Sign conventions

Axes, positive directions and how to read a diagram without guessing — the page that prevents most result confusion.

Theory notes 3 min read

Getting a sign convention wrong invalidates everything downstream. Read this once and the "why is this moment negative?" question disappears.

Global axes

A right-handed Cartesian system: $X$ and $Y$ horizontal, $Z$ vertical and positive upwards. Gravity therefore acts in negative Z, so a downward load is entered as negative in the global system, or as a positive magnitude with a downward direction, depending on how you apply it.

Rotations are positive counter-clockwise about the positive axis, viewed looking back along that axis towards the origin: the standard right-hand rule.

Local member axes

Every member has its own system:

Axis	Direction
$x$	Along the member, from start node to end node. Always
$y$ , $z$	Perpendicular to $x$ and to each other, right-handed. Their orientation is set per member, in the Local coordinate system group of the properties panel

Two consequences:

The start node defines the direction of $x$ . Draw a member the other way and its local $x$ reverses, taking $y$ and $z$ with it. Two identical columns drawn in opposite directions report moments of opposite sign for the same physical behaviour.
Which of $y$ and $z$ is the section's strong axis is a setting, not a given. A column rotated 90° about its own axis bends the other way, and neither the geometry nor the solve will complain. Display local axes before reading $M_{y}$ or $M_{z}$ on any member, and orient similar members the same way.

Internal forces

Internal forces are reported in the local system, on the section, using the convention that the values act on the positive face of a cut:

Quantity	Positive means
$N$	Tension in the member
$V_{y}$ , $V_{z}$	Shear acting in the positive local $y$ or $z$ direction on the positive face
$T$	Torsion about the local $x$ axis, by the right-hand rule
$M_{y}$	Bending about the local $y$ axis
$M_{z}$	Bending about the local $z$ axis

A viewport plotting the normal force N on the steel hall under the self-weight case, with negative values labelled on the columns — Normal force N in the steel hall under self-weight alone. The columns carry compression, so their labelled values are negative; the bracing and the rafters show small values of either sign.LCS1 · self-weight

Bending diagram convention

$M_{y}$ positive corresponds to tension on the positive local $z$ face of the section. Whether that face is the top or the bottom of a beam depends on which way its local $z$ points, so the sign on its own does not tell you sagging from hogging.

The diagram does. Bending moment diagrams are drawn on the tension side of the member, the convention most European practice uses, so the picture shows directly which face is in tension, whatever the axes:

Behaviour	Where the diagram is drawn
Sagging — tension at the bottom of a beam	Below the beam
Hogging — tension at the top of a beam	Above the beam

Global axes, local member direction, and the two conventions that confuse most: axial force is positive in tension, and a moment diagram is drawn on the tension side — below the beam for sagging, whatever the local axes say.

Surface results

For plates, walls and shells, results are per unit width in the surface's local system:

Quantity	Positive means
$m_{x}$	Bending about the local $y$ axis, tension on the bottom surface
$m_{y}$	Bending about the local $x$ axis, tension on the bottom surface
$m_{x y}$	Twisting moment
$n_{x}$ , $n_{y}$	Membrane tension
$n_{x y}$	In-plane shear

The surface's local axes come from its definition, so check them before interpreting $m_{x}$ versus $m_{y}$ on any surface not aligned with the global axes. "Bottom" means the negative local $z$ face of the surface, which for a floor slab modelled the usual way is the soffit.

Reactions

Reactions are reported in the global system and act on the structure. A downward gravity load produces a positive upward vertical reaction. The sum of reactions must balance the sum of applied loads in each direction, per load case: the check described in Your first analysis.

Practical habits

Draw members consistently (columns bottom-to-top, beams left-to-right) so local axes are predictable across the model.
Display local axes before interpreting any result on a sloping or rotated member.

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