"""OpenSees Example 2b. Nonlinear Cantilever Column: Uniaxial Inelastic Section. OpenSees Wiki: https://opensees.berkeley.edu/wiki/index.php?title=OpenSees_Example_2b._Nonlinear_Cantilever_Column:_Uniaxial_Inelastic_Section This is the first nonlinear cantilever example in the OpenSees tutorial sequence. The column uses: - uniaxial elastic axial response - uniaxial bilinear flexural response - a SectionAggregator that combines P and Mz into one section - a force-based nonlinear beam-column element Run from the repository root: python examples/ex2b_canti2d_inelastic_section.py Produces ``examples/ex2b_canti2d_inelastic_section.osmodel``. """ from __future__ import annotations from pathlib import Path import math import sys if __package__ is None or __package__ == "": sys.path.insert(0, str(Path(__file__).resolve().parents[1] / "src")) from otko.core import ( # noqa: E402 AggregatorDOF, ElasticUniaxial, ForceBeamColumn, LinearTimeSeries, NodalLoad, Node, PathTimeSeries, PlainLoadPattern, Project, ProjectMeta, PushoverCase, SectionAggregator, StaticCase, Steel01, TransientCase, UniformExcitationPattern, UnitSystem, ) from otko.services import load_project, save_project # noqa: E402 from otko.services.peer_record import parse_plain_values # noqa: E402 # Geometry / mass variables. L_COL = 432.0 WEIGHT = 2000.0 H_COL = 60.0 B_COL = 60.0 G_ACCEL = 386.4 P_COL = WEIGHT MASS = P_COL / G_ACCEL A_COL = B_COL * H_COL * 1000.0 IZ_COL = (1.0 / 12.0) * B_COL * H_COL**3 # Material / section variables. FC = -4.0 E_C = 57.0 * math.sqrt(-FC * 1000.0) EI_COL = E_C * IZ_COL EA_COL = E_C * A_COL MY_COL = 130000.0 PHI_Y_COL = 0.65e-4 EI_COL_CRACK = MY_COL / PHI_Y_COL HARDENING_RATIO = 0.01 NUM_INT_PTS = 5 # Analysis variables. N_GRAVITY = 10 GRAVITY_STEP = 1.0 / N_GRAVITY PUSH_TARGET = 0.05 * L_COL PUSH_STEP = 0.001 * L_COL H_LOAD = WEIGHT GROUND_DT = 0.01 GROUND_FACTOR = 1.0 ANALYSIS_DT = 0.01 ANALYSIS_STEPS = 1000 DAMPING_RATIO = 0.02 _ROOT = Path(__file__).resolve().parent GROUND_MOTION_FILE = _ROOT / "data" / "BM68elc.acc" REFERENCE_PUSH_TCL = _ROOT / "data" / "Ex2b.Canti2D.InelasticSection.Push.tcl.txt" REFERENCE_EQ_TCL = _ROOT / "data" / "Ex2b.Canti2D.InelasticSection.EQ.tcl.txt" def _ground_motion_values() -> list[float]: return parse_plain_values(GROUND_MOTION_FILE) def build_ex2b_canti2d_inelastic_section() -> Project: values = _ground_motion_values() return Project( meta=ProjectMeta( name="OpenSees Ex 2b - Nonlinear Cantilever Column", author="OpenSees Wiki / Silvia Mazzoni & Frank McKenna", description=( "Nonlinear cantilever with an aggregated uniaxial section: " "elastic axial P plus bilinear inelastic Mz in one force-based element." ), units=UnitSystem.US_IN_KIP, ), ndm=2, ndf=3, nodes=[ Node( id=1, name="Base", coords=(0.0, 0.0, 0.0), restraint=(True, True, False, False, False, True), ), Node( id=2, name="Top", coords=(0.0, L_COL, 0.0), mass=(MASS, 1.0e-9, 0.0, 0.0, 0.0, 0.0), ), ], materials=[ Steel01( id=2, name="Col-Flex", Fy=MY_COL, E0=EI_COL_CRACK, b=HARDENING_RATIO, ), ElasticUniaxial( id=3, name="Col-Axial", E=EA_COL, ), ], sections=[ SectionAggregator( id=1, name="Col-Section", pairings=[ AggregatorDOF(material_id=3, dof="P"), AggregatorDOF(material_id=2, dof="Mz"), ], ), ], elements=[ ForceBeamColumn( id=1, name="Column", nodes=(1, 2), section_id=1, integration_points=NUM_INT_PTS, geom_transf="Linear", ), ], time_series=[ LinearTimeSeries(id=1, name="Gravity"), LinearTimeSeries(id=200, name="Lateral"), PathTimeSeries( id=400, name="BM68elc", dt=GROUND_DT, factor=GROUND_FACTOR, values=values, file_path=str(GROUND_MOTION_FILE.name), ), ], load_patterns=[ PlainLoadPattern( id=1, name="Gravity", time_series_id=1, nodal_loads=[ NodalLoad(node_id=2, forces=(0.0, -P_COL, 0.0, 0.0, 0.0, 0.0)), ], ), PlainLoadPattern( id=200, name="Pushover-X", time_series_id=200, nodal_loads=[ NodalLoad(node_id=2, forces=(H_LOAD, 0.0, 0.0, 0.0, 0.0, 0.0)), ], ), UniformExcitationPattern( id=400, name="GroundMotion-X", direction=1, accel_series_id=400, ), ], analyses=[ StaticCase( id=1, name="Gravity", pattern_ids=[1], n_steps=N_GRAVITY, load_factor_increment=GRAVITY_STEP, system="BandGeneral", constraints="Plain", integrator="LoadControl", algorithm="Newton", test="NormDispIncr", tolerance=1e-8, max_iter=6, ), PushoverCase( id=2, name="Push", preload_case_ids=[1], pattern_ids=[200], control_node=2, control_dof=1, target_disp=PUSH_TARGET, step_size=PUSH_STEP, base_nodes=[1], system="BandGeneral", constraints="Plain", algorithm="Newton", test="EnergyIncr", tolerance=1e-8, max_iter=6, ), TransientCase( id=3, name="Earthquake", preload_case_ids=[1], pattern_ids=[400], dt=ANALYSIS_DT, n_steps=ANALYSIS_STEPS, system="SparseGeneral", constraints="Transformation", integrator="Newmark", integrator_params=(0.5, 0.25), algorithm="ModifiedNewton", test="EnergyIncr", tolerance=1e-8, max_iter=10, rayleigh_mode1_damping=DAMPING_RATIO, ), ], ) def main() -> None: project = build_ex2b_canti2d_inelastic_section() project.validate_references() gm = next(ts for ts in project.time_series if ts.id == 400) print(f"Built '{project.meta.name}'") print( f" LCol={L_COL}, EA={EA_COL:.1f}, My={MY_COL:.1f}, " f"EIcr={EI_COL_CRACK:.1f}, b={HARDENING_RATIO}" ) print(f" Gravity + pushover + earthquake cases: {len(project.analyses)}") print(f" Ground motion file: {GROUND_MOTION_FILE.name}") print(f" Reference Tcls: {REFERENCE_PUSH_TCL.name}, {REFERENCE_EQ_TCL.name}") print(f" Record points: {len(gm.values)}, dt = {GROUND_DT}s, factor = {GROUND_FACTOR}") 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()