How Do You Calculate the Maximum Axial Compressive Load for a Steel Punch?

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To calculate the maximum axial compressive load for a steel punch with a circumference of 25mm, first determine the diameter and then the cross-sectional area using the formula πr². With a maximum compressive stress of 235 MN/m² and a safety factor of 3, the allowable stress is 78.3 MN/m². The maximum load can then be calculated by multiplying this allowable stress by the cross-sectional area. There is no need to calculate the slenderness ratio for this specific problem. Understanding these calculations is essential for ensuring the structural integrity of the steel punch.
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I have a question on axial loads. I can get to a certain point but can't quite work out how to used the forumla properly. The question is

Given that the maximum compressive stress for steel is 235MN/m2. Using a factor of saftey of 3, determin the maximum axial compressive load that can be applied to a steel punch with a 25mm circumferance.

So far i work out we need to find the area of the punch, which we work out diameter first then half it and work out area using pie x r squared. This is fairly easy but now i know the forumla to use but do i need to work out the slenderness ratio first?

cheers
 
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I think you should keep it simple:

With a safety factor of 3 the maximum compressive stress that should be applied to the punch is 78.3 MN/m^2. The maximum load that it should experience can be calculated by using the cross sectional area that you calculated.
 
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