Question

The assembly is composed of a solid steel alloy rod (Est200 GPa; Vst- 0.32) inside a hollow copper alloy tube (Ecu 101 GPa; vst 0.35). Both the rod and the tube are fixed to a rigid support at A. The length of the assembly is 0.5 m. As shown in figure (b), the diameter of the rod is d1 60 mm, and the outer diameter of the tube is d2-90 mm. The inner diameter of the tube is 70 mm (a) Initially (not shown on the diagram), a clockwise torque T1 is applied to the tube only, which twists the tube such that the angle of twist of the tube at B is 0.05 radians clockwise. . Determine the torque T (b) Next, with the tube in its twisted position and the rod in its original untwisted position, a rigid cap is attached to both the rod and the tube, as shown in figure (a). After the cap is attached, the torque T1 is released so that there is no external load on the assembly. As a result, the entire assembly cross- section at B rotates slightly counterclockwise. In its final position, determine: . the internal torque in the rod and the internal torque in Rod (1) dy Tube (2) the tube. (Hint: a free-body diagram will establish the relationship between Ttube and Trod.) . the angle of twist of the rod relative to its initial untwisted position and the angle of twist of the tube relative to its initial untwisted position (before Ti was applied). (Hint: first write a compatibility equation that relates the angles of twist Øtube and Ørod.)

Answer 1

Gevenoata U竺0.35 tube Tube-l dji cel dt

N02 tee Glce : 200 Gist : イ645GPa Copper ct QCI35) tO

0-03 Gcu Jcu 2 416 10 O-SIN 1-616 tylbo 30936823 66 N-mm

system wi aet a Sysem Subecte 1-0 in Counter cloctwise direction leabe Trad T 0 rad rod tube tabe To d q 6 380133 62 tube

Trod iube- Sad 2.ssu rod309368 33-66 o09 3683366 89 6 433 N-m tube 864 33 m

2 10 6380xIo rad 0.06 Y Caculate retative to s untuv tube. tabe 0.01211 Counter CocK- re