# How to determine the deflection of a wire mesh under wind load?

I am trying to extend a metal wire mesh over a large distance, while tensioning it to limit the deflection of the mesh due to the wind as much as possible. After doing some research I came across Roark's Formulas for Stress and Strain, which has a number of formulas regarding the deflection of flat rectangular plates under a variety of support conditions. In particular, I have been trying to use this formula, for a plate under a uniform transverse distributed load, with tension applied to its short edges: However, this is assuming it is a solid plate, not a welded wire mesh. I have tried to use these equations, but with the distributed load from the wind only applied to the percentage of the area taken up by the wires of the mesh. The other problem I have run into while using theses formulas is that there are only values of the three coefficients for values of P/Pe up to 5, and I would like to investigate the effects tensioning the mesh would have with higher values of this ratio. There are other ways of preventing the mesh from deflecting besides tensioning it, but I would like to investigate this method, as well as learn about the behavior of the mesh in a broader sense.

Are there any formulas/methods of calculating the deflection of a mesh due to wind out there? Or is there a way to use Roarks to solve this problem? Any advice or direction to additional resources is appreciated!

• This is a complex and highly nonlinear problem. For example the results will almost certainly depend on the stiffness of the supports as well as everything else. Either find a civil engineering code that specifies how to design wire mesh fences, or be prepared to learn a lot about multi-physics computer simulation! – alephzero Feb 18 at 17:35

An approximate solution is to assume a deflection shape similar to the diagram below $$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$$and solve it by using strip concrete slab method on FEM software or energy methods using the hyperbolic surface as a guess deflection shape. Just don't expect it can be done in a few days. 