# What thickness of steel sheet do I need to achieve a given strength?

I have a customer that originally bought 0.0351" thick sheet steel, CSA grade, G90 zinc coating. They moved to 0.0236" Grade80, G90 to cut costs. The thinner, harder steel satisfied their customer's strength requirements. Their customer would now like a heavier zinc coating (G110) for corrosion protection but our customer wants to keep the total metal thickness the same meaning the base metal thickness will need to decrease. Strength is determined by the base metal thickness, not the zinc coating! What is the formula to determine how thin I can go and stay within the strength requirements of my customer's customer?

Now- Here is where you are going to beat me up. I do not know the strength requirements yet of my customer's customer. If I assume that requirement to be 'x', I could still calculate strength.

• Without knowing the requirements, there really isn't any way to answer this. @wasabi tried to give you some general considerations, but it still isn't an answer. The items mentioned might not even be relevant to the way that this part is loaded. It would be much better if you could wait until you know more of your requirements. – hazzey Jun 23 '15 at 18:06

## 1 Answer

The requisite thickness is a function of the applied loads.

If your sheet suffers only tension, then the calculation is trivial: the total applied tensile force divided by the sheet's cross-sectional area has to be less than the allowable (not characteristic) stress in the steel. This assumes the force is evenly applied along the sheet. If, however, the load is applied only at a given point, a more detailed analysis is required (finite elements are your friends). Since the stress is a function of area, the strength of your sheet is proportional to the thickness (halve the thickness, halve the strength).

If the sheet suffers only compression, then you need to check how the sheet will collapse: by stress (unlikely, only if a very short sheet) or by buckling. The allowable compression force by stress is obtained in the same way as in tension: allowable stress times cross-sectional area (assuming distributed load). By buckling the absolute maximum value is given by Euler: $$F = \dfrac{\pi^2EI}{(kL)^2}$$ where $EI$ is the sheet's stiffness and $kL$ is the effective length (a function of the boundary conditions). This is the absolute maximum, but no code will ever allow you to get close to this value. Since this is a function of the sheet's moment of inertia, the strength is a function of the orientation of the sheet. The lower value is obviously given for the sheet's "weak axis", so here the strength is also linearly proportional to thickness (double the thickness, double the strength).

If the sheet suffers only bending, then the orientation does matter: assuming the sheet is parallel to the floor, then the stress is a function of the cube of the thickness (double the thickness, eight times the strength... half the thickness, an eighth of the strength).

So in order to know whats the requisite thickness for your customer's customer, you need to know precisely what your customer's customer needs the piece for.