We need to design a bracket to take some kind of repeated bending load. One end is clamped stationary between a couple of plates, and a uniaxial, fully-reversed load with a maximum of 300 lbf rides on the end at a distance of a away from where it’s clamped. There’s a fillet where it clamps into the wall to try and keep it from fretting on a sharp corner. We’ll say it’s machined steel with an ultimate tensile strength of 82000 psi and an elastic modulus of 28 x 10^6 psi. We need it to survive basically forever. We aren’t given any dimensions, so we need to figure out exactly what this part has to look like. (Problem adapted from Machine Design: An Integrated Approach, 4th Ed., by Robert L. Norton.)
This is a pretty complicated problem - although we’re given a basic shape, we need to design this piece more or less from scratch. Here’s the basic process we’ll follow for this and other fatigue design problems:
- Initial estimated design
- Calculate nominal stresses
- Apply fatigue stress concentration factor
- Calculate principal stresses
- Calculate corrected endurance limit or fatigue strength
- Calculate safety factor
- Modify design
This gets long and ugly, but none of the individual pieces are too bad.
The cool thing is being able to write code (either in a spreadsheet or another program like octave/matlab) to solve the problem by iterations for you.
YES. A thousand times yes. If you have access to a spreadsheet or similar, by all means, do out the math, plug in your numbers, and let the program do the heavy lifting for the iterations.
Code, easy engineering, school is pointless. Yes.
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