Defining Connector Spring Stiffness

Using the spring connection between the superstructure and the substructure or at the bottom of columns gives you the flexibility to model simple or complex connections or boundary conditions. The abstract keyword connection types, e.g., pin, free, etc., provide for typical connections and are usually adequate for most cases. However, there are situations in which more control is needed to specify connections. For example, if you use special bearings between the superstructure and an abutment, and the stiffness might affect the bridge design, or the stiffness of a pile footing might be an important contribution, selecting a spring connection allows you to include the stiffness in the analysis model.

Another instance you might consider using a spring connection type is if your bridge contains monolithic or diaphragm wall abutments. Although CIP RC/PT Girder does not directly model these abutment types, you can model them by reducing the stiffness of the abutment/soil/foundation system to a 3-by-3 stiffness matrix at the top of the wall and using it as the connection spring constants.

Perform the following steps to define the connector spring stiffness:

Grid Definitions

• Kh: Enter the horizontal translational degree-of-freedom.

• Kv: Enter the vertical translational degree-of-freedom.

• Kr: Enter the rotational degree-of-freedom.

Technical Discussion

The ability to add user-computed stiffness into the analysis model is an important feature for an analysis program like CIP RC/PT Girder. The computation of the stiffness coefficients is done outside of the program and is dependent on a variety of parameters, in addition to how rigorous the calculation needs to be. For example, in some situations it may be adequate to compute just the diagonal coefficients (e.g., Kh-Kh, Kv-Kv, or Kr-Kr) and ignore any coupling effects. In other situations, ignoring the coupling between degrees-of-freedom can effect the accuracy of the results.

If you are using stiffness coefficients to model a bearing connection at an abutment, pier, or span hinge, then part of the stiffness coefficient calculations depend on the number, size, and location of the bearings as well as the material of the bearings. If the springs are used to model a complex pile footing containing battered piles in soft soil, then the stiffness matrix can be complicated to obtain and possess complex couplings.

CIP RC/PT Girder performs the analysis using standard matrix structural analysis techniques: element stiffness and load matrices are formed, summed into the system matrix, and then displacements are obtained by solving the resulting system of equations. Since the solution of the system of equations performs many floating-point operations, the relative size of coefficients in the system stiffness matrix can introduce round-off errors.

Typically, structural analysis stiffness matrices are well-conditioned and solving the system of equations is not a problem although specifying atypical values for element properties, such as a very small or very large moment of inertia, can cause ill-conditioning problems. However, if it is possible to introduce discrete stiffness terms that are computed outside the normal element stiffness formulations, such as using a spring-type connection, then it is possible to cause numerical round-off errors. Be aware that specifying very large stiffness terms (the order of 1015 or greater) or coupling coefficients that are incorrect (in value or in sign) can potentially cause numerical round-off errors.