pycba.nonlinear.NonlinearResult#

class NonlinearResult(collapse_lambda, collapsed, hinge_events, node_coords, final_moments, final_R, support_coords=<factory>, lambda_history=<factory>, moment_history=<factory>, final_displacements=<factory>)[source]#

Bases: object

Results container for a nonlinear beam analysis.

collapse_lambda#

Load factor at collapse (static) or front-axle position in metres at collapse (moving load). If no collapse occurred, this is the final value reached.

Type:

float

collapsed#

True if a collapse mechanism was detected.

Type:

bool

hinge_events#

Chronological list of yield and plastic-hinge events.

Type:

list[HingeEvent]

node_coords#

Global coordinates of all mesh nodes.

Type:

ndarray

final_moments#

Nodal bending moments at the end of the analysis.

Type:

ndarray

final_R#

Final element-end stiffness-reduction parameters.

Type:

ndarray, shape (n_elem, 2)

support_coords#

Global x-coordinates of the support locations.

Type:

ndarray

lambda_history#

Recorded load-factor (or position) snapshots.

Type:

list[float]

moment_history#

Recorded moment-distribution snapshots (same length as lambda_history).

Type:

list[ndarray]

Methods

plot_beam_state

Plot the beam with hinge locations and optional vehicle position.

plot_collapse

Plot the deformed shape at collapse, with the plastic hinges marked.

plot_hinge_history

Plot the hinge formation sequence along the beam.

plot_moments

Plot the bending moment distribution at collapse.

Attributes

collapse_lambda

collapsed

hinge_events

node_coords

final_moments

final_R

support_coords

lambda_history

moment_history

final_displacements

plot_moments(Mp=None, ax=None, units=None)[source]#

Plot the bending moment distribution at collapse.

If moment history snapshots were recorded (via record_every), they are shown as light traces behind the final distribution.

Parameters:

  • Mp (float, optional) – Plastic moment capacity. If given, horizontal dashed lines are drawn at +/- Mp.

  • ax (matplotlib Axes, optional) – Axes to plot on. If None, a new figure is created.

  • units (str or pycba.units.UnitSystem, optional) – Display unit system for the labels (see pycba.set_units()).

Returns:

ax

Return type:

matplotlib Axes

plot_hinge_history(moving=False, ax=None, units=None)[source]#

Plot the hinge formation sequence along the beam.

Each event is shown as a marker at (x, stage) where x is the hinge location on the beam.

For static analysis, stage is the load factor at which the event occurred. The beam line is drawn at $lambda = 1$.

For moving-load analysis (moving=True), stage is the front-axle position when the event occurred — showing where the load was when each hinge formed.

Parameters:

  • moving (bool, optional) – If True, label the y-axis as front-axle position. Default False (load factor).

  • ax (matplotlib Axes, optional) – Axes to plot on. If None, a new figure is created.

  • units (str or pycba.units.UnitSystem, optional) – Display unit system for the labels (see pycba.set_units()).

Returns:

ax

Return type:

matplotlib Axes

plot_beam_state(vehicle=None, ax=None, units=None)[source]#

Plot the beam with hinge locations and optional vehicle position.

Draws the beam, supports, and marks yield/hinge locations along the beam line. If vehicle is given and the analysis collapsed, axle positions at collapse are shown above the beam.

Parameters:

  • vehicle (pycba.Vehicle, optional) – Vehicle object. Axle positions are drawn at the collapse position (collapse_lambda).

  • ax (matplotlib Axes, optional) – Axes to plot on. If None, a new figure is created.

  • units (str or pycba.units.UnitSystem, optional) – Display unit system for the labels (see pycba.set_units()).

Returns:

ax

Return type:

matplotlib Axes

plot_collapse(scale=None, ax=None, units=None)[source]#

Plot the deformed shape at collapse, with the plastic hinges marked.

The undeformed beam is drawn in grey and the (exaggerated) collapse deflected shape overlaid, with a large marker at every plastic‑hinge location — the standard collapse‑mechanism picture for a plastic analysis.

Parameters:

  • scale (float, optional) – Deflection exaggeration factor. By default the shape is auto‑scaled so the largest deflection spans a sensible fraction of the beam length.

  • ax (matplotlib Axes, optional) – Axes to plot on; a new figure is created if None.

  • units (str or pycba.units.UnitSystem, optional) – Display unit system for the distance axis (see pycba.set_units()).

Returns:

ax

Return type:

matplotlib Axes