Beam formulas on elastic foundation 5

[mte12]

Has anyone used the formulas in Roark's for beams on elastic foundation, Table 8.5.
Case 2 in Table 8.5, I presume can be used for a beam on ground, without restraints, and evenly loaded with a distributed load.

For some reason, the formulas don't seem to give the same answer as a check in a computer model.

The beam is very stiff, I'm sure the response depends on this, the formulas do have the parameter for inertia, but still getting unexpected results.

Is someone has used and verified, please post a snapshot with sample data to follow.

 

[mte12]

Thanks centondollar, do you remember the literature which suggest increasing stiffness towards the edges?

 

[centondollar]

Here is some reading from structure magazine

https://www.structuremag.org/?p=7840

This article describes the concept of making a three-dimensional non-linear soil model (soil as solid elements, slab/footing as plate or beam elements) and then iterating the subgrade modulus in a separate linear discrete spring model until deflections and contact pressures are nearly identical (error smaller than some tolerance):

https://geotechsimulation.com/2018/02/12/subgrade-reaction-modulus-of-footings/

 

[IDS]

For in-practice analysis and design (as opposed to academic research) a 3D FEA is overkill, and with current computer hardware and software a beam on springs analysis is an over-simplification that introduces significant uncertainty in the results, for little or no saving in time.

A 2D plane strain FEA including the footing and the supporting soil allows the soil properties to be determined from provided basic soil parameters and removes the inaccuracies due to edge effects inherent in a beam on springs model.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[mte12]

OK thanks but please note that I do not have access to FEA software.

 

[Denial]

I feel the need to point out that even if never used for beams on elastic foundations (because of limitations in the Winkler representation of the foundation), the Winkler-style beam-on-elastic-foundation mathematical model gives (by mathematical analogy) an EXACT model for the stresses and deflections in an axisymmetric cylinder subjected to axisymmetric radial loadings.[ ] Very useful for pipes and circular tanks under pressure loadings.

 

[centondollar]

A 2D plane strain FEA including the footing and the supporting soil allows the soil properties to be determined from provided basic soil parameters and removes the inaccuracies due to edge effects inherent in a beam on springs model.

What you describe is a simplification of a full 3D model, which is also unnecessary given modern computing power. If it is also an elastic solution (parameters of the soil being e.g., elastic modulus, shear modulus and poisson's ratio), the accuracy is unlikely to be good. Also, although edge effects of the spring model are removed in a 2D or 3D model, there will still be edge-effects in such models unless the soil basin (vertical and horizontal extent of the soil in a 2D model) is extremely large.

 

[IDS]

centondollar - The point is that a 2D analysis addresses the significant over-simplifications in a beam and spring model, and can be set up and analysed in much the same time as a beam and spring model. Non-linear soil behaviour can be included just as easily in a 2D analysis as 3D, and allowance for sliding at the soil-structure interface can also be included when it is significant (often it isn't). Yes, the width and depth of the soil model needs to be large enough to make edge effects insignificant, but how is that a problem?

There are of course times when a 3D analysis will be required, but for any problem where a beam and spring model is considered suitable, a 2D plane strain FEA can give more reliable results with less need for empirical adjustment of soil properties depending on the size of the footing.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[centondollar]

One significant problem with a 2D soil model is that it is suitable only for 2D superstructures, such as simple frames. A 3D model is in most cases the next logical step to take after considering spring models.