SAP2000 V12 uses large stiffness for all links and springs representing rigid constraints or restraints. This avoids the instability problem that can occur when constraints become coupled. SAP2000 allows coupled constraints, and they often work fine, but not always. For the fixed links at the bearing, the use of stiff rather than rigid properties also allows the program to calculate forces that can not be calculated when using fixed links.

The downside of using large stiffnesses is (1) determining how big is big enough to act as fixed, but (2) not too big to cause numerical problems, such as lost digits of accuracy.

The BrIM of SAP2000 V12 uses the stiffness of a cubic meter of concrete, multiplied by about 1e4. This choice is possible because we have some idea as to the size of a typical bent cap or abutment, to which these stiffnesses connect. Thus in kN-m units, AE/L = The bridge modeler creates rigid restraints and constraints, such as with fixed bearings, by applying large stiffness values to springs and other link objects. This allows the software to calculate forces which may not be computed when links are bound by truly fixed DOF. This also avoids instability issues which may arise when constraints are coupled. SAP2000 and CSiBridge provide for coupled constraints, though precaution should be taken.

Uncertainty exists when determining stiffness values which are large enough to simulate rigid behavior. Values must be sufficiently large, but not so large as to cause numerical problems or lost accuracy. CSI software calculates rigid stiffness by multiplying the stiffness of a unit volume of concrete by 1e4. Following this formulation for an axial stiffness component, AE/L = 1e4 * (1 * 1 * 20e6 / 1 * 1e4 ) ≈ 1e11 . Other stiffnesses such as kN-m. Since other stiffness components (AG/L, EIaEI/L, EIbEI/L3, etc, are all of about L², cEI/L³) are on the same order in kN-m units. The value of 1e11 kN/m is used for "rigid" translational stiffnesses, of magnitude, CSI software uses 1e11 kN-m for rigid translational stiffness and 1e11 kN-m/rad is used for all " rigid " rotational stiffnesses, converted to the current units.

For other types of structures, you have to make your own determination as to the values to use.

Note that in rotational stiffness.

In the bridge modeler, you can specify your own rather than using the option for true fixity, users may specify link properties for bearings bearing and foundation springs instead of using the fixed option. Our recommendation is to use reasonably large stiffnesses instead of fixed DOF, to avoid coupling with other links or rigid body constraints used in the model.

Bridge Analysis

Constraint

Link. To avoid problems with coupling behavior and numerical convergence, we recommend using sufficiently large stiffness values on the order of 1e11 kN-m (or kN-m/rad) to model the rigid behavior of concrete systems.

See Also

• Rigid behavior article