# Constraints

Constraints are where a condition is applied to a degree of freedom in the model. They may be defined as:

Constraints can all be represented as constraints equations:

## Restraints

Restraints specify degrees of freedom that are restrained from movement such that $u_{i} = 0$.

In GSA, restraints can be applied in **Node properties**:

If using staged analysis, restraints can be defined differently for each stage. See the references entry on generalised restraints entry for further guidance on restraints that move between stages.

## Settlements

Settlements are when a degree of freedom is forced into a displaced position such that $u_{i} = settlement$.

Settlements can be applied to any restrained node by applying a settlement load. A different settlement can be defined for each load case.

## Joints

Joints describe the condition where two degrees of freedom in the model are linked in a given direction such that $u_{si} = u_{mi}$.

They relate the displacement or force at the *constrained degree of freedom,* ($s$) to the *primary degree of freedom* ($m$).

Note:Joints are an artificial feature and might not give an equilibrium condition if the nodes are not coincident or have the same axes.

## Rigid constraints

Rigid constraints are similar to joints in that it relates the constrained degrees of freedom to the primary degree of freedom. However, unlike joints, they are a set of constraint equations that maintain equilibrium.

For a rigid constraint in the $x-y$ plane, the equations are:

Rigid constraints can be applied in all directions or applied to a specified plane.

- The primary node can be restrained
*or*constrained by another constraint. - The constrained node
*cannot*be restrained or be a constrained by another constraint. - A rigid constraint can be considered as a rigid body or rigid plane, depending on the type of its property.

The rigid constraint can have the following properties:

Plane | Properties |
---|---|

All | Rigid constraint applied to all directions (a rigid body) |

XY plane | Rigid constraint applied to XY plane only (a rigid plane) |

YZ plane | Rigid constraint applied to YZ plane only (a rigid plane) |

ZX plane | Rigid constraint applied to ZX plane only (a rigid plane) |

Pin all | Same as 'All', except that the constrained node moment will not be transferred to the primary node. |

Pin XY plane | Same as 'XY plane', except that the constrained node moment will not be transferred to the primary node. |

Pin YZ plane | Same as 'YZ plane', except that the constrained node moment will not be transferred to the primary node. |

Pin ZX plane | Same as 'ZX plane', except that the constrained node moment will not be transferred to the primary node. |