Calculations on Statically Indeterminate Beams

[kcarey]

I am a mechanical engineer in Australia, with 4 years Project Engineering experience & a passion for maths. I am currently not working (I just had a bub), & am doing some self study to get my design skills up to scratch.

I am doing a small job for my dad (draftsman), which is basically a statically indeterminate monorail supported from (3)in one case & (5) in another case equi-distanced floor beams. (assume 4 bolt pinned connections at each support. The monorail spans across (4) chain conveyors & will be used to remove any (1) of the drives at any one time. For this reason, I am planning on assuming that the load will act central between (2) of the equi-spaced support beams, which would offer the maximum moment & deflection.

As these are statically indeterminate, I am aware that the thorough way of designing this would be to use the moment-area method or similar, but my question is.....


ie. if you have an arrangement as follows:

V
......................
^ 2 ^ 2 ^

Can you assume a simply supported beam of length 2 with the load acting in the centre, or would you treat the centre support as redundant & design for a length of 4 as an additional safety factor?- the latter would result in a very bulky 1000kg monorail.

What would you do if it was a similar set up only with 5 supports?

Sometimes, I feel that I might be paying too much attention to detail (this is why I am looking for a simple method of calculating this type of loading)

P.S. I know that in this case, I can easily overdesign the I beam, but I need to understand how to calculate it properly first to give me confidence in more critical design. As far as the rest of the design & beam selection goes, I think I'm alright there!

 

[Qshake]

For continuous beams with 3 or more supports, the maximum response will not occur at the midspan of the supported lengths. the maximum deflection and moment will occur at approximately the 6/10 point as measured from the left support. This, of course, assumes that the beam is of constant flexural rigidity.

Incidentally, the moment area method is based on having a moment diagram for which to perform a graphical integration. If you don't have that...you certainly can't get it from the moment area method.

There is nothing wrong with the simple beam assumption as for sizing the member for shear, moment, and deflection. However, this requires that the maximum positive moment is greater than the maximum negative moment for the continous case. That may or may not be the case for your project.

 

[prex]

Why should you discard a support? Are you uncertain of its strength? And if so, why not discarding one of the two others, or even all the three? I see no reason for that: take the supports you have and make sure they are capable of taking the reaction, equal to the load for a moving load
(plus dead weight contributions and deceleration load).
For a continuous beam over equal spans with a single concentrated load the maximum moment (and deflection) is only slightly different from that of two simply supported (unconnected) beams. If I were you I would go for such a simple calculation. Only if you find that a standard beam size is only a little (a few percent) underdesigned, you could refine the calculation to decide whether that beam is usable or not.

prex

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