If the system is initially stress-free.

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Calculate the temperature change that will cause a tensile stress of 90 MPa in the brass rod. Assume that both rods are subjected to the change in temperature. Solution Problem Four steel bars jointly support a mass of 15 Mg as shown in Fig. Each bar has a cross-sectional area of mm2. Such a bar is said to be in torsion. Solved Problems in Torsion Problem A steel shaft 3 ft long that has a diameter of 4 in. Determine the maximum shearing stress and the angle of twist. What maximum shearing stress is developed? Solution Problem A steel marine propeller shaft 14 in. What power can be transmitted by the shaft at 20 Hz?

Solution Problem A 2-in-diameter steel shaft rotates at rpm. If the shearing stress is limited to 12 ksi, determine the maximum horsepower that can be transmitted. Solution Problem A steel propeller shaft is to transmit 4.

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Solution Problem An aluminum shaft with a constant diameter of 50 mm is loaded by torques applied to gears attached to it as shown in Fig. Solution Problem A flexible shaft consists of a 0. Determine the maximum length of the shaft if the shearing stress is not to exceed 20 ksi. What will be the angular deformation of one end relative to the other end?

Solution Problem Determine the maximum torque that can be applied to a hollow circular steel shaft of mm outside diameter and an mm inside diameter without exceeding a shearing stress of 60 MPa or a twist of 0. Solution Problem The steel shaft shown in Fig. Solution Problem A 5-m steel shaft rotating at 2 Hz has 70 kW applied at a gear that is 2 m from the left end where 20 kW are removed. At the right end, 30 kW are removed and another 20 kW leaves the shaft at 1.

Solution Problem A compound shaft consisting of a steel segment and an aluminum segment is acted upon by two torques as shown in Fig. Solution Problem A hollow bronze shaft of 3 in. The two shafts are then fastened rigidly together at their ends. What torque can be applied to the composite shaft without exceeding a shearing stress of psi in the bronze or 12 ksi in the steel?

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Solution Problem A solid aluminum shaft 2 in. Determine the maximum shearing stress in each segment and the angle of rotation of the free end. Solution Problem The compound shaft shown in Fig. P is attached to rigid supports. Solution Problem In Prob. What torque T is required? Solution Problem A torque T is applied, as shown in Fig. P, to a solid shaft with built-in ends. How would these values be changed if the shaft were hollow? Solution Problem A solid steel shaft is loaded as shown in Fig.

Determine the maximum shearing stress developed in each segment. For the bronze segment AB, the maximum shearing stress is limited to psi and for the steel segment BC, it is limited to 12 ksi. Solution Problem The two steel shaft shown in Fig.

P, each with one end built into a rigid support have flanges rigidly attached to their free ends. The shafts are to be bolted together at their flanges.

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Determine the maximum shearing stress in each shaft after the shafts are bolted together. Solution Flanged Bolt Couplings In shaft connection called flanged bolt couplings see figure above , the torque is transmitted by the shearing force P created in he bolts that is assumed to be uniformly distributed. For any number of bolts n, the torque capacity of the coupling is If a coupling has two concentric rows of bolts, the torque capacity is where the subscript 1 refer to bolts on the outer circle an subscript 2 refer to bolts on the inner circle.

See figure. For rigid flanges, the shear deformations in the bolts are proportional to their radial distances from the shaft axis. Determine the torque capacity of the coupling if the allowable shearing stress in the bolts is 40 MPa.

Determine the torque capacity of the coupling if the allowable shearing stress in the bolts is psi. Solution Problem A flanged bolt coupling consists of eight mmdiameter steel bolts on a bolt circle mm in diameter, and six mmdiameter steel bolts on a concentric bolt circle mm in diameter, as shown in Fig. What torque can be applied without exceeding a shearing stress of 60 MPa in the bolts? Determine the shearing stress in the bolts. Solution Problem Determine the number of mm-diameter steel bolts that must be used on the mm bolt circle of the coupling described in Prob.

What torque can be applied without exceeding psi in the steel or psi in the aluminum? Solution Problem A plate is fastened to a fixed member by four mm diameter rivets arranged as shown in Fig. Compute the maximum and minimum shearing stress developed. P to the fixed member. Using the results of Prob. What additional loads P can be applied before the shearing stress in any rivet exceeds psi?

Solution Problem The plate shown in Fig. P is fastened to the fixed member by five mm-diameter rivets. Compute the value of the loads P so that the average shearing stress in any rivet does not exceed 70 MPa. Determine the wall thickness t so as not to exceed a shear stress of 80 MPa. What is the shear stress in the short sides? Neglect stress concentration at the corners. Solution Problem A tube 0.

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What torque will cause a shearing stress of psi? Determine the smallest permissible dimension a if the shearing stress is limited to psi. Solution Problem A tube 2 mm thick has the shape shown in Fig.

Assume that the shearing stress at any point is proportional to its radial distance. This formula neglects the curvature of the spring. For heavy springs and considering the curvature of the spring, a more precise formula is given by: A. Use Eq.