*5-24. The copper pipe has an outer diameter of 2.50 in. and an inner diameter of 2.30 in. If it is tightly secured to the wall at C and a uniformly distributed torque is applied to it as shown, determine the shear stress developed at points A and B. These points lie on the pipe’s outer surface. Sketch the shear stress on volume elements located at A and B.
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5-22. The solid shaft is subjected to the distributed and concentrated torsional loadings shown. Determine the required diameter d of the shaft to the nearest mm if the allowable shear stress for the material is Tallow = 50 MPa.
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•5—21. The 60-mm-diameter solid shaft is subjected to the distributed and concentrated torsional loadings shown. Determine the absolute maximum and minimum shear stresses on the outer surface of the shaft and specify their locations, measured from the fixed end A.
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*5-20. Two wrenches are used to tighten the pipe. If the pipe is made from a material having an allowable shear stress of Tallow = 85 MPa, determine the allowable maximum force P that can be applied to each wrench. The pipe has an outer diameter of 25 mm and inner diameter of 20 mm.
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5-19. Two wrenches are used to tighten the pipe. If P = 300 N is applied to each wrench, determine the maximum torsional shear stress developed within regions AB and BC. The pipe has an outer diameter of 25 mm and inner diameter of 20 mm. Sketch the shear stress distribution for both cases.
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5-17. The rod has a diameter of 1 in. and a weight of 10 lb/ft. Determine the maximum torsional stress in the rod at a section located at A due to the rod’s weight.
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5-15. The solid shaft is made of material that has an allowable shear stress of Tallow = 10 MPa. Determine the required diameter of the shaft to the nearest mm.
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5-13. If the applied torque on shaft CD is T’ = 75 N. m, determine the absolute maximum shear stress in each shaft. The bearings B, C, and D allow free rotation of the shafts, and the motor holds the shafts fixed from rotating.
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5-14. The solid 50-mm-diameter shaft is used to transmit the torques applied to the gears. Determine the absolute maximum shear stress in the shaft.
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5-12. The motor delivers a torque of 50 N. m to the shaft AB. This torque is transmitted to shaft CD using the gears at E and F. Determine the equilibrium torque T’ on shaft CD and the maximum shear stress in each shaft. The bearings B, C, and D allow free rotation of the shafts.
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