249 lines
8.8 KiB
Python
249 lines
8.8 KiB
Python
|
"""Moment-Curvature Example — OpenSees Examples Manual, Example 2.
|
|||
|
|
|
|||
|
|
Reinforced-concrete column cross-section, fibre discretisation, axial
|
|||
|
|
preload + monotonic moment pushover. Mirrors the OpenSees Tcl script
|
|||
|
|
at https://opensees.berkeley.edu/wiki/index.php?title=Moment_Curvature_Example
|
|||
|
|
|
|||
|
|
Model
|
|||
|
|
-----
|
|||
|
|
Two coincident nodes linked by a ``zeroLengthSection`` carrying the
|
|||
|
|
RC fibre section. Node 1 is fully restrained; node 2 is free in Ux
|
|||
|
|
(so axial can shorten) and Rz (the curvature DOF). A constant axial
|
|||
|
|
load P = -180 kip is applied first via LoadControl(0); then a
|
|||
|
|
linear reference moment pattern (Mz = 1 kip·in) is added and
|
|||
|
|
DisplacementControl on DOF 3 ramps the curvature to μ·Ky where
|
|||
|
|
μ = 15 and Ky is the elastic yield curvature estimate.
|
|||
|
|
|
|||
|
|
Units: kip, in, ksi (UnitSystem.US_IN_KIP).
|
|||
|
|
|
|||
|
|
GUI walkthrough: File → Open → moment_curvature.osmodel, Options →
|
|||
|
|
Set Display Units → US (in, kip, kip·s²/in, s, ksi), Analyze → Run →
|
|||
|
|
MK, Display → Show Pushover Curve.
|
|||
|
|
"""
|
|||
|
|
|
|||
|
|
from __future__ import annotations
|
|||
|
|
|
|||
|
|
from pathlib import Path
|
|||
|
|
|
|||
|
|
from otko.core import (
|
|||
|
|
Concrete01,
|
|||
|
|
ConstantTimeSeries,
|
|||
|
|
CoordinateGridSystem,
|
|||
|
|
FiberSection,
|
|||
|
|
GridSystem,
|
|||
|
|
LinearTimeSeries,
|
|||
|
|
NodalLoad,
|
|||
|
|
Node,
|
|||
|
|
PlainLoadPattern,
|
|||
|
|
Project,
|
|||
|
|
ProjectMeta,
|
|||
|
|
PushoverCase,
|
|||
|
|
RectangularPatch,
|
|||
|
|
Steel01,
|
|||
|
|
StraightLayer,
|
|||
|
|
UnitSystem,
|
|||
|
|
ZeroLengthSectionElement,
|
|||
|
|
make_grid_lines,
|
|||
|
|
)
|
|||
|
|
from otko.services import load_project, save_project
|
|||
|
|
|
|||
|
|
|
|||
|
|
# Cross-section parameters (kip-in-ksi, from the Tcl example).
|
|||
|
|
COL_WIDTH = 15.0 # z-direction dimension
|
|||
|
|
COL_DEPTH = 24.0 # y-direction dimension
|
|||
|
|
COVER = 1.5
|
|||
|
|
AS_BAR = 0.60 # area of one #7 rebar
|
|||
|
|
|
|||
|
|
FY = 60.0 # steel yield stress, ksi
|
|||
|
|
E_STEEL = 30000.0 # steel Young's modulus, ksi
|
|||
|
|
HARDENING = 0.01 # strain-hardening ratio
|
|||
|
|
|
|||
|
|
P_AXIAL = -180.0 # kip, compression
|
|||
|
|
MU = 15 # target curvature ductility
|
|||
|
|
NUM_INCR = 100 # DisplacementControl increments
|
|||
|
|
|
|||
|
|
|
|||
|
|
def build_moment_curvature() -> Project:
|
|||
|
|
"""Build the OpenSees Example 2 Moment-Curvature project."""
|
|||
|
|
y1 = COL_DEPTH / 2.0 # 12
|
|||
|
|
z1 = COL_WIDTH / 2.0 # 7.5
|
|||
|
|
d = COL_DEPTH - COVER # 22.5
|
|||
|
|
|
|||
|
|
# Yield curvature estimate, assumed elastic + top/bottom steel only.
|
|||
|
|
eps_y = FY / E_STEEL # 0.002
|
|||
|
|
ky = eps_y / (0.7 * d) # ≈ 1.27e-4
|
|||
|
|
max_k = ky * MU # ≈ 1.905e-3
|
|||
|
|
d_k = max_k / NUM_INCR # per-step curvature increment
|
|||
|
|
|
|||
|
|
return Project(
|
|||
|
|
meta=ProjectMeta(
|
|||
|
|
name="Moment-Curvature (OpenSees Ex 2)",
|
|||
|
|
author="OpenSees Examples Manual",
|
|||
|
|
description=(
|
|||
|
|
"RC column fibre section — constant axial P + DisplacementControl "
|
|||
|
|
"curvature pushover. Kip-in-ksi units throughout."
|
|||
|
|
),
|
|||
|
|
units=UnitSystem.US_IN_KIP,
|
|||
|
|
),
|
|||
|
|
ndm=2, ndf=3,
|
|||
|
|
coord_systems=[
|
|||
|
|
# A tiny grid at the section origin so the two coincident
|
|||
|
|
# nodes have a visual anchor in the canvas.
|
|||
|
|
CoordinateGridSystem(
|
|||
|
|
name="Global",
|
|||
|
|
grid=GridSystem(
|
|||
|
|
x_grid_lines=make_grid_lines("X", [0.0]),
|
|||
|
|
y_grid_lines=make_grid_lines("Y", [0.0]),
|
|||
|
|
z_grid_lines=make_grid_lines("Z", [0.0]),
|
|||
|
|
),
|
|||
|
|
),
|
|||
|
|
],
|
|||
|
|
nodes=[
|
|||
|
|
# Node 1 — fully clamped.
|
|||
|
|
Node(id=1, name="Support",
|
|||
|
|
coords=(0.0, 0.0, 0.0),
|
|||
|
|
restraint=(True, True, False, False, False, True)),
|
|||
|
|
# Node 2 — free in Ux and Rz (axial + curvature).
|
|||
|
|
Node(id=2, name="Crown",
|
|||
|
|
coords=(0.0, 0.0, 0.0),
|
|||
|
|
restraint=(False, True, False, False, False, False)),
|
|||
|
|
],
|
|||
|
|
materials=[
|
|||
|
|
# Core concrete — confined (tag 1).
|
|||
|
|
Concrete01(id=1, name="Core-Conc",
|
|||
|
|
fpc=-6.0, epsc0=-0.004,
|
|||
|
|
fpcu=-5.0, epsU=-0.014),
|
|||
|
|
# Cover concrete — unconfined (tag 2).
|
|||
|
|
Concrete01(id=2, name="Cover-Conc",
|
|||
|
|
fpc=-5.0, epsc0=-0.002,
|
|||
|
|
fpcu=0.0, epsU=-0.006),
|
|||
|
|
# Reinforcing steel — bilinear hardening (tag 3).
|
|||
|
|
Steel01(id=3, name="Steel-60",
|
|||
|
|
Fy=FY, E0=E_STEEL, b=HARDENING),
|
|||
|
|
],
|
|||
|
|
sections=[
|
|||
|
|
FiberSection(
|
|||
|
|
id=1, name="RC-Column",
|
|||
|
|
patches=[
|
|||
|
|
# Core — confined concrete inside the rebar ring.
|
|||
|
|
RectangularPatch(
|
|||
|
|
material_id=1, n_fib_y=10, n_fib_z=1,
|
|||
|
|
y_i=COVER - y1, z_i=COVER - z1,
|
|||
|
|
y_j=y1 - COVER, z_j=z1 - COVER,
|
|||
|
|
),
|
|||
|
|
# Top cover (unconfined).
|
|||
|
|
RectangularPatch(
|
|||
|
|
material_id=2, n_fib_y=10, n_fib_z=1,
|
|||
|
|
y_i=-y1, z_i=z1 - COVER,
|
|||
|
|
y_j=y1, z_j=z1,
|
|||
|
|
),
|
|||
|
|
# Bottom cover.
|
|||
|
|
RectangularPatch(
|
|||
|
|
material_id=2, n_fib_y=10, n_fib_z=1,
|
|||
|
|
y_i=-y1, z_i=-z1,
|
|||
|
|
y_j=y1, z_j=COVER - z1,
|
|||
|
|
),
|
|||
|
|
# Left cover.
|
|||
|
|
RectangularPatch(
|
|||
|
|
material_id=2, n_fib_y=2, n_fib_z=1,
|
|||
|
|
y_i=-y1, z_i=COVER - z1,
|
|||
|
|
y_j=COVER - y1, z_j=z1 - COVER,
|
|||
|
|
),
|
|||
|
|
# Right cover.
|
|||
|
|
RectangularPatch(
|
|||
|
|
material_id=2, n_fib_y=2, n_fib_z=1,
|
|||
|
|
y_i=y1 - COVER, z_i=COVER - z1,
|
|||
|
|
y_j=y1, z_j=z1 - COVER,
|
|||
|
|
),
|
|||
|
|
],
|
|||
|
|
layers=[
|
|||
|
|
# Top rebar (3 × #7).
|
|||
|
|
StraightLayer(
|
|||
|
|
material_id=3, n_bars=3, bar_area=AS_BAR,
|
|||
|
|
y_start=y1 - COVER, z_start=z1 - COVER,
|
|||
|
|
y_end=y1 - COVER, z_end=COVER - z1,
|
|||
|
|
),
|
|||
|
|
# Middle rebar (2 × #7).
|
|||
|
|
StraightLayer(
|
|||
|
|
material_id=3, n_bars=2, bar_area=AS_BAR,
|
|||
|
|
y_start=0.0, z_start=z1 - COVER,
|
|||
|
|
y_end=0.0, z_end=COVER - z1,
|
|||
|
|
),
|
|||
|
|
# Bottom rebar (3 × #7).
|
|||
|
|
StraightLayer(
|
|||
|
|
material_id=3, n_bars=3, bar_area=AS_BAR,
|
|||
|
|
y_start=COVER - y1, z_start=z1 - COVER,
|
|||
|
|
y_end=COVER - y1, z_end=COVER - z1,
|
|||
|
|
),
|
|||
|
|
],
|
|||
|
|
),
|
|||
|
|
],
|
|||
|
|
elements=[
|
|||
|
|
ZeroLengthSectionElement(
|
|||
|
|
id=1, name="MK-Link",
|
|||
|
|
nodes=(1, 2), section_id=1,
|
|||
|
|
),
|
|||
|
|
],
|
|||
|
|
time_series=[
|
|||
|
|
ConstantTimeSeries(id=1, name="AxialP"),
|
|||
|
|
LinearTimeSeries(id=2, name="RefMoment"),
|
|||
|
|
],
|
|||
|
|
load_patterns=[
|
|||
|
|
# Constant axial preload at node 2 — Fx = P (compression).
|
|||
|
|
PlainLoadPattern(
|
|||
|
|
id=1, name="AxialP",
|
|||
|
|
time_series_id=1,
|
|||
|
|
nodal_loads=[
|
|||
|
|
NodalLoad(node_id=2,
|
|||
|
|
forces=(P_AXIAL, 0, 0, 0, 0, 0)),
|
|||
|
|
],
|
|||
|
|
),
|
|||
|
|
# Linear reference moment — Mz = 1.0, DisplacementControl
|
|||
|
|
# scales this as it ramps curvature.
|
|||
|
|
PlainLoadPattern(
|
|||
|
|
id=2, name="RefMoment",
|
|||
|
|
time_series_id=2,
|
|||
|
|
nodal_loads=[
|
|||
|
|
NodalLoad(node_id=2,
|
|||
|
|
forces=(0, 0, 0, 0, 0, 1.0)),
|
|||
|
|
],
|
|||
|
|
),
|
|||
|
|
],
|
|||
|
|
analyses=[
|
|||
|
|
PushoverCase(
|
|||
|
|
id=1, name="MK",
|
|||
|
|
pattern_ids=[1, 2],
|
|||
|
|
control_node=2, control_dof=3, # Rz = curvature
|
|||
|
|
target_disp=max_k,
|
|||
|
|
step_size=d_k,
|
|||
|
|
base_nodes=[1],
|
|||
|
|
test="NormUnbalance",
|
|||
|
|
tolerance=1e-9, max_iter=25,
|
|||
|
|
),
|
|||
|
|
],
|
|||
|
|
)
|
|||
|
|
|
|||
|
|
|
|||
|
|
def main() -> None:
|
|||
|
|
project = build_moment_curvature()
|
|||
|
|
project.validate_references()
|
|||
|
|
y1 = COL_DEPTH / 2.0
|
|||
|
|
eps_y = FY / E_STEEL
|
|||
|
|
ky = eps_y / (0.7 * (COL_DEPTH - COVER))
|
|||
|
|
print(f"Built '{project.meta.name}'")
|
|||
|
|
print(f" ndm={project.ndm}, ndf={project.ndf}, units={project.meta.units.value}")
|
|||
|
|
print(f" Estimated yield curvature Ky = {ky:.4e} 1/in")
|
|||
|
|
print(f" Target (mu * Ky) = {ky * MU:.4e} 1/in (mu = {MU})")
|
|||
|
|
|
|||
|
|
out_path = Path(__file__).with_suffix(".osmodel")
|
|||
|
|
save_project(project, out_path)
|
|||
|
|
print(f"Saved -> {out_path}")
|
|||
|
|
|
|||
|
|
restored = load_project(out_path)
|
|||
|
|
restored.validate_references()
|
|||
|
|
assert restored.model_dump(by_alias=True) == project.model_dump(by_alias=True)
|
|||
|
|
print("Round-trip OK.")
|
|||
|
|
|
|||
|
|
|
|||
|
|
if __name__ == "__main__":
|
|||
|
|
main()
|