Stiffness values for Expansion and Fixed Bearing

[Dwaipayan Sharma]

Hi,

I am working on Midas and wondering about the stiffness while defining the expansion and fixed bearing.
I am trying to define them using elastic link and define stiffness for both translation and rotation.

What should I use the stiffness values for both types in general?
SDx SDy SDz & SRx SRy SRz ???

Thanks!

 

[BridgeSmith]

The stiffness of a fixed bearing should be set to the bending stiffness of the anchor bolts over the height over which they can bend.

The stiffness of an expansion bearing should be input as whatever it is.

For elastomeric bearings, it's deformation * shear modulus * plan area of the bearing / total height of the elastomer (bearing height minus combined reinforcement thickness).

For sliding bearings, it's coefficient of friction * vertical reaction.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[centondollar]

Just a note, BridgeSmith:

deformation*shear modulus*plan area / total height gives units [m] * [N/m^2] * [m^2] / [m] = [N], so it cannot be a stiffness value.

Similarly, "friction*reaction" gives a force, which is also not a stiffness parameter. Dividing by some expected lateral deformation "delta_max" (k_lateral = friction*reaction / delta_max) will give a translational stiffness.

 

[BridgeSmith]

deformation*shear modulus*plan area / total height gives units [m] * [N/m^2] * [m^2] / [m] = [N], so it cannot be a stiffness value.

Correct. That formula gives you force for a given deformation. For the stiffness value, the deformation would be dropped out of that equation, and you'd have units of N/m (or in our case, kips/in). We directly calculate the force at the maximum deformation of the pad. Sorry for the confusion.

Similarly, "friction*reaction" gives a force, which is also not a stiffness parameter. Dividing by some expected lateral deformation "delta_max" (k_lateral = friction*reaction / delta_max) will give a translational stiffness.

With a sliding bearing, there is no 'stiffness' to calculate, since the force doesn't change based on the amount of movement. The force is the same for an 1/8" of movement as it is for 3" - still COF*vertical force.

Btw, to the OP - rotational stiffness is typically low, and ignored in the designs we work on, but if you want to calculate it, AASHTO has vertical deformation checks for steel reinforced elastomeric bearings that could be adapted to calculate the resistance to rotation provided by that type of bearing. For a sliding bearing, since stiffness of the components is very high, you'd probably calculate rotational 'stiffness' as a moment due to the eccentricity of the load, as it shifts towards the edge of the bearing plate/sliding plate.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[centondollar]

Right, but then the force is just a binary parameter determining whether or not sliding occurs - that is not what I would characterize as "stiffness".

Interesting discussion nonetheless.

 

[BridgeSmith]

Right, but then the force is just a binary parameter determining whether or not sliding occurs - that is not what I would characterize as "stiffness".

Generally (for bridge bearings, anyway), what is of interest is the force applied to the foundation or substructure, which the foundation or substructure has to resist.

Rod Smith, P.E., The artist formerly known as HotRod10