Statically Indeterminate Problem

[kklinger]

Does anyone know of a good book on Statically Indeterminate Problems? If you go to Amazon.com, it will list 30 books with little or no detail about them. I am looking to verify my reactions that I obtained using FEA. I tried using the 3 Moment equation with a little bit of success. My problem has 3 loads + gravity, but 6 simple supports (can't change geometry but x-section is uniform) and 7 spans (2 cantilevers). Therefore, the beam is pushing down on some supports and pulling up on others. I may have read that the 3 Moment equation method might not be valid for this case.

 

[rb1957]

3 moment should be fine (pushing down or pulling up reactions), i'd check your sums.

you note 6 supports, 7 spans, 2 cantilevers ??? doesn't add up in my mind ... 6 supports would yield 5 spans; unless you've got two different beams spread over 6 supports, then the key question is are the beams joined together ?

if they are using the same supports, but free to bend independently, then you can consider them independently, and sum the support reactions. if the two beams are effectively welded together so that their bending is constrained along their length, then they'll act as a single beam, with an increased moment of inertia. if the two beams are welded together at the supports only, then they'll intercahange moment at these supports (they're constrained to have the same slope) and this is something that 3 moments might have trouble with.

try also moment distribution method in Bruhn, or unit load method ... this will give you 4 simultaneous equations to solve (your problem has 4 redundancies).

good luck

 

[14159]

I have two books that would be good candidates:

Structural Analysis by Harold Laurson (or Laursen, can't remember)

Mechanics of Materials by Ferdinand P. Beer and Russell Johnston

DBD

 

[14159]

Another thought:

In the past when I've done something like this, I'll check the solutions against a known solution rather than trying to recalculate the solution using a theoretical method. Once I obtain agreement for known problems, I gain confidence in the program and my ability to use the program.

I usually use the AISC Steel Manual deflection and moment diagrams for this. They have a lot of cases in there including some with cantilevers and multiple spans.

That would be a heck of a lot more efficient than recalculating reactions, etc using classical structural analysis methods.

DBD

 

[corus]

If you're using a reputable FEA code then there's no need to verify the reaction force distribution other than to check your input by comparing the total load with the total reaction force.
The idea of FE is that you can do calculations accurately and quickly. If you're re-doing the calculation by hand, then there's not much point.

corus

 

[HemiBuell]

I disagree Corus. In my brief FEA work I always felt some supporting information must be provided. A simple hand calculation to verify deflections is easy to do. I always felt confident in my design after I completed some sort of FEA, simple calculation and also a controlled lab experiment.

This might also pertain to the safety factor being used and also the application. FEA and a safety factor of 5 might negate the need for calculations. But the risk of human life or large amounts of money needs verification.

 

[mrMikee]

All good software including FEA will generally do what you tell it to do. But that's also the problem in that you need to make a model relevant to what you need to solve. In my opinion it is really a confidence builder to see a new program duplicate known results, at least for me. This can be in the form of hand calcs, example problems, solutions from textbooks, etc. You need to be able to recognize when things look right and when they go wrong, because sometimes they will go wrong.

A book that has a fairly complete set of beam tables that might help is the "Design of Welded Structures" by Blodgett. It is clearly a design book and NOT a structural analysis book, but it is a good reference that most structural engineers should have.

-Mike

 

[JStephen]

With a normal beam problem, you take the loads, look in beam tables, find equations for deflections, and calculate deflections, slope, etc.

With statically indeterminate problem, you can't do this because you don't know some of the loads. But, once you have analyzed it with the FEM/ structural software, you DO know the loads- take those loads, calculate deflections, slopes, shearing forces, etc. The "check" is then whether your slopes are uniform at fixed connection points, etc. IE, it's much easier to show your answers are right than to independently FIND the answers, and that's the approach I would take.