geometry problem

This page:

say 84.127 and 84.285

Assuming perfect conditions, cut, weld, etc., you would need 84.1269" for the 2" droop and 84.2854" for the 3" droop.

Good luck

Assuming the sheet will follow a circular arc. Here's a calculator and derivation calcs.

Cool calculator. As you can only shear to about 0.100 accuracy, I'll plan on

84.25 on one side and 84.5 on the other to make the sag 3" on one end and 4" on the other.

karl

Without using any mathematical formula you can find out the length of the arc by running a narrow flat metal tape (approx equal to the sheet metal thickness that you would weld) in between the two points of connections (which is 84" apart measured straight) and let it sag 2" or 3" from the top level. Measure how much tape is required to bridge the curved span that will conform to your desired specification. That is the amount of sheet metal width that you will need.

And here I was going to be a smart ass and say "just a bit longer than 84 inches".

Silly me.

Do you have to center the steel between the iron, or can you let it ride on the face? If you can let it ride on the face of the iron, just cut it a bit long and jig it up to sag the right amount, then weld away.

I expect a metal tape measure would work just as well. I like your solution.

Dan

I found this site quite a while back after a lot of looking. I needed to calculate the actual length of a roadway that ran a long distance, but had a curve in it. My boss used to just guess, and was really impressed when I showed him this site. A very handy thing for lots of uses.

Steve

For that matter it doesn't have to be metal. A "dressmaker's" fabric tape would give the same answer. Well, not strictly. A fabric tape will be close to a catenery. The calculators described in other postings probably assume a circular arc. The exact shape of the metal sheet under the combined influence of compression and gravity will depend on its thickness and its orientation (if the angle irons are not at the same level). But for 2 - 3 inches bow in an 84 inch span there won't be much practical difference for a roof (although it could matter for a microwave reflector).

| >> Without using any mathematical formula you can find out the length of the | >> arc by running a narrow flat metal tape (approx equal to the sheet metal | >> thickness that you would weld) in between the two points of connections | >> (which is 84" apart measured straight) and let it sag 2" or 3" from the | >> top | >> level. Measure how much tape is required to bridge the curved span that | >> will | >> conform to your desired specification. That is the amount of sheet metal | >> width that you will need. | >

| >

| > I expect a metal tape measure would work just as well. I like your | > solution. | >

| > Dan | | For that matter it doesn't have to be metal. A "dressmaker's" fabric tape | would give the same answer. Well, not strictly. A fabric tape will be close | to a catenery. The calculators described in other postings probably assume a | circular arc. The exact shape of the metal sheet under the combined | influence of compression and gravity will depend on its thickness and its | orientation (if the angle irons are not at the same level). But for 2 - 3 | inches bow in an 84 inch span there won't be much practical difference for a | roof (although it could matter for a microwave reflector). |

It's actually a parabolic curve with a possible vertex location at (0,0) and the two welded end coordinates either at (-42, 2) and (42, 2) or (-42, 3) and (42, 3).