From 759d5e3baebe67c9ad996194939c3f376e21706b Mon Sep 17 00:00:00 2001 From: smillmorel Date: Mon, 21 Sep 2026 19:16:57 -0400 Subject: [PATCH] Refine beam section figure and derive As from bars - Derive As from the provided longitudinal bars instead of taking it as input; drop the redundant As_bars output and update tests. - Draw a fixed schematic 1 in cover and pin the bottom bars to the stirrup's bottom leg so the figure no longer depends on cover or d. - Fixed stirrup stroke with a rounded 3 pt corner radius. - Right-align the figure, constrain its caption to the image width, and shorten the caption to "Beam cross-section". - Document input.yaml fields. --- concrete-beam/assets/beam-section.typ | 55 +- concrete-beam/beam_section.py | 90 +- concrete-beam/calc.py | 12 +- concrete-beam/concrete-beam.pdf | 1106 ++++++++++++------------- concrete-beam/concrete-beam.typ | 11 +- concrete-beam/input.yaml | 21 +- concrete-beam/results.json | 17 +- concrete-beam/test_concrete_beam.py | 8 +- 8 files changed, 639 insertions(+), 681 deletions(-) diff --git a/concrete-beam/assets/beam-section.typ b/concrete-beam/assets/beam-section.typ index 3f62aa3..e5d2a3b 100644 --- a/concrete-beam/assets/beam-section.typ +++ b/concrete-beam/assets/beam-section.typ @@ -1,35 +1,28 @@ // Generated by beam_section.py from input.yaml - do not edit by hand. #let beam-section() = { - box(width: 302pt, height: 246pt)[ - #place(dx: 80pt, dy: 34pt, rect(width: 112pt, height: 168pt, fill: rgb("#f2f2f2"), stroke: 1pt + black)) - #place(dx: 103.6pt, dy: 57.62pt, rect(width: 64.75pt, height: 120.8pt, radius: 1.5pt, stroke: 5.25pt + black)) - #place(dx: 106.2pt, dy: 162.6pt, circle(radius: 4.375pt, fill: black)) - #place(dx: 157pt, dy: 162.6pt, circle(radius: 4.375pt, fill: black)) - #place(dx: 106.2pt, dy: 60.25pt, circle(radius: 3.5pt, fill: black)) - #place(dx: 158.8pt, dy: 60.25pt, circle(radius: 3.5pt, fill: black)) - #place(line(start: (80pt, 218pt), end: (192pt, 218pt), stroke: 0.6pt + black)) - #place(line(start: (80pt, 214pt), end: (80pt, 222pt), stroke: 0.6pt + black)) - #place(line(start: (192pt, 214pt), end: (192pt, 222pt), stroke: 0.6pt + black)) - #place(dx: 80pt, dy: 221pt, box(width: 112pt, align(center)[$b_w = 8 " in"$])) - #place(line(start: (68pt, 34pt), end: (68pt, 202pt), stroke: 0.6pt + black)) - #place(line(start: (64pt, 34pt), end: (72pt, 34pt), stroke: 0.6pt + black)) - #place(line(start: (64pt, 202pt), end: (72pt, 202pt), stroke: 0.6pt + black)) - #place(dx: 2pt, dy: 113pt, text(size: 8pt)[$h = 12 " in"$]) - #place(line(start: (50pt, 34pt), end: (50pt, 167pt), stroke: 0.6pt + black)) - #place(line(start: (46pt, 34pt), end: (54pt, 34pt), stroke: 0.6pt + black)) - #place(line(start: (46pt, 167pt), end: (54pt, 167pt), stroke: 0.6pt + black)) - #place(dx: 2pt, dy: 95.5pt, text(size: 8pt)[$d = 9.5 " in"$]) - #place(line(start: (162.2pt, 63.75pt), end: (204pt, 52pt), stroke: 0.5pt + rgb("#626b73"))) - #place(dx: 160.8pt, dy: 62.25pt, circle(radius: 1.5pt, fill: black)) - #place(dx: 208pt, dy: 46pt, text(size: 7.5pt)[2 No. 4 hanger \ bars]) - #place(line(start: (168.4pt, 118pt), end: (204pt, 114pt), stroke: 0.5pt + rgb("#626b73"))) - #place(dx: 166.9pt, dy: 116.5pt, circle(radius: 1.5pt, fill: black)) - #place(dx: 208pt, dy: 108pt, text(size: 7.5pt)[No. 3 stirrup \ at 6 in o.c.]) - #place(line(start: (161.4pt, 167pt), end: (204pt, 184pt), stroke: 0.5pt + rgb("#626b73"))) - #place(dx: 159.9pt, dy: 165.5pt, circle(radius: 1.5pt, fill: black)) - #place(dx: 208pt, dy: 178pt, text(size: 7.5pt)[2 No. 5 bottom \ $A_s = 0.62 " in"^2$]) - #place(line(start: (103.6pt, 178.4pt), end: (40pt, 228pt), stroke: 0.5pt + rgb("#626b73"))) - #place(dx: 102.1pt, dy: 176.9pt, circle(radius: 1.5pt, fill: black)) - #place(dx: 2pt, dy: 232pt, text(size: 7.5pt)[cover = 1.5 in]) + box(width: 180pt, height: 180pt)[ + #place(dx: 48pt, dy: 28pt, rect(width: 76pt, height: 114pt, fill: rgb("#f2f2f2"), stroke: 1pt + black)) + #place(dx: 58.5pt, dy: 38.5pt, rect(width: 55pt, height: 93pt, radius: 3pt, stroke: 2pt + black)) + #place(dx: 59.5pt, dy: 124.6pt, circle(radius: 2.969pt, fill: black)) + #place(dx: 106.6pt, dy: 124.6pt, circle(radius: 2.969pt, fill: black)) + #place(dx: 59.5pt, dy: 39.5pt, circle(radius: 2.375pt, fill: black)) + #place(dx: 107.8pt, dy: 39.5pt, circle(radius: 2.375pt, fill: black)) + #place(line(start: (48pt, 158pt), end: (124pt, 158pt), stroke: 0.6pt + black)) + #place(line(start: (48pt, 155pt), end: (48pt, 161pt), stroke: 0.6pt + black)) + #place(line(start: (124pt, 155pt), end: (124pt, 161pt), stroke: 0.6pt + black)) + #place(dx: 48pt, dy: 161pt, box(width: 76pt, align(center, text(size: 7pt)[$b_w = 8 " in"$]))) + #place(line(start: (42pt, 28pt), end: (42pt, 142pt), stroke: 0.6pt + black)) + #place(line(start: (39pt, 28pt), end: (45pt, 28pt), stroke: 0.6pt + black)) + #place(line(start: (39pt, 142pt), end: (45pt, 142pt), stroke: 0.6pt + black)) + #place(dx: 0.5pt, dy: 82pt, text(size: 7pt)[$h = 12 " in"$]) + #place(line(start: (110.1pt, 41.88pt), end: (129pt, 42pt), stroke: 0.5pt + rgb("#626b73"))) + #place(dx: 108.6pt, dy: 40.38pt, circle(radius: 1.5pt, fill: black)) + #place(dx: 132pt, dy: 37pt, text(size: 7pt)[2 No. 4 hanger \ bars]) + #place(line(start: (113.5pt, 85pt), end: (129pt, 82pt), stroke: 0.5pt + rgb("#626b73"))) + #place(dx: 112pt, dy: 83.5pt, circle(radius: 1.5pt, fill: black)) + #place(dx: 132pt, dy: 77pt, text(size: 7pt)[No. 3 stirrup \ at 6 in o.c.]) + #place(line(start: (109.5pt, 127.5pt), end: (129pt, 128pt), stroke: 0.5pt + rgb("#626b73"))) + #place(dx: 108pt, dy: 126pt, circle(radius: 1.5pt, fill: black)) + #place(dx: 132pt, dy: 123pt, text(size: 7pt)[2 No. 5 bottom \ $A_s = 0.6136 " in"^2$]) ] } diff --git a/concrete-beam/beam_section.py b/concrete-beam/beam_section.py index 3752d00..bff3c6a 100644 --- a/concrete-beam/beam_section.py +++ b/concrete-beam/beam_section.py @@ -6,11 +6,15 @@ from pathlib import Path HERE = Path(__file__).resolve().parent -SCALE = 14.0 # points per inch -LEFT = 80.0 -RIGHT = 110.0 -TOP = 34.0 -BOTTOM = 44.0 +SCALE = 9.5 # points per inch +LEFT = 48.0 +RIGHT = 56.0 +TOP = 28.0 +BOTTOM = 38.0 + +STIRRUP_STROKE = 2.0 # drawn stirrup line width, points +STIRRUP_RADIUS = 3.0 # drawn stirrup corner radius, points +DRAW_COVER = 1.0 # schematic cover shown in the drawing, inches MUTED = 'rgb("#626b73")' @@ -19,9 +23,9 @@ def _f(value: float) -> str: return f"{value:.4g}" -def _centers(size: float, number: int, bw: float, cover: float, stirrup_db: float) -> list[float]: +def _centers(size: float, number: int, bw: float, edge: float) -> list[float]: half = size / 2.0 - left = cover + stirrup_db + half + left = edge + half right = bw - left if number == 1: return [bw / 2.0] @@ -32,10 +36,7 @@ def render(values: dict) -> str: s = SCALE bw = float(values["bw"]) h = float(values["h"]) - d = float(values["d"]) - cover = float(values["cover"]) stirrup_size = int(values["stirrup_size"]) - stirrup_db = float(values["stirrup_db"]) stirrup_spacing = float(values["stirrup_spacing"]) bar_size = int(values["bar_size"]) bar_db = float(values["bar_db"]) @@ -58,11 +59,12 @@ def render(values: dict) -> str: def sy(y_in: float) -> float: return oy + (h - y_in) * s - inset = cover + stirrup_db / 2.0 - y_bottom = h - d - bottom = _centers(bar_db, n_bars, bw, cover, stirrup_db) - top_y = h - (cover + stirrup_db + top_bar_db / 2.0) - top = _centers(top_bar_db, n_top_bars, bw, cover, stirrup_db) + edge = DRAW_COVER + STIRRUP_STROKE / s + inset = DRAW_COVER + STIRRUP_STROKE / s / 2.0 + y_bottom = edge + bar_db / 2.0 + bottom = _centers(bar_db, n_bars, bw, edge) + top_y = h - (edge + top_bar_db / 2.0) + top = _centers(top_bar_db, n_top_bars, bw, edge) lines: list[str] = [] add = lines.append @@ -77,7 +79,7 @@ def render(values: dict) -> str: add( f" #place(dx: {_f(sx(inset))}pt, dy: {_f(sy(h - inset))}pt, " f"rect(width: {_f((bw - 2.0 * inset) * s)}pt, height: {_f((h - 2.0 * inset) * s)}pt, " - f"radius: 1.5pt, stroke: {_f(stirrup_db * s)}pt + black))" + f"radius: {_f(STIRRUP_RADIUS)}pt, stroke: {_f(STIRRUP_STROKE)}pt + black))" ) for x_in in bottom: @@ -100,47 +102,31 @@ def render(values: dict) -> str: ) for tick in (ox, ox + w_sec): add( - f" #place(line(start: ({_f(tick)}pt, {_f(dim_y - 4)}pt), end: ({_f(tick)}pt, {_f(dim_y + 4)}pt), " + f" #place(line(start: ({_f(tick)}pt, {_f(dim_y - 3)}pt), end: ({_f(tick)}pt, {_f(dim_y + 3)}pt), " f"stroke: 0.6pt + black))" ) add( f" #place(dx: {_f(ox)}pt, dy: {_f(dim_y + 3)}pt, " - f'box(width: {_f(w_sec)}pt, align(center)[$b_w = {_f(bw)} " in"$]))' + f'box(width: {_f(w_sec)}pt, align(center, text(size: 7pt)[$b_w = {_f(bw)} " in"$])))' ) - x_h = ox - 12.0 + x_h = ox - 6.0 add( f" #place(line(start: ({_f(x_h)}pt, {_f(oy)}pt), end: ({_f(x_h)}pt, {_f(oy + h_sec)}pt), " f"stroke: 0.6pt + black))" ) for tick in (oy, oy + h_sec): add( - f" #place(line(start: ({_f(x_h - 4)}pt, {_f(tick)}pt), end: ({_f(x_h + 4)}pt, {_f(tick)}pt), " + f" #place(line(start: ({_f(x_h - 3)}pt, {_f(tick)}pt), end: ({_f(x_h + 3)}pt, {_f(tick)}pt), " f"stroke: 0.6pt + black))" ) add( - f" #place(dx: 2pt, dy: {_f(oy + h_sec / 2.0 - 5)}pt, " - f'text(size: 8pt)[$h = {_f(h)} " in"$])' + f" #place(dx: 0.5pt, dy: {_f(oy + h_sec / 2.0 - 3)}pt, " + f'text(size: 7pt)[$h = {_f(h)} " in"$])' ) - x_d = ox - 30.0 - d_end = oy + d * s - add( - f" #place(line(start: ({_f(x_d)}pt, {_f(oy)}pt), end: ({_f(x_d)}pt, {_f(d_end)}pt), " - f"stroke: 0.6pt + black))" - ) - for tick in (oy, d_end): - add( - f" #place(line(start: ({_f(x_d - 4)}pt, {_f(tick)}pt), end: ({_f(x_d + 4)}pt, {_f(tick)}pt), " - f"stroke: 0.6pt + black))" - ) - add( - f" #place(dx: 2pt, dy: {_f((oy + d_end) / 2.0 - 5)}pt, " - f'text(size: 8pt)[$d = {_f(d)} " in"$])' - ) - - label_x = ox + w_sec + 16.0 - lead_x = ox + w_sec + 12.0 + label_x = ox + w_sec + 8.0 + lead_x = ox + w_sec + 5.0 def leader(fx: float, fy: float, lx: float, ly: float) -> None: add( @@ -149,28 +135,22 @@ def render(values: dict) -> str: ) add(f" #place(dx: {_f(fx - 1.5)}pt, dy: {_f(fy - 1.5)}pt, circle(radius: 1.5pt, fill: black))") - leader(sx(top[-1]), sy(top_y), lead_x, oy + 18.0) + leader(sx(top[-1]), sy(top_y), lead_x, oy + 14.0) add( - f" #place(dx: {_f(label_x)}pt, dy: {_f(oy + 12)}pt, " - f"text(size: 7.5pt)[{n_top_bars} No. {top_bar_size} hanger \\ bars])" + f" #place(dx: {_f(label_x)}pt, dy: {_f(oy + 9)}pt, " + f"text(size: 7pt)[{n_top_bars} No. {top_bar_size} hanger \\ bars])" ) - leader(sx(bw - inset), sy(h / 2.0), lead_x, oy + h_sec / 2.0 - 4.0) + leader(sx(bw - inset), sy(h / 2.0), lead_x, oy + h_sec / 2.0 - 3.0) add( - f" #place(dx: {_f(label_x)}pt, dy: {_f(oy + h_sec / 2.0 - 10)}pt, " - f"text(size: 7.5pt)[No. {stirrup_size} stirrup \\ at {_f(stirrup_spacing)} in o.c.])" + f" #place(dx: {_f(label_x)}pt, dy: {_f(oy + h_sec / 2.0 - 8)}pt, " + f"text(size: 7pt)[No. {stirrup_size} stirrup \\ at {_f(stirrup_spacing)} in o.c.])" ) - leader(sx(bottom[-1]), sy(y_bottom), lead_x, oy + h_sec - 18.0) + leader(sx(bottom[-1]), sy(y_bottom), lead_x, oy + h_sec - 14.0) add( - f" #place(dx: {_f(label_x)}pt, dy: {_f(oy + h_sec - 24)}pt, " - f'text(size: 7.5pt)[{n_bars} No. {bar_size} bottom \\ $A_s = {_f(As)} " in"^2$])' - ) - - leader(sx(inset), sy(inset), 40.0, oy + h_sec + 26.0) - add( - f" #place(dx: 2pt, dy: {_f(oy + h_sec + 30)}pt, " - f'text(size: 7.5pt)[cover = {_f(cover)} in])' + f" #place(dx: {_f(label_x)}pt, dy: {_f(oy + h_sec - 19)}pt, " + f'text(size: 7pt)[{n_bars} No. {bar_size} bottom \\ $A_s = {_f(As)} " in"^2$])' ) add(" ]") diff --git a/concrete-beam/calc.py b/concrete-beam/calc.py index c880e97..7c8fe95 100644 --- a/concrete-beam/calc.py +++ b/concrete-beam/calc.py @@ -63,7 +63,6 @@ def compute(inp: dict) -> dict: d = quantity(inp["d"], "in", "d") fc = quantity(inp["fc"], "ksi", "fc") fy = quantity(inp["fy"], "ksi", "fy") - As = quantity(inp["As"], "in**2", "As") concrete_density = quantity(inp["concrete_density"], "pcf", "concrete_density") cover = quantity(inp["cover"], "in", "cover") stirrup_size = bar_number(inp["stirrup_size"], "stirrup_size") @@ -73,6 +72,11 @@ def compute(inp: dict) -> dict: top_bar_size = bar_number(inp["top_bar_size"], "top_bar_size") n_top_bars = count(inp["n_top_bars"], "n_top_bars") + stirrup_db = stirrup_size / 8.0 + bar_db = bar_size / 8.0 + top_bar_db = top_bar_size / 8.0 + As = n_bars * math.pi * bar_db**2 / 4.0 + self_weight = (bw * h / 144.0) * concrete_density / 1000.0 wD = D * tributary / 1000.0 + self_weight wL = L * tributary / 1000.0 @@ -97,11 +101,6 @@ def compute(inp: dict) -> dict: Vc = 2.0 * math.sqrt(fc * 1000.0) * bw * d / 1000.0 phiVc = 0.75 * Vc - stirrup_db = stirrup_size / 8.0 - bar_db = bar_size / 8.0 - top_bar_db = top_bar_size / 8.0 - As_bars = n_bars * math.pi * bar_db**2 / 4.0 - bottom_centroid = h - d min_bottom_centroid = cover + stirrup_db + bar_db / 2.0 if bottom_centroid < min_bottom_centroid: @@ -153,7 +152,6 @@ def compute(inp: dict) -> dict: "top_bar_size": top_bar_size, "n_top_bars": n_top_bars, "top_bar_db": q(top_bar_db), - "As_bars": q(As_bars), }, "checks": { "flexure": { diff --git a/concrete-beam/concrete-beam.pdf b/concrete-beam/concrete-beam.pdf index 1b60d97..7e978bc 100644 --- a/concrete-beam/concrete-beam.pdf +++ b/concrete-beam/concrete-beam.pdf @@ -2,46 +2,46 @@ % 1 0 obj -<> +<> endobj 2 0 obj -<> +<> endobj 3 0 obj -<> +<> endobj 4 0 obj -<> +<> endobj 5 0 obj -<> +<> endobj 6 0 obj -<> +<> endobj 7 0 obj <> endobj 8 0 obj -<>/K[188 0 R]/ParentTree<>/ParentTreeNextKey 2>> +<>/K[187 0 R]/ParentTree<>/ParentTreeNextKey 2>> endobj 9 0 obj -[11 0 R 13 0 R 12 0 R 13 0 R 13 0 R 17 0 R 17 0 R 18 0 R 22 0 R 14 0 R 26 0 R 29 0 R 29 0 R 29 0 R 29 0 R 29 0 R 30 0 R 30 0 R 30 0 R 30 0 R 30 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 31 0 R 33 0 R 33 0 R 33 0 R 33 0 R 33 0 R 32 0 R 32 0 R 32 0 R 32 0 R 32 0 R 32 0 R 32 0 R 32 0 R 32 0 R 33 0 R 27 0 R 27 0 R 36 0 R 37 0 R 37 0 R 37 0 R 37 0 R 37 0 R 39 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 42 0 R 44 0 R 47 0 R 47 0 R 47 0 R 47 0 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Numbers come from `calc == Section and Reinforcement -#figure( +#align(right, block(width: 2.5in, figure( beam-section(), - caption: [ - Beam cross-section: #n.bw in × #n.h in, No. #n.stirrup_size stirrups at #n.stirrup_spacing in - on center, and #n.n_bars No. #n.bar_size longitudinal bars (A_s = #n.As in²). - ], -) + caption: [Beam cross-section], +))) == Loads and Beam Demand @@ -75,7 +72,7 @@ Simple-span rectangular beam under uniform gravity load. Numbers come from `calc #calcline([$d = #n.d " in"$], [Effective depth]) #calcline([$f'_c = #n.fc " ksi"$], [Concrete compressive strength]) #calcline([$f_y = #n.fy " ksi"$], [Steel yield strength]) -#calcline([$A_s = #n.As " in"^2$], [Provided tension steel (2 No. 5)]) +#calcline([$A_s = #n.As " in"^2$], [Provided tension steel (#n.n_bars No. #n.bar_size)]) #calcline( [$a = A_s f_y / (0.85 f'_c b_w) = #round(n.a, digits: 3) " in"$], [Equivalent compression-block depth], diff --git a/concrete-beam/input.yaml b/concrete-beam/input.yaml index 91635fe..b6fc292 100644 --- a/concrete-beam/input.yaml +++ b/concrete-beam/input.yaml @@ -1,23 +1,42 @@ +# Project name shown in the Typst report header. project: "Deer Creek Shoring" +# Person or organization shown in the Typst report footer. prepared_by: "Conemco Engineering" +# Simple span used for the moment and shear demands. span: "16 ft" +# Tributary width carried by the beam. tributary: "6.25 ft" +# Dead load including superimposed dead (psf). D: "55 psf" +# Live load (psf). L: "20 psf" +# Beam web width b_w. bw: "8 in" +# Overall beam depth h. h: "12 in" +# Effective depth to the tension-steel centroid, used for flexure. d: "9.5 in" +# Concrete compressive strength f'_c. fc: "3.0 ksi" +# Steel yield strength f_y. fy: "60 ksi" -As: "0.62 in**2" +# Concrete unit weight used for the beam self-weight. concrete_density: "150 pcf" +# Factored load combination applied to the demands. load_combination: "1.2D + 1.6L" +# Clear cover from the concrete face to the stirrup. cover: "1.5 in" +# Stirrup bar number (#3). stirrup_size: 3 +# Stirrup spacing along the span, on center. stirrup_spacing: "6 in" +# Bottom (tension) longitudinal bar number (#5). bar_size: 5 +# Number of bottom longitudinal bars. n_bars: 2 +# Top (hanger) longitudinal bar number (#4). top_bar_size: 4 +# Number of top hanger bars. n_top_bars: 2 diff --git a/concrete-beam/results.json b/concrete-beam/results.json index 3120cbd..9ca010d 100644 --- a/concrete-beam/results.json +++ b/concrete-beam/results.json @@ -19,12 +19,12 @@ "d": 9.5, "fc": 3.0, "fy": 60.0, - "As": 0.62, - "a": 1.823529, - "et": 0.010285, + "As": 0.613592, + "a": 1.804683, + "et": 0.010423, "phi": 0.9, - "Mn": 26.623529, - "phiMn": 23.961176, + "Mn": 26.377285, + "phiMn": 23.739557, "As_min": 0.253333, "Vc": 8.325383, "phiVc": 6.244037, @@ -37,18 +37,17 @@ "bar_db": 0.625, "top_bar_size": 4, "n_top_bars": 2, - "top_bar_db": 0.5, - "As_bars": 0.613592 + "top_bar_db": 0.5 }, "checks": { "flexure": { "demand": 23.44, - "capacity": 23.961176, + "capacity": 23.739557, "ok": true }, "minimum_steel": { "demand": 0.253333, - "capacity": 0.62, + "capacity": 0.613592, "ok": true }, "shear": { diff --git a/concrete-beam/test_concrete_beam.py b/concrete-beam/test_concrete_beam.py index 6a59edb..9aa94d6 100644 --- a/concrete-beam/test_concrete_beam.py +++ b/concrete-beam/test_concrete_beam.py @@ -40,10 +40,10 @@ def test_example_demands(result): def test_example_flexure(result): v = result["values"] - assert v["a"] == pytest.approx(1.823529, rel=1e-5) - assert v["et"] == pytest.approx(0.010283, rel=1e-3) + assert v["a"] == pytest.approx(1.804683, rel=1e-5) + assert v["et"] == pytest.approx(0.010423, rel=1e-3) assert v["phi"] == pytest.approx(0.9) - assert v["phiMn"] == pytest.approx(23.961176, rel=1e-5) + assert v["phiMn"] == pytest.approx(23.739557, rel=1e-5) assert result["checks"]["flexure"]["ok"] is True @@ -67,7 +67,7 @@ def test_reinforcement_geometry(result): assert v["top_bar_size"] == 4 assert v["n_top_bars"] == 2 assert v["top_bar_db"] == pytest.approx(0.5) - assert v["As_bars"] == pytest.approx(2 * math.pi * 0.625**2 / 4.0, rel=1e-6) + assert v["As"] == pytest.approx(2 * math.pi * 0.625**2 / 4.0, rel=1e-6) def test_rejects_depth_without_room_for_bars():