1. Why Elastomeric Bearings?
In the beginning, bridges were built with materials like stone or timber. The nature of those structures made it possible to place them directly into the supporting elements or even the soil itself. Furthermore, there was not the awareness and the knowledge about structural seismic performance that we have today. With new and specialized materials and the need to protect the structures from events like earthquakes, structural bearings have begun, and there are currently many options for different types of bridges.
Elastomeric bearings are frequently used elements of all structural bearings to support concrete superstructures and transmit the loads to the substructures. This type of bearing has also shown adequate behavior in other types of materials and types of structures.
Figure 1. Elastomeric bearing pad in a concrete bridge
The design of elastomeric bearings deals with the equilibrium between having sufficient stiffness that can withstand the imposed vertical loads and enough flexibility to allow for the expected deformations. The stiffness and flexibility requirements are enhanced with steel plates and rubber, respectively. Then, elastomeric bearings can either be plain or reinforced with internal steel plates.
Figure 2. Plain (left) and reinforced (right) elastomeric bearing pads (Dacheng Rubber Co., Ltd. catalog)
As reference values for proper use, reinforced elastomeric bearings can usually be used for (vertical) loads up to 3500 kN, translations up to 100 mm, rotations up to 0,04 radians (for typical bending behavior), and have a low initial and maintenance cost (AISI and NSBA, 1996).
2. The Need for Including Elastomeric Bearings in the Structural Model
Figure 3. Bridge support drawing and structural model in midas Civil
In terms of the required information for design, it makes perfect sense that we need to calculate the expected deformations of the bearing because they are related to stiffness/flexibility, as stated before. Thanks to the advanced computer software for structural analysis and design of bridges, such as midas Civil, it is advisable to include the stiffness of the bearings in the finite element model to ease up the iteration process and take advantage of the design capabilities.
For bridges where the structural analysis must include both the superstructure and substructure, the inclusion of the bearing properties is natural. The model is usually employed for seismic analysis, where the flexibilization effect of the elastomers (whether they are or not dampers) is beneficial for the reduction of seismic force to be resisted by the substructure, especially if the bridge supports are rigid. A helpful comparison of an actual bridge modeled with and without elastomeric bearings by Akogul and Celik (2008) proved this effect and even found that it may not be beneficial for cases where supports have low lateral stiffness compared to the bearings.
An additional reason to include the bearings stiffnesses in the model is that the program's displacements can be used to define the expansion joint sizes.
3. Stiffness of Elastomeric Bearings
One can quickly determine stiffness expressions for the elastomeric bearings with the help of Solid Mechanics. Still, there are variables where we do not have analytical expressions yet, primarily due to the inherent nonlinear behavior of the rubber. Still, some empirical relations have proven to be accurate for bridge design.
International codes usually have design methods that include those factors, and the stiffnesses can be derived. The following are references to the clauses of some of those international codes:
The only standard that explicitly includes the expressions for the elastomeric bearing stiffnesses from the previous is the Australian standard (clause 12.7). The expressions shown in this article for rectangular bearings are from this code.
Figure 4. Strains in a Steel Reinforced Elastomeric Bearing (AISI and NSBA, 1996)
Compression stiffness equation
Rotational stiffness equation
4. Tips for Modeling of Elastomeric Bearings for Bridges
Here is a list of tips for the appropriate modeling of elastomeric bearings for bridges:
Figure 5. Elastomeric bearing stiffness input in midas Civil according to this article's variables
Figure 6. Usage of elastic links and other elements in midas Civil for structural elastomeric bearing connection