Tapered beam question 2

[Rrs1021]

I'm having some trouble understanding how to calculate the moment of inertia for a beam a certain X length that tapers at each end, and how to find the plastic and elastic section modulus after that. Would I have to set it up as a function that gives you the moment of inertia at any point as it runs through the beam? Thank you

 

[BAretired]

The moment of inertia and section modulus are variable in the tapered sections. If you can express the depth in terms of the position x along the beam, then you can express the other properties as a continuous function within the taper.

Alternatively, if that proves too cumbersome, you could divide the tapered portions into smaller sections, each with its average depth and moment of inertia. Accuracy improves as the number of sections increases.

BA

 

[GregLocock]

I would definitely use a model with multiple sections in it. Check the result against your standard equations for a uniform beam.

https://en.smath.com/wiki/GetFile.aspx?File=Examples/finger4.pdf

shows a similar approach for a different problem, in that case the large deflection behavior of a cantilever. Varying EI along its length would be trivial.

Section 8.8 in Roarke deals with beams of variable section.


Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[BAretired]

I have found Newmark's numerical procedures to be very handy through the years since graduation. If you are interested, here are a few notes. If you scan through these pages, you will see a couple of examples of tapered members.

http://www.slideruleera.net/Numerical Procedures for Indeterminate Structures.pdf

BA

 

[Rrs1021]

Thank you for the responses everyone, I'm still new here and I appreciate the help