Well it depends upon a lot of stuff, like the properties and temperature of the wire, and the span/sag ratio. The wire will take the shape of the catenary (hyperbolic functions, kind of tough to calculate manually), however, if the sag is relatively small in comparison to the span (say the sag is less than about 10 percent of the span), then the catenary curve is very closely approximated by a parbolic curve using the following equation: [tex] T=wl^2/(8d)[/tex], where w is the weight of the wire per unit length, l is the horizontal span between supports, d is the sag, and T is the horizontal tension in the cable. So, given T, l, and w, you can easily calculate d (the sag at the low point of the curve). If it is less than 10% or so of l, you plot the parabolic curve, and can then get sags at various points using the parabolic properties of that curve. Temperature and live loadis will affect sag/tension values, but if you're just looking at one tension at a given temperature under the wire dead load weight only, you need not go further.I am looking for a formula to calculate the deflection(sag) in steel wire that is supported between two points with a known tension. I want to be able to calculate the deflection(sag) at any point along the wire.
Oh, I was assuming a larger wire with higher tensions and spans. Nonetheless, the same formula applies. But first be sure you're using a very high strength steel, otherewise even your meager 30 pounds will snap it in half, because you are using such small diameter wire.Thanks for quick response; I really need to be able to find deflection along any point in the wire. I'm lloking at .016" dia wire with spans from 10 feet to 100 feet and wire tension of 30 pounds.
Yow, that's a close tolerance. Let me give you a sample calc based on the parabolic approximation, but don't use it for actual design!The wire sag is used for turbine machinery alignment; the internal parts of the turbine must be accurately aligned to a centerline. The wire is the centerline reference but the wire sag must be accounted for to get accurate centerline. Alignment of the turbine components has to be within thousants of an inch.