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History-free snapshot of the private development repository at 77a82eb. Code, docs and the public catalogue only: no plant or job knowledge layers, no client, job or producer names (tools/scrub.py clean against the widened term list; a second word-level grep clean). The intro deck is left out because its slide images cannot be checked for job drawings.
197 lines
8.9 KiB
Python
197 lines
8.9 KiB
Python
# -*- coding: utf-8 -*-
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"""The insulated-sandwich SECTION path in `section.py` / `capacity.py`.
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Every expected number here is arithmetic done by hand, written out beside it,
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and -- where a golden figure exists -- pinned to the value Eriksson Wall's own
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section table prints, NOT to the code's own expression. A pin that recomputes
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both sides agrees with any refactor, including a wrong one.
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THE GOLDEN PIECE is WPB3.0 Run 1 (docs/eriksson-wall-algorithms.md sec.12 and
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the extracted `WPB3.0.md`): a horizontal insulated wall panel, layup
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3 in. concrete + 4 in. insulation + 4 in. concrete = 11 in. envelope
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at a clear width of 24 ft = 288 in (no opening at the checked station).
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Eriksson reports, for this section (p.11 of that packet):
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Area 2016.00 in2 Cy 5.79 in Izz 29955.43 in4 Sb 5177.48 St 5744.88
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which is the FULLY-COMPOSITE transformed section of the two concrete wythes
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about their common centroid, with the insulation EXCLUDED. That is what
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`section.NetSection` must reproduce for a sandwich, and it is what closes the
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"treated as a solid 11 in prism" defect: the solid idealisation would give
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Izz = 288*11^3/12 = 31944 and S = 288*11^2/6 = 5808, both larger than the real
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section (unconservative), and its shear b*d would be 288*0.8*11, a third too
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large -- see `test_shear_bd_drops_by_the_36_percent_the_parity_run_found`.
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The task framed Eriksson's treatment as NON-composite; the golden figures do
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not bear that out (Area 2016 is BOTH wythes, and Izz 29955 is their composite
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inertia, not one wythe's), so this implements and pins the composite section
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Eriksson actually reports. The %composite knock-down Eriksson then applies
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(95% for stress/strength, 35% for in-place deflection) and the strand
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development layer are out of scope here; the more conservative non-composite /
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structural-wythe-alone bounds live in `sandwich.py`.
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"""
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import math
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import pytest
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from panellift import capacity, section
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from panellift.model import Panel, Stage
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ENVELOPE = 11.0
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WIDTH_FT = 24.0
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B_IN = WIDTH_FT * 12.0 # 288 in
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def wpb3_source():
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"""`source` as the exporter writes it for the WPB3.0 layup.
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3 in wythe at the form face (z 0-3), 4 in insulation (z 3-7), 4 in wythe
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(z 7-11). The order does not change Area / Izz / the governing S; it only
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labels which face is Sb and which is St.
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"""
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return {
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'solid_parts': [
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{'counted': True, 'z0_in': 0.0, 'z1_in': 3.0,
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'material': 'WYTHE 3IN', 'density_pcf': 150.0, 'volume_ft3': 1.0},
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{'counted': False, 'z0_in': 3.0, 'z1_in': 7.0,
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'material': 'INSULATION', 'density_pcf': 2.0, 'volume_ft3': 1.0},
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{'counted': True, 'z0_in': 7.0, 'z1_in': 11.0,
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'material': 'WYTHE 4IN', 'density_pcf': 150.0, 'volume_ft3': 1.0},
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],
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'envelope_thickness_in': ENVELOPE,
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}
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def wpb3_panel():
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return Panel(mark='WPB3', length_ft=24.0, width_ft=WIDTH_FT,
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thickness_in=ENVELOPE, unit_weight_pcf=150.0,
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fci_psi=3500.0, fc_psi=6000.0, source=wpb3_source())
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def _mid_net(panel):
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return section.NetSection(panel, panel.length_ft / 2.0)
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# ------------------------------------------------ the section, vs the golden
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def test_area_is_both_wythes_with_the_insulation_excluded():
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# A = b * (t1 + t2) = 288 * (3 + 4) = 2016.00 in2, NOT 288*11 = 3168.
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net = _mid_net(wpb3_panel())
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assert net.is_sandwich is True
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assert net.area_in2 == pytest.approx(2016.0, abs=1e-6)
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def test_centroid_is_the_composite_neutral_axis():
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# zbar = (A1*z1 + A2*z2)/A, wythes at z=1.5 and z=9:
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# = (3*1.5 + 4*9)/7 = (4.5 + 36)/7 = 5.785714 in -> Eriksson Cy 5.79
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net = _mid_net(wpb3_panel())
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assert net.zbar_in == pytest.approx(5.7857143, abs=1e-6)
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def test_through_thickness_inertia_matches_the_reported_izz():
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# Iz = b*[ t1^3/12 + t1*(z1 - zbar)^2 + t2^3/12 + t2*(z2 - zbar)^2 ]
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# = 288*[ 3^3/12 + 3*(1.5-5.785714)^2 + 4^3/12 + 4*(9-5.785714)^2 ]
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# = 288*[ 2.25 + 55.1020 + 5.3333 + 41.3265 ] = 288*104.0119 = 29955.4
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net = _mid_net(wpb3_panel())
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assert net.iz_in4 == pytest.approx(29955.43, abs=0.5) # reported 29955.43
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def test_the_two_faces_have_the_unequal_moduli_eriksson_prints():
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# c_form = 5.785714 (to z=0), c_far = 11 - 5.785714 = 5.214286 (to z=11)
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# Sb = 29955.43 / 5.785714 = 5177.5 (Eriksson 5177.48)
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# St = 29955.43 / 5.214286 = 5744.9 (Eriksson 5744.88)
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net = _mid_net(wpb3_panel())
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assert net.c_form_in == pytest.approx(5.7857143, abs=1e-6)
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assert net.c_far_in == pytest.approx(5.2142857, abs=1e-6)
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sb = net.iz_in4 / net.c_form_in
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st = net.iz_in4 / net.c_far_in
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assert sb == pytest.approx(5177.48, abs=1.0)
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assert st == pytest.approx(5744.88, abs=1.0)
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# sz_in3 is the GOVERNING (smaller) modulus, the one that decides tension.
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assert net.sz_in3 == pytest.approx(min(sb, st), abs=1e-6)
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def test_the_solid_idealisation_would_have_overstated_this_section():
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"""The number the refusal was built on: the solid 11 in prism is bigger
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than the real composite section, both in I and S -- unconservative."""
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net = _mid_net(wpb3_panel())
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solid_iz = B_IN * ENVELOPE ** 3 / 12.0 # 31944.0
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solid_sz = B_IN * ENVELOPE ** 2 / 6.0 # 5808.0
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assert solid_iz > net.iz_in4 # 31944 > 29955
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assert solid_sz > net.sz_in3 # 5808 > 5177
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# --------------------------------------------------------------- shear b*d
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def test_shear_bd_drops_by_the_36_percent_the_parity_run_found():
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"""docs sec.3.1: for a sandwich d_v = 0.8*th uses the CONCRETE depth (the
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summed wythes), not the envelope. Here that is 0.8*7 vs 0.8*11, so the
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shear area is 7/11 of the solid one -- a 36.4% drop, which is exactly the
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WPB3.0 shear residual the harness traced to b*d not excluding insulation.
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"""
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net = _mid_net(wpb3_panel())
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assert net.shear_thickness_in == pytest.approx(7.0) # concrete, not 11
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stage = Stage(name='strip', multiplier=1.4, fc_psi=3500.0)
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pt = capacity.detailed_shear_at(wpb3_panel(), stage,
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x=12.0, moment_lbft=5000.0, shear_lb=8000.0)
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solid_bd = net.width_in * capacity.pci.DV_OVER_H_SHEAR * ENVELOPE
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assert pt.bd_in2 == pytest.approx(solid_bd * 7.0 / 11.0, rel=1e-9)
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drop = 1.0 - pt.bd_in2 / solid_bd
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assert drop == pytest.approx(4.0 / 11.0, abs=1e-6) # 0.3636...
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# --------------------------------------- contiguous two-layer -> merged solid
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def test_a_contiguous_two_concrete_body_is_the_merged_solid():
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"""An architectural face cast monolithically on a structural wythe (no
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insulation gap) is not a hole in the middle -- its composite section is
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simply the solid over the whole concrete span, and that is what comes
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out. 4 in (z0-4) + 12 in (z4-16) contiguous -> a solid 16 in section."""
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src = {'solid_parts': [
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{'counted': True, 'z0_in': 4.0, 'z1_in': 16.0, 'material': 'STRUCT',
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'density_pcf': 150.0, 'volume_ft3': 1.0},
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{'counted': True, 'z0_in': 0.0, 'z1_in': 4.0, 'material': 'ARCH',
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'density_pcf': 150.0, 'volume_ft3': 1.0}],
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'envelope_thickness_in': 16.0}
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panel = Panel(mark='C', length_ft=20.0, width_ft=5.0, thickness_in=12.0,
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source=src)
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net = section.NetSection(panel, 10.0)
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b = 5.0 * 12.0
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assert net.area_in2 == pytest.approx(b * 16.0) # all 16 in concrete
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assert net.zbar_in == pytest.approx(8.0) # mid-depth: solid
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assert net.iz_in4 == pytest.approx(b * 16.0 ** 3 / 12.0)
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assert net.shear_thickness_in == pytest.approx(16.0)
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# --------------------------------------------- the solid path does not move
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def test_a_solid_panel_is_untouched():
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"""No source -> not a sandwich -> the familiar b*t, b*t^2/6, b*t^3/12,
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d_v = 0.8*t, centroid t/2. Byte-for-byte what it always was."""
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panel = Panel(mark='S', length_ft=20.0, width_ft=5.0, thickness_in=8.0)
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net = section.NetSection(panel, 10.0)
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b = 5.0 * 12.0
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assert net.is_sandwich is False
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assert net.area_in2 == pytest.approx(b * 8.0)
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assert net.zbar_in == pytest.approx(4.0)
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assert net.c_form_in == pytest.approx(4.0)
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assert net.c_far_in == pytest.approx(4.0)
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assert net.iz_in4 == pytest.approx(b * 8.0 ** 3 / 12.0)
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assert net.sz_in3 == pytest.approx(b * 8.0 ** 2 / 6.0)
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assert net.shear_thickness_in == pytest.approx(8.0)
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def test_the_free_functions_follow_the_same_section():
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"""`section.area_in2` / `section_modulus_in3` / `inertia_in4` are what
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`statics` (EI) and `layout` read; they must be the sandwich section too."""
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panel = wpb3_panel()
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x = 12.0
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net = section.NetSection(panel, x)
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assert section.area_in2(panel, x) == pytest.approx(net.area_in2, abs=1e-6)
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assert section.inertia_in4(panel, x) == pytest.approx(net.iz_in4, abs=1e-6)
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assert section.section_modulus_in3(panel, x) == pytest.approx(net.sz_in3,
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abs=1e-6)
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