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Replies

  • skipper

    Member • Jul 22, 2009

    Ahem; there are several ways to approach this. One is to get a good engineering calc, like a HP say, and download a public domain copy of the software for beam calculations.

    You need the partial diff for the internal variation in the modulus, along the beam length...?
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  • witamserdecznie

    Member • Jul 23, 2009

    I am only interested in hand calculations. Calculating this in a software would be easy and without any pleasure - that is not a point.

    I was thinking about tackling this using double integration for varies spans, that would give numerous of integration constants but by recognizing boundary conditions should be possible to be solved. However I am not sure what would be the steps of calculations and how to combine it all together. Therefore any help here will be appriciated (calculations step by step preferred).

    If you have other ideas how to calculate it using double integration then please write below.
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  • skipper

    Member • Jul 24, 2009

    Have you looked at the differential solutions that correspond to Bernoulli-Euler equations? Can you extrapolate on the double integral formula you're looking for?
    What's being integrated and inside which bounds?
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  • witamserdecznie

    Member • Jul 24, 2009

    that is where my problem is, I looked at Bernoulli-Euler equations but do not know how to apply it to continuous beams. That is what I would like to find out.

    on the Internet all I could find were single span examples and all continuous beams are calculated by Macaulay's method (which is simplified Bernoulli-Euler method and is excellent but applies only to beams of constant stiffness).

    Do you know how to calculate this example by using Bernoulli-Euler?
    [​IMG]
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  • skipper

    Member • Jul 24, 2009

    That eqn is for a beam with uniform stiffness/elasticity. The PDE version is more general.
    Are you familiar with the various methods used for structural analysis? I haven't done much myself, but I understand inertial moments and loading problems in general (EE for example uses a very similar approach, but different physical constructions of resistance and impedance).

    You might want to look at finite element analysis. I think the important thing is to restrict the problem to one that fits a standard solution (always approximate).

    Mathematical methods for determining the beam forces (internal forces of the beam and the forces that are imposed on the beam support) include the "<a href="https://en.wikipedia.org/wiki/Moment_distribution_method" target="_blank" rel="nofollow noopener noreferrer">Moment Distribution Method</a>", the force or <a href="https://en.wikipedia.org/wiki/Flexibility_method" target="_blank" rel="nofollow noopener noreferrer">Flexibility Method</a> and the <a href="https://en.wikipedia.org/wiki/Direct_stiffness_method" target="_blank" rel="nofollow noopener noreferrer">Direct Stiffness Method</a>.
    <a href="https://en.wikipedia.org/wiki/Beam_%28structure%29" target="_blank" rel="nofollow noopener noreferrer">Beam %28Structure%29</a>
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  • jhbalaji

    Member • Jul 26, 2009

    skipper
    That eqn is for a beam with uniform stiffness/elasticity. The PDE version is more general.
    Are you familiar with the various methods used for structural analysis? I haven't done much myself, but I understand inertial moments and loading problems in general (EE for example uses a very similar approach, but different physical constructions of resistance and impedance).

    You might want to look at finite element analysis. I think the important thing is to restrict the problem to one that fits a standard solution (always approximate).

    <a href="https://en.wikipedia.org/wiki/Beam_%28structure%29" target="_blank" rel="nofollow noopener noreferrer">Beam %28Structure%29</a>
    Thanks for this mate..
    Now only know about it...
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  • witamserdecznie

    Member • Jul 30, 2009

    jhbalaji, I have seen your comments (my favourite: too long, not reading) and you are a very good example of a word "useless".

    improve
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  • witamserdecznie

    Member • Jul 30, 2009

    skipper,

    I am familiar with few of those methods and most of them are not very practical. I am interested in methods like PDE. But my main question here would be how to apply this method in continuous beam to calculate deflection??

    I do not want to go into finite element analysis as that is not an appropriate method for this rank of problem.

    The methods you have listed under "for determining forces in beam" are to calculate reactions etc. I am already using moment distribution method to calculate those and although iterative it works very well. So I am not interested in forces/reactions. I am interested in calculating deflection of continuous beams.

    Any one can solve the above problem using partial differential equation?
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