// Assumed inputs (define these in your app): // diagram_type: s - simply supported, b - built in fixed, c - cantilever // span (m), udl (kN/m), elast_mod (N/mm^2), mom_in*1000000 (mm^4) // wload (kN) or sometimes used as udl depending on your diagram type // a_var (m), b_var (m), load_n (individual load), n_var (number of segments) // ---------------- helpers (put once) ---------------- const roundTo = (x, dp = 2) => { const p = Math.pow(10, dp); return Math.round(x * p) / p; }; const fmt = (x, dp = 2) => { const v = Number(x); if (!Number.isFinite(v)) return "—"; const av = Math.abs(v); if (av !== 0 && (av >= 1e6 || av < 1e-3)) return v.toExponential(2); return String(roundTo(v, dp)); }; // Deflection formatting: 4 significant figures, NO exponential/engineering notation const fmtDefl = (x, sig = 4) => { const v = Number(x); if (!Number.isFinite(v)) return "—"; if (v === 0) return "0"; const av = Math.abs(v); const exp = Math.floor(Math.log10(av)); const dp = Math.max(0, sig - (exp + 1)); const p = Math.pow(10, dp); const r = Math.round(v * p) / p; return r.toFixed(dp); }; // MathML helper: force left alignment + consistent sizing + no italics const mathWrapLeft = (inner) => `

${inner}

`; const mathML_basic_values = ({ coeffNum, coeffDen, WN, Lmm, E, I, deltaMm }) => mathWrapLeft(` Δ = ${coeffNum} ${coeffDen} ⋅ ${fmt(WN)} ⋅ ${fmt(Lmm)}3 ${fmt(E)} ⋅ ${fmt(I)} = ${fmtDefl(deltaMm, 4)} mm `); const mathML_s4_values = ({ WN, Lmm, E, I, aEff, L, deltaMm }) => mathWrapLeft(` Δ = ${fmt(WN)} ⋅ ${fmt(Lmm)}3 48 ⋅ ${fmt(E)} ⋅ ${fmt(I)} ⋅ [ 3⋅${fmt(aEff)} ${fmt(L)} − 4 ⋅ ( ${fmt(aEff)}${fmt(L)} ) 3 ] = ${fmtDefl(deltaMm, 4)} mm `); const mathML_kn_values = ({ k, WN, Lmm, n, E, I, deltaMm }) => mathWrapLeft(` Δ = ${fmt(k)} ⋅ ${fmt(WN)} ⋅ ${fmt(Lmm)}3 192 ⋅ (${fmt(n)}−1) ⋅ ${fmt(E)} ⋅ ${fmt(I)} = ${fmtDefl(deltaMm, 4)} mm `); // UPDATED: c3 uses (L - a) instead of b const mathML_c3_values = ({ WN, aMm, LaMm, E, I, deltaMm }) => mathWrapLeft(` Δ = ${fmt(WN)} ⋅ ${fmt(aMm)}3 ${fmt(E)} ⋅ ${fmt(I)} ⋅ 13 ⋅ [ 1 + 3⋅${fmt(LaMm)} 2⋅${fmt(aMm)} ] = ${fmtDefl(deltaMm, 4)} mm `); let wloadMathML = ""; // ---------------- main logic ---------------- let deflection_equation_values = ""; // NOTE: wload is assigned in cases (as per your original code) if (diagram_type == "s1") { hide_W = 0; wload = span * udl; // m * kN/m = kN // Create MathML string wloadMathML = `

W = w \cdot L

W = ${udl} \cdot ${span} = ${wload} kN

`; deflection = (5 / 384) * Math.pow(span * 1000, 3) * wload * 1000 / (elast_mod * mom_in * 1000000); deflection_equation = mathWrapLeft(` Δ = 5384 ⋅ W ⋅ L3 E ⋅ I `); const Lmm = span * 1000; const WN = wload * 1000; deflection_equation_values = mathML_basic_values({ coeffNum: "5", coeffDen: "384", WN, Lmm, E: elast_mod, I: mom_in * 1000000, deltaMm: deflection, }); } else if (diagram_type == "s2") { hide_W = 0; wload = udl * span / 2; // m * kN/m = kN wloadMathML = `

W = \frac{peak_load \cdot L}{2}

W = \frac{${udl} \cdot ${span}}{2} = ${wload} kN

`; deflection = (1 / 60) * Math.pow(span * 1000, 3) * wload * 1000 / (elast_mod * mom_in * 1000000); deflection_equation = mathWrapLeft(` Δ = 160 ⋅ W ⋅ L3 E ⋅ I `); const Lmm = span * 1000; const WN = wload * 1000; deflection_equation_values = mathML_basic_values({ coeffNum: "1", coeffDen: "60", WN, Lmm, E: elast_mod, I: mom_in * 1000000, deltaMm: deflection, }); } else if (diagram_type == "s3") { hide_W = 1; udl = wload; // (kept as per your original) deflection = (1 / 48) * Math.pow(span * 1000, 3) * wload * 1000 / (elast_mod * mom_in * 1000000); deflection_equation = mathWrapLeft(` Δ = 148 ⋅ W ⋅ L3 E ⋅ I `); const Lmm = span * 1000; const WN = wload * 1000; deflection_equation_values = mathML_basic_values({ coeffNum: "1", coeffDen: "48", WN, Lmm, E: elast_mod, I: mom_in * 1000000, deltaMm: deflection, }); } else if (diagram_type == "s4") { hide_W = 1; // Use aEff = a if a < L/2 else (L - a) const aEff = (a_var < span / 2) ? a_var : (span - a_var); deflection = ((1 / 48) * Math.pow(span * 1000, 3) * wload * 1000 / (elast_mod * mom_in * 1000000)) * ((3 * aEff) / span - (4 * Math.pow((aEff / span), 3))); deflection_equation = mathWrapLeft(` Δ = W ⋅ L3 48 ⋅ E ⋅ I ⋅ [ 3⋅a L − 4 ⋅ ( aL ) 3 ] , where a = min ( a , L − a ) `); const Lmm = span * 1000; const WN = wload * 1000; deflection_equation_values = mathML_s4_values({ WN, Lmm, E: elast_mod, I: mom_in * 1000000, aEff, L: span, deltaMm: deflection, }); } else if (diagram_type == "s5") { hide_W = 1; // kept as per your original wload = load_n * (n_var - 1); const n = Number(n_var); if (n % 2 === 1) { k_var = ((n - (1 / n)) * (3 - (0.5 * (1 - (1 / Math.pow(n, 2)))))); } else if (n % 2 === 0) { k_var = n * (3 - (0.5 * (1 + (4 / Math.pow(n, 2))))); } deflection = (k_var * wload * 1000 * Math.pow(span * 1000, 3)) / (192 * (n - 1) * elast_mod * mom_in * 1000000); deflection_equation = mathWrapLeft(` Δ = k ⋅ W ⋅ L3 192 ⋅ (n−1) ⋅ E ⋅ I `); const Lmm = span * 1000; const WN = wload * 1000; deflection_equation_values = mathML_kn_values({ k: k_var, WN, Lmm, n, E: elast_mod, I: mom_in * 1000000, deltaMm: deflection, }); } else if (diagram_type == "b1") { hide_W = 0; wload = span * udl; // Create MathML string wloadMathML = `

W = w \cdot L

W = ${udl} \cdot ${span} = ${wload} kN

`; deflection = (1 / 384) * Math.pow(span * 1000, 3) * wload * 1000 / (elast_mod * mom_in * 1000000); deflection_equation = mathWrapLeft(` Δ = 1384 ⋅ W ⋅ L3 E ⋅ I `); const Lmm = span * 1000; const WN = wload * 1000; deflection_equation_values = mathML_basic_values({ coeffNum: "1", coeffDen: "384", WN, Lmm, E: elast_mod, I: mom_in * 1000000, deltaMm: deflection, }); } else if (diagram_type == "b2") { hide_W = 0; wload = udl * span / 2; wloadMathML = `

W = \frac{peak_load \cdot L}{2}

W = \frac{${udl} \cdot ${span}}{2} = ${wload} kN

`; deflection = (1.4 / 384) * Math.pow(span * 1000, 3) * wload * 1000 / (elast_mod * mom_in * 1000000); deflection_equation = mathWrapLeft(` Δ = 1.4384 ⋅ W ⋅ L3 E ⋅ I `); const Lmm = span * 1000; const WN = wload * 1000; deflection_equation_values = mathML_basic_values({ coeffNum: "1.4", coeffDen: "384", WN, Lmm, E: elast_mod, I: mom_in * 1000000, deltaMm: deflection, }); } else if (diagram_type == "b3") { hide_W = 1; udl = wload; // kept as per your original deflection = (1 / 192) * (Math.pow(span * 1000, 3) * wload * 1000 / (elast_mod * mom_in * 1000000)); deflection_equation = mathWrapLeft(` Δ = 1192 ⋅ W ⋅ L3 E ⋅ I `); const Lmm = span * 1000; const WN = wload * 1000; deflection_equation_values = mathML_basic_values({ coeffNum: "1", coeffDen: "192", WN, Lmm, E: elast_mod, I: mom_in * 1000000, deltaMm: deflection, }); } else if (diagram_type == "b4") { hide_W = 1; wload = load_n * (n_var - 1); const n = Number(n_var); if (n % 2 === 1) { k_var = ((n - (1 / n)) * (1 - (0.5 * (1 - (1 / Math.pow(n, 2)))))); } else if (n % 2 === 0) { k_var = (3 - (0.5 * (1 + (4 / Math.pow(n, 2))))) * n - (2 * (n - (1 / n))); } deflection = (k_var * wload * 1000 * Math.pow(span * 1000, 3)) / (192 * (n - 1) * elast_mod * mom_in * 1000000); deflection_equation = mathWrapLeft(` Δ = k ⋅ W ⋅ L3 192 ⋅ (n−1) ⋅ E ⋅ I `); const Lmm = span * 1000; const WN = wload * 1000; deflection_equation_values = mathML_kn_values({ k: k_var, WN, Lmm, n, E: elast_mod, I: mom_in * 1000000, deltaMm: deflection, }); } else if (diagram_type == "c1") { hide_W = 0; wload = span * udl; // Create MathML string wloadMathML = `

W = w \cdot L

W = ${udl} \cdot ${span} = ${wload} kN

`; deflection = (1 / 8) * Math.pow(span * 1000, 3) * wload * 1000 / (elast_mod * mom_in * 1000000); deflection_equation = mathWrapLeft(` Δ = 18 ⋅ W ⋅ L3 E ⋅ I `); const Lmm = span * 1000; const WN = wload * 1000; deflection_equation_values = mathML_basic_values({ coeffNum: "1", coeffDen: "8", WN, Lmm, E: elast_mod, I: mom_in * 1000000, deltaMm: deflection, }); } else if (diagram_type == "c2") { hide_W = 0; wload = udl * span / 2; wloadMathML = `

W = \frac{peak_load \cdot L}{2}

W = \frac{${udl} \cdot ${span}}{2} = ${wload} kN

`; deflection = (1 / 15) * Math.pow(span * 1000, 3) * wload * 1000 / (elast_mod * mom_in * 1000000); deflection_equation = mathWrapLeft(` Δ = 115 ⋅ W ⋅ L3 E ⋅ I `); const Lmm = span * 1000; const WN = wload * 1000; deflection_equation_values = mathML_basic_values({ coeffNum: "1", coeffDen: "15", WN, Lmm, E: elast_mod, I: mom_in * 1000000, deltaMm: deflection, }); } else if (diagram_type == "c3") { hide_W = 1; // UPDATED: use (L - a) instead of b_var const bEff = span - a_var; deflection = ((Math.pow(a_var * 1000, 3) * wload * 1000) / (elast_mod * mom_in * 1000000)) * (1 / 3) * (1 + (3 * (bEff * 1000) / (2 * (a_var * 1000)))); deflection_equation = mathWrapLeft(` Δ = W⋅a3 E⋅I ⋅ 13 ⋅ [ 1+ 3⋅ (L−a) 2⋅a ] `); const WN = wload * 1000; const aMm = a_var * 1000; const LaMm = (span - a_var) * 1000; deflection_equation_values = mathML_c3_values({ WN, aMm, LaMm, E: elast_mod, I: mom_in * 1000000, deltaMm: deflection, }); } // Output to console (or inject into HTML) if (diagram_type == "s1") { console.log(wloadMathML); } if (diagram_type == "s2") { console.log(wloadMathML); } if (diagram_type == "b1") { console.log(wloadMathML); } if (diagram_type == "b2") { console.log(wloadMathML); } if (diagram_type == "c1") { console.log(wloadMathML); } if (diagram_type == "c2") { console.log(wloadMathML); } // Console output similar to your original (but now includes both equations) const deflRounded = Math.round(deflection * 100) / 100; console.log(deflection_equation + "
" + deflection_equation_values);

AS/NZS 3679 Structural Steel Open Sections