A circular tube is subjected to torsion by torques T applied at the ends. The bar is 0.75 m long and the inside and outside diameter are 35 mm and 46 mm respectively. It is determined by measurement that the angle of twist is 3.20 degrees when the torque is 600 N-m. (a) Calculate the maximum shear stress in the tube. (b) Calculate the shear modulus of elasticity. (c) Calculate the maximum shear strain in radians

Let’s consider a rod having a solid circular cross-section with diameter of 6 mm and it is made of a material having a Young’s modulus E = 200 Gpa and a Poisson’s ratio of 0.3. If a tensile force F is subjected to that rod cross-section, the diameter becomes 5.998 mm. determine the applied force F.

Question 2. A circular aluminum tube subjected to pure torsion by torques T (see figure 2) has an outer radius 12 equal to 1.5 times the inner radius ₁. (a) If the maximum shear strain in the tube is measured as 400x106 rad, what is the shear strain y at the inner surface? (b) If the maximum allowable rate of twist is 0.125 degrees per meter and the maximum shear strain is to be kept at 400x105 rad by adjusting the torque T, what is the minimum required outer radius (12) min? T Figure 2: cylindrical shaft

A motor driving a solid circular steel shaft transmits 30 kW to a gear at B (as shown). The allowable shear stress in the steel is 40 MPa. G=70 GA (a) What is the required diameter d of the shaft if it is operated at 1500 rpm? (b) What is the required diameter d if it is operated at 3000 rpm? (c) If the length of the shaft from the motor to the gear is 1 m, what are the angles of twist for the two speeds of rotation? Motor Motor

A steel and aluminum shafts with rigidity of (Gs = 77 GPa) and (Ga = 27 GPa) respectively. As shown in Fig. 3, the tube are connected to a fixed support and to a rigid disk. A torque of T = 6, 325 N-m is applied at the end. Determine the shear stresses in the steel shaft and aluminum tube. Note that the displacement in such problem is rotational displacement and the the stresses is calculated based on TX r/j 8 mm Aluminum tube 76 mm [50 mm ' Steel shaft 500 mm Fig. 3

The hollow ACB shaft made of steel has an inner diameter of 40 mm and an outer diameter of 50 mm and is fixed against rotation at the A and B ends. As shown in the figure of a rod welded vertically to the shaft at point C of the shaft, P forces are applied to the ends in the horizontal direction. If the maximum allowable slip on the ACB shaft is 45 MPa, determine the largest value of the P force. stretching

Find the resulting strains in a unidirectional lamina subjected to normal tensile stresses of 20MPa in the longitudinal direction, compressive stress of 5MPA in the transverse direction, and a negative shear stress of 1.0MPa. The lamina properties are: EL =20 GPa, ET = 2 GPa, GLT = 0.7 GPa, and vLT = 0.35.

The copper pipe [G = 7,000 ksi] has an outside diameter of 3.000 in. and a wall thickness of 0.125 in. The pipe is subjected to a uniformly distributed torque of t= 70 Ib-ft/ft along its entire length. Using a = 2.0 ft, b = 4.0 ft, and c = 8.5 ft, determine (a) the maximum shear stress in the pipe. (b) the rotation angle oc at the free end of the shaft. B Answers: (a) Tmax = i psi (b) Фс- і rad

The 12 kN.m torque is applied to the free end of the 5-m steel shaft. The angle of rotation of the shaft is to be limited to 3o. (a)Find the diameter d of the smallest shaft that can be used. (b) What will be the maximum shear stress in the shaft? Use G = 83 GPa for steel.

A shaft composed of three segments and fastened to rigid supports. Determine the maximum shear stress developed in each segment. (Please don't skip any mathematical step and please show all the working)