concrete-beam/assets/beam-section.typ

@@ -0,0 +1,28 @@
+// Generated by beam_section.py from input.yaml - do not edit by hand.
+#let beam-section() = {
+  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) #4"))
+    #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, "#3 @ 6″"))
+    #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) #5"))
+  ]
+}

concrete-beam/beam_section.py

@@ -0,0 +1,180 @@
+from __future__ import annotations
+
+import sys
+from pathlib import Path
+
+
+HERE = Path(__file__).resolve().parent
+
+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")'
+
+
+def _f(value: float) -> str:
+    return f"{value:.4g}"
+
+
+def _centers(size: float, number: int, bw: float, edge: float) -> list[float]:
+    half = size / 2.0
+    left = edge + 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"])
+    stirrup_size = int(values["stirrup_size"])
+    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"])
+
+    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
+
+    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
+    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: {_f(STIRRUP_RADIUS)}pt, stroke: {_f(STIRRUP_STROKE)}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 - 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, text(size: 7pt)[$b_w = {_f(bw)} " in"$])))'
+    )
+
+    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 - 3)}pt, {_f(tick)}pt), end: ({_f(x_h + 3)}pt, {_f(tick)}pt), "
+            f"stroke: 0.6pt + black))"
+        )
+    add(
+        f"    #place(dx: 0.5pt, dy: {_f(oy + h_sec / 2.0 - 3)}pt, "
+        f'text(size: 7pt)[$h = {_f(h)} " in"$])'
+    )
+
+    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(
+            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 + 14.0)
+    add(
+        f"    #place(dx: {_f(label_x)}pt, dy: {_f(oy + 9)}pt, "
+        f'text(size: 7pt, "({n_top_bars}) #{top_bar_size}"))'
+    )
+
+    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 - 8)}pt, "
+        f'text(size: 7pt, "#{stirrup_size} @ {_f(stirrup_spacing)}″"))'
+    )
+
+    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 - 19)}pt, "
+        f'text(size: 7pt, "({n_bars}) #{bar_size}"))'
+    )
+
+    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())

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")
@@ -46,8 +63,19 @@ 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")
+    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")
+
+    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
@@ -73,6 +101,14 @@ def compute(inp: dict) -> dict:
     Vc = 2.0 * math.sqrt(fc * 1000.0) * bw * d / 1000.0
     phiVc = 0.75 * Vc
 
+    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 +142,16 @@ 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),
         },
         "checks": {
             "flexure": {
@@ -131,6 +177,17 @@ 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 else HERE / "input.yaml"
     output_path = Path(sys.argv[2]) if len(sys.argv) > 2 else input_path.with_name("results.json")
@@ -139,6 +196,9 @@ def main() -> int:
     result = compute(inp)
     write_results(result, output_path)
     print(output_path)
+    section_path = HERE / "assets" / "beam-section.typ"
+    _load_section_module().write_fragment(result["values"], section_path)
+    print(section_path)
     return 0
 
 

concrete-beam/concrete-beam.typ

@@ -1,4 +1,5 @@
 #import "assets/sheet.typ": calcline, calcsheet, check
+#import "assets/beam-section.typ": beam-section
 
 #let data = json("results.json")
 #let n = data.values
@@ -37,6 +38,13 @@ Simple-span rectangular beam under uniform gravity load. Numbers come from `calc
   caption: [#n.span ft simply supported beam, #n.bw in × #n.h in rectangular section.],
 )
 
+== Section and Reinforcement
+
+#align(right, block(width: 2.5in, figure(
+  beam-section(),
+  caption: [Beam cross-section],
+)))
+
 == Loads and Beam Demand
 
 #calcline([$L = #n.span " ft"$], [Simple span])
@@ -64,7 +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],

concrete-beam/input.yaml

@@ -1,15 +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

concrete-beam/results.json

@@ -19,25 +19,35 @@
     "d": 9.5,
     "fc": 3.0,
     "fy": 60.0,
-    "As": 0.62,
+    "As": 0.613592,
-    "a": 1.823529,
+    "a": 1.804683,
-    "et": 0.010285,
+    "et": 0.010423,
     "phi": 0.9,
-    "Mn": 26.623529,
+    "Mn": 26.377285,
-    "phiMn": 23.961176,
+    "phiMn": 23.739557,
     "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
   },
   "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": {

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
@@ -31,10 +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["a"] == pytest.approx(1.804683, rel=1e-5)
-    assert v["et"] == pytest.approx(0.010283, rel=1e-3)
+    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
 
 
@@ -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"] == 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