Chapter 6 (Torsion) - T6 1. The splined ends and gears attached to the A992 steel shaft (G = 75 GPa) are subjected to the torques shown in Figure 1. The shaft has a diameter of 40 mm. a) Draw the internal torque diagram from A to D. b) Calculate the maximum shear stress of the shaft, in MPa. c) Determine the angle of twist of end B with respect to end A, in degree. 200 N-m 600 N-m 400 mm 400 N-m 1200 N-m 500 mm Figure 1 600 mm B

The two solid shafts are connected by the gears shown. The motor constantly supplies 20 kW of power at 15 Hz to system at A. The yield shear stress is 140 MPa for shaft (1) and 220 MPa for the shaft (2), and over all factor of safety is 2. a) Find the diameter of both shafts. b) If the modulus of rigidity of shaft (2) G is 77.2 GPa, calculate the relative angle of twist D with respect to C. 30 teeth B (1) 48 teeth Tp 0.8 m

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400 mm Fr= 800 150mm C 600 N -Fa = 400 150mm Ft = Draw bending torsional moments, shear forces and normal force diagrams for the given gear shaft system.

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The shaft shown in the figure is machined from AISI 1040 CD steel. The shaft rotates at 1600 rpm and is supported in rolling bearings at A and B. The applied forces are F₁ = 1600 lbf and F2 = 640 lbf. A steady torque of 1600 lbf-in is being transmitted through the shaft between the points of application of the forces. 1 / in ] A in [lin -10 in- F₁ in F₂ -10 in- All fillets in R. 12in] 3 in The value of the notch sensitivity is The value of the fatigue stress concentration factor is in NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. What is the value of the theoretical stress concentration factor for torsion, the notch sensitivity, and the fatigue stress concentration factor? (You must provide an answer before moving to the next part.) The value of the theoretical stress concentration factor for torsion is

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a) Figure Q5 shows a 1.4 m long steel shaft that consists of a hollow segment AB and a solid segment BC. The shaft is fixed at C and is subjected to two external torques TA and TB at points A and B, respectively. The torque developed at the fixed end C is 750 kN.m in the direction as indicated in the figure. i) Determine the values of TA and TB if the corresponding angle of twist of end A is zero. ii) Calculate the maximum shear stress developed in the shaft. Give your comment whether the shaft will fail or not if the allowable shear stress of the shaft is 75 MPa. 750 kN.m 1.4 m 0.8 m C 160 mm B Тв 200 mm- ΤΑ Section a-a Figure Q5 = [Ans: a) i) T 332 kN.m, TB=1082 kN.m, ii) TCB,max = 60 MPa, TBA,max=45 MPa]

The spur gear arrangement shown in the figure has a pinion (diver Gear A) that rotates at 625 rpm, an idler Gear B and a driven gear (Gear C). The gears have a module of 5 mm and a pressure angle of 20 degrees. Given the number of teeth as shown in the figure, determine: i) ii) iii) The pitch diameters of each of the gears. The torque that each shaft is required to transmit. The forces on each of the gears 40 teeth 490⁰ B 70 teeth 50 teeth