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.
Applied Local loads and the member-frame display use this geometric axis. A section's principal-axis angle Alpha does not rotate the authored load glyph.
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 roll the physical section and its result axes by +90°. Channel meaning remains section-attached: Mz is major-axis bending, My is minor-axis bending, Vy is major/web shear, and Vz is minor shear. Design engines consume those channels directly.
- For sections with a non-zero principal-axis rotation (single angles, Z-purlins), authored Local loads remain in the displayed geometric frame. Analysis resolves them onto the physical principal axes, and member-result diagrams use those same physical axes. The rendered section geometry and authored local-axis triad do not include Alpha.
- Sideways is the only supported user roll. Arbitrary or inverted section-roll metadata is rejected before analysis; it is not silently interpreted differently by the solver, renderer, and design engine.
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 (-)
At any position, imagine cutting the member and retaining the portion extending from the cut toward Node B. The outward normal of its cut face is local −x. Vy is positive when the force acting on this face points in local +y; Vz is positive when it points in local +z.
T is the torque acting on the same Node-B-side cut face. Positive torsion acts about local +x according to the Right-Hand Rule.
My is bending in the local x–z plane; Mz is bending in the local x–y plane. Member bending results use the solver's recovered beam sign convention. The frontend evaluates the bending stress as sigma_x = Mz*y/Iz + My*z/Iy in the final section-attached local axes.
- Positive Mz produces tension on the local +y side; negative Mz produces tension on the local −y side.
- Positive My produces tension on the local +z side; negative My produces tension on the local −z side.
Bending-moment diagrams are drawn on the corresponding Tension Side.
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
σx and σy are tension-positive in the plate local x and y directions. τxy is the in-plane shear component in the local plate frame.
Maximum and minimum principal membrane stresses σ1 and σ2 keep their sign. Equivalent fibre-stress contours use the top and bottom surface states and are unsigned. Rankine reports the maximum principal-stress magnitude; Bach applies the maximum principal-strain criterion.
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.