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I am trying to figure out how to design how thick a material has to be so that the bar shown in picture 1 stays intact when a user is running on it.

Background: The project is a treadmill and the user is going to be running on the rods shown in the first picture. The total length of the bar should be about 1 meter or 3.5 ft. The main restraint is the budget. I am able to weld also. Most likely I'll need to use steel, but I don't know how to calculate how thick the steel needs to be in order for the bar not the collapse under the pressure of the user walking on it(user weighs max 200 pounds). Also, the shape of the bar is a little different than the first picture. The bar is going to look like picture 2. The bars are going to be 7/8 inch wide and 1 meter long/3.5 ft long. Each bar is going to have a rectangular cut in the middle that is 3/8 inch wide.

Task: Based on the research I've done, I believe I need to calculate the bending stress. Overall, I don't know which equations to use for this situations (I tried the load at the mid point formula but I am very confused) and how to design the bar (thickness)so that it can carry the weight of a running 200 pounds person without collapsing.

Any help would be extremely appreciated. Thank you!!!

[![enter image description here][1]][1]

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  • $\begingroup$ 200 lbs - I wish... you may need to increase that. $\endgroup$
    – Solar Mike
    Commented May 10 at 10:19
  • $\begingroup$ I suggest you read up on the dynamics of running. WAG the shock is of the order of 4g on a rigid surface, but your ankle breaking trampoline is not rigid, so it'll be less. $\endgroup$
    – Greg Locock
    Commented May 10 at 23:03
  • $\begingroup$ Additionally you may want to look at a different criteria than failure due to a single load. You may want to look at cyclic load and fatigue failure. I am not that knowledgeable on the topic but my understanding is the closer your applied load is the the capacity of the material, the quicker it will fail from fatigue loading. The other thing to consider is deflection criteria. How far can you let the support bend before it conflicts with other parts of your machine. Back in the day, conveyor belts and treadmills could be made with wood slats. Probably cheaper than steel. $\endgroup$
    – Forward Ed
    Commented May 18 at 0:46

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