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支援等高度熱軋型鋼與變高度焊接板梁牛腿。提供垂直動力衝擊與雙向側力組合下的彎剪壓、扭矩檢核，以及彈性法全周銲縫強度分析、AISC J10 柱翼緣局部彎曲與柱腹板局部屈服/挫屈五大檢核。
| 檢核項目 (Limit State) | DCR 值 | 狀態 |
|---|---|---|
| 牛腿強軸抗彎 (Mx Bending) | 0.180 | 安全 |
| 牛腿弱軸抗彎 (My Bending) | 0.052 | 安全 |
| 牛腿軸力檢核 (Pu Axial) | 0.017 | 安全 |
| 牛腿彎壓/拉互制檢核 (Interaction) | 0.240 | 安全 |
| 牛腿強軸抗剪 (Vy Shear) | 0.435 | 安全 |
| 牛腿弱軸抗剪 (Vx Shear) | 0.022 | 安全 |
| 連接銲縫強度 (Weld Connection) | 0.816 | 安全 |
| 柱翼緣局部彎曲 (Column Flange Bending) | 0.512 | 安全 |
| 柱腹板局部屈服 (Column Web Yielding) | 0.458 | 安全 |
| 柱腹板局部挫屈 (Column Web Crippling) | 0.292 | 安全 |
| 柱腹板橫向挫屈 (Column Web Buckling) | 0.362 | 安全 |
Vu (設計垂直力) = Pv * (1 + βv / 100) = 250.0 * (1 + 0.25) = 312.50 kN Pu (設計軸力) = Ps = 50.00 kN Vux (弱軸設計剪力) = Pl = 25.00 kN ds (側力偏心高度) = h_cr + H_2 / 2 = 200 + 400 / 2 = 400.0 mm Mux (強軸根部彎矩) = Vu * e + |Ps| * ds = 312.50 * 0.2 + 50.0 * 0.4 = 82.50 kN-m Muy (弱軸根部彎矩) = Pl * e = 25.00 * 0.2 = 5.00 kN-m Tu (扭矩) = Pl * ds = 25.00 * 0.4 = 10.00 kN-m
Ag (斷面積) = 2 * B_bf * t_bf + (H_2 - 2 * t_bf) * t_bw = 2 * 200 * 16 + (400 - 2 * 16) * 10 = 10080 mm² (100.80 cm²) Ix (強軸慣性矩) = 27760 cm⁴ Iy (弱軸慣性矩) = 2136 cm⁴ Sx (強軸彈性模數) = Ix / (H_2 / 2) = 1388.0 cm³ Sy (弱軸彈性模數) = Iy / (B_bf / 2) = 213.6 cm³ Zx (強軸塑性模數) = B_bf * t_bf * (H_2 - t_bf) + t_bw * (H_2 - 2 * t_bf)² / 4 = 1567.4 cm³ Zy (弱軸塑性模數) = 2 * t_bf * B_bf² / 4 + (H_2 - 2 * t_bf) * t_bw² / 4 = 329.2 cm³
λ_f (寬厚比) = B_bf / (2 * t_bf) = 200 / (2 * 16) = 6.25 λ_p (緊密限值) = 0.38 * √(E / F_y) = 0.38 * √(200000 / 325) = 9.43 翼緣狀態: 塑性屈服 (Plastic Yielding) Mnx (名義抗彎強度) = 509.39 kN-m φMnx (設計抗彎強度) = 0.90 * Mnx = 458.45 kN-m DCR = Mux / φMnx = 82.50 / 458.45 = 0.180
Mny (名義弱軸抗彎強度) = min(F_y * Z_y, 1.6 * F_y * S_y) = 106.99 kN-m φMny (設計抗彎強度) = 0.90 * Mny = 96.29 kN-m DCR = Muy / φMny = 5.00 / 96.29 = 0.052
Pn_yield (屈服強度) = F_y * A_g = 325 * 100.80 * 0.1 = 3276.00 kN 控制極限狀態: 斷面屈服 (Yielding) Pn (名義軸向強度) = 3276.00 kN φPn (設計軸向強度) = 0.90 * Pn = 2948.40 kN DCR = |Pu| / φPn = 50.00 / 2948.40 = 0.017
Pr/Pc = 50.00 / 2948.40 = 0.017 < 0.2
DCR = Pr/(2*Pc) + (Mrx/Mcx + Mry/Mcy)
= 0.008 + (82.5/458.5 + 5.0/96.3) = 0.240Aw (剪力腹板面積) = (H_2 - 2 * t_bf) * t_bw = (400 - 2 * 16) * 10 = 3680 mm² h/t_w = 36.80, kv = 5.34 (無加勁板) h/tw = 36.8 ≤ 2.24√(E/Fy) = 55.6 → Cv = 1.0, φv = 1.00 Vny (名義剪力強度) = 0.6 * F_y * Aw * Cv = 0.6 * 325 * 36.80 * 1.000 * 0.1 = 717.60 kN φVny (設計剪力強度) = 1 * Vny = 717.60 kN DCR = Vu / φVny = 312.50 / 717.60 = 0.435
A_flanges (兩側翼緣面積) = 2 * B_bf * t_bf = 2 * 200 * 16 = 6400 mm² Vnx (名義剪力強度) = 0.6 * F_y * A_flanges = 0.6 * 325 * 64.00 * 0.1 = 1248.00 kN φVnx (設計剪力強度) = 0.90 * Vnx = 1123.20 kN DCR = Vux / φVnx = 25.00 / 1123.20 = 0.022
te_f (翼緣填角銲喉深) = 0.707 * a_f = 0.707 * 10.0 = 7.07 mm te_w (腹板線喉深) = 1.414 * a_w = 1.414 * 8.0 = 11.31 mm (雙面銲) Aw_weld (總銲縫線面積) = 6991 mm² Iwx (銲縫強軸線慣性矩) = 1.512e+8 mm⁴ Iwy (銲縫弱軸線慣性矩) = 9.471e+6 mm⁴ Jw (銲縫線極慣性矩) = 1.607e+8 mm⁴ f_n (軸向應力) = Pu / Aw_weld = 7.15 MPa f_mx (彎矩強軸) = Mux * y / Iwx = 109.11 MPa f_my (彎矩弱軸) = Muy * x / Iwy = 52.79 MPa 四角點正應力: [169.0, 63.5, -49.2, -154.7] MPa f_total (最不利角點) = 169.05 MPa v_total (合成剪應力，含扭矩) = √[ (f_vx + τ_tx)² + (f_vy + τ_ty)² ] = 53.39 MPa σ_w (最不利點焊縫合成應力) = √(f_total² + v_total²) = 177.28 MPa F_w (銲縫設計強度) = 217.18 MPa (銲條 F_EXX = 70 ksi) DCR = σ_w / F_w = 177.28 / 217.18 = 0.816
Ft_raw (集中力) = Mux / (H_2 - t_bf) + Pu / 2 = 82.50 / 0.384 + 50.00 / 2 = 239.84 kN Ft (拉力集中力) = 239.84 kN Rn (名義抗彎強度) = 6.25 * t_cf² * F_yc = 6.25 * 16² * 325 * 10⁻³ = 520.00 kN φRn (設計強度) = 0.90 * Rn = 468.00 kN DCR = Ft / φRn = 239.84 / 468.00 = 0.512
k (翼緣趾部距離) = t_cf + r_c = 16 + 13 = 29.0 mm Rn (名義局部屈服強度) = F_yc * t_cw * (5*k + N_b) = 325 * 10 * (5 * 29.0 + 16) * 10⁻³ = 523.25 kN φRn (設計強度) = 1.00 * Rn = 523.25 kN DCR = max(Ft, Fc) / φRn = 239.84 / 523.25 = 0.458
Fc (集中壓力) = Mux / (H_2 - t_bf) - Pu / 2 = 189.84 kN
Rn (名義局部挫屈強度) = 0.80 * t_cw² * [ 1 + 3 * (N_b / d_c) * (t_cw / t_cf)¹.5 ] * √(E * F_yc * t_cf / t_cw)
= 0.80 * 10² * [ 1 + 3 * (16 / 390) * (10 / 16)¹.5 ] * √(200000 * 325 * 16 / 10) * 10⁻³ = 865.46 kN
φRn (設計強度) = 0.75 * Rn = 649.09 kN
DCR = Fc / φRn = 189.84 / 649.09 = 0.292hw (柱腹板淨高) = d_c - 2*k = 390 - 2 * 29.0 = 332.0 mm Rn (名義挫屈強度) = 24 * t_cw³ * √(E * F_yc) / hw = 24 * 10³ * √(200000 * 325) / 332.0 * 10⁻³ = 582.81 kN φRn (設計強度) = 0.90 * Rn = 524.53 kN DCR = Fc / φRn = 189.84 / 524.53 = 0.362
所有柱子局部應力檢核均安全 (DCR <= 1.0)，可不配置橫向加勁板。