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25592fa6c2
ci / test (push) Successful in 6m14s
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.
111 lines
4.4 KiB
Python
111 lines
4.4 KiB
Python
# -*- coding: utf-8 -*-
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"""The beam solver must reproduce PCI Figure 8.3.2 from first principles.
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This is the test the whole design rests on. Figure 8.3.2's coefficients are
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not a separate method -- they are the closed-form solution of a uniformly
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loaded beam with two overhangs, with the supports placed where the positive
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and negative moments come out equal. If our solver cannot land on 0.0214 with
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the supports there, it cannot be trusted with the supports somewhere else,
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which is the only case anyone actually needs it for.
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"""
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import math
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from panellift import pci, section, statics
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from panellift.model import Stage
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from conftest import ASPIRE, LENGTH_FT, WIDTH_FT
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def test_optimal_support_fraction_is_the_root_of_the_quadratic():
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a = pci.OPTIMAL_TWO_LINE_FRACTION
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assert abs(4 * a ** 2 + 4 * a - 1) < 1e-12
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assert abs(a - 0.20710678) < 1e-7
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def test_closed_form_coefficient_is_pcis_0_0214():
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"""M = w*(aL)^2/2 with a = (sqrt(2)-1)/2 gives 0.02145, printed as 0.0214."""
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a = pci.OPTIMAL_TWO_LINE_FRACTION
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coefficient = a ** 2 / 2.0
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assert abs(coefficient - 0.0214) < 0.0001
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def test_solver_reproduces_my_coefficient(solid_panel, rolling):
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"""The numerical diagram must match 0.0214 w a b^2 to within 0.5%."""
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stage = Stage(name='unfactored', multiplier=1.0, fc_psi=4000.0)
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result = statics.analyse(solid_panel, stage, rolling,
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reconcile_weight=False)
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w_psf = section.unit_weight_psf(solid_panel)
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_, expected = pci.fig_832_four_point(w_psf, WIDTH_FT, LENGTH_FT)
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_, m_pos = result.diagram.max_positive
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_, m_neg = result.diagram.max_negative
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assert abs(m_pos - expected) / expected < 0.005
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assert abs(abs(m_neg) - expected) / expected < 0.005
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def test_positive_and_negative_moments_are_equal_at_the_optimum(solid_panel,
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rolling):
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"""That equality is the definition of the Figure 8.3.2 layout."""
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stage = Stage(name='unfactored', multiplier=1.0, fc_psi=4000.0)
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result = statics.analyse(solid_panel, stage, rolling,
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reconcile_weight=False)
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_, m_pos = result.diagram.max_positive
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_, m_neg = result.diagram.max_negative
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assert abs(m_pos - abs(m_neg)) / m_pos < 0.01
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def test_unit_weight_matches_the_article(solid_panel):
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assert abs(section.unit_weight_psf(solid_panel) -
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ASPIRE['w_psf']) < 0.1
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def _peak_abs_moment(result):
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"""The governing moment, whichever sign it has.
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Bunching the picks inboard turns the panel into two long cantilevers, and
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then the whole interior hogs -- the largest positive moment is zero, at
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the ends. Comparing only sagging would read that as an improvement.
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"""
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_, positive = result.diagram.max_positive
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_, negative = result.diagram.max_negative
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return max(abs(positive), abs(negative))
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def test_moving_the_supports_inboard_raises_the_governing_moment(solid_panel,
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rolling):
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"""A sanity check that the solver is solving, not returning a constant."""
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stage = Stage(name='unfactored', multiplier=1.0, fc_psi=4000.0)
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optimum = _peak_abs_moment(
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statics.analyse(solid_panel, stage, rolling, reconcile_weight=False))
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for lifter in solid_panel.lifters:
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lifter.x = LENGTH_FT / 2.0 + math.copysign(
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4.0, lifter.x - LENGTH_FT / 2.0)
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moved = _peak_abs_moment(
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statics.analyse(solid_panel, stage, rolling, reconcile_weight=False))
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assert moved > optimum * 1.5
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def test_the_optimum_layout_really_is_the_optimum(solid_panel, rolling):
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"""No other support position beats (sqrt(2)-1)/2. Worth proving once.
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This is what makes the PCI layout a benchmark the report can measure a
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detailer's actual layout against, rather than just another arrangement.
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"""
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stage = Stage(name='unfactored', multiplier=1.0, fc_psi=4000.0)
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best = _peak_abs_moment(
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statics.analyse(solid_panel, stage, rolling, reconcile_weight=False))
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for fraction in (0.10, 0.15, 0.18, 0.23, 0.26, 0.30):
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left = fraction * LENGTH_FT
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for lifter in solid_panel.lifters:
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lifter.x = left if lifter.x < LENGTH_FT / 2.0 else LENGTH_FT - left
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trial = _peak_abs_moment(
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statics.analyse(solid_panel, stage, rolling,
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reconcile_weight=False))
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assert trial >= best * 0.999, (
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'fraction {0} beat the supposed optimum'.format(fraction))
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