Homework Assignment 3

Given torque of and structural steel with the yield strength of , perform the following steps:

a) (20 points) Design the diameter of a circular shaft such that the shaft can safely withstand the applied torque. Derive all the equations and perform analytical calculations either using a calculator or MATLAB. This problem is actually solved over here.

b) (20 points) Consider the design shown in figures 1, 2, and 3 below. The diameter is calculated in part (a) of this assignment. Assume that the force couple consisting of two forces is creating the torque. Assuming that , find the value of force that will produce the torque of (whose value is given at the beginning of the assignment).

c) (20 points) For the computed diameter and computed force , use Fusion 360 to perform static stress analysis. Demonstrate that the calculated stress distribution matched the theoretical predictions (see here). That is, demonstrate that the stress values reach the highest values close to the edge of the cylinder. Ignore the top rectangular part, and choose the cutting plane at 1 [m] from the top.

d) (10 points) What is the maximal stress? Is the maximal stress computed using Fusion 360 close to the theoretical prediction in part (a)?

e) (30 points) Perform shape optimization using the method explained in this YouTube video Remove the unnecessary material and change the cross-section shape (watch the video). Make sure that the stress is still in the acceptable range. Is the final result similar to a shaft with a ring cross-section?

Submission instructions:

1. Submission deadline is Wednesday, 10/13/2021, at 11 AM (after the class).
2. Only printed copies should be submitted in person. I do not accept electronic submissions.
3. Please do not copy solutions from other students. This should be your original work.
4. Hand-written solutions will not be accepted. You are not allowed to write text and graphs using handwritting. Graphs should be made using appropriate software. You are allowed to write equations using handwritting.
5. Extra points will be given to students who write everything (equations + text+graphs) using software. A good program for writting engineering homework assignments is Latex. You will get extra points if you use Latex. You can use different Latex editors, a good choice is given here. Below, you can find a video tutorial on how to start with Latex.