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- The steel hollow shaft is rigidly attached to a solid bronze shaft by a bolt coupling. A maximum torque T can be applied to the ends of the shaft without failure. Use G = 83 GPa for steel and G = 35 GPa for bronze. 100 mm † 70 mm 70 mm 1.5 m 2 m 1. Determine the maximum torque Tin kN-m without exceeding a shear stress of 70 MPa in steel and 50 MPa for bronze. C) 8.56 A) 10.44 Determine the maximum torque T in kN-m without exceeding an angle of twist of 2.5° in the 3.5-m length. A) 1.20 Determine the number of 16 mm bolts required to attach the two shafts if the B) 9.82 D) 7.35 2. B) 13.51 C) 2.40 D) 12.68 3. allowable shear stress in each bolt is 30 MPa and the diameter of bolt circle is 150 mm. A) 4 B) 5 C) 6 D) 7 O 1A 1B 10 1D 2A O 28 O 20 O 2D O 3A O 3B O 30 3D O O OQuestion 3 3.1 The short column in Figure 3 has a rectangle cross-section 80 mm x 50 mm. If the maximum compressive stress in the column is not to exceed 115 MPa, determine the magnitude of the greatest allowable vertical load P which can be carried. 30 mm 80 mm Fig. 1A hollow titanium [G=31 GPa] shaft has an outside diameter of D = 57 mm and a wall thickness of t = 1.61 mm. The maximum shear stress in the shaft must be limited to 246 MPa. Determine: (a) the maximum power P that can be transmitted by the shaft if the rotation speed must be limited to 22 Hz. (b) the magnitude of the angle of twist & in a 690-mm length of the shaft when 80 kW is being transmitted at 11 Hz. Answers: (a) P = i (b) = i kW.
- Mechanics of Deformable Bodies 6 in. in.- 5 in. 4 in. A steel tube with the cross section shown carries a torque T. The tube is 6ft and has a constant wall thickness of 3/8in. (a)Compute the torsional stiffness k=TTO of the tube. (b) If the tube is twisted through 0.5°, determine the shear stress in the wall of the tube. Use G=12x 106psi.Situation 5: A solid shaft is partially inserted in a hollow shaft where it snuggly fits and is rigidly attached on the wall of the hollow shaft. Solid shaft SECTION VIEW Hollow shaft Embedment Consider the following: Torque, T9 KN-m A What is the stress (MPa) of the hollow shaft at section A? B. What is the stress (MPa) of the solid shaft at section C? C. What is the stress (MPa) of the hollow shaft at section B? Properties of the hollow shaft: Length =4m Outer diameter - 80 mm Inner diameter = 40 mm Shear modulus = 96 GPa D. What is the stress (MPa) of the solid shaft at section B? E. What is the angle of twist (rad) of the entire assembly? Properties of the solid shaft: Length - 2.5 m Shear modulus = 112 GPa Length of embedment = 0.5m5 - An aluminum circular shaft, fixed at both ends, is loaded by torques applied at points B and C, as shown in the figure. The bar material has a shear modulus G = 85 GPa. Plot the maximum shear stress and angle of twist along the length of the shaft. A D TB 0.5m Tc 0.9m с 0.4m 40mm ↑ TB-10KN-m Tc=15KN.m
- PROBLEM 3 A compound shaft consisting of a 50mm diameter bronze segment and a 75mm diameter aluminum segment is subjected to two torques shown. Determine the maximum permissible value of T if the stress of bronze is limited to 60Mpa, the stress in aluminum is limited to 70mpa and the angle of twist of the free end is 10 deg. G for aluminum= 28GPA and G for bronze = 35 GPa. 27 37 Aluminum bronze it 2M 2The solid shaft, made of three different materials, carries the two torques shown. (a) Calculate the maximum shear stress in each material. (b) Find the angle of rotation of the free end of the shaft. The shear moduli are 28 GPa for the aluminum, 83 GPa for steel and 35 GPa for bronze. Aluminum 100 mm -3 m- 4 kN.m Steel 75 mm -2 m 1.5 kN - m Bronze |--15m-lSectian 300 800 ISM P= 300 kl, e = 250mm From the given figure shown, Calculate the stress at the top located in the centerline of the beam. (MPa)
- A flat steel bar, 25mm wide by 6mm thick and 1 m long, is bent by couple applied at the ends so that the midpoint deflection is 20mm. Use E=200 GN/m^2. Compute: a. the maximum stress in the bar (MPa) b. the magnitude of the couples(N-mm) Round to the nearest whole number.The following shaft consists of a 3.50 m long steel shaft and a 2.00 m long aluminum tube. The steel and aluminum are rigidly bonded together in the first 2.00 m. The applied torque T is 50 kN-m. The data is listed in the table. Determine: The maximum shear stress in the aluminum (composite section). The maximum shear stress in the steel (composite section). The maximum stress in the steel. The total deformation of the shaft at the free end.A hollow titanium [G = 46 GPa] shaft has an outside diameter of D = 56 mm and a wall thickness of t = 1.88 mm. The maximum shear stress in the shaft must be limited to 243 MPa. Determine: (a) the maximum power P that can be transmitted by the shaft if the rotation speed must be limited to 27 Hz. (b) the magnitude of the angle of twist in a 830-mm length of the shaft when 75 kW is being transmitted at 9 Hz. Answers: (a) P = i (b) = kW.