Truss Camber calculations
A work sheet to assist in determineing the proper cambering of a truss (may be used for beams as well) based on truss geometry and a specified camber.
Sometimes (acutally all the time) it amazes me what was accomplished without computers; This is interesting, but it is not emperical. It is based on a uniformily loaded truss in which the deflection is primairly due flexure (as opposed to shear deformation). The method also assumes equally spaced panel points.
Added an equation to accomplish the same, but not restricted to equally spaced panel points.
Thanks for the post,
Thank you for the added content. In reviewing your formulation it is quite apparent that the guys who figured this out used the moment diagram. Your final formula is identical to mine except that mine assumes discrete equal intervals. My n is L/2 and my i is your x. Simply moving things around and substituting we get the same formula. I do appreciate the added knowledge, maybe now I won't forget how it was originally derived.
My intent in preparing the worksheet was to preserve a method of calculation that anyone can use. I fear that we will forget the simple way of doing things and be tied to the computer for even these simplist of tasks. My recent search of the internet, and my library of books (some over a hundred years old) for this camber calcualtion method turned up empty; I had forgotten the procedure as I do not often use it so I had to recreate from my memory, and that too is starting to go.
So I hope that the basic procedure and formula, though equal panel point spacing is assumed it does work for varying panel points within reason, or at least with very little effect on the end result, will be of assistance to some one. I appreciate the added information as it will show the underlying math and perhaps record the means of doing a precise calcualtion -- for those who insist on precision. Something that is lost and will never return though is that these calcualtions would have been done with log tables and for those of you too young to know what these are they predated slide rules and for those who have never seen one of those they predate calculators. Log tables are just a book full of numbers used to assist in doing calculations.
Now what I am looking for is the formulation for a helix.
I appreciate the intent, there is value in it. A compendium of such techniques would be very interesting and might help keep things in perspective. But I fear with programs that design whole buildings available, that after a few years out of college, many engineers may not even be able to design a beam with a calculator.