Question

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A solid steel shaft AC is fixed to a rigid wall at its end A and is connected to a solid aluminum shaft CD at its other end C. The torques Ti and Tz are applied at the sections R and D, respectively, as shown in the figure. All the dimensions are given in the figure and the weight of the shafts are neglected. The shear modulus of steel is Gst 78 GPa and the shear modulus of aluminum is GAl 27 GPa. 20 cm 10 cm ? 45 cm Steel Aluminum T,= 7 kNm WALL diameter- 35 cm diameter 20 cm (a) Draw a free-body diagram of the shaft and find the reaction torque at A. (b) Draw free-body diagrams for each part and calculate the internal torque for (c) Calculate the polar moment of inertia, J, of the steel shaft and the polar (d) Calculate the maximum and minimum shear stresses in magnitude in the parts AB and BD moment of inertia, J, of the aluminum shaft. steel shaft and the maximum and minimum shear stresses in magnitude in the aluminum shaft. (e) Calculate the maximum and minimum shear strain in magnitude in the steel shaft and the maximum and minimum shear strain in magnitude in the aluminum shaft (f) Calculate the angle of rotation of: i. section D relative to section C ii. section C relative to section B iii. section B relative to section A (g) Calculate the angle of rotation of section D with respect to section A.

Answer 1

AL 句 . ㄙㄧ la pola. mom 3 AL 3 2 Aluri^iur) 0-31 Cactel. z 2.122 x lo