Best Practices for defining Restraints and Constraints in SAP2000 Structural Models

Properly defining constraints and restraints is crucial to ensure accurate structural analysis. This article discusses the risks of assigning multiple forms of restraint to the same joint, explains how links with “fixed” degrees of freedom (DOFs) work in practice, and proposes robust alternatives to avoid numerical inconsistencies. 

1. Avoid mixing Constraints and Restraints

It is not recommended that restrained degrees of freedom also be constrained, although it is permitted. Similarly, it is not recommended that a given degree of freedom be included in more than one constraint. These overlaps can lead to: 

• Exclusion of reaction components: When a joint is subject to a constraint (e.g., a rigid diaphragm) and also has a defined restraint at the same DOF, SAP2000 may ignore contributions to the reaction from joints connected by constraints. 
• Redundancy consequences: Overlapping constraints can create conflicting equations in the stiffness matrix, adversely affecting numerical stability. 
• Potential impact on dynamic analysis: Modal results (frequencies, mode shapes) can be distorted by contradictory mass and stiffness assignments. 

Recommendation: Each degree of freedom should be controlled by at most one restraint or constraint, regardless of whether it is a rigid diaphragm constraint, a rigid body constraint, a support restraint, or a “Fixed” link. 

2. Links with Fixed Degrees of Freedom act as Constraints

As discussed in the article Fixed DOF in Links, any link defined with fixed DOFs is internally treated as a constraint. Therefore, connecting such a link to joints that already have any kind of restraint or constraint—for example: 

• Restraints 
• Other constraints 
• Other links with fixed DOFs 

results in an overlap of constraint equations. Common consequences include: 

• Omission of force components from the constraint in the final reaction output; 
• Failure to apply imposed ground displacements at the supported joints; 
• Complications in obtaining vibration modes. 

3. Alternatives to replace Fixed Degrees of Freedom or Restraints

To prevent redundancy without duplicating constraints or mixing constraints with restraints, you can use: 

a) Non-Fixed Rigid Links 

• Assign large stiffness values (e.g., 1e11 kN/m for translations or 1e11 kN·m/rad for rotations), as suggested in the Rigid behavior article and exemplified in Section 3.3.4 of the SAP2000 Advanced course. 
• Additional Benefits: A high-stiffness link behaves almost rigidly while still allowing output of internal forces. Besides that, its properties can be modified in Staged Construction load cases. 

  

   

b) Elastic Supports (Springs)

• Define joint springs or 1-joint links with suitably high stiffness to simulate fixed supports. 
• Useful Application: When you need to assign constraints to joints that are physically supported, modeling the support as a rigid spring can help avoid mixing constraints and restraints on the same DOF. 

4. Practical Case: How to Substitute a Restraint Connected to a Constraint

problem: Defining a discrete support for a concrete core (modeled with shell elements) to simulate the rotational stiffness of the foundation, without mixing constraints and restraints.

Solution: 

1. Place a joint at the footing’s center of gravity—this can coincide with the core’s centroid if the foundation is centered. 
2. Assign a BODY constraint to all joints at the base of the core plus the newly created joint, ensuring that loads transfer to the support without localized deformations. 
3. At the new joint, assign a Joint Spring with very high translational stiffnesses (e.g., 1e11 kN/m) and the desired rotational stiffness values to simulate the soil’s flexibility under rotation. 

   

    

This approach keeps the model simple with respect to ignoring differential settlements: 

• Translational movements are effectively restrained for all vertical elements (the support is very stiff), 
• While the foundation’s rotational stiffness is still accounted for. 

By using only a single Joint Spring instead of defining a restraint for translations plus another Joint Spring for rotations, you avoid mixing restraints and constraints on the same support joint, which is already constrained by the BODY constraint. 

If you used a restraint to fix translations, you would risk losing reaction data for that core, as explained in Sections 1 and 2 above. 
 

5. Conclusion  

Applying multiple constraints or restraints to the same joint often leads to analysis conflicts, since no degree of freedom should be doubly controlled. A link with “fixed” DOFs is inherently treated as a constraint, so it is essential to ensure it is not applied to joints already restricted by other means. 

Instead of fixing link DOFs outright, it is typically safer to use high stiffness values, or to use rigid joint springs rather than restraints. These practices reduce the likelihood of conflicting constraints and preserve the availability of force output data at the “nearly rigid” connections. 

Seemingly simple situations can produce unexpected results if you assign more than one restriction per joint, for example:  

• A story joint with a rigid diaphragm constraint, connected to a link with “Fixed DOFs,” which can cause issues in modal analysis results. 
• Joints with both restraints and constraints, leading to potential loss of reported reaction forces (both local or “Base Reactions”). 

By avoiding these overlaps, you ensure consistent results, clearer interpretation of reaction forces, and robust dynamic behavior throughout the analysis process.