Wire Sag Revisited, deflection of a pretensioned extensible cable

[skipm]

In the previous thread (404-60468) EnglishMuffin cited the equation ymax= L*(3*w*L/(64EA))^(1/3) to determine sag of a horizontal extensible cable whose length equals the span from Roark's formulas. He also proposed an equation where the cable is shorter than the span as ymax=w*L^2/(8*A*E*(1-LC/L)).

We make a woven metal wire mesh that is hung on exterior structures that is subjected to wind loading. The mesh is made of interlinked flattened wire spirals that are springy and hinge freely. A link chain fence is a crude approximation of the mesh construction. We have wind tunnel data for loading and load vs. elongation data that a psuedo E value have been derrived from. Using this data, the first equation will estimate the deflection of a strip of mesh hung between anchor points who's length is equal to the span. We would like to be able to estimate the effect of pretension on the mesh's deflection and thus the resulting mesh tension. The problem with the second equation is that as the pretension (mesh stretch) is reduced to zero (equal lengths), the calculated deflection increased to infinity instead of the value of the first equation.

I am looking an equation that will factor in the pretension and estimate the sag. If it would be helpfull, I can supply actual values or clarify details of the application.

Thanks Skip

 

[skipm]

To update, it works! Got more precise in the displacement measurements, added more data points, and calculated E correctly based on a unit width of mesh and then used an area of 1 (everything is being calculated per foot of width). A linear curvefit was applied to the load/elongation data. The length of the test panel divided by the slope is the E value. The initial preload is the equivalent tension based upon the b intercept elongation. A panel preloaded to this initial value will sag to the predicted value to within .030 in a 16' span. A panel tensioned beyond the initial preload also is very close (use the total preload, not initial plus offset, not additive).

Thanks again Prex and EnglishMuffin.

Skip