{
    "slug": "k-factor-bend-allowance",
    "title": "K-Factor and Bend Allowance for Sheet Metal Bending",
    "description": "K factors by material and thickness for air bending, bottoming and coining per DIN 6935, with bend allowance and deduction worked examples for 90-degree bends.",
    "lang": "en",
    "tables": [
        {
            "caption": "K factors by material, thickness and bend method (calculated DIN 6935 + published ranges)",
            "columns": [
                "Material",
                "t (mm)",
                "V die (mm)",
                "R_i (mm)",
                "R/t",
                "K DIN 6935",
                "K air (DIN ↔ published)",
                "K bottoming",
                "K coining",
                "y = K·t (mm)",
                "Source"
            ],
            "rows": [
                {
                    "Material": "DC01 mild steel",
                    "t (mm)": "0.5",
                    "V die (mm)": "6",
                    "R_i (mm)": "0.96",
                    "R/t": "1.92",
                    "K DIN 6935": "0.40",
                    "K air (DIN ↔ published)": "0.40–0.43",
                    "K bottoming": "0.44–0.47",
                    "K coining": "0.41–0.46",
                    "y = K·t (mm)": "0.20",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "DC01 mild steel",
                    "t (mm)": "0.8",
                    "V die (mm)": "6",
                    "R_i (mm)": "0.96",
                    "R/t": "1.20",
                    "K DIN 6935": "0.34",
                    "K air (DIN ↔ published)": "0.34–0.43",
                    "K bottoming": "0.44–0.47",
                    "K coining": "0.41–0.46",
                    "y = K·t (mm)": "0.27",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "DC01 mild steel",
                    "t (mm)": "1.0",
                    "V die (mm)": "8",
                    "R_i (mm)": "1.28",
                    "R/t": "1.28",
                    "K DIN 6935": "0.35",
                    "K air (DIN ↔ published)": "0.35–0.43",
                    "K bottoming": "0.44–0.47",
                    "K coining": "0.41–0.46",
                    "y = K·t (mm)": "0.35",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "DC01 mild steel",
                    "t (mm)": "1.5",
                    "V die (mm)": "12",
                    "R_i (mm)": "1.92",
                    "R/t": "1.28",
                    "K DIN 6935": "0.35",
                    "K air (DIN ↔ published)": "0.35–0.43",
                    "K bottoming": "0.44–0.47",
                    "K coining": "0.41–0.46",
                    "y = K·t (mm)": "0.53",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "DC01 mild steel",
                    "t (mm)": "2.0",
                    "V die (mm)": "16",
                    "R_i (mm)": "2.56",
                    "R/t": "1.28",
                    "K DIN 6935": "0.35",
                    "K air (DIN ↔ published)": "0.35–0.43",
                    "K bottoming": "0.44–0.47",
                    "K coining": "0.41–0.46",
                    "y = K·t (mm)": "0.70",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "DC01 mild steel",
                    "t (mm)": "3.0",
                    "V die (mm)": "25",
                    "R_i (mm)": "4.00",
                    "R/t": "1.33",
                    "K DIN 6935": "0.36",
                    "K air (DIN ↔ published)": "0.36–0.43",
                    "K bottoming": "0.44–0.47",
                    "K coining": "0.41–0.46",
                    "y = K·t (mm)": "1.07",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "DC01 mild steel",
                    "t (mm)": "4.0",
                    "V die (mm)": "32",
                    "R_i (mm)": "5.12",
                    "R/t": "1.28",
                    "K DIN 6935": "0.35",
                    "K air (DIN ↔ published)": "0.35–0.43",
                    "K bottoming": "0.44–0.47",
                    "K coining": "0.41–0.46",
                    "y = K·t (mm)": "1.40",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "DC01 mild steel",
                    "t (mm)": "6.0",
                    "V die (mm)": "50",
                    "R_i (mm)": "8.00",
                    "R/t": "1.33",
                    "K DIN 6935": "0.36",
                    "K air (DIN ↔ published)": "0.36–0.43",
                    "K bottoming": "0.44–0.47",
                    "K coining": "0.41–0.46",
                    "y = K·t (mm)": "2.14",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "DX51D+Z galvanized",
                    "t (mm)": "0.8",
                    "V die (mm)": "6",
                    "R_i (mm)": "0.96",
                    "R/t": "1.20",
                    "K DIN 6935": "0.34",
                    "K air (DIN ↔ published)": "0.34–0.43",
                    "K bottoming": "0.44–0.47",
                    "K coining": "0.41–0.46",
                    "y = K·t (mm)": "0.27",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "DX51D+Z galvanized",
                    "t (mm)": "1.5",
                    "V die (mm)": "12",
                    "R_i (mm)": "1.92",
                    "R/t": "1.28",
                    "K DIN 6935": "0.35",
                    "K air (DIN ↔ published)": "0.35–0.43",
                    "K bottoming": "0.44–0.47",
                    "K coining": "0.41–0.46",
                    "y = K·t (mm)": "0.53",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "DX51D+Z galvanized",
                    "t (mm)": "3.0",
                    "V die (mm)": "25",
                    "R_i (mm)": "4.00",
                    "R/t": "1.33",
                    "K DIN 6935": "0.36",
                    "K air (DIN ↔ published)": "0.36–0.43",
                    "K bottoming": "0.44–0.47",
                    "K coining": "0.41–0.46",
                    "y = K·t (mm)": "1.07",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "304 stainless",
                    "t (mm)": "0.8",
                    "V die (mm)": "8",
                    "R_i (mm)": "1.60",
                    "R/t": "2.00",
                    "K DIN 6935": "0.40",
                    "K air (DIN ↔ published)": "0.40–0.45",
                    "K bottoming": "0.46–0.48",
                    "K coining": "0.44–0.47",
                    "y = K·t (mm)": "0.32",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "304 stainless",
                    "t (mm)": "1.5",
                    "V die (mm)": "16",
                    "R_i (mm)": "3.20",
                    "R/t": "2.13",
                    "K DIN 6935": "0.41",
                    "K air (DIN ↔ published)": "0.41–0.45",
                    "K bottoming": "0.46–0.48",
                    "K coining": "0.44–0.47",
                    "y = K·t (mm)": "0.61",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "304 stainless",
                    "t (mm)": "3.0",
                    "V die (mm)": "32",
                    "R_i (mm)": "6.40",
                    "R/t": "2.13",
                    "K DIN 6935": "0.41",
                    "K air (DIN ↔ published)": "0.41–0.45",
                    "K bottoming": "0.46–0.48",
                    "K coining": "0.44–0.47",
                    "y = K·t (mm)": "1.23",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "316L stainless",
                    "t (mm)": "1.0",
                    "V die (mm)": "10",
                    "R_i (mm)": "2.10",
                    "R/t": "2.10",
                    "K DIN 6935": "0.41",
                    "K air (DIN ↔ published)": "0.41–0.45",
                    "K bottoming": "0.46–0.48",
                    "K coining": "0.44–0.47",
                    "y = K·t (mm)": "0.41",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "316L stainless",
                    "t (mm)": "2.0",
                    "V die (mm)": "20",
                    "R_i (mm)": "4.20",
                    "R/t": "2.10",
                    "K DIN 6935": "0.41",
                    "K air (DIN ↔ published)": "0.41–0.45",
                    "K bottoming": "0.46–0.48",
                    "K coining": "0.44–0.47",
                    "y = K·t (mm)": "0.82",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "316L stainless",
                    "t (mm)": "3.0",
                    "V die (mm)": "32",
                    "R_i (mm)": "6.72",
                    "R/t": "2.24",
                    "K DIN 6935": "0.41",
                    "K air (DIN ↔ published)": "0.41–0.45",
                    "K bottoming": "0.46–0.48",
                    "K coining": "0.44–0.47",
                    "y = K·t (mm)": "1.23",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "5052-H32 aluminium",
                    "t (mm)": "0.8",
                    "V die (mm)": "6",
                    "R_i (mm)": "0.96",
                    "R/t": "1.20",
                    "K DIN 6935": "0.34",
                    "K air (DIN ↔ published)": "0.34–0.40",
                    "K bottoming": "0.42–0.46",
                    "K coining": "0.38–0.44",
                    "y = K·t (mm)": "0.27",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "5052-H32 aluminium",
                    "t (mm)": "1.5",
                    "V die (mm)": "12",
                    "R_i (mm)": "1.92",
                    "R/t": "1.28",
                    "K DIN 6935": "0.35",
                    "K air (DIN ↔ published)": "0.35–0.40",
                    "K bottoming": "0.42–0.46",
                    "K coining": "0.38–0.44",
                    "y = K·t (mm)": "0.53",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "5052-H32 aluminium",
                    "t (mm)": "3.0",
                    "V die (mm)": "25",
                    "R_i (mm)": "4.00",
                    "R/t": "1.33",
                    "K DIN 6935": "0.36",
                    "K air (DIN ↔ published)": "0.36–0.40",
                    "K bottoming": "0.42–0.46",
                    "K coining": "0.38–0.44",
                    "y = K·t (mm)": "1.07",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "6061-T6 aluminium *",
                    "t (mm)": "1.0",
                    "V die (mm)": "10",
                    "R_i (mm)": "1.80",
                    "R/t": "1.80",
                    "K DIN 6935": "0.39",
                    "K air (DIN ↔ published)": "0.39–0.45",
                    "K bottoming": "0.46–0.48",
                    "K coining": "0.44–0.47",
                    "y = K·t (mm)": "0.39",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "6061-T6 aluminium *",
                    "t (mm)": "2.0",
                    "V die (mm)": "20",
                    "R_i (mm)": "3.60",
                    "R/t": "1.80",
                    "K DIN 6935": "0.39",
                    "K air (DIN ↔ published)": "0.39–0.45",
                    "K bottoming": "0.46–0.48",
                    "K coining": "0.44–0.47",
                    "y = K·t (mm)": "0.78",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "6061-T6 aluminium *",
                    "t (mm)": "3.0",
                    "V die (mm)": "32",
                    "R_i (mm)": "5.76",
                    "R/t": "1.92",
                    "K DIN 6935": "0.40",
                    "K air (DIN ↔ published)": "0.40–0.45",
                    "K bottoming": "0.46–0.48",
                    "K coining": "0.44–0.47",
                    "y = K·t (mm)": "1.20",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "C110 copper",
                    "t (mm)": "1.0",
                    "V die (mm)": "8",
                    "R_i (mm)": "1.28",
                    "R/t": "1.28",
                    "K DIN 6935": "0.35",
                    "K air (DIN ↔ published)": "0.35–0.40",
                    "K bottoming": "0.42–0.46",
                    "K coining": "0.38–0.44",
                    "y = K·t (mm)": "0.35",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "C110 copper",
                    "t (mm)": "2.0",
                    "V die (mm)": "16",
                    "R_i (mm)": "2.56",
                    "R/t": "1.28",
                    "K DIN 6935": "0.35",
                    "K air (DIN ↔ published)": "0.35–0.40",
                    "K bottoming": "0.42–0.46",
                    "K coining": "0.38–0.44",
                    "y = K·t (mm)": "0.70",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "C260 brass",
                    "t (mm)": "1.0",
                    "V die (mm)": "8",
                    "R_i (mm)": "1.28",
                    "R/t": "1.28",
                    "K DIN 6935": "0.35",
                    "K air (DIN ↔ published)": "0.35–0.40",
                    "K bottoming": "0.42–0.46",
                    "K coining": "0.38–0.44",
                    "y = K·t (mm)": "0.35",
                    "Source": "S1/S2/S3"
                },
                {
                    "Material": "C260 brass",
                    "t (mm)": "2.0",
                    "V die (mm)": "16",
                    "R_i (mm)": "2.56",
                    "R/t": "1.28",
                    "K DIN 6935": "0.35",
                    "K air (DIN ↔ published)": "0.35–0.40",
                    "K bottoming": "0.42–0.46",
                    "K coining": "0.38–0.44",
                    "y = K·t (mm)": "0.70",
                    "Source": "S1/S2/S3"
                }
            ]
        },
        {
            "caption": "What K-factor should I use for 2 mm mild steel in air bending?",
            "columns": [
                "Step",
                "Quantity",
                "Value",
                "Note"
            ],
            "rows": [
                {
                    "Step": "1",
                    "Quantity": "R/t",
                    "Value": "2.0 / 2.0 = 1.00",
                    "Note": "DIN 6935: k = 0.65 + 0.5·log10(1.00) = 0.65"
                },
                {
                    "Step": "2",
                    "Quantity": "K = k/2",
                    "Value": "0.325",
                    "Note": "Table value rounds to 0.33; this example carries the unrounded value"
                },
                {
                    "Step": "3",
                    "Quantity": "BA = (π/180)·A·(R + K·t), A = 90°",
                    "Value": "4.163 mm",
                    "Note": "1.5708 × 2.65"
                },
                {
                    "Step": "4",
                    "Quantity": "OSSB = (R + t)·tan(A/2)",
                    "Value": "4.000 mm",
                    "Note": "4.0 × tan 45°"
                },
                {
                    "Step": "5",
                    "Quantity": "Flat legs from 50/30 outside",
                    "Value": "46.000 / 26.000 mm",
                    "Note": "A_flat = 50 − OSSB, B_flat = 30 − OSSB"
                },
                {
                    "Step": "6",
                    "Quantity": "L = A + B + BA",
                    "Value": "76.16 mm",
                    "Note": "BD = 2×4.000 − 4.163 = 3.837; 50 + 30 − 3.837 = 76.163 ✓"
                },
                {
                    "Step": "7",
                    "Quantity": "If CAD default K = 0.44",
                    "Value": "L = 76.52 mm (+0.361)",
                    "Note": "BA = 4.524 mm; four bends accumulate about 1.4 mm"
                }
            ]
        },
        {
            "caption": "Why do CAD programs default to a K-factor of 0.44?",
            "columns": [
                "Condition",
                "Which K",
                "Typical value",
                "Next step"
            ],
            "rows": [
                {
                    "Condition": "Ductile mild steel, air bending, R/t 0.5–3",
                    "Which K": "DIN 6935 Table / formula",
                    "Typical value": "0.25–0.40",
                    "Next step": "Test bend, back-solve the real K"
                },
                {
                    "Condition": "Mild steel, CAD default, V = 6–8t",
                    "Which K": "Published medium air (t–3t)",
                    "Typical value": "0.43 (defaults 0.44–0.45)",
                    "Next step": "Use only when tooling and material match; otherwise switch to DIN"
                },
                {
                    "Condition": "304/316 stainless, air bending",
                    "Which K": "DIN 6935 at R/t 2.0–2.2",
                    "Typical value": "0.40–0.41 (316 shop data up to 0.50)",
                    "Next step": "Check springback, cracking and die wear"
                },
                {
                    "Condition": "5052-H32 aluminium, air bending",
                    "Which K": "DIN 6935 at R/t 1.2–1.3",
                    "Typical value": "0.34–0.36",
                    "Next step": "Check cracking; soft temper takes the low end"
                },
                {
                    "Condition": "6061-T6 aluminium, air bending",
                    "Which K": "Published hard air / DIN upper bound",
                    "Typical value": "0.39–0.45",
                    "Next step": "Test bend mandatory; T6 cracks — prefer a larger radius"
                },
                {
                    "Condition": "C110 copper / C260 brass",
                    "Which K": "DIN 6935 at R/t 1.28",
                    "Typical value": "0.35",
                    "Next step": "Confirm annealed temper; hard temper takes the upper bound"
                },
                {
                    "Condition": "Bottoming",
                    "Which K": "Published t–3t tier of the class",
                    "Typical value": "0.42–0.48",
                    "Next step": "Never reuse an air-bending K"
                },
                {
                    "Condition": "Coining",
                    "Which K": "Published t–3t tier of the class",
                    "Typical value": "0.38–0.47",
                    "Next step": "Note coining sits below bottoming in the published table (see the coin-vs-bottom question)"
                },
                {
                    "Condition": "R/t > 5",
                    "Which K": "K = 0.50",
                    "Typical value": "0.50",
                    "Next step": "Neutral axis back at mid-thickness"
                },
                {
                    "Condition": "R/t < 0.5",
                    "Which K": "DIN Table low end",
                    "Typical value": "0.15–0.25",
                    "Next step": "High cracking risk — open the radius or change material"
                },
                {
                    "Condition": "New material / new tooling / no data",
                    "Which K": "Test bend, back-solve",
                    "Typical value": "measured",
                    "Next step": "Lock the measured K into the CAD material library"
                }
            ]
        },
        {
            "caption": "How does K-factor change with inside radius?",
            "columns": [
                "R/t",
                "k (DIN 6935)",
                "K = k/2",
                "y/t",
                "Note"
            ],
            "rows": [
                {
                    "R/t": "0.05",
                    "k (DIN 6935)": "0.00",
                    "K = k/2": "0.00",
                    "y/t": "0.00",
                    "Note": "Neutral axis on the inside surface; cracking risk — do not design here"
                },
                {
                    "R/t": "0.07",
                    "k (DIN 6935)": "0.06",
                    "K = k/2": "0.03",
                    "y/t": "0.03",
                    "Note": "Source-table value; the DIN formula itself gives 0.07 (k) at this R/t — upstream document is internally inconsistent here"
                },
                {
                    "R/t": "0.10",
                    "k (DIN 6935)": "0.15",
                    "K = k/2": "0.08",
                    "y/t": "0.08",
                    "Note": ""
                },
                {
                    "R/t": "0.20",
                    "k (DIN 6935)": "0.30",
                    "K = k/2": "0.15",
                    "y/t": "0.15",
                    "Note": ""
                },
                {
                    "R/t": "0.25",
                    "k (DIN 6935)": "0.35",
                    "K = k/2": "0.18",
                    "y/t": "0.18",
                    "Note": ""
                },
                {
                    "R/t": "0.33",
                    "k (DIN 6935)": "0.41",
                    "K = k/2": "0.21",
                    "y/t": "0.21",
                    "Note": ""
                },
                {
                    "R/t": "0.50",
                    "k (DIN 6935)": "0.50",
                    "K = k/2": "0.25",
                    "y/t": "0.25",
                    "Note": ""
                },
                {
                    "R/t": "0.75",
                    "k (DIN 6935)": "0.59",
                    "K = k/2": "0.30",
                    "y/t": "0.30",
                    "Note": ""
                },
                {
                    "R/t": "1.00",
                    "k (DIN 6935)": "0.65",
                    "K = k/2": "0.33",
                    "y/t": "0.33",
                    "Note": ""
                },
                {
                    "R/t": "1.25",
                    "k (DIN 6935)": "0.70",
                    "K = k/2": "0.35",
                    "y/t": "0.35",
                    "Note": ""
                },
                {
                    "R/t": "1.50",
                    "k (DIN 6935)": "0.74",
                    "K = k/2": "0.37",
                    "y/t": "0.37",
                    "Note": ""
                },
                {
                    "R/t": "1.75",
                    "k (DIN 6935)": "0.77",
                    "K = k/2": "0.39",
                    "y/t": "0.39",
                    "Note": ""
                },
                {
                    "R/t": "2.00",
                    "k (DIN 6935)": "0.80",
                    "K = k/2": "0.40",
                    "y/t": "0.40",
                    "Note": ""
                },
                {
                    "R/t": "2.50",
                    "k (DIN 6935)": "0.85",
                    "K = k/2": "0.43",
                    "y/t": "0.43",
                    "Note": ""
                },
                {
                    "R/t": "3.00",
                    "k (DIN 6935)": "0.89",
                    "K = k/2": "0.45",
                    "y/t": "0.45",
                    "Note": ""
                },
                {
                    "R/t": "3.50",
                    "k (DIN 6935)": "0.92",
                    "K = k/2": "0.46",
                    "y/t": "0.46",
                    "Note": ""
                },
                {
                    "R/t": "4.00",
                    "k (DIN 6935)": "0.95",
                    "K = k/2": "0.48",
                    "y/t": "0.48",
                    "Note": ""
                },
                {
                    "R/t": "4.50",
                    "k (DIN 6935)": "0.98",
                    "K = k/2": "0.49",
                    "y/t": "0.49",
                    "Note": ""
                },
                {
                    "R/t": "5.00",
                    "k (DIN 6935)": "1.00",
                    "K = k/2": "0.50",
                    "y/t": "0.50",
                    "Note": "R/t ≥ 5: neutral axis at mid-thickness"
                }
            ]
        },
        {
            "caption": "What is the difference between air bending, bottoming and coining in K-factor?",
            "columns": [
                "Material class",
                "Bend method",
                "R = 0–t",
                "R = t–3t",
                "R > 3t"
            ],
            "rows": [
                {
                    "Material class": "Soft (aluminium 5052, copper, brass)",
                    "Bend method": "Air bending",
                    "R = 0–t": "0.33",
                    "R = t–3t": "0.40",
                    "R > 3t": "0.50"
                },
                {
                    "Material class": "Soft (aluminium 5052, copper, brass)",
                    "Bend method": "Bottoming",
                    "R = 0–t": "0.42",
                    "R = t–3t": "0.46",
                    "R > 3t": "0.50"
                },
                {
                    "Material class": "Soft (aluminium 5052, copper, brass)",
                    "Bend method": "Coining",
                    "R = 0–t": "0.38",
                    "R = t–3t": "0.44",
                    "R > 3t": "0.50"
                },
                {
                    "Material class": "Medium (mild steel, galvanized)",
                    "Bend method": "Air bending",
                    "R = 0–t": "0.38",
                    "R = t–3t": "0.43",
                    "R > 3t": "0.50"
                },
                {
                    "Material class": "Medium (mild steel, galvanized)",
                    "Bend method": "Bottoming",
                    "R = 0–t": "0.44",
                    "R = t–3t": "0.47",
                    "R > 3t": "0.50"
                },
                {
                    "Material class": "Medium (mild steel, galvanized)",
                    "Bend method": "Coining",
                    "R = 0–t": "0.41",
                    "R = t–3t": "0.46",
                    "R > 3t": "0.50"
                },
                {
                    "Material class": "Hard (304/316 stainless)",
                    "Bend method": "Air bending",
                    "R = 0–t": "0.40",
                    "R = t–3t": "0.45",
                    "R > 3t": "0.50"
                },
                {
                    "Material class": "Hard (304/316 stainless)",
                    "Bend method": "Bottoming",
                    "R = 0–t": "0.46",
                    "R = t–3t": "0.48",
                    "R > 3t": "0.50"
                },
                {
                    "Material class": "Hard (304/316 stainless)",
                    "Bend method": "Coining",
                    "R = 0–t": "0.44",
                    "R = t–3t": "0.47",
                    "R > 3t": "0.50"
                }
            ]
        },
        {
            "caption": "How do I calculate bend allowance?",
            "columns": [
                "Term",
                "Formula",
                "Reading"
            ],
            "rows": [
                {
                    "Term": "K factor",
                    "Formula": "K = y / t, 0 ≤ K ≤ 0.5",
                    "Reading": "Neutral-axis offset from the inside surface over thickness"
                },
                {
                    "Term": "Neutral radius",
                    "Formula": "R_neutral = R_i + K × t",
                    "Reading": "The arc radius that actually keeps its length"
                },
                {
                    "Term": "Bend allowance BA",
                    "Formula": "BA = (π/180) × A × (R_i + K × t)",
                    "Reading": "Arc length of the neutral axis through the bend"
                },
                {
                    "Term": "Outside setback OSSB",
                    "Formula": "OSSB = (R_i + t) × tan(A/2)",
                    "Reading": "Tangent length from the apex to the bend tangent points"
                },
                {
                    "Term": "Bend deduction BD",
                    "Formula": "BD = 2 × OSSB − BA",
                    "Reading": "What the two outside corners lose versus the flat pattern"
                },
                {
                    "Term": "Flat length L",
                    "Formula": "L = A + B + BA (flat legs); L = A_out + B_out − BD (outside dims)",
                    "Reading": "Both give the same answer when K is right — mixing BA and BD is the classic flat-pattern error"
                },
                {
                    "Term": "Angle convention",
                    "Formula": "A = 180° − included angle",
                    "Reading": "90° bend: A = 90; 60° included: A = 120; 120° included: A = 60"
                }
            ]
        },
        {
            "caption": "How do I calculate bend deduction?",
            "columns": [
                "Case",
                "Item",
                "Value"
            ],
            "rows": [
                {
                    "Case": "90°, t 2.0, R 2.0",
                    "Item": "OSSB = (2+2)·tan45°",
                    "Value": "4.000 mm"
                },
                {
                    "Case": "90°, t 2.0, R 2.0",
                    "Item": "BD = 2×4.000 − 4.163",
                    "Value": "3.837 mm"
                },
                {
                    "Case": "90°, t 2.0, R 2.0",
                    "Item": "L = 50 + 30 − 3.837",
                    "Value": "76.163 mm"
                },
                {
                    "Case": "A=120°, t 1.5, R 3.0, 304",
                    "Item": "K = (0.65 + 0.5·log10 2)/2",
                    "Value": "0.4003"
                },
                {
                    "Case": "A=120°, t 1.5, R 3.0, 304",
                    "Item": "BA = 2.0944 × (3 + 0.4003×1.5)",
                    "Value": "7.541 mm"
                },
                {
                    "Case": "A=120°, t 1.5, R 3.0, 304",
                    "Item": "OSSB = 4.5 × tan60°",
                    "Value": "7.794 mm"
                },
                {
                    "Case": "A=120°, t 1.5, R 3.0, 304",
                    "Item": "L = 52.206 + 32.206 + 7.541",
                    "Value": "91.95 mm"
                },
                {
                    "Case": "A=120°, t 1.5, R 3.0, 304",
                    "Item": "BD check: 60 + 40 − (2×7.794 − 7.541)",
                    "Value": "91.952 mm ✓"
                },
                {
                    "Case": "A=120°, t 1.5, R 3.0, 304",
                    "Item": "If hard-air K 0.45 instead",
                    "Value": "L = 92.11 mm (+0.156 vs DIN 0.40: 0.16 mm per bend)"
                }
            ]
        },
        {
            "caption": "What V-die opening should I use for 2 mm mild steel?",
            "columns": [
                "t (mm)",
                "V (mm)",
                "R_i (mm)",
                "Min flange (mm)",
                "Tonnage (t/m)",
                "Source"
            ],
            "rows": [
                {
                    "t (mm)": "0.5",
                    "V (mm)": "6",
                    "R_i (mm)": "0.96",
                    "Min flange (mm)": "—",
                    "Tonnage (t/m)": "—",
                    "Source": "practical min V6, calc"
                },
                {
                    "t (mm)": "0.8",
                    "V (mm)": "6",
                    "R_i (mm)": "0.96",
                    "Min flange (mm)": "—",
                    "Tonnage (t/m)": "—",
                    "Source": "S3 method, calc"
                },
                {
                    "t (mm)": "1.0",
                    "V (mm)": "8",
                    "R_i (mm)": "1.3",
                    "Min flange (mm)": "> 5.5",
                    "Tonnage (t/m)": "8",
                    "Source": "S3"
                },
                {
                    "t (mm)": "1.5",
                    "V (mm)": "12",
                    "R_i (mm)": "2.0",
                    "Min flange (mm)": "> 8.5",
                    "Tonnage (t/m)": "10",
                    "Source": "S3"
                },
                {
                    "t (mm)": "2.0",
                    "V (mm)": "16",
                    "R_i (mm)": "2.6",
                    "Min flange (mm)": "> 11.0",
                    "Tonnage (t/m)": "12",
                    "Source": "S3"
                },
                {
                    "t (mm)": "2.5",
                    "V (mm)": "20",
                    "R_i (mm)": "3.3",
                    "Min flange (mm)": "> 14.0",
                    "Tonnage (t/m)": "14",
                    "Source": "S3"
                },
                {
                    "t (mm)": "3.0",
                    "V (mm)": "25",
                    "R_i (mm)": "4.0",
                    "Min flange (mm)": "> 17.5",
                    "Tonnage (t/m)": "16",
                    "Source": "S3"
                },
                {
                    "t (mm)": "4.0",
                    "V (mm)": "32",
                    "R_i (mm)": "5.0",
                    "Min flange (mm)": "> 22.0",
                    "Tonnage (t/m)": "22",
                    "Source": "S3"
                },
                {
                    "t (mm)": "5.0",
                    "V (mm)": "40",
                    "R_i (mm)": "6.5",
                    "Min flange (mm)": "> 28.0",
                    "Tonnage (t/m)": "27",
                    "Source": "S3"
                },
                {
                    "t (mm)": "6.0",
                    "V (mm)": "50",
                    "R_i (mm)": "8.0",
                    "Min flange (mm)": "> 35.0",
                    "Tonnage (t/m)": "32",
                    "Source": "S3"
                }
            ]
        },
        {
            "caption": "What K-factor should I use for 304 stainless?",
            "columns": [
                "Caliber",
                "K at R≈t",
                "Applies to",
                "Source"
            ],
            "rows": [
                {
                    "Caliber": "Shop-measured caliber",
                    "K at R≈t": "0.46",
                    "Applies to": "304, air bending, R = t",
                    "Source": "S4"
                },
                {
                    "Caliber": "Shop-measured caliber",
                    "K at R≈t": "0.50",
                    "Applies to": "316, air bending, R = t",
                    "Source": "S4"
                },
                {
                    "Caliber": "Published hard class (t–3t)",
                    "K at R≈t": "0.45",
                    "Applies to": "Generic 304/316 hard tier — does not separate 304 from 316",
                    "Source": "S2/S5"
                },
                {
                    "Caliber": "DIN 6935 at R/t = 2",
                    "K at R≈t": "0.40",
                    "Applies to": "Geometry only — no work-hardening difference",
                    "Source": "S1/S6"
                },
                {
                    "Caliber": "This page, Table 2",
                    "K at R≈t": "0.41–0.45",
                    "Applies to": "316 takes the upper bound; test-bend",
                    "Source": "S1/S2/S3"
                }
            ]
        },
        {
            "caption": "What K-factor should I use for 5052 aluminium?",
            "columns": [
                "Caliber",
                "K",
                "Applies to",
                "Source"
            ],
            "rows": [
                {
                    "Caliber": "Shop-measured (R = t)",
                    "K": "0.33",
                    "Applies to": "5052-H32, air bending",
                    "Source": "S4"
                },
                {
                    "Caliber": "Published soft air (t–3t)",
                    "K": "0.40",
                    "Applies to": "Generic soft aluminium",
                    "Source": "S2/S5"
                },
                {
                    "Caliber": "DIN 6935 (R/t = 1.2)",
                    "K": "0.345",
                    "Applies to": "Geometry only",
                    "Source": "S1/S6"
                },
                {
                    "Caliber": "This page, Table 2",
                    "K": "0.34–0.40",
                    "Applies to": "Soft temper low end, hard temper or wide V high end",
                    "Source": "S1/S2/S3"
                }
            ]
        },
        {
            "caption": "Can I use one K-factor for all thicknesses?",
            "columns": [
                "t (mm)",
                "V (mm)",
                "R_i (mm)",
                "R/t",
                "K DIN 6935"
            ],
            "rows": [
                {
                    "t (mm)": "0.5",
                    "V (mm)": "6",
                    "R_i (mm)": "0.96",
                    "R/t": "1.92",
                    "K DIN 6935": "0.40"
                },
                {
                    "t (mm)": "0.8",
                    "V (mm)": "6",
                    "R_i (mm)": "0.96",
                    "R/t": "1.20",
                    "K DIN 6935": "0.34"
                },
                {
                    "t (mm)": "2.0",
                    "V (mm)": "16",
                    "R_i (mm)": "2.56",
                    "R/t": "1.28",
                    "K DIN 6935": "0.35"
                },
                {
                    "t (mm)": "3.0",
                    "V (mm)": "25",
                    "R_i (mm)": "4.00",
                    "R/t": "1.33",
                    "K DIN 6935": "0.36"
                },
                {
                    "t (mm)": "6.0",
                    "V (mm)": "50",
                    "R_i (mm)": "8.00",
                    "R/t": "1.33",
                    "K DIN 6935": "0.36"
                }
            ]
        },
        {
            "caption": "How do I measure the real K-factor for my press brake?",
            "columns": [
                "Step",
                "Rule",
                "Value"
            ],
            "rows": [
                {
                    "Step": "1",
                    "Rule": "Strip",
                    "Value": "200 × 50 mm, bend at 90° mid-length"
                },
                {
                    "Step": "2",
                    "Rule": "Measure both outside flanges A_out + B_out",
                    "Value": "BD = 200 − (A_out + B_out)"
                },
                {
                    "Step": "3",
                    "Rule": "Back-solve",
                    "Value": "K = [2(R+t)tan(A/2) − BD] / [(π/180)·A·t] − R/t"
                },
                {
                    "Step": "4",
                    "Rule": "Write into CAD material library",
                    "Value": "per material + tooling pair"
                }
            ]
        },
        {
            "caption": "Where is the neutral axis in a bend?",
            "columns": [
                "Case",
                "K",
                "t (mm)",
                "y = K·t (mm)",
                "Neutral radius"
            ],
            "rows": [
                {
                    "Case": "DC01 2.0 mm, R/t 1.28",
                    "K": "0.35",
                    "t (mm)": "2.0",
                    "y = K·t (mm)": "0.70",
                    "Neutral radius": "R + 0.70 mm (R_i 2.56 → neutral 3.26 mm)"
                },
                {
                    "Case": "DC01 3.0 mm, R/t 1.33",
                    "K": "0.36",
                    "t (mm)": "3.0",
                    "y = K·t (mm)": "1.07",
                    "Neutral radius": "R + 1.07 mm"
                },
                {
                    "Case": "304 1.5 mm, R/t 2.13",
                    "K": "0.41",
                    "t (mm)": "1.5",
                    "y = K·t (mm)": "0.61",
                    "Neutral radius": "R + 0.61 mm"
                },
                {
                    "Case": "DC01 6.0 mm, R/t 1.33",
                    "K": "0.36",
                    "t (mm)": "6.0",
                    "y = K·t (mm)": "2.14",
                    "Neutral radius": "R + 2.14 mm"
                }
            ]
        },
        {
            "caption": "Why does coining sometimes show a lower K than bottoming?",
            "columns": [
                "Method",
                "Soft K (t–3t)",
                "Medium K (t–3t)",
                "Hard K (t–3t)",
                "Source"
            ],
            "rows": [
                {
                    "Method": "Bottoming",
                    "Soft K (t–3t)": "0.46",
                    "Medium K (t–3t)": "0.47",
                    "Hard K (t–3t)": "0.48",
                    "Source": "S2/S5"
                },
                {
                    "Method": "Coining",
                    "Soft K (t–3t)": "0.44",
                    "Medium K (t–3t)": "0.46",
                    "Hard K (t–3t)": "0.47",
                    "Source": "S2/S5"
                },
                {
                    "Method": "Expectation",
                    "Soft K (t–3t)": "—",
                    "Medium K (t–3t)": "—",
                    "Hard K (t–3t)": "—",
                    "Source": "—"
                },
                {
                    "Method": "Second source confirming the ranking",
                    "Soft K (t–3t)": "none found",
                    "Medium K (t–3t)": "none found",
                    "Hard K (t–3t)": "none found",
                    "Source": "GAP"
                }
            ]
        }
    ]
}