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john237084

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## Homework Statement

Hi all, I was wondering if anyone can help with this?

A uniform Steel strut (material Modulus of Elasticity 210 GN/m2, Poisson’s Ratio 0.3) of length 400mm and width 80 mm is restrained as appropriate at one end and under an axial tensile load of 20 KN applied to the other end face. It has been initially designed with a thickness of 5mm. This gives a hand calculated stress value of 50 MN/ m2, which is a quarter of the material’s Yield Stress, of 200 MN/m2, giving a factor of safety of four.

The strut now requires a round ended slot in the centre, right through, of Length L and width W. Determine the minimum thickness of strut of the same length, width and material, capable of withstanding the same tensile force with the same factor of safety. Assume Von Mises failure criterion apply, i.e. the maximum Von Mises (unaveraged) stress should not exceed 50 MN/m2. Your final thickness must be an integer millimetre value to use standard size material.

## Homework Equations

Kt = σmax/σnom

ratio for Kt = hole diameter/plate width

σnom = P/A, A = smallest cross sectional area at the section with the highest stress.

σmax = Kt*(P/A)

A = t*40 t = thickness.

## The Attempt at a Solution

Petersons chart 4.1 shows d/W to be 0.5 = Kt of 2.16. For a finite plate with a central hole in uniaxial stress.

σnom = σmax/Kt = 23.148 Mn/m2, through trial and error 21.6mm x 40mm = 864mm2 = 0.000864m2.(Which is obviously a plate thickness of 22mm for the integer value)

σnom = 20*10^3/864*10^-6 = 23.148148 Mn/m2, to prove this I put it back into σmax = Kt*(P/A) and it = 2.16*(20*10^3/864*10^-6) = 50MN/m2

So I modeled this thickness (21.6mm) to see if it gave a max stress of 50 Mn/m2 and it didn't. So I modeled some smaller thicknesses and found through modelling that the FEA results showed 16.5mm to be 49.9 MN/m2 max stress?

Is this because you don't take the shear stress into account and the software does?

So if you could help I'd really appreciate it. Am I using the wrong K? I looked for a formulae for a slot but the only one I could find is for a vertical slot, not a horizontal slot?

Also am I right to assume that von-mises failure criterion, in simple tension, is the same as the yield stress of 200 MN/m2?

Sorry if this seems long winded and a bit hard to understand, but I'm new to this stuff and quite long in the tooth. I really apreciate you taking the time to look, I'm not looking for someone to answer the whole thing, but I would like to know that I'm not wasting my time.

Thanks in advance.

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