Sign Conventions

Understanding the coordinate systems and positive directions used in AutoCalcs is essential for accurate modeling and result interpretation.

Key Principle: Right-Hand Rule

AutoCalcs consistently uses the Right-Hand Rule for all coordinate systems and rotations. Point your right thumb in the positive axis direction, and your curled fingers indicate the positive rotation/moment direction.

Global Coordinate System

The global system defines the position of all nodes in 3D space. It is a strictly Y-Up system:

  • X-Axis: Horizontal (Red) → Positive to the Right
  • Y-Axis: Vertical (Green) ↑ Positive Upwards (Elevation)
  • Z-Axis: Depth (Blue) ↗ Positive Outwards/Forwards
+Y (Up) ^ | | | +----------> +X (Right) / / v +Z (Forward/Out)

Member Local Axes

Each member has its own local coordinate system (x, y, z) that moves and rotates with the member. This is crucial for interpreting internal forces like bending moments and shear.

Local x-axis (Longitudinal)

Defined by the line connecting Node A (Start) to Node B (End). Positive direction is from Node A → Node B.

Local y-axis

Perpendicular to the local x-axis. For a typical horizontal beam, local y points Up vertically (aligned with global +Y). For a vertical column drawn bottom-to-top, local y aligns with global −X.
For sections where the principal axes are not aligned with the geometric axes (single angles, Z-purlins, cold-formed channels with non-zero Alpha), local y points along the section's principal minor axis, not the geometric minor.

Local z-axis

Perpendicular to both x and y, defined by the Right-Hand Rule ($z = x \times y$). For a typical horizontal beam, local z is horizontal. For a vertical column drawn bottom-to-top, local z aligns with global +Z.

Section orientation caveats

  • By default local y = section minor axis and local z = section major axis, so Mz is major-axis bending and My is minor-axis bending.
  • Members flagged sideways have their section axes swapped (geometric minor and major exchange roles), so Mz then drives minor-axis bending and My drives major-axis bending. Demands and capacities are swapped accordingly inside the design engines.
  • For sections with a non-zero principal-axis rotation (single angles, Z-purlins), the local y/z axes follow the principal axes, not the geometric ones. Internal force diagrams are reported in this principal frame.

Positive Sign Conventions

Analysis Results

Displacements (Dx, Dy, Dz)

Follow Global Axes (+X Right, +Y Up, +Z Forward)

Rotations (Rx, Ry, Rz)

Follow Right-Hand Rule about Global Axes

Reactions

Forces acting ON the structure from supports. Follow Global Axes.

Internal Forces

Axial Force (P)

Tension is Positive (+)
Compression is Negative (-)

Shear Force (Vy, Vz)

Positive when acting in the positive local y / z axis direction on a positive face. Vy is the shear in the local-y direction; Vz is the shear in the local-z direction.

Torsion (T)

Moment about the member's local x-axis (twist). Right-Hand Rule about local x.

Bending Moment (My, Mz)

My is bending about the local y-axis (drives local-z deflection); Mz is bending about the local z-axis (drives local-y deflection). Right-Hand Rule about the respective local axis. Diagrams are drawn on the Tension Side.

As vector components, these are the local-frame member-end forces Fx, Fy, Fz, Mx, My, Mz — same letters used by the load-input API below, but for results the engineering names P / Vy / Vz / T / My / Mz are used in the member-analysis dialog, force diagrams, and design output (P ↔ Fx, Vy ↔ Fy, Vz ↔ Fz, T ↔ Mx).

Load Inputs

Each load specifies an axis frame. Member point and distributed loads expose a Local / Global selector; node loads and self-weight are always global.

  • Node Loads (FX, FY, FZ; MX, MY, MZ): Always follow global axes. e.g. −10 kN on FY is a downward gravity point load at the node.
  • Member Force Loads — Global frame: Components follow global X, Y, Z. Use this for gravity, wind, or any load whose direction is fixed in space regardless of member orientation.
  • Member Force Loads — Local frame: Components follow the member's local x (longitudinal), y, and z axes — and rotate with the member. Use this for lateral pressures normal to a sloped beam, axial pre-loads along the member, etc.
  • Moment Loads: Follow the Right-Hand Rule about the chosen-frame axis.
  • Distributed Loads: Same Local/Global selector as point loads. A typical UDL gravity load is Global −Y; a normal-to-beam pressure on a sloped roof rafter is Local −y.

Naming convention: lower-case Fx/Fy/Fz (and Mx/My/Mz) are local-frame components; upper-case FX/FY/FZ (and MX/MY/MZ) are global-frame components. Same letters, the case picks the frame.