1. Objective: To determine the internal torque and the associated shear stress for statically indeterminate problems. T A C B L AC L CB L 1)Reaction at A and B. 2)Internal torque at segment AC and CB. 3)Stress at AC and CB. Find,

2. Dr. H. Ali Al-Gadhib T AB TATA TBTB TATA T AC T AC = T A T CB TBTB T CB = T B Equation of equilibrium. T B – T + T A = 0 ---------------- A Where T A and T B are reactions at supports. T CB – T + T AC = 0 ---------------- B Equation of equilibrium. Equation A is of better form…

3. Dr. H. Ali Al-Gadhib T AC L AC + T CB L CB = 0 ---------------- C Solving equations B & C for the internal torque (T AC and T CB ) and then find reactions and stress.

4. Dr. H. Ali Al-Gadhib Example: The solid steel shaft as shown in figure has a diameter of 20 mm. If it is subject to the two torques, determine the reactions at the fixed support A and B.

5. Dr. H. Ali Al-Gadhib Solution: Equation of equilibrium.

6. Dr. H. Ali Al-Gadhib Compatibility:

7. Dr. H. Ali Al-Gadhib Example: The shaft as shown in figure is made from a steel tube, which is bonded to a brass core. If a torque of T = 250 N·m is applied at its end, plot the shear-stress distribution along a radial line of its cross-sectional area. Take G st = 80 GPa, G br = 36 GPa.

8. Dr. H. Ali Al-Gadhib Solution: Equilibrium. Compatibility.

9. Dr. H. Ali Al-Gadhib Solving Eqs. 1 and 2, we get

10. Dr. H. Ali Al-Gadhib