> For the complete documentation index, see [llms.txt](https://docs.openbrim.org/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.openbrim.org/templates/openbrimfea/geometry-fea/springs-fea.md).

# Springs \[FEA]

A Spring (also called a link) is a two-node connector element with a defined stiffness in each of six directions, independent of any material or section. Where a node's own DOF values describe a support to ground, a Spring describes a connection **between two points in the model**.

Use it for bearings, isolators, shear keys, expansion-joint restrainers, soil springs alongside a pile, and any connection whose stiffness is known directly as force per unit displacement rather than derived from geometry.

A Spring contributes to the **stiffness matrix** only. It carries no mass and generates no load.

{% hint style="danger" %}
The stiffness columns use the same sign convention as node supports:

Entering **1** does not make a direction rigid; it creates a spring of stiffness 1 force unit per length unit, which for any real structure behaves as free.
{% endhint %}

| Value                 | Meaning                                                  |
| --------------------- | -------------------------------------------------------- |
| **0**                 | **Free** — no connection in that direction (the default) |
| **negative** (use −1) | **Rigid** — the two nodes are tied in that direction     |
| **positive**          | **Elastic spring** of that stiffness                     |

## Geometry

**Node 1 / Node 2:** The two joints the spring connects. These are **connectivity** parameters: they determine what is joined and, with the nodes' positions, the direction the spring acts in.

The two nodes are very often **coincident** — a bearing modelled as a zero-length link between the girder soffit node and the pier-top node. That is the normal arrangement, and it is why **Merge w/Same Loc Node** must usually be turned OFF on those nodes: if they merge, the spring has nothing left to connect and its stiffness disappears from the model with no warning.

The spring acts in **global** directions. Define together with the six stiffness values; a spring with both nodes set but every stiffness at 0 connects nothing.

**Tx / Ty / Tz:** Translational stiffness along each global axis, in force per unit length.

**Rx / Ry / Rz:** Rotational stiffness about each global axis, in moment per unit angle.

*Engineering influence, common to all six.* Each direction is independent — this is a diagonal stiffness, not a coupled one. Increasing a stiffness transfers more force through the connection and reduces relative movement between the two nodes; decreasing it toward zero lets them move independently and sheds that load elsewhere. What matters is the value **relative to** the members either side: a bearing stiffness that behaves as nearly rigid under a flexible pier is nearly free under a stiff one, so a number copied from another project without checking that ratio can behave completely differently.

A value of 0 means no connection in that direction — exactly how a guided bearing is modelled: rigid across the bearing line, free along it. Setting every direction rigid turns the spring into a full moment connection and defeats the purpose of modelling a bearing at all.

Very large positive values are a poor way to express "rigid": they add terms orders of magnitude larger than the surrounding structure, degrade conditioning, and produce noisy reactions and spurious high-frequency modes. Use a negative value.

Results sensitive to these: the force transferred through the connection, the distribution of lateral load between substructure elements, and — because a soft link lengthens periods — the whole dynamic response of an isolated structure.

**Group:** The FE Group used for construction-stage activation and selection. A spring whose group is inactive in a stage does not exist in that stage, which is how a temporary bearing or a restrainer installed partway through erection is modelled.

## Gap

**Tx Gap / Ty Gap / Tz Gap:** A translational gap, in length units, that must close before the spring engages in that direction.

**Rx Gap / Ry Gap / Rz Gap:** A rotational gap, in angle units, before the rotational spring engages.

*Engineering influence.* A gap makes the connection **nonlinear and one-sided**: the nodes move freely relative to one another until the gap closes, then the stiffness applies. This is the natural model for a shear key with a construction clearance, an expansion joint that closes under thermal contraction, or a restrainer cable that acts only once slack is taken up. Zero (the default) means the spring engages immediately.

Gaps are honoured only in a **nonlinear** analysis. In a linear static, modal or response-spectrum case the connection is linearized per the Stiffness Option settings and the gap has no effect — which is why a shear key entered with a gap can appear to carry load from the very first increment of a linear run.

Related to this, one-sided behaviour is expressed through the stiffness value itself rather than the gap column: a bracketed stiffness `[value]` denotes a **tension-only** (hook) spring and `[-value]` a **compression-only** (gap) spring. A shear key that must only push is entered as a negative-bracketed stiffness, not as a plain number with a gap.

Increasing a gap delays engagement and increases relative movement before load transfers. Results sensitive to it: the order in which restraints engage, displacements at low load, and any envelope spanning load levels either side of closure.

## Stiffness Option

These twelve columns decide what stiffness a **nonlinear** spring contributes when the analysis being run is **linear**. A linear static, modal, response-spectrum or non-FNA time-history case cannot represent gapping or a one-sided link, so it must substitute a constant stiffness.

**Tx / Ty / Tz / Rx / Ry / Rz Linear Mode:**

| Mode                    | Meaning                                                        |
| ----------------------- | -------------------------------------------------------------- |
| **Nonlinear** (default) | tangent/initial stiffness taken from the current state         |
| **Initial Stiffness**   | always the slope of the nonlinear curve at zero displacement   |
| **Effective Stiffness** | the constant value typed in the matching Eff. Stiffness column |

**Tx / Ty / Tz Eff. Stiffness** and **Rx / Ry / Rz Eff. Stiffness:** The constant stiffness used when that direction's Linear Mode is Effective Stiffness. Ignored in the other two modes.

*Engineering influence.* This is where a seismic isolator's design assumption is expressed. **Initial Stiffness** gives small-amplitude behaviour — shorter periods, higher spectral accelerations — appropriate for serviceability or wind-vibration checks. **Effective Stiffness** lets you enter the secant stiffness at the expected design displacement, which is what isolation design normally requires; it lengthens periods, generally lowers force demand, and increases displacement demand. The two can differ by a factor of several, and neither is universally conservative.

An Effective Stiffness of zero removes the connection entirely from every linear analysis, which commonly makes a linear case unstable on a model whose nonlinear case solves without complaint.

{% hint style="warning" %}
The twelve Stiffness Option columns and the 6×6 Stiffness Matrix are **not declared in the object type**. They remain writable from the agent API and `set_parameter` — those resolve any field the object exposes in its sheet — but they carry no unit category, no dropdown option list, and no authorability from a library template. Scripted writes bypass the sheet's own conversion, so a Linear Mode must be given as its raw number (0 Nonlinear, 1 Initial Stiffness, 2 Effective Stiffness).
{% endhint %}

## Settings

**Use Nonlinear Penalty:** Whether the nonlinear penalty formulation enforces this spring's nonlinear conditions. Defaults to YES. It changes **how** the condition is enforced numerically, not what the condition is; turning it off is a convergence-troubleshooting measure for a nonlinear case that will not converge, not a modelling decision.

## Stiffness Matrix

**6x6 Stiffness Matrix:** A full 6×6 stiffness matrix for the connection, edited in its own sub-sheet, for links whose behaviour is **coupled** between directions.

*Engineering influence.* The six values above form only the diagonal; they cannot express that a horizontal translation also produces a moment, as an eccentric or extended bearing does. A matrix produced by an **Equivalent Stiffness** point, or supplied by a bearing manufacturer, is normally full. It should be symmetric and positive-definite; one that is not can make the global system indefinite and cause the solve to fail. Leave empty when the diagonal values suffice.

## Verification

* Check the spring's force and the relative displacement between its two nodes; their ratio must return the stiffness you entered. This is the fastest way to catch a direction entered as 1 when −1 was meant, or a spring whose nodes were merged away.
* Confirm the two nodes still exist separately in the assembled model. If a coincident pair merged, the spring is inert.
* Check that a direction left at 0 shows genuine relative movement; if it does not, something else is connecting the nodes.
* For a guided bearing, confirm the reaction appears only in the restrained direction.
* For a gap, run the nonlinear case either side of closure and confirm engagement at the right relative displacement.
* Run a modal analysis on an isolated structure and confirm the isolated period matches a hand calculation from the effective stiffness and the supported mass.
* Compare a single bearing against a hand calculation: force = stiffness × relative displacement.

## Common mistakes

* **Leaving Merge w/Same Loc Node ON at a zero-length link**, merging the two nodes and silently deleting the connection.
* **Entering 1 to mean rigid**, producing an essentially free direction.
* **Using a huge stiffness instead of −1**, degrading matrix conditioning.
* **Making every direction rigid**, turning a bearing into a moment connection that attracts load the real bearing cannot carry.
* **Entering gaps and running a linear analysis**, where they are ignored.
* **Leaving Linear Mode at Nonlinear for an isolator** and reading modal periods based on the small-amplitude stiffness rather than the design displacement.
* **Copying bearing stiffnesses between projects** without checking them against the substructure stiffness they sit on.
* **Setting Effective Stiffness to zero**, removing the link from every linear analysis.


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