My friends and I are designing a bench press spotter. Essentially, when the user needs help lifting the barbell due to muscle fatigue, an arm on each side of the user raises to provide assistance. These arms are essentially cantilever beams. We determined that a rectangular beam would experience the least amount of stress when the bar provides a force equal to half its weight on each arm but we need to maximize the aspect ratio of the height and the width of the rectangle.
Our professor said to use fore-aft forces when doing this. Basically he means that if the user ends up tipping the bar and one end of the bar hits one of the arms at an angle without touching the other then the bar provides a force on the corner of the rectangular arm and this force is greater than if it touches each arm at the same time. Is there a way using forces to analyze the best dimensions for this?