313 lines
12 KiB
Python
313 lines
12 KiB
Python
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"""Elastic Frame Example — OpenSees Examples Manual, Example 4.
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3-story 3-bay 2D elastic moment-resisting frame under gravity
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(distributed beam loads) + a lateral reference pattern (point loads
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at each floor's leftmost joint) + a 5-mode eigenvalue analysis.
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Matches the Tcl walkthrough at:
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https://opensees.berkeley.edu/wiki/index.php?title=Elastic_Frame_Example
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Model (kip-in-ksi, ndm=2, ndf=3):
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Floor 3 (z = 486") 13 ──beam19── 14 ──beam20── 15 ──beam21── 16
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│ │ │ │
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col9 col10 col11 col12
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│ │ │ │
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Floor 2 (z = 324") 9 ──beam16── 10 ─beam17── 11 ──beam18── 12
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│ │ │ │
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col5 col6 col7 col8
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│ │ │ │
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Floor 1 (z = 162") 5 ──beam13── 6 ─beam14── 7 ──beam15── 8
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│ │ │ │
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col1 col2 col3 col4
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│ │ │ │
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Base (z = 0") 1 2 3 4
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(fixed) (fixed) (fixed) (fixed)
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x = 0 360 720 1080
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Sections (AISC W-shapes):
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- Exterior column (lines 1, 4): W14X257 A=75.6 Iz=3400
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- Interior column (lines 2, 3): W14X311 A=91.4 Iz=4330
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- Floor-1 beam: W33X118 A=34.7 Iz=5900
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- Floor-2 beam: W30X116 A=34.2 Iz=4930
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- Floor-3 beam: W24X68 A=20.1 Iz=1830
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- E = 29000 ksi for all.
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Columns use the PDelta geometric transformation to capture P-Δ; beams
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use Linear. Gravity is a Constant time series with a uniform
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distributed load per beam (reference tributary intensity Load / 4 /
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bay — matches the Tcl ``eleLoad -type -beamUniform [expr -Load/(4*bay)]``).
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The lateral pattern uses a Linear time series with single-node point
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loads (220 / 180 / 90 kip at floors 1 / 2 / 3 respectively).
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Expected results (verified against the Tcl reference):
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- Gravity ΣFy at base: ≈ 2505 kip (Σw · Σbeam-length · 3 floors)
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- Gravity+Lateral ΣFx: ≈ -490 kip
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- First five periods (s): 1.0256, 0.3498, 0.1919, 0.1562, 0.1307
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GUI walkthrough: File → Open → elastic_frame.osmodel → Analyze →
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Run → "Gravity + Lateral" → Display → Show Force Diagram / Modal.
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"""
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from __future__ import annotations
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from pathlib import Path
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from otko.core import (
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ConstantTimeSeries,
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CoordinateGridSystem,
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ElasticBeamColumn,
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ElasticSection,
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GridSystem,
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LinearTimeSeries,
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ModalCase,
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NodalLoad,
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Node,
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PlainLoadPattern,
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Project,
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ProjectMeta,
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StaticCase,
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UniformElementLoad,
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UnitSystem,
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make_grid_lines,
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)
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from otko.services import load_project, save_project
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# Frame geometry (inches).
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BAY = 360.0 # 30 ft — bay width
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H_STORY = 162.0 # 13.5 ft — story height
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N_BAYS = 3
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N_STORIES = 3
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# Material + section (kip, in, ksi).
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E = 29000.0
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# Column sections — exterior W14X257 vs interior W14X311.
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A_COL_EXT, IZ_COL_EXT = 75.6, 3400.0
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A_COL_INT, IZ_COL_INT = 91.4, 4330.0
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# Beam sections — per floor.
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A_BEAM_F1, IZ_BEAM_F1 = 34.7, 5900.0 # W33X118 (floor 1)
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A_BEAM_F2, IZ_BEAM_F2 = 34.2, 4930.0 # W30X116 (floor 2)
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A_BEAM_F3, IZ_BEAM_F3 = 20.1, 1830.0 # W24X68 (floor 3)
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# Gravity loading (total weight per floor, kip).
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LOAD_F1 = 1185.0
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LOAD_F2 = 1185.0
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LOAD_F3 = 970.0
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# Lateral loading (kip, applied at each floor's leftmost joint, +X).
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P_F1 = 220.0
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P_F2 = 180.0
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P_F3 = 90.0
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# Gravity constant.
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G = 386.4 # in/s²
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# ─── ID layout ─────────────────────────────────────────────────────
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# Nodes: row-major, starting from (x=0, y=0). 4 columns × 4 rows = 16.
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# row r (0=base, 1=floor-1, 2=floor-2, 3=floor-3), col c (0..3):
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# id = 1 + r*4 + c
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#
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# Elements:
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# cols 1..12 : columns (bottom-to-top, left-to-right within each story)
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# cols 13..21 : beams (bottom-to-top, left-to-right within each floor)
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#
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def _node_id(row: int, col: int) -> int:
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return 1 + row * (N_BAYS + 1) + col
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def _col_id(story: int, col: int) -> int:
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# Story 1..3, col 0..3.
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return (story - 1) * (N_BAYS + 1) + col + 1
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def _beam_id(floor: int, bay: int) -> int:
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# Floor 1..3, bay 0..(N_BAYS-1).
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n_cols_total = N_STORIES * (N_BAYS + 1) # 12
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return n_cols_total + (floor - 1) * N_BAYS + bay + 1
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def build_elastic_frame() -> Project:
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nodes: list[Node] = []
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m_floor = {
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1: LOAD_F1 / ((N_BAYS + 1) * G), # mass per node at floor 1
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2: LOAD_F2 / ((N_BAYS + 1) * G),
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3: LOAD_F3 / ((N_BAYS + 1) * G),
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}
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for r in range(N_STORIES + 1):
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for c in range(N_BAYS + 1):
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nid = _node_id(r, c)
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x = c * BAY
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y = r * H_STORY
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if r == 0:
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# Base nodes: fix tx, ty, rz (the only active DOFs in ndm=2 ndf=3).
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restraint = (True, True, False, False, False, True)
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mass = (0.0,) * 6
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else:
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# Floor nodes: all 6 slots free. The runner's dof_idx
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# picks only (tx, ty, rz) = (0, 1, 5) out of this tuple
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# when emitting 2D. A stray True at index 5 would fix Rz
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# at every floor node and make the frame act rigid-joint.
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restraint = (False,) * 6
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m = m_floor[r]
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mass = (m, m, 0.0, 0.0, 0.0, 0.0)
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nodes.append(Node(
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id=nid, name=f"N{nid}",
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coords=(x, y, 0.0),
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restraint=restraint, mass=mass,
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))
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# Sections: exterior col, interior col, beam-F1, beam-F2, beam-F3.
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sections = [
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ElasticSection(id=1, name="W14X257-ColExt",
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E=E, A=A_COL_EXT, Iz=IZ_COL_EXT,
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Iy=IZ_COL_EXT, G=11200.0, J=1.0),
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ElasticSection(id=2, name="W14X311-ColInt",
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E=E, A=A_COL_INT, Iz=IZ_COL_INT,
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Iy=IZ_COL_INT, G=11200.0, J=1.0),
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ElasticSection(id=3, name="W33X118-Beam1",
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E=E, A=A_BEAM_F1, Iz=IZ_BEAM_F1,
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Iy=IZ_BEAM_F1, G=11200.0, J=1.0),
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ElasticSection(id=4, name="W30X116-Beam2",
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E=E, A=A_BEAM_F2, Iz=IZ_BEAM_F2,
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Iy=IZ_BEAM_F2, G=11200.0, J=1.0),
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ElasticSection(id=5, name="W24X68-Beam3",
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E=E, A=A_BEAM_F3, Iz=IZ_BEAM_F3,
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Iy=IZ_BEAM_F3, G=11200.0, J=1.0),
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]
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# Elements — 12 columns (PDelta) + 9 beams (Linear).
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elements: list[ElasticBeamColumn] = []
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for s in range(1, N_STORIES + 1):
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for c in range(N_BAYS + 1):
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sec_id = 1 if c in (0, N_BAYS) else 2 # exterior vs interior
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elements.append(ElasticBeamColumn(
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id=_col_id(s, c), name=f"Col-S{s}-C{c}",
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nodes=(_node_id(s - 1, c), _node_id(s, c)),
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section_id=sec_id, geom_transf="PDelta",
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))
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beam_sec = {1: 3, 2: 4, 3: 5}
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for f in range(1, N_STORIES + 1):
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for b in range(N_BAYS):
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elements.append(ElasticBeamColumn(
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id=_beam_id(f, b), name=f"Beam-F{f}-B{b}",
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nodes=(_node_id(f, b), _node_id(f, b + 1)),
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section_id=beam_sec[f], geom_transf="Linear",
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))
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# Gravity distributed load per beam: w = -Load / (4 × bay). The Tcl
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# reference divides by 4 (number of column lines), not by the number
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# of bays — so the distributed load represents a *reference* tributary
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# intensity, not the total floor weight spread over all beams.
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# Corresponding reference values: w1 = w2 = -0.8229 kip/in, w3 = -0.6736.
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floor_total = {1: LOAD_F1, 2: LOAD_F2, 3: LOAD_F3}
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gravity_element_loads = [
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UniformElementLoad(
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element_id=_beam_id(f, b),
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wy=-floor_total[f] / ((N_BAYS + 1) * BAY),
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)
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for f in range(1, N_STORIES + 1)
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for b in range(N_BAYS)
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]
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# Lateral point loads at each floor's leftmost joint (+X).
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lateral_nodes = {
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_node_id(1, 0): P_F1,
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_node_id(2, 0): P_F2,
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_node_id(3, 0): P_F3,
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}
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return Project(
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meta=ProjectMeta(
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name="Elastic Frame (OpenSees Ex 4)",
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author="OpenSees Examples Manual",
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description=(
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"3-story 3-bay 2D elastic frame, AISC W-shape sections, "
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"gravity (distributed) + lateral (point) + 5-mode eigen."
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),
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units=UnitSystem.US_IN_KIP,
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),
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ndm=2, ndf=3,
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coord_systems=[
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CoordinateGridSystem(
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name="Global",
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grid=GridSystem(
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x_grid_lines=make_grid_lines(
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"X", [c * BAY for c in range(N_BAYS + 1)],
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),
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y_grid_lines=make_grid_lines(
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"Y", [r * H_STORY for r in range(N_STORIES + 1)],
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),
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z_grid_lines=make_grid_lines("Z", [0.0]),
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),
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),
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],
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nodes=nodes,
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sections=sections,
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elements=elements,
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time_series=[
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ConstantTimeSeries(id=1, name="Gravity"),
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LinearTimeSeries(id=2, name="Lateral"),
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],
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load_patterns=[
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PlainLoadPattern(
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id=1, name="Gravity",
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time_series_id=1,
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element_loads=gravity_element_loads,
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),
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PlainLoadPattern(
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id=2, name="Lateral",
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time_series_id=2,
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nodal_loads=[
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NodalLoad(node_id=nid, forces=(P, 0, 0, 0, 0, 0))
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for nid, P in lateral_nodes.items()
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],
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),
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],
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analyses=[
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# Gravity alone — ΣFy at base should equal +3340 kip.
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StaticCase(
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id=1, name="Gravity",
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pattern_ids=[1],
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n_steps=1, load_factor_increment=1.0,
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system="BandGeneral", constraints="Transformation",
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integrator="LoadControl", algorithm="Linear",
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test="NormDispIncr", tolerance=1e-10, max_iter=10,
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),
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# Gravity + lateral — ΣFx at base should equal -490 kip.
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StaticCase(
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id=2, name="Gravity+Lateral",
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pattern_ids=[1, 2],
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n_steps=1, load_factor_increment=1.0,
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system="BandGeneral", constraints="Transformation",
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integrator="LoadControl", algorithm="Linear",
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test="NormDispIncr", tolerance=1e-10, max_iter=10,
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),
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# Eigen analysis on the lumped-mass model — 5 modes.
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ModalCase(id=3, name="Modal-5", n_modes=5),
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],
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)
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def main() -> None:
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project = build_elastic_frame()
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project.validate_references()
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print(f"Built '{project.meta.name}'")
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print(f" ndm={project.ndm}, ndf={project.ndf}, "
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f"units={project.meta.units.value}")
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print(f" {len(project.nodes)} nodes, {len(project.elements)} elements")
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print(f" Total gravity load: {LOAD_F1 + LOAD_F2 + LOAD_F3:.0f} kip")
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print(f" Total lateral load: {P_F1 + P_F2 + P_F3:.0f} kip")
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out_path = Path(__file__).with_suffix(".osmodel")
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save_project(project, out_path)
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print(f"Saved -> {out_path}")
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restored = load_project(out_path)
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restored.validate_references()
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assert restored.model_dump(by_alias=True) == project.model_dump(by_alias=True)
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print("Round-trip OK.")
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if __name__ == "__main__":
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main()
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