feat(bearing): 교대만 있을 때 A1 ↔ A2 현(chord) 짝 받침

교각 없이 A1 · A2만 불러온 다경간 곡선교(운곡교 광주·완도, 358 m, 방위각 8° 차)는 거더 짝 허용오차
(방위각 ≤ 0.1°)를 넘어 짝이 없었다. 교각이 0기일 때만, A1 받침과 A2 받침을 잇는 현의 방향이 두
방위각의 평균과 0.1° 이내인 받침을 짝으로 한다(원곡선이면 정확히 같다). 같은 노선·같은 번호가 117″,
다른 후보는 1176″ 이상이라 하나로 정해진다.
- S = Δz / 현 길이 (교량 전체 평균 경사), S 근거 '계산', 짝 받침 표시 "A2-광주-① (현)"
- 방위각 검사 칸은 "현 117″ (참고)": 한 거더용 10″ 규칙이 아니므로 WS01은 내지 않음
- 교각이 하나라도 있으면 쓰지 않음. 단경간 직선(A1·A2 방위각 같음)은 기존 거더 짝으로 처리
- 테스트: 곡선 두 노선 합성 10쌍(노선·번호 일치), 교대 카드 표시, 교각 있을 때 미적용
- 브라우저: 운곡교AA.xlsx A1-광주 ①–⑤ ↔ A2-광주 ①–⑤ (현), S −1.900 ~ −1.892 %

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

src/core/bearing-pair.ts

@@ -45,6 +45,8 @@ export interface BearingPair {
   slopePct: number;
   /** The structure on the higher end: the 오르막 쪽 where T1 sits for both bearings. */
   uphill: string;
+  /** girder = the two ends of one girder; chord = A1 ↔ A2 of a bridge loaded without piers (현, chordPairs). */
+  kind: 'girder' | 'chord';
   warnings: PairWarning[];
 }
 
@@ -87,13 +89,41 @@ export function girderPairs(structures: PairStructure[]): BearingPair[] {
       pairs.push({
         from: { structure: here.name, no: b.no }, to: { structure: best.c.structure, no: best.c.no },
         distanceM, offsetM: best.offset, azimuthDiffDeg: best.dAz, directionDeg, fromCheckSec, toCheckSec,
-        slopePct, uphill: best.c.z > b.z ? best.c.structure : here.name, warnings,
+        slopePct, uphill: best.c.z > b.z ? best.c.structure : here.name, warnings, kind: 'girder',
       });
     }
   }
   return pairs;
 }
 
+/**
+ * A1 ↔ A2 pairs when no pier is loaded (교대만, 검토 2026-11-06). Over several spans the azimuths of the two ends differ
+ * (곡선, 운곡교 8°), so the girder test fails; the chord from b to c then runs along the mean of the two azimuths (exact on a
+ * circular arc). The partner is the end bearing whose chord is within 0.1° of that mean (WS04 when two are), and S is the
+ * whole-bridge average Δz / chord. The check value is chord − mean azimuth, for reference only (no WS01).
+ */
+export function chordPairs(starts: PairStructure[], ends: PairStructure[]): BearingPair[] {
+  const pairs: BearingPair[] = [];
+  for (const here of starts) for (const b of here.bearings) {
+    const candidates = ends.flatMap((s) => s.bearings.map((c) => {
+      const d = { e: c.x - b.x, n: c.y - b.y };
+      const directionDeg = (Math.atan2(d.e, d.n) / DEG + 360) % 360;
+      const mean = (b.azimuthDeg + c.azimuthDeg + (Math.abs(b.azimuthDeg - c.azimuthDeg) > 180 ? 360 : 0)) / 2 % 360;
+      return { c, structure: s.name, d, directionDeg, dev: angleDiffDeg(directionDeg, mean) };
+    })).filter((t) => t.dev <= PAIR_AZIMUTH_TOL_DEG).sort((p, q) => p.dev - q.dev);
+    if (!candidates.length) continue;
+    const best = candidates[0];
+    const distanceM = Math.hypot(best.d.e, best.d.n);
+    pairs.push({
+      from: { structure: here.name, no: b.no }, to: { structure: best.structure, no: best.c.no },
+      distanceM, offsetM: 0, azimuthDiffDeg: angleDiffDeg(best.c.azimuthDeg, b.azimuthDeg), directionDeg: best.directionDeg,
+      fromCheckSec: best.dev * 3600, toCheckSec: best.dev * 3600, slopePct: ((best.c.z - b.z) / distanceM) * 100,
+      uphill: best.c.z > b.z ? best.structure : here.name, warnings: candidates.length > 1 ? ['WS04'] : [], kind: 'chord',
+    });
+  }
+  return pairs;
+}
+
 /** The pair a bearing belongs to, on either end; undefined when it has none (then WS03 with a fallback S, not done here). */
 export function pairOf(pairs: BearingPair[], structure: string, no: number): BearingPair | undefined {
   return pairs.find((p) => (p.from.structure === structure && p.from.no === no) || (p.to.structure === structure && p.to.no === no));