Spring force calculation

1. Diamond
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## Spring force calculation

I looked into spring force and got lost in the math. If I take a spring steel rod say 24 inches long and one inch in diameter. Fixed at one end and free to move up and down at the other end. If, for example, 1,000 pounds moves it down say 1 inch.
If I reduce the diameter so the cross section is 1/2 of the original will it move down 2 inches from the same 1,000 pound loading.
All this assumes we stay within the load of the spring so no hysteresis to worry about.
I am just guessing here but I would think the cross section area is directly related to spring force. I imagine there is a little more to it then that but I assume it should be true at low speeds in the mid range of loading.
Of course all sample springs are identical materials and heat treating.
Bill D.

2. Aluminum
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Originally Posted by Bill D
I looked into spring force and got lost in the math. If I take a spring steel rod say 24 inches long and one inch in diameter. Fixed at one end and free to move up and down at the other end. If, for example, 1,000 pounds moves it down say 1 inch.
If I reduce the diameter so the cross section is 1/2 of the original will it move down 2 inches from the same 1,000 pound loading.
All this assumes we stay within the load of the spring so no hysteresis to worry about.
I am just guessing here but I would think the cross section area is directly related to spring force. I imagine there is a little more to it then that but I assume it should be true at low speeds in the mid range of loading.
Of course all sample springs are identical materials and heat treating.
Bill D.
Deflection difference will be a factor of about 15 not 2. Look up round bar deflection calculation. It calculates for you.

3. Diamond
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The on-line spring calculators are common enough. A few minutes playing around will give you more insight than 100 replies on any internet forum.

4. Diamond
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Thanks for the replys. For some reason I forgot to include "online calculator" as part of my search terms. I found several and now I can play around and see the results change. Interesting to see the differences between slight changes in flat or round stock.
Bill D

5. I’m sure the on-line calculators are great, but machinery’s handbook will also walk you through the design of a spring step-by-step if you’re interested. Good luck!

6. Aluminum
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This is a Solid Mechanics problem. There are equations to calculate rod deflections based on support and loading. The determining factors are the diameter of the rod, the length of the rod, and the moment created by the force. Here is a link to a video on this topic. Hopefully this helps.