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When Purdue University football fans failed to topple the goal posts after an important win, Purdue professor, Dr. A.F. (Skip) Grandt, Jr. had an inspiration for a creative exam problem*.  Can you solve this mean stress problem he posed for his students?

Frustrated by their unsuccessful efforts to tear down the goal posts following several recent football victories, a group of students decide to cut notches in the posts to hasten the nucleation of fatigue cracks as they plan to bend the goal posts back and forth following their next victory. During a full-scale fatigue test of one of the notched posts, it is discovered that ten students can exert a nominal cyclic stress amplitude +/- S that causes a crack to form in 10,000,000 reversals. Since the students don’t expect the stadium guards to allow them to remain on the field for the time required to apply 10,000,000 reversals (and since the students are anxious to return to their studies following the game), it is decided to recruit more students in order apply a larger cyclic stress, and, thus, hasten the fatigue failure of the goal posts.

Question:
How many students are required to develop fatigue cracks in the goal posts in 100 reversals?
Your assumptions:

Solution: Click here to view the solution.

*[Problem 9.13 from A. F. Grandt, Jr., Fundamentals of Structural Integrity – Damage Tolerant Design and Nondestructive Evaluation, John Wiley & Sons, 2004.]