Dr. Vance closed the book. "Remember, Leo: Torque isn't just force times distance. It's stress times radius, integrated over area. Chapter 3 is about respecting that integration."
"Material spec says yield shear strength is 60 MPa," Leo said. "We're below yield. So why did it fail?" "Because you didn't check the angle of twist ," Dr. Vance said. "Turn to Equation 3-15." Mechanics Of Materials 7th Edition Chapter 3 Solutions
"2.4 degrees of twist over 2.5 meters is acceptable," Leo said. It's stress times radius, integrated over area
"Exactly," said Dr. Vance. "The Resilient was overloaded by cyclic torque. Now go re-design the shaft diameter using Equation 3-9: (J = \pi d^4/32). Solve for (d) using (\tau_allow = 60/2.5 = 24) MPa." So why did it fail
Setting: Engineering Lab, Coast Guard Inspection Yard. 2:00 AM.
Leo solved: [ d = \sqrt[3]\frac16T\pi \tau_allow ] [ d = \sqrt[3]\frac16(4000)\pi (24\times10^6) = 0.094 \text m \approx 94 \text mm ]