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Deflection of a solid body with different cross sectional areas

by ladil123
Tags: deflection, solid body
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ladil123
#1
Jan15-09, 09:17 AM
P: 45
Hello!

I want to know the deflection at certain points in a solid body with different cross sectional areas. A force (F) is applied at one of the different sections. I want to know the deflection where the force is applied and what the deflection is on the other parts of the body.
Im going to need to calculate the deflection on different geometries but if anyone could help me with the one that is on the picture below maybe I start to remember how to do it... The solid body is all round.
The only material constant i want to use is the E-modulus.

Thanks for helping me

Daniel
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skeleton
#2
Jan15-09, 10:53 AM
P: 86
In contrast, a uniform beam with a an offset point load has a deflection at the point of loading to be:

defl(P) = P*a^3*b^3 / 3*E*I*L^3

However, you have modeled a beam consisting of three segments. I would direct you to any good book on "Mechanics of Materials" under structural engineering. It would give the principles for you then to develop equations for this problem. Guaranteed, you won't find a pre-assembled solution as this problem is too irregular in itself.

As you presented it, the problem is well defined (said to be determinant). That is, you have sufficient data to determine the deflection.

Frankly, we use a "Frame Analysis" computer program to frequently solve such problems. There are oodles of such programs; you could probably find some rudimentary ones free on the internet. That would be able to calculate deflections at all points, but of course only for numerically defined problems. I suggest you go that route.
ladil123
#3
Jan16-09, 02:28 AM
P: 45
Thank you!

If I want to do this very easy, can I combine the deflection of one specific beam with different boundary conditions at the end of the beam and with equlibrium solve the problem.

I dont really need the to know the deflection all over the beam, just where its maximum is= where the force is applied (obviously) and at the end of the different sections.

English is not my first language so I hope I made it somewhat clear.

skeleton
#4
Jan16-09, 06:45 PM
P: 86
Deflection of a solid body with different cross sectional areas

Yes, in theory you could determine the deflections by maintaining compatible boundary conditions. In reality, this is usually more difficult then the alternative. The most common method is to model the beam with varying sectional properties. As said earlier, most method is to use a computer program.

I would suggest the following program (FastFrame), which is free and perhaps one of the best for its price:

http://www.enercalc.com/support/downloads.asp

Maximum deflection in not coincident in location with applied force unless the location is symmetric (ie: at mid point).

Usually the maximum deflection is not trivial for non-trivial configurations. As such, we structural engineers usually check the deflection incrementally along the entire length of the beam (eg: in 1/10*length intervals).


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