Deflection of beam check... 4

[Bert2]

Hi,

Its been a while since ive needed to calculate the defelection of a beam, in doing so i have came up with two quite different answers, using Macauleys and the direct deflection equation. calcs attached, any pointers in my errors would be soundly appreciated.

Thanks!

 

[Bert2]

thanks desertfox! great help as always!!!

 

[desertfox]

Hi Bert2

your welcome!

 

[IDS]

Some belated comments on this problem:

- You really need to have an idea of the expected magnitude of deflections to pick up gross errors straight away, but even without that it's obvious that a deflection approaching 1 billion light years is a little on the high side.

- A few minutes entering the deflection formula in a spreadsheet would pick up the error with the sign of the exponents, but that then gives a deflection of 8.3E-18 mm, which is also obviously much too small, being much less than the diameter of an iron atom.

- The E value for steel used in the original calc was in Pa (N/m^2), whereas the load was in KN, so one or the other needs to be adjusted. This was obviously picked up in later iterations, but no-one mentioned it. Correcting this brings the deflection up to 8.3E-15 mm, but this is still obviously much too small.

- I don't know how the units of mm^4 for deflection in the original calc were arrived at, but this should have rung alarm bells, because it should have been in m (as the span length) and not raised to the fourth power.

- I don't agree that Macaulay's Method is inapplicable to this problem. With a uniform load over the full length it reduces to the integration method. It doesn't provide any advantage for this case, but checking this sort of simple example does provide a quick check that the method is being applied properly.

- I have recently posted a spreadsheet for analysing continuous beams using Macaulay's Method on my blog. It now allows for single or multi-span beams with cantilevers and spring supports (translation and/or rotation) and optionally shear deflection. There are six posts on the subject, the first one (including a link to the latest version of the spreadsheet) being:

http://newtonexcelbach.wordpress.com/2011/11/12/beam-actions-and-deflections-by-macaulays-method/

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/