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 (Minor Axis)

Perpendicular to the x-axis. For horizontal members, this points Up vertically. For vertical columns, the orientation depends on the default rotation, but generally points in the positive global Z direction unless rotated.
Controls bending resistance against lateral/sideways loads (Minor Axis Bending).

Local z-axis (Major Axis)

Perpendicular to both x and y, defined by the Right-Hand Rule ($z = x \times y$). For typical horizontal beams, this axis is horizontal.
Controls bending resistance against vertical loads (Major Axis Bending).

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 (Fx)

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

Shear Force (Fy, Fz)

Positive when acting in positive local axis direction on a positive face.

Bending Moment (My, Mz)

Follows Right-Hand Rule about local axes. Default displays moment on the Tension Side.

Load Inputs

When applying loads, symbols indicate the positive direction:

  • Force Loads (Fx, Fy, Fz): Follow Global Axes direction. (e.g., -10kN Fy is a downward gravity load).
  • Moment Loads (Mx, My, Mz): Follow Right-Hand Rule about the axis.
  • Distributed Loads: Specified in Global or Local axes. Downward gravity load on a beam is typically Global -Y or Local -y.