feat(core): coping main bars C1–C8 (plan C3) and column rebar C4

- Nominal bar diameters (H29 28.6, S32 31.8, …) as used by the documents. With
  them, C7/C8 l_s = 1.3·l_d(28.6, fck 27) = 1717.6, which is the document's 1717.
- C1–C8 (코핑철근.md §5): width layout 127 · 110.5 · 21@125 · 110.5 · 127 with 24
  bars (12 + 12); heights 43.284 / 43.227 / 43.170; top bar lengths 12744 /
  12629.6 / 12515.2; bottom pieces ≈ 7448.
- C4 (기둥철근.md): P1 r 875 and P2 r 843.2; couplers P1 +3/6/9/12 m, P2 +150;
  230 + 230 main pieces and 368 couplers; tie radius 900.45; P3 38 at @300 from
  2.340; P5 19 at @120; P4 8 at @120 from −0.060; P6 8 levels × 4 = 32, length
  ≈ 2071.
- Not yet: C4 interference checks (P4 vs B11, Q-C9), bar lengths of P3/P5/P4
  and coupler shapes, the coping/column drawing checks, and the ③ screen.

Co-Authored-By: Claude Haiku 5.5 <noreply@anthropic.com>

src/core/rebar/column.ts

@@ -0,0 +1,123 @@
+import { developmentLength, hookLength, NOMINAL_DIAMETER } from './common';
+
+/**
+ * 기둥 철근 C4 (plan C4). Source: RAG/기둥철근 (1).md, 2026-10-22 최종 정리. Type-1 원형 중실 기둥.
+ * Lengths in mm, heights in mm from the 확대기초 상면 (up +).
+ */
+export interface ColumnInput {
+  /** 기둥 지름 D. */
+  D: number;
+  /** 기둥 높이 H_c (확대기초 상면 ~ 코핑 Level 하면). */
+  Hc: number;
+  /** 기둥 중심 위치의 코핑 높이 h_cop. */
+  hcop: number;
+  /** 기둥 면 ~ P1 중심 피복 c. */
+  c: number;
+  /** P1 위 끝의 코핑 상면 아래 깊이 e_P1. */
+  eP1: number;
+  /** 띠철근 구간 위 끝의 코핑 상면 아래 깊이 e_top. */
+  eTop: number;
+  /** 확대기초 깊이 H_f (for P4). */
+  Hf: number;
+  /** 주철근 원주 등분 수 n_div. */
+  nDiv: number;
+  /** 주철근 커플러 간격 (확대기초 상면부터). */
+  ctcCoupler: number;
+  /** P2 커플러를 P1보다 올리는 높이. */
+  dzCp2: number;
+  ctcP3: number;
+  ctcP5: number;
+  ctcP4: number;
+  /** P4 구간 깊이 비율 r_P4. */
+  rP4: number;
+  ctcP6: number;
+}
+
+/** 예제 운곡교 P1 (기둥철근.md §1.2 기본값). */
+export const COLUMN_P1: ColumnInput = {
+  D: 2000,
+  Hc: 12703,
+  hcop: 2644,
+  c: 125,
+  eP1: 200,
+  eTop: 1623,
+  Hf: 2000,
+  nDiv: 46,
+  ctcCoupler: 3000,
+  dzCp2: 150,
+  ctcP3: 300,
+  ctcP5: 120,
+  ctcP4: 120,
+  rP4: 0.5,
+  ctcP6: 1800,
+};
+
+const dS32 = NOMINAL_DIAMETER.S32;
+const dH19 = NOMINAL_DIAMETER.H19;
+const dH16 = NOMINAL_DIAMETER.H16;
+const round = (v: number, d = 1) => Math.round(v * 10 ** d) / 10 ** d;
+
+export function columnRebar(x: ColumnInput = COLUMN_P1) {
+  // P1 and P2 main bars (기둥철근.md §3)
+  const r1 = x.D / 2 - x.c;
+  const r2 = r1 - dS32;
+  const zTop1 = x.Hc + x.hcop - x.eP1;
+  const lD2 = developmentLength(dS32, 500, 27);
+  const zTop2 = x.Hc + lD2;
+  const couplerLevels = Array.from({ length: Math.max(0, Math.floor(zTop1 / x.ctcCoupler) - 1) }, (_, i) => (i + 1) * x.ctcCoupler);
+  const couplersP1 = couplerLevels.length;
+  const mainLines = x.nDiv;
+  const mainP1 = mainLines * (couplersP1 + 1);
+  const mainP2 = mainLines * (couplersP1 + 1);
+  const couplers = couplersP1 * x.nDiv * 2;
+
+  // Ties (기둥철근.md §4–§6)
+  // Tie radius r_t = r_1 + (d_P1 + d_P3)/2 (기둥철근.md §4.1)
+  const tieRadius = r1 + (dS32 + dH19) / 2;
+  const zTopT = x.Hc + x.hcop - x.eTop;
+  const lEmin = Math.max(x.D, zTopT / 6, 450);
+  const n5 = Math.floor(lEmin / x.ctcP5);
+  const lE = Math.max(lEmin, n5 * x.ctcP5 + x.ctcP5 / 2);
+  const p3 = Array.from({ length: Math.floor((zTopT - lE) / x.ctcP3) + 1 }, (_, k) => lE + k * x.ctcP3);
+  const n5all = Math.floor(lE / x.ctcP5);
+  const p5 = Array.from({ length: n5all }, (_, j) => lE - (j + 1) * x.ctcP5);
+  const z5last = lE - n5all * x.ctcP5;
+  const m4 = Math.floor((z5last + x.rP4 * x.Hf) / x.ctcP4);
+  const p4 = Array.from({ length: m4 }, (_, j) => z5last - (j + 1) * x.ctcP4);
+
+  // P6 crossties (기둥철근.md §7): 4 bars per 단, from the first P4
+  const z4first = p4.length ? p4[0] : z5last;
+  const p6Levels: number[] = [];
+  for (let z = z4first; z <= x.Hc; z += x.ctcP6) p6Levels.push(z);
+  const p6Straight = 2 * tieRadius;
+  const p6Hook = hookLength('tie90', dH16);
+  const p6Length = p6Straight + 2 * p6Hook;
+
+  return {
+    r1: round(r1),
+    r2: round(r2),
+    angleStepDeg: 360 / x.nDiv,
+    zTop1: round(zTop1),
+    zTop2: round(zTop2),
+    couplerP1: couplerLevels,
+    couplerP2: couplerLevels.map((z) => z + x.dzCp2),
+    mainP1,
+    mainP2,
+    couplers,
+    tieRadius: round(tieRadius, 2),
+    tieCircumference: round(2 * Math.PI * tieRadius, 1),
+    zTopT: round(zTopT),
+    lEmin: round(lEmin),
+    lE: round(lE),
+    p3,
+    p5,
+    p4,
+    p6Levels,
+    p6Count: p6Levels.length * 4,
+    p6Length: round(p6Length, 1),
+    p4SemicircleLength: round(Math.PI * tieRadius, 1),
+    p3Count: p3.length,
+    p5Count: p5.length,
+    p4Count: p4.length,
+  };
+}

src/core/rebar/common.ts

@@ -23,6 +23,20 @@ export function spliceLength(db: number, fy: number, fck: number, lambda = MATER
   return 1.3 * developmentLength(db, fy, fck, lambda);
 }
 
+/** Nominal diameters d (mm) of the bar sizes used in the documents (코핑철근.md, 기둥철근.md). */
+export const NOMINAL_DIAMETER = {
+  D13: 12.7,
+  H16: 15.9,
+  H19: 19.1,
+  D22: 22.2,
+  H25: 25.4,
+  H29: 28.6,
+  S32: 31.8,
+  D35: 34.9,
+} as const;
+
+export type BarSize = keyof typeof NOMINAL_DIAMETER;
+
 export type HookKind = 'main90' | 'tie90' | 'stirrup135';
 
 /**

src/core/rebar/coping-main.ts

@@ -0,0 +1,80 @@
+import { hookLength, NOMINAL_DIAMETER, spliceLength } from './common';
+
+/**
+ * C1–C8 상·하면 주철근 (plan C3 continued). Source: RAG/코핑철근.md §5, 2026-10-22 최종 정리.
+ * Lengths in mm, heights in m (EL).
+ */
+export const MAIN = {
+  /** 피복 (최외측 철근 중심까지). */
+  cover: 100,
+  /** 기본 간격 s_m and minimum end gap g_min. */
+  spacing: 125,
+  endGapMin: 80,
+  /** 상면 단 간격 s_lay (EL, m) and its horizontal step (mm). */
+  layEl: 0.057,
+  layHorizontal: 57.2,
+  /** 90° 갈고리 l_h (mm, as in the document). */
+  hook: 472,
+  /** 하면 경사 구간 수평 길이 (mm, each side) and Level width. */
+  slopeEach: 5067.8,
+  level: 2100,
+} as const;
+
+export interface WidthLayout {
+  /** Edge bar centre from the coping side face: c + (d_st + d_m)/2. */
+  yE: number;
+  /** Clear length between the two edge bars: B − 2·y_e. */
+  S: number;
+  /** Bars inside the edge bars: n (so n + 3 in all, including the two edges and the two 110.5 ends). */
+  n: number;
+  /** Equal end gap g = (S − n·s_m)/2. */
+  g: number;
+  /** Bars in all: n + 3. */
+  count: number;
+  /** Bars per cycle (alternating): 12 / 12 for 24. */
+  cyclePerKind: number;
+  /** Dimension string, e.g. "127 · 110.5 · 21@125 · 110.5 · 127". */
+  text: string;
+}
+
+/** 폭 방향 배치 (코핑철근.md §5.1). d_st = H25 stirrup, d_m = H29 main. */
+export function widthLayout(B: number, dSt = NOMINAL_DIAMETER.H25, dM = NOMINAL_DIAMETER.H29): WidthLayout {
+  const yE = MAIN.cover + (dSt + dM) / 2;
+  const S = B - 2 * yE;
+  const n = Math.floor((S - 2 * MAIN.endGapMin) / MAIN.spacing);
+  const g = (S - n * MAIN.spacing) / 2;
+  const count = n + 3;
+  const r = (v: number) => Math.round(v * 10) / 10;
+  return {
+    yE: r(yE),
+    S: r(S),
+    n,
+    g: r(g),
+    count,
+    cyclePerKind: count / 2,
+    text: `${r(yE)} · ${r(g)} · ${n}@${MAIN.spacing} · ${r(g)} · ${r(yE)}`,
+  };
+}
+
+/** Top-layer EL of the k-th row (k = 1, 2, 3): z_k = z_1 − (k − 1)·s_lay (m). */
+export function topRowEl(z1: number, k: number): number {
+  return Math.round((z1 - (k - 1) * MAIN.layEl) * 1000) / 1000;
+}
+
+/** Length of one top bar on row k: path L − 2·(c + (k−1)·step), plus two 90° hooks. */
+export function topBarLength(L: number, k: number): number {
+  const path = L - 2 * (MAIN.cover + (k - 1) * MAIN.layHorizontal);
+  return path + 2 * MAIN.hook;
+}
+
+/**
+ * Bottom bar C7·C8 (spliced at the column centre, 하면 겹침이음). Each piece:
+ * path/2 + l_s/2 + l_h, with path = 2·slope + Level and l_s = 1.3·l_d for H29 (nominal 28.6, fck 27, fy 400).
+ */
+export function bottomPiece(fck = 27): { path: number; ls: number; piece: number } {
+  const path = 2 * MAIN.slopeEach + MAIN.level;
+  const ls = spliceLength(NOMINAL_DIAMETER.H29, 400, fck);
+  const lh = hookLength('main90', NOMINAL_DIAMETER.H29);
+  return { path, ls, piece: path / 2 + ls / 2 + lh };
+}
+

tests/rebar-column.test.ts

@@ -0,0 +1,63 @@
+import { describe, expect, it } from 'vitest';
+import { columnRebar } from '../src/core/rebar/column';
+
+const c = columnRebar();
+
+describe('기둥 철근 C4 (기둥철근.md, plan C4)', () => {
+  it('P1 radius 875, P2 radius 843.2 (touching; centre gap = d_P1)', () => {
+    expect(c.r1).toBe(875);
+    expect(c.r2).toBe(843.2);
+    expect(c.angleStepDeg).toBeCloseTo(360 / 46, 9);
+  });
+
+  it('heights: P1 top 15147, P2 top ≈ 14539 (l_d of S32 at fck 27, 1836.9 ≈ the document 1836)', () => {
+    expect(c.zTop1).toBe(15147);
+    expect(Math.abs(c.zTop2 - 14539)).toBeLessThan(1);
+  });
+
+  it('couplers P1 at +3 / 6 / 9 / 12 m, P2 at +150 above each', () => {
+    expect(c.couplerP1).toEqual([3000, 6000, 9000, 12000]);
+    expect(c.couplerP2).toEqual([3150, 6150, 9150, 12150]);
+  });
+
+  it('main bar pieces 230 + 230, couplers 4 × 46 × 2 = 368', () => {
+    expect(c.mainP1).toBe(230);
+    expect(c.mainP2).toBe(230);
+    expect(c.couplers).toBe(368);
+  });
+
+  it('tie radius 900.45, circumference ≈ 5657.7', () => {
+    expect(c.tieRadius).toBe(900.45);
+    expect(c.tieCircumference).toBeCloseTo(5657.7, 1);
+  });
+
+  it('P3: l_e = 2340, 38 ties from 2.340 at @300 (top 13.440)', () => {
+    expect(c.zTopT).toBe(13724);
+    expect(c.lE).toBe(2340);
+    expect(c.p3Count).toBe(38);
+    expect(c.p3[0]).toBe(2340);
+    expect(c.p3[c.p3.length - 1]).toBe(13440);
+  });
+
+  it('P5: 19 ties @120 from 2.220 down to 0.060', () => {
+    expect(c.p5Count).toBe(19);
+    expect(c.p5[0]).toBe(2220);
+    expect(c.p5[c.p5.length - 1]).toBe(60);
+  });
+
+  it('P4: 8 ties @120 from −0.060 to −0.900 (none removed in the example)', () => {
+    expect(c.p4Count).toBe(8);
+    expect(c.p4[0]).toBe(-60);
+    expect(c.p4[c.p4.length - 1]).toBe(-900);
+  });
+
+  it('P4 semicircle ≈ 2828.9', () => {
+    expect(c.p4SemicircleLength).toBeCloseTo(2828.9, 0);
+  });
+
+  it('P6: 8 levels from −0.060 to 12.540, 4 bars each = 32, length ≈ 2071', () => {
+    expect(c.p6Levels).toEqual([-60, 1740, 3540, 5340, 7140, 8940, 10740, 12540]);
+    expect(c.p6Count).toBe(32);
+    expect(c.p6Length).toBeCloseTo(2071, 0);
+  });
+});

tests/rebar-coping-main.test.ts

@@ -0,0 +1,45 @@
+import { describe, expect, it } from 'vitest';
+import { developmentLength, hookLength, NOMINAL_DIAMETER, spliceLength } from '../src/core/rebar/common';
+import { bottomPiece, topBarLength, topRowEl, widthLayout } from '../src/core/rebar/coping-main';
+
+describe('C1–C8 상·하면 주철근 (코핑철근.md §5, plan C3)', () => {
+  it('nominal diameters: H29 28.6, S32 31.8 (documents use these, not the round numbers)', () => {
+    expect(NOMINAL_DIAMETER.H29).toBe(28.6);
+    expect(NOMINAL_DIAMETER.S32).toBe(31.8);
+  });
+
+  it('width layout for B 3100: edge 127, ends 110.5, 21@125, 24 bars (12 + 12)', () => {
+    const w = widthLayout(3100);
+    expect(w.yE).toBe(127);
+    expect(w.S).toBe(2846);
+    expect(w.n).toBe(21);
+    expect(w.g).toBe(110.5);
+    expect(w.count).toBe(24);
+    expect(w.cyclePerKind).toBe(12);
+    expect(w.text).toBe('127 · 110.5 · 21@125 · 110.5 · 127');
+  });
+
+  it('heights: 43.284 / 43.227 / 43.170 for the three top rows', () => {
+    expect(topRowEl(43.284, 1)).toBe(43.284);
+    expect(topRowEl(43.284, 2)).toBe(43.227);
+    expect(topRowEl(43.284, 3)).toBe(43.17);
+  });
+
+  it('top bar lengths 12744 / 12629.6 / 12515.2 (path + 2 × 472 hook)', () => {
+    expect(topBarLength(12000, 1)).toBeCloseTo(12744, 0);
+    expect(topBarLength(12000, 2)).toBeCloseTo(12629.6, 0);
+    expect(topBarLength(12000, 3)).toBeCloseTo(12515.2, 0);
+  });
+
+  it('bottom piece ≈ 7448 with l_s = 1717.6 (1.3 × l_d of H29 at fck 27) — the document shows 1717', () => {
+    const b = bottomPiece();
+    expect(b.path).toBeCloseTo(12235.6, 6);
+    expect(b.ls).toBeCloseTo(1717.6, 0);
+    expect(b.piece).toBeCloseTo(7448, 0);
+  });
+
+  it('hook 472 (16.5 × 28.6) and splice from the same formula as C1', () => {
+    expect(hookLength('main90', NOMINAL_DIAMETER.H29)).toBeCloseTo(472, 0);
+    expect(spliceLength(NOMINAL_DIAMETER.H29, 400, 27)).toBeCloseTo(1.3 * developmentLength(NOMINAL_DIAMETER.H29, 400, 27), 9);
+  });
+});