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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) ≈ 1e11 kN-m. Since other stiffness components (AG/L, aEI/L, bEI/L2, cEI/L3) are on the same order of magnitude, CSI software uses 1e11 kN-m for rigid translational stiffness and 1e11 kN-m/rad for rigid rotational stiffness.

 

In the bridge modeler, rather than using the option for true fixity, users may specify link properties for bearing and foundation springs. 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.

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