Question

Torque T, Angle of twiste (IT TOTO- Area A E10.11 Deriving indices for torsion (Figure E10.8). A shaft of length L, loaded in torsion, must support a specified torque T* without failing and be as cheap as possible. Section shape is a variable and "failure" again means the first onset of plasticity. Derive the material index. The table summarizes the requirements. Figure E10.8 Function Constraints • Cheap shaft • Specified failure torque T* • Length L specified • Minimize material cost C • Choice of material • Section shape and scale Objective Free variables

Answer 1

Given: Torque and length are specified. By torsion equation: I = = = = I J RL R de outer radius. Inner radius, t = R-k " can't be altered. I TI = 0 [where I GJ material property br & means shape and scale and I polar moment of inertia. can be altered. where I = I lacer)" - (2474) i I & GI , which means it is is more then the torque allowable will be more but it will cost and will be expensive, So, if we choose a particular cheap material we choose a particular cheap material and alter the thickness the rod can withstand the specified torque and lengtha Meano altering the polar moment of inertia. (I)