Modeling elastomeric Bearings 1

[Dor4oSokol]

Hi friends

I am tying modeling an elastomeric bearing for horizontal forces simulation.

I am usin the following formulae:
a-Dimension of bearing in direction paralel to beam axis
b-Dimension of bearing in direction Normal to beam axis
h- total hight of bearing
hc-total height of elastomer layers
Ec-Modulus for concrete used in modeling
G-* Modulus of the elastomer
Ic- Second moment of inertia for concrete section having hight h wich have same properties as bearing

Ic=(G*a*b*h^3)/(3*hc*Ec)
ac=Sqrt4(12*Ic)-The dimension of square section for member used in model.
As final the member of concrete section with Ec ac*ac*h
is used to model bearing for horizontal forces.

Is this O'k?

Also is there any idea how to model elastomeric bearings in SAP2000???(both horizontal and vertical actions)
Any ideas will be helpful.

Thanks to all of you

Dor4o Sokol

 

[Dinosaur]

Let's take it step by step;

The force to displace an elastomeric pad one unit is . . .

F = G x A / h

where G is the shear modulus (psi)
A is the plan area of the pad (sq in)
h is the height of the elastomer without shims (in)
F would then be in (lb/in)

Using a vertically oriented beam element fixed at one end and pinned at the other the force required to produce a unit displacement is . . .

F = 3 x Ec x I* / h^3

where Ec is the modulus of elasticity of concrete (psi)
I* is the unknown modified moment of inertia of your special bearing element (in^4)
h is the bearing height (in)

By substitution you can solve for the modified moment of inertia for your element as . . .

I* = G x A x h^2 / (3 x Ec)

Use a circular section when using this element because the pad has equal stiffness for longitudinal and transverse movement. If you know the vertical stiffness of the pad, you can use a similar method to determine the modified area (A*) of this beam. The important trick is to make sure you pin one end of your special beam element so only negligable moment is introduced into the cap or beam. This is the method I advocated in a project two years past.

After looking at your formula and mine, they appear the same except yours allows you to use a bearing depth equal to the overall depth of the pad which may silence the most eager critics. Good Luck.

 

[zliazmei]

Good question

I agree with both of you.
Think that as here is A question for horizontal forces, Dor40's decision is more applicapable.

Just one problem.
This formulea is based on the asumption that bearing is square or circular.
If it is not I would try to find not I only Ec.
Lets explain.
1/Paralel to axis
I1=a^3*b/12
E1=(Ga*b*h^3)/(3*hc*I1)
2/Normal to the axis
I2=a*b^3/12
E2=(Ga*b*h^3)/(3*hc*I2)

Ofcourse this will require software that is posible to use orthortopic matherial.
In SAP2000 it is posible to be done.
Using modifivation factor for A the vertical forces think are not a problem.

Zlia Zmei

 

[ludvik]

Even easier than using a beam element with stiffness properties equal to your bearing is to use a two noded spring element. Simply assign the actual bearing stiffnesses to the element and you are done.(Note that in SAP2000, two noded springs are called NLLink elements (non-linear link) because the element has the capacity for both linear and non linear properties).

I strongly advocate inputing the stiffness directly into the NLLink element on the grounds that it eliminates one level of calculation, and is thus one less potential bug. (Bugs are my sworn enemy).

btw: Has anyone come across any technical papers for modeling bearings? Bearings have an important determining role in the seismic behavior of a bridge, yet frequently bearing models are crude.

Particularly of interest is how to model non-linear bearing behavior in a linear model (a response spectrum analysis). For example, what is the best way to model an expansion bearing which relies on teflon coated sliding surfaces?

 

[Dor4oSokol]

Thanks All,

About bearings with different dimensions:
If k=b/a then
ac=sqrt4(12Ic/k) and bc=ac*k

Other question:
Has anybody tryed to model bearing with solid elements. Mean al steel and elastomeric layers with their properties?
If yes any comments will be efficient.

Thanks

 

[mxa23]

On another note, I'm modeling a multi-span bridge for seismic using SEISAB which will have elastomeric bearing pads on each abutment. This will be modeled using spring constants. Does anyone know how to calculate the stiffness for a bearing pad?

thanks!

 

[Dinosaur]

mxa23,

My post back in April discusses how to compute the stiffness of an elastomeric pad. F = G x A / h

Good Luck