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, right-handed system:
- X-Axis: Global X, shown in red. In the standard front view it appears left/right on screen.
- Y-Axis: Global Y, shown in green. Positive Y is vertical upwards/elevation.
- Z-Axis: Global Z, shown in blue. In the standard front view positive Z points out of the screen toward you.
The viewport is orbitable, so the red X and blue Z axes will not always appear as fixed left/right screen directions. Use the bottom-left axis gizmo and colour labels to read the current camera projection; the model coordinates themselves remain global X, Y, Z.
Use the left sidebar display controls to show the global axes, member local frames, and plate local frames directly in the 3D view.
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.
Toggle Member Local Frame in the left sidebar to display each member's local x, y, and z axes on the model. This is the fastest way to confirm member load directions, result planes, and sideways section orientation before interpreting diagrams.
Plate Local Axes
Each plate group has a local surface frame. The local axes are fixed by the plate geometry, not by the order you clicked the corners, so copied or mirrored plates keep a consistent result convention.
- Local x is the global X direction projected onto the plate surface. If that projection is not usable, the frame falls back to a stable in-plane direction.
- Local y lies in the plate surface and completes the right-handed local frame.
- Local z is the plate surface normal, canonicalised to point upward where possible. For vertical walls, global X and then global Z are used to break ties.
Toggle Plate Local Frame in the left sidebar to display each plate group's local x/y axes and +z surface normal. This is useful for checking pressure direction and for interpreting plate result components such as Mx, My, Sx, and Sy.
Positive Sign Conventions
Analysis Results
Follow global X, Y, Z axes. Positive Y is upwards/elevation; X and Z screen directions depend on camera orientation.
Follow Right-Hand Rule about Global Axes
Forces acting ON the structure from supports. Follow Global Axes.
Internal Forces
Tension is Positive (+)
Compression is Negative (-)
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.
Moment about the member's local x-axis (twist). Right-Hand Rule about local x.
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.
Fx, Fy, Fz, Mx, My, Mz, the 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).Plate Result Signs
Plate Bending and Shear
Plate deflection components follow global displacement signs. Vertical displacement follows global Y, so downward gravity deflection is normally negative Y.
Displayed plate bending moments are sagging-positive. A positive Mx or My corresponds to tension on the plate's local -z face and compression on the +z face.
Reported in the plate local x and y directions. Use the Plate Local Frame display when comparing component signs between adjacent plate groups.
Plate Membrane and Design Moments
Sx and Sy are tension-positive in the plate local x and y directions. Txy is the in-plane shear component in the local plate frame.
Principal membrane stresses keep their sign. Equivalent stress contours use the top and bottom fibre states; von Mises, Tresca, Bach and Rankine are unsigned.
Wood-Armer values are design demand moments for orthogonal reinforcement layers. Top means the +local z face shown by the plate normal/local-axis display; bottom means the opposite -local z face. These are local plate faces, not necessarily global up and down.
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.
- Plate Surface Pressure: Normal: Positive pressure acts along the plate local +z normal. On a flat roof/slab whose +z points upward, use a negative pressure for a downward gravity load.
- Plate Surface Pressure: Global X/Y/Z: The load direction follows the fixed global axis and is resolved onto the plate surface by the solver.
- 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.