in the directions shown in the figure. The magnitudes of the torques are T1= 1000 lb-in., T2= T4= 500 lb-in., and T3= T5= 800 lb-in. The tube has an outside diameter of d2= 1.0 in. The allowable shear stress is 12,000 psi and the allowable rate of twist is 2.0°/ft. Determine the maximum permissible inside diameter d1, of the tube.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.Two 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.