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Tutorial 6 MECH 101 Liang Tengfei [email protected] Office phone : 2358-8811 Mobile : 6497-0191 Office hour : 14:00-15:00 Fri 1 Outline Common problems in HW #3 Stress in an inclined plane Torsi0nal shaft Stress in an inclined plane Determine the stress acting on inclined section. Where the area of cross section is 1mm2, the angle is 30o. P=500N 375MPa 217MPa 1 cos (1 cos 2 ) 2 2 sin cos max x , at 0; 1 2 max x , at 450 ; 1 (sin 2 ) 2 practice 30.960 Pmax 1.53KN Basic concepts about torsional loading of shafts One important assumption: when a circular shaft, whether solid or tubular, is subjected to torsion, each cross section remains plane and simply rotates about the axis of the member. Torsional Shaft d ( x ) s r dx d ( x) : the rate of change of the angle of twist dx s r ( x) d ( x ) ( x) s r dx T dA s A for uniform shaft, const L r dA 2 A s r J Example 1 A shaft shown below is attached to a wall at its left end and is in equilibrium when subjected to the two torques. The shear modulus is 12,000 ksi. Determine (a) The maximum shearing stress in the shaft. (b) The rotation of end B of the 6-in segment with respect to end A (c) The rotation of end C of the 4-in segment with respect to end B (d) The rotation of end C with respect to end A. Solution FBD at A TAB 20 5 0 FBD at B TAB 15kip ft TBC 5 0 TBC 5kip ft From the above analysis, we can obtain a torque diagram which represents the torque distribution in the shaft. Solution (a) Maximum shearing stress We have known What is JAB and JBC ? Solution (b) The rotation of end B of the 6-in segment with respect to end A Apply the equation for rotation B / A T L L GJ TAB LAB 15(12)(9)(12) 0.012733rad GAB J AB 12000(127.23) (c) The rotation of end C of the 4-in segment with respect to end B Similarly C / B TCB LCB 5(12)(5)(12) 0.011938rad GCB J CB 12000(25.13) (d) The rotation of end C with respect to end A C / A C / B B / A (0.011938) (0.012733) 0.000795rad. Example 2