diff --git a/concrete-beam/assets/beam-section.typ b/concrete-beam/assets/beam-section.typ new file mode 100644 index 0000000..3f62aa3 --- /dev/null +++ b/concrete-beam/assets/beam-section.typ @@ -0,0 +1,35 @@ +// 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]) + ] +} diff --git a/concrete-beam/beam_section.py b/concrete-beam/beam_section.py new file mode 100644 index 0000000..3752d00 --- /dev/null +++ b/concrete-beam/beam_section.py @@ -0,0 +1,201 @@ +from __future__ import annotations + +import sys +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 + +MUTED = 'rgb("#626b73")' + + +def _f(value: float) -> str: + return f"{value:.4g}" + + +def _centers(size: float, number: int, bw: float, cover: float, stirrup_db: float) -> list[float]: + half = size / 2.0 + left = cover + stirrup_db + half + right = bw - left + if number == 1: + return [bw / 2.0] + return [left + index * (right - left) / (number - 1) for index in range(number)] + + +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"]) + n_bars = int(values["n_bars"]) + top_bar_size = int(values["top_bar_size"]) + top_bar_db = float(values["top_bar_db"]) + n_top_bars = int(values["n_top_bars"]) + As = float(values["As"]) + + w_sec = bw * s + h_sec = h * s + width = LEFT + w_sec + RIGHT + height = TOP + h_sec + BOTTOM + ox = LEFT + oy = TOP + + def sx(x_in: float) -> float: + return ox + x_in * s + + 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) + + lines: list[str] = [] + add = lines.append + add("// Generated by beam_section.py from input.yaml - do not edit by hand.") + add("#let beam-section() = {") + add(f" box(width: {_f(width)}pt, height: {_f(height)}pt)[") + + add( + f" #place(dx: {_f(ox)}pt, dy: {_f(oy)}pt, " + f'rect(width: {_f(w_sec)}pt, height: {_f(h_sec)}pt, fill: rgb("#f2f2f2"), stroke: 1pt + black))' + ) + 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))" + ) + + for x_in in bottom: + r = bar_db / 2.0 * s + add( + f" #place(dx: {_f(sx(x_in) - r)}pt, dy: {_f(sy(y_bottom) - r)}pt, " + f"circle(radius: {_f(r)}pt, fill: black))" + ) + for x_in in top: + r = top_bar_db / 2.0 * s + add( + f" #place(dx: {_f(sx(x_in) - r)}pt, dy: {_f(sy(top_y) - r)}pt, " + f"circle(radius: {_f(r)}pt, fill: black))" + ) + + dim_y = oy + h_sec + 16.0 + add( + f" #place(line(start: ({_f(ox)}pt, {_f(dim_y)}pt), end: ({_f(ox + w_sec)}pt, {_f(dim_y)}pt), " + f"stroke: 0.6pt + black))" + ) + 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"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)[$b_w = {_f(bw)} " in"$]))' + ) + + x_h = ox - 12.0 + 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"stroke: 0.6pt + black))" + ) + add( + f" #place(dx: 2pt, dy: {_f(oy + h_sec / 2.0 - 5)}pt, " + f'text(size: 8pt)[$h = {_f(h)} " in"$])' + ) + + 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 + + def leader(fx: float, fy: float, lx: float, ly: float) -> None: + add( + f" #place(line(start: ({_f(fx)}pt, {_f(fy)}pt), end: ({_f(lx)}pt, {_f(ly)}pt), " + f"stroke: 0.5pt + {MUTED}))" + ) + 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) + 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])" + ) + + leader(sx(bw - inset), sy(h / 2.0), lead_x, oy + h_sec / 2.0 - 4.0) + 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.])" + ) + + leader(sx(bottom[-1]), sy(y_bottom), lead_x, oy + h_sec - 18.0) + 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])' + ) + + add(" ]") + add("}") + return "\n".join(lines) + "\n" + + +def write_fragment(values: dict, path: Path) -> None: + path.write_text(render(values), encoding="utf-8") + + +def main(argv: list[str] | None = None) -> int: + argv = sys.argv[1:] if argv is None else argv + input_path = Path(argv[0]) if argv else HERE / "input.yaml" + output_path = Path(argv[1]) if len(argv) > 1 else HERE / "assets" / "beam-section.typ" + + import yaml + import calc + + with input_path.open(encoding="utf-8") as handle: + result = calc.compute(yaml.safe_load(handle)) + write_fragment(result["values"], output_path) + print(output_path) + return 0 + + +if __name__ == "__main__": + raise SystemExit(main()) diff --git a/concrete-beam/calc.py b/concrete-beam/calc.py index 86a1b08..c880e97 100644 --- a/concrete-beam/calc.py +++ b/concrete-beam/calc.py @@ -36,6 +36,23 @@ def quantity(value, unit: str, name: str) -> float: return magnitude +def count(value, name: str, minimum: int = 1) -> int: + try: + number = int(value) + except (TypeError, ValueError) as exc: + raise ValueError(f"{name}: expected an integer, got {value!r}") from exc + if number < minimum: + raise ValueError(f"{name} must be >= {minimum}") + return number + + +def bar_number(value, name: str) -> int: + number = count(value, name, minimum=3) + if number > 18: + raise ValueError(f"{name} must be between 3 and 18") + return number + + def compute(inp: dict) -> dict: span = quantity(inp["span"], "ft", "span") tributary = quantity(inp["tributary"], "ft", "tributary") @@ -48,6 +65,13 @@ def compute(inp: dict) -> dict: 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") + stirrup_spacing = quantity(inp["stirrup_spacing"], "in", "stirrup_spacing") + bar_size = bar_number(inp["bar_size"], "bar_size") + n_bars = count(inp["n_bars"], "n_bars") + top_bar_size = bar_number(inp["top_bar_size"], "top_bar_size") + n_top_bars = count(inp["n_top_bars"], "n_top_bars") self_weight = (bw * h / 144.0) * concrete_density / 1000.0 wD = D * tributary / 1000.0 + self_weight @@ -73,6 +97,19 @@ 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: + raise ValueError("effective depth d is too large for the specified cover and bars") + inner_width = bw - 2.0 * (cover + stirrup_db) + if n_bars * bar_db > inner_width: + raise ValueError("bottom bars do not fit within the stirrup width") + def q(value: float) -> float: return round(value, 6) @@ -106,6 +143,17 @@ def compute(inp: dict) -> dict: "As_min": q(As_min), "Vc": q(Vc), "phiVc": q(phiVc), + "cover": q(cover), + "stirrup_size": stirrup_size, + "stirrup_spacing": q(stirrup_spacing), + "stirrup_db": q(stirrup_db), + "bar_size": bar_size, + "n_bars": n_bars, + "bar_db": q(bar_db), + "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": { @@ -131,6 +179,17 @@ def write_results(result: dict, path: Path) -> None: path.write_text(json.dumps(result, indent=2) + "\n", encoding="utf-8") +def _load_section_module(): + import importlib.util + + spec = importlib.util.spec_from_file_location("beam_section", HERE / "beam_section.py") + if spec is None or spec.loader is None: + raise SystemExit("Could not load beam_section.py") + module = importlib.util.module_from_spec(spec) + spec.loader.exec_module(module) + return module + + def main() -> int: input_path = Path(sys.argv[1]) if len(sys.argv) > 1 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Numbers come from `calc caption: [#n.span ft simply supported beam, #n.bw in × #n.h in rectangular section.], ) +== Section and Reinforcement + +#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). + ], +) + == Loads and Beam Demand #calcline([$L = #n.span " ft"$], [Simple span]) diff --git a/concrete-beam/input.yaml b/concrete-beam/input.yaml index 698db78..91635fe 100644 --- a/concrete-beam/input.yaml +++ b/concrete-beam/input.yaml @@ -13,3 +13,11 @@ fy: "60 ksi" As: "0.62 in**2" concrete_density: "150 pcf" load_combination: "1.2D + 1.6L" + +cover: "1.5 in" +stirrup_size: 3 +stirrup_spacing: "6 in" +bar_size: 5 +n_bars: 2 +top_bar_size: 4 +n_top_bars: 2 diff --git a/concrete-beam/results.json b/concrete-beam/results.json index db84d98..3120cbd 100644 --- a/concrete-beam/results.json +++ b/concrete-beam/results.json @@ -27,7 +27,18 @@ "phiMn": 23.961176, "As_min": 0.253333, "Vc": 8.325383, - "phiVc": 6.244037 + "phiVc": 6.244037, + "cover": 1.5, + "stirrup_size": 3, + "stirrup_spacing": 6.0, + "stirrup_db": 0.375, + "bar_size": 5, + "n_bars": 2, + "bar_db": 0.625, + "top_bar_size": 4, + "n_top_bars": 2, + "top_bar_db": 0.5, + "As_bars": 0.613592 }, "checks": { "flexure": { diff --git a/concrete-beam/test_concrete_beam.py b/concrete-beam/test_concrete_beam.py index ad4ad51..6a59edb 100644 --- a/concrete-beam/test_concrete_beam.py +++ b/concrete-beam/test_concrete_beam.py @@ -1,5 +1,6 @@ from pathlib import Path import importlib.util +import math import pytest @@ -13,6 +14,14 @@ spec.loader.exec_module(calc_module) compute = calc_module.compute +def _load(name: str, filename: str): + spec = importlib.util.spec_from_file_location(name, HERE / filename) + assert spec is not None and spec.loader is not None + module = importlib.util.module_from_spec(spec) + spec.loader.exec_module(module) + return module + + @pytest.fixture def result(): import yaml @@ -44,3 +53,35 @@ def test_example_min_steel_and_shear(result): assert v["phiVc"] == pytest.approx(6.244016, rel=1e-4) assert result["checks"]["minimum_steel"]["ok"] is True assert result["checks"]["shear"]["ok"] is True + + +def test_reinforcement_geometry(result): + v = result["values"] + assert v["cover"] == pytest.approx(1.5) + assert v["stirrup_size"] == 3 + assert v["stirrup_db"] == pytest.approx(0.375) + assert v["stirrup_spacing"] == pytest.approx(6.0) + assert v["bar_size"] == 5 + assert v["n_bars"] == 2 + assert v["bar_db"] == pytest.approx(0.625) + 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) + + +def test_rejects_depth_without_room_for_bars(): + import yaml + + with (HERE / "input.yaml").open(encoding="utf-8") as handle: + inp = yaml.safe_load(handle) + inp["d"] = "11.9 in" + with pytest.raises(ValueError): + compute(inp) + + +def test_section_fragment_is_current(result): + module = _load("beam_section", "beam_section.py") + expected = module.render(result["values"]) + actual = (HERE / "assets" / "beam-section.typ").read_text(encoding="utf-8") + assert actual == expected