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Modulus of elasticity without the weight

Modulus of elasticity, coefficient of elasticity, Young's modulus, or simply stiffness: These are all terms used to describe a materials ability to resist deformation WHEN STRESSED. What is it called and how do I find the deflection when stressed only by its own weight. For example: What is the minimum thickness required for a piece of 7075-T6 aluminum to prevent sagging less than .003 inch over a 10 foot span with no additional weight applied?

Lon Freeman
- Hot Springs, Arkansas, USA


This is engineering work, Lon, and it would be illegal to practice unlicensed engineering. But assuming it's something for personal use, and trivial like a decoration (you said the only loading is its own weight), and you are just looking for thumb rules like a carpenter or electrician or plumber would use:

You might ignore the end conditions and figure the item to be a simply supported beam subjected to uniform loading. The deflection formula for midspan could be figured using standard beam formulas as shown in Machinery's Handbook

Of course you don't know the weight because you don't know the thickness yet, so assume a thickness like 1 inch and see where you are, then use successive refinement. You need to know Young's modulus for the aluminum, and you have to calculate the moment of inertia, again assuming a thickness.

Crane rails are often allowed to deflect 1 part in 450 or 1 part in 600. One part in 600 would be .2", so you can see that .003" is a pretty small deflection and the plate in question would have to be thicker than you might first think. Just a 2nd warning that you really shouldn't be thinking about designing it. Even if you did study and understood the beam formulas you could very easily miss another crucial issue like lateral instability -- the section twisting or turning in some fashion so that you no longer have the moment of inertia that you planned on.

Ted Mooney,
Ted Mooney, P.E.
Striving to live Aloha - Pine Beach, New Jersey

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