Beam on a Elastic Foundation

[Pwilliams]

I am using sap 2000 to model a beam on an elastic foundation. My question is how do you model the spring at the end of the beam. The spring force is calculated by calculating the vertical modulus of sub grade reaction using Terzaghi equation, then to obtain the node spring reaction you multiplied the modulus sub grade reaction times the beam width times member length. For the interior spring this is not a problem, but for the end spring the member length is the distance to the next node/spring. Then should the end spring be placed between the end node and the adjacent node or at the end????

 

[Riz]

The spring stiffness is the product of modulus of subgrade reaction and area of soil lumped to the supported joint.
Your calcs seem to be okay, except that if u locate the spring away from the end than u will have a tension built up on the bottom. This might be excessive.
U can do either of the following:
1. Locate springs at the supports only, or;
2. Locate springs at suitable intervals including ends.
Note: if there are no columns at the end than u can not locate spring at that point as cantilever action can not be alleviated.
A PDelta analysis will be more useful.
I am not sure with SAP 2000, but have done the same on Staad.

 

[Pwilliams]

Thanks for your response I appreciate the input. SAP 2000 and STAAD.Pro 2001 have the same capabilities. Both programs have the capabilities of infinite numbers of springs, but this all depends on the speed of your computer. You have pointed out something that I missed in analyzing my model. The P-delta effects will magnify the moment in the column thus in turn magnifying the moment into the foundation. To add more clarification to my original question, the columns are not located at the ends and the springs in the model are spaced 6" apart. The interior spring are calc by lumping the area of soil to the spring, thus 6" times the modulus of sub grade reaction. I still do not feel confident in lumping 6" of soil to the end springs. Should I approach this in the same way as you would in analyzing a finite plate model, by refining the model mesh? I should refine the spacing of the springs to 4" spacing. Then run the model, and compare the deflection to the 6" spaced spring. What are your thoughts on this?

Williams

 

[Riz]

I need more information! What is it supporting? Etc,ETc,ETC. Location of spring is a judgement of various cases but largely depends on what the superstructure is.

 

[ishvaaag]

If I divide the beam in equal segments and inner nodes have spring constant 2 kip/in, I put to end nodes (of equal segments division) 1 kip/in. This I consider accurate enough, for, what is the ability of these models to deliver proper assessment or the soil response?. I don't put the same spring at ends ecause it would result in significantly higher responses than correct if segments are big...but you can make them small.