Sign conventions

GenSec uses a consistent right-hand coordinate system throughout. Understanding the sign conventions is essential for interpreting results correctly.

Coordinate system

The origin is at the bottom-left corner of the section bounding box.

  • \(x\)-axis: horizontal, pointing right (section width direction).

  • \(y\)-axis: vertical, pointing up (section height direction).

For sections created with parametric primitives (primitives) or via YAML, this convention is enforced automatically.

Strain sign convention

\[\begin{split}\varepsilon > 0 \quad &\Longrightarrow \quad \text{tension} \\ \varepsilon < 0 \quad &\Longrightarrow \quad \text{compression}\end{split}\]

Force and moment signs

The moment convention follows directly from the fiber integration (see The fiber method):

\[\begin{split}M_x &= \sum_i \sigma_i \, A_i \, (y_i - y_{\text{ref}}) \\ M_y &= \sum_i \sigma_i \, A_i \, (x_i - x_{\text{ref}})\end{split}\]

Strain plane

The strain at any fiber location \((x_i, y_i)\) is given by:

\[\varepsilon(x, y) = \varepsilon_0 + \chi_x \, (y - y_{\text{ref}}) + \chi_y \, (x - x_{\text{ref}})\]

where:

  • \(\varepsilon_0\) is the strain at the reference point (centroid by default),

  • \(\chi_x\) is the curvature about the \(x\)-axis [1/mm],

  • \(\chi_y\) is the curvature about the \(y\)-axis [1/mm].

Uniaxial bending corresponds to \(\chi_y = 0\).

Embedded vs. external rebars

For rebars that lie inside the bulk material (the default, embedded: true), GenSec subtracts the displaced bulk material to avoid double-counting the area occupied by the bar:

\[F_{\text{net},i} = \bigl[\sigma_{\text{rebar}}(\varepsilon_i) - \sigma_{\text{bulk}}(\varepsilon_i)\bigr] \, A_{s,i}\]

For external elements — CFRP strips bonded to the surface, steel plates, external tendons — set embedded: false. The full rebar stress is used without subtracting the bulk:

\[F_{\text{net},i} = \sigma_{\text{rebar}}(\varepsilon_i) \, A_{s,i}\]

This distinction is critical for accurate results when mixing materials.

Units

GenSec works with a consistent set of units internally:

Quantity

Unit

Length

mm

Stress

MPa

Force

N

Moment

N·mm

Curvature

1/mm

Strain

—

YAML input uses kN and kN·m for demands (N_kN, Mx_kNm, My_kNm) for convenience. The conversion happens automatically in the YAML loader.