Visualization and Results¶

Once the analysis has run, BeamLab lets you inspect internal forces, displacements and rotations, either in the 2D or in the 3D view. This page explains how to read them, which axes they refer to, and which sign convention is used.

Global axes and local axes¶

Global axes¶

• Y is the vertical axis of the project (positive upwards). Gravity acts along -Y.
• In a 2D project, the structure is drawn in the XY plane.
• In a 3D project, X and Z are the two horizontal axes.

Local axes of a beam¶

Each beam has its own local axes (x, y, z), built automatically from its two nodes:

The axes always form a right-handed system (x × y = z).

The local axes depend only on the position of the nodes, not on the direction in which the beam was drawn: a horizontal beam drawn from right to left has the same z axis (pointing up) as the same beam drawn from left to right. Only its x axis, and therefore the position of its first and second ends, are reversed.

Strong axis and weak axis¶

The orientation of a section is set with the beam property orientation:

• Strong axis (default): the section is placed so that its strong axis is y. The height of the section is along z, so bending in the vertical plane (rotation about y) uses the strong-axis inertia Iyy. The weak axis is z.
• Weak axis: the section is turned by 90° about the beam axis. Bending in the vertical plane then uses the weak-axis inertia Izz.

In a 2D project, there is a single bending plane (the plane of the structure). It uses Iyy with a strong-axis orientation and Izz with a weak-axis orientation.

Rotating a structure¶

Results are invariant when the structure is rotated about the vertical axis Y (loads rotated with it). For a rotation about any other axis (for example about Z in a 2D project), the structure is no longer in the same position with respect to the vertical: the axial force N, the torsion T, the reactions and the displacements are unchanged, but the sign of the shear forces and bending moments of a member can change, because its "top" fibre is not the same any more.

Sign convention¶

All results follow one consistent convention, summarized in the figure below.

Internal forces in beams¶

General principles¶

Internal forces are expressed in the local coordinate system of each beam (see above):

• x runs along the beam, from its first node to its second node;
• y and z are the transverse axes of the cross-section.

The diagrams are plotted along each member, and the values at both ends of a member are the forces that the rest of the structure transmits to it.

Forces and moments are related to each other:

• the shear force is the derivative of the bending moment along the beam;
• a distributed load makes the shear force vary linearly (for a uniform load), and the bending moment vary parabolically.

Forces available in 2D¶

In a 2D project, three internal forces are available. They are the forces of the bending plane, which is the plane of the structure (XY): the shear force is named Vz and the moment My, as for the vertical plane of a 3D beam.

Normal force (N)

Shear force (Vz)

Bending moment (My)

Additional forces in 3D¶

A 3D project adds the out-of-plane forces (the bending in the horizontal plane) and the torsion. Warping models also provide the bimoment.

In 3D, Vz and My are the forces of the vertical plane (for a non-vertical beam), and Vy and Mz those of the horizontal plane.

Shear force (Vy)

Bending moment (Mz)

Torsion moment (Mx)

Bimoment (B)

Displacements and rotations¶

General principles¶

Displacements are expressed in the global coordinate system of the project (X, Y, Z), not in the local axes of the beams. This guarantees that two beams sharing a node always show the same displacement at that node.

• Displacements are shown in mm.
• Rotations are shown in mrad.
• Diagrams are drawn with a color scale (from green to red) that goes from the smallest to the largest displayed value.

Available components¶

Wireframe or full view¶

The deformed shape can be displayed either:

• as a wireframe (the beams are drawn as lines), or
• as a full view (the beams are drawn with their actual cross-section).

The wireframe view is available only when the material is custom.

Twist of the beams¶

In 3D projects, when a beam undergoes a torsional rotation, its twist can be visualized in the 3D view: the cross-section rotates progressively about the beam axis along its length. Twist visualization can be disabled in the legend.

Export to Excel¶

The exported workbook contains the full description of the project and its results, organized in several sheets: