MomentCurvature

class opstool.anlys.MomentCurvature(sec_tag, axial_force=0)

Bases: object

Moment-Curvature Analysis for Fiber Section in OpenSeesPy.

Parameters

sec_tagint,

The previously defined section Tag.

axial_forcefloat, optional

Axial load, compression is negative, by default 0

Methods

analyze	Performing Moment-Curvature Analysis.
bilinearize	Bilinear Approximation of Moment-Curvature Relation.
get_M	Get the moment array.
get_M_phi	Get the moment and curvature array.
get_curvature	Get the curvature array.
get_fiber_data	All fiber data.
get_limit_state	Get the curvature and moment corresponding to a certain limit state.
get_moment	Get the moment array.
get_phi	Get the curvature array.
plot_M_phi	Plot the moment-curvature relationship.
plot_fiber_responses	Plot the fiber responses.
set_cycle_path	set a deformation cycle path.

analyze(axis='y', max_phi=0.5, incr_phi=0.0001, limit_peak_ratio=0.8, cycle_analyze=False, smart_analyze=True, debug=False)

Performing Moment-Curvature Analysis.

Parameters

axisstr, optional, “y” or “z”

The axis of the section to be analyzed, by default “y”.

max_phifloat, optional

The maximum curvature to analyze, by default 0.5.

incr_phifloat, optional

Curvature analysis increment, by default 1e-4.

limit_peak_ratiofloat, optional

A ratio of the moment intensity after the peak used to stop the analysis., by default 0.8, i.e., a 20% drop after peak.

cycle_analyzebool, optional

Whether to perform cyclic analysis, by default False.

smart_analyzebool, optional

Whether to use smart analysis options, by default True.

debug: bool, optional

Whether to use debug mode when smart analysis is True, by default, False.

Note

The termination of the analysis depends on whichever reaches max_phi or post_peak_ratio first.

set_cycle_path(max_phi, n_cycle=20, n_hold=1)

set a deformation cycle path.

Parameters

max_phifloat

Peak of the path.

n_cycleint, optional

Number of cycles, by default 20

n_holdint, optional

The number of repetitions for each cycle., by default 1

Note

The total number of cycles is n_cycle * n_hold.

Returns

1D Arraylike.

Displacement path sequence

plot_M_phi(ax=None)

Plot the moment-curvature relationship.

Parameters

axmatplotlib.axes.Axes, optional

The axes to plot the moment-curvature relationship, by default None.

plot_fiber_responses(return_ax=False)

Plot the fiber responses.

Parameters

return_ax: bool, default=False

If True, return the axes for the plot of matplotlib.

get_phi()

Get the curvature array.

Returns

phi: 1D array-like

Curvature array.

get_curvature()

Get the curvature array.

Returns

phi: 1D array-like

Curvature array.

get_M()

Get the moment array.

Returns

m: 1D array-like

Moment array.

get_moment()

Get the moment array.

Returns

m: 1D array-like

Moment array.

get_M_phi()

Get the moment and curvature array.

Returns

(1D array-like, 1D array-like)

(Curvature array, Moment array)

get_fiber_data()

All fiber data.

Return type:

DataArray

Returns

FiberData: xr.DataArray

All fiber data. “Steps” is the number of steps in the analysis. “Fibers” is the number of fibers in the section. “Properties” is the properties of the fibers, including “yloc”, “zloc”, “area”, “mat”, “stress”, “strain”.

get_limit_state(matTag=1, threshold=0.0, peak_drop=False)

Get the curvature and moment corresponding to a certain limit state.

Parameters

matTagUnion[list[int], int]

The OpenSeesPy material Tag used to determine the limit state., by default 1

thresholdUnion[list[float], float]

The strain threshold used to determine the limit state by material matTag, by default 0. The positive and negative signs are meaningful for tension and compression.

Note

If matTag is a list, the length of matTag and threshold should be the same. As long as any material reaches its corresponding threshold, it will be set to the limit state.

peak_dropUnion[float, bool], optional, by default False.

If True, A default 20% drop from the peak value of the moment will be used as the limit state; If float in [0, 1], this means that the ratio of ultimate strength to peak value is specified by this value, for example, peak_drop = 0.3, the ultimate strength = 0.7 * peak. matTag and threshold are not needed.

Note

When using peak_drop, matTag and strain threshold will be ignored!

Returns

(float, float)

(Limit Curvature, Limit Moment)

Examples

>>> sec = MomentCurvature(sec_tag=1)
>>> sec.analyze(axis="y", max_phi=1.0, incr_phi=1e-4, limit_peak_ratio=0.8)
>>> # Get the limit state by material Tag 1 and strain threshold 0.002
>>> sec.get_limit_state(matTag=1, threshold=0.002)
>>> sec.get_limit_state(peak_drop=0.20)

bilinearize(phiy, My, phiu, plot=False, ax=None)

Bilinear Approximation of Moment-Curvature Relation.

Parameters

phiyfloat

The initial yield curvature.

Myfloat

The initial yield moment.

phiufloat

The limit curvature.

plotbool, optional

If True, plot the bilinear approximation, by default, False.

axmatplotlib.axes.Axes, optional

The axes to plot the bilinear approximation, by default None.

Returns

(float, float)

(Equivalent Curvature, Equivalent Moment)