Solver nodes

In the Tekla Structural Designer Solver View, a solver node represents a point where structural members connect or where loads and supports are applied. Each node has six degrees of freedom (DOF), which define its potential for movement and rotation. These DOFs are defined relative to the node’s own coordinate system, known as the User Coordinate System (UCS). The UCS may align with the global coordinate system, but it can also be rotated to match the orientation of the member or support it's associated with, such as a skewed column or an inclined support.

Fixed degrees of freedom

When one or more of a node's six DOFs are restrained (fixed), the solver view indicates this using specific symbols:

A single arrow pointing in a specific direction indicates a translational fixity. The node is prevented from moving along that axis.
A double arrow around a specific axis indicates a rotational fixity. The node is prevented from rotating about that axis.

The table below outlines the above conventions:


DOF	Symbol
Translationally fixed in Fx, Fy, Fz. Rotationally released: Mx, My, Mz
Translationally fixed: Fx, Fy, Fz Rotationally fixed: Mx, My, Mz

For instructions on how to restrain DOFs, see creating a support

Inclined and rotated UCS

The UCS does not necessarily have to match the global coordinate system, for example:

If you rotate a supported column around its axis, the UCS would rotate to match the column.
If you incline and rotate a support applied to a node, the UCS would also incline and rotate.

Coincident solver nodes

Coincident solver nodes are two or more nodes that occupy the same physical location within the model. These nodes are automatically generated when required to model specific release conditions, allowing for different elements at the same location to behave independently in certain DOFs.

To make these nodes easier to visualize, you can use the Highlight coincident nodes command on the Solver ribbon, as they can be difficult to see without zooming in.

Coincident nodes can be either coupled or uncoupled, depending on their intended function.

Coupled coincident solver nodes

Coupled coincident nodes are constrained to move together in one or more DOFs. This relationship is indicated in the solver view by a dotted triangle symbol above the nodes.

One node is designated as the Leader and the other as the Follower. The Leader/Follower relationship and the specific DOFs that are coupled are detailed in the node properties.


Solver node	Tooltip	Node properties
Leader
Follower

A common application for coupled coincident nodes is to model a specific end release, such as a vertical load release on an A-brace or V-brace. In such a scenario, the nodes are coupled in the global X and Y directions, allowing them to move together under lateral loads, but they are uncoupled in the global Z direction, allowing them to move independently under vertical loads.

Coupled Coincident Node Example:

Consider the following ‘A brace’ example. Only one of the brace pairs (the highlighted pair) has had a vertical release applied to end 2 as shown below.

After analysing the model, if you open a Solver View, and click Highlight coincident nodes on the ribbon, a single pair of the coincident nodes are identified at the point where the vertical load release was applied.

Zooming in, by highlighting one of the coincident nodes you can see that they are coupled and a leader/follower relationship has been established.

By switching to a results view and displaying the deflections you can see:

Under lateral loading, because solver node 163 is coupled to solver node 157 in the global X and Y directions, the two nodes and the elements connected to them move together.
Under vertical loading, because solver node 163 is not coupled to solver node 157 in the global Z direction, the two nodes and elements connected to them move independently.

Uncoupled coincident solver nodes

Uncoupled coincident nodes are not linked by a Leader/Follower relationship, allowing them to move independently in all DOFs. This is used to model a disconnected or discontinuous connection between adjacent members, such as a Disconnected wall panel edge connected to a Fixed wall panel.

The solver view uses a V-shaped symbol to indicate uncoupled coincident nodes.

The tooltip for these nodes simply provides their coordinates, as there is no Leader/Follower relationship to display. The nodes at the disconnected edge of the wall panels are free to move independently, as confirmed by the deflected shape in the results view.

Coincident Solver Node Example:

Consider the following core wall example with a wind load applied in global X as shown below:

In a Review View, you can use the Show/Alter State> Releases command to set one of the edges as Disconnected.

After analysing the model, if you open a Solver View, and click Highlight coincident nodes on the ribbon, all of the coincident nodes are identified.

Zooming in, you would see that the coincident nodes are uncoupled as no leader/follower relationship is required at a disconnected edge.

In a Results View, the deflected shape for the wind in X loadcase confirms that the solver nodes move independently at the disconnected edge.

Uncoupled coincident solver nodes with zero-length 1D elements

A third type of coincident node configuration involves uncoupled nodes that are linked by a zero-length 1D element.

This type of 1D element is represented in the solver view by an inclined line extending from the coincident nodes.

The properties of this element, including its local coordinate system and rotational stiffness values, can be reviewed in the Properties window.

Zero-length 1D elements are currently used to model:

A pinned wall panel edge connected to a fixed wall panel

This element is axially rigid, preventing translational movement between the nodes. By default, the link’s local Y-axis is aligned with the wall edge, and its rotational stiffness about this axis is set to zero to represent the pinned condition. This provides a superior solution for a pinned connection, as it can model the release regardless of the edge’s orientation. This is in contrast to the Leader/Follower relationship, which is limited to global axes.
A hinge joint along a slab edge

This element has a rotational release about Y only, which can either be free or be assigned a stiffness.
A vertical sliding joint along a slab edge

This element is axially rigid in the X and Y direction, but released or sprung in the Z direction. Rotationally it can either be free or assigned a stiffness about X and Y.

Pinned Wall Edge Example:

This example uses the same core wall with a wind load applied in global X as the uncoupled coincident solver nodes example in the previous section:

In a Review View, the Show/Alter State> Releases command is used to set one of the edges as Pinned.

After analyzing the model, if you open a Solver View, and click Highlight coincident nodes on the ribbon, the coincident nodes are identified once again.

Note: To aid visualization the opacity of Solver 2D Elements has been reduced in Settings>Scene>Colors.

Zooming in, you would once again see that the coincident nodes are uncoupled. But this time a zero-length solver element is also present.

When the solver element is selected, its properties can be reviewed.

The XYZ coordinate system of the 1D solver element (the link) is determined by the pinned wall edge. When 2D Elements > Local Axes are enabled in Scene Content, you can observe that the local y (green) axes of the 2D elements align with this edge. Consequently, the 1D solver element’s Y direction also follows the edge, while the X direction remains perpendicular within the wall plane and the Z direction is normal to the wall.

The edge is pinned, which is why the link’s rotational stiffness in Y direction is set to zero, while the rotational stiffness in X and Z is rigid.

In a Results View, the deflected shape for the wind in X loadcase confirms that the edge is pinned.

Slab Edge Hinge Joint Example:

This example consists of two walls and a flat slab. A uniform downwards load acts on the slab.

In a Review View, the Show/Alter State> Releases command is used to set one of the slab edges as a Hinge joint.

Assuming the option to mesh slabs in 3D analysis has not been selected, after analysis you would proceed as follows in order to see the coincident solver nodes and zero-length 1D elements:

Open a Sub Model view and set it to a Solver View regime.
In the Solver ribbon set the Method to FE chase-down.

If the option to mesh slabs in 3D analysis has been selected, after analysis you could proceed as follows instead:

Open a Structural view and set it to a Solver View regime.
In the Solver ribbon set the Method to the 3D analysis type that has been performed.

The quickest way to then locate the coincident nodes is to click Highlight coincident nodes on the ribbon.

Note: To aid visualization the opacity of Solver 2D Elements has been reduced in Settings>Scene>Colors.

Zooming in, (and switching off the 2D elements for clarity) you would see the coincident nodes are uncoupled and a zero-length solver element is also present.

When the solver element is selected, its properties can be reviewed.

The XYZ coordinate system of the zero-length 1D solver element (the link) is determined by the released slab edge. When 2D Elements > Local Axes are enabled in Scene Content, you can observe that the local y (green) axes of the 2D elements align with this edge. Consequently, the 1D solver element’s Y direction also follows the edge, while the X direction remains perpendicular within the slab plane and the Z direction is normal to the slab.

The edge is pinned, which is why the link’s rotational stiffness in Y direction is set to zero, while the rotational stiffness in X and Z is rigid.

In a Results View, the deflected shape for the uniform downwards load confirms that the edge is acting as a hinge.

Diaphragm constraints

Within the solver view, the symbols for nodes change to indicate whether they are constrained by a rigid diaphragm.

Hollow circles represent nodes that are not constrained by a rigid diaphragm.
Filled circles represent nodes that are constrained by a rigid diaphragm.

Nodes constrained by a rigid diaphragm are forced to maintain their relative distances in-plane, as if they were part of a rigid plate. The specific diaphragm number is listed in the node properties. If needed, individual solver nodes can be manually excluded from their constraining diaphragm. For instructions on how to do this, see: Include or remove solver nodes from the diaphragm.

For further information about diaphragms, see: Overview of diaphragm action in roof panels and slabs.

Solver node properties

When in a Solver View, solver node properties are displayed in the Properties Window as shown below.


Property	Description
Fx, Fy, Fz	The translational degrees of freedom at the node. Fixed Pinned Coupled to <joint number>
Fx, Fy, Fz	The rotational degrees of freedom at the node. Fixed Pinned Coupled to <joint number>
Coordinate	The node location.
P-Delta	When using second-order analysis the accuracy of the result will increase with the number of nodes within members. Within a member the number of internal nodes is determined by the number of incoming members. Tekla Structural Designer will add a P-Delta node into a beam or column if there are no incoming members. See also: Member second-order (P-δ) effects
Exclude from Diaphragm	If checked, the node has been excluded from the diaphragm. For instructions on how to do this, see: Include or remove solver nodes from the diaphragm Note that in a Solver View, you can only exclude a node from a diaphragm when Working Solver Model is selected as the method on the Solver ribbon.
Diaphragm #	Specifies the diaphragm number to which the node is connected. (Not displayed when viewing the "Working Solver Model").