steel-structure-design

name

steel-structure-design

description

Structural steel design — AISC 360 LRFD/ASD, member selection (W-shapes, HSS, channels), axial compression (λ, Fcr, KL/r slenderness), beam bending (Lb unbraced length, Cb, Lp, Lr, lateral-torsional buckling), combined loading (H1-1a/b interaction), connection design (bolted: ASTM A325/A490, welded: fillet weld E70XX), seismic design (AISC 341 SMF/IMF/OMF), drift limits, composite beams (AISC Chapter I), and wind/seismic load combinations.

Structural Steel Design — Complete Skill

Design Basis (AISC 360)

LRFD vs. ASD

LRFD (Load and Resistance Factor Design): φ × R_n ≥ Σ (γᵢ × Qᵢ) [φ = resistance factor; R_n = nominal strength; γᵢ = load factor; Qᵢ = load effect] φ factors: φ_c = 0.90 (compression); φ_b = 0.90 (bending); φ_v = 1.00 (shear); φ_t = 0.90 (tension)

LRFD load combinations (ASCE 7-22): 1.4D; 1.2D+1.6L; 1.2D+1.6S+(L or 0.5W); 1.2D+1.0W+L+0.5S; 0.9D+1.0W; 0.9D+1.0E+... [D = dead; L = live; S = snow; W = wind; E = earthquake]

ASD (Allowable Strength Design): R_n / Ω ≥ Σ Qᵢ [Ω = safety factor; Ω_c = 1.67 compression; Ω_b = 1.67 bending; Ω_v = 1.50 shear]

Yield strength F_y and ultimate F_u: ASTM A992 (W-shapes): F_y = 345 MPa (50 ksi); F_u = 448 MPa (65 ksi) → standard for W-shapes ASTM A36: F_y = 248 MPa (36 ksi); F_u = 400 MPa (58 ksi) → plates, older shapes ASTM A500 Grade C (HSS): F_y = 317 MPa (46 ksi); F_u = 427 MPa (62 ksi) ASTM A572 Grade 50: F_y = 345 MPa; F_u = 448 MPa (plates, channels, angles)

Tension Members (AISC Chapter D)

Tensile yielding: T_ny = F_y × A_g [φ_t = 0.90]

Tensile rupture (at net section): T_nu = F_u × A_e [A_e = U × A_n; U = shear lag factor; A_n = net area = A_g - bolt holes; φ_t = 0.75] U = 1 - x̄/L [x̄ = connection eccentricity; L = connection length; from AISC Table D3.1]

Design tension: T_n = min(T_ny, T_nu); verify φ_t T_n ≥ T_u (LRFD)

Compression Members (AISC Chapter E)

Column Buckling

Slenderness ratio: KL/r [K = effective length factor; L = unbraced length; r = radius of gyration; minimum r governs] K values: pinned-pinned = 1.0; fixed-pinned = 0.7; fixed-fixed = 0.5; fixed-free = 2.0

Critical stress F_cr (AISC E3): When KL/r ≤ 4.71√(E/F_y): Fcr = [0.658^(F_y/F_e)] × F_y [inelastic buckling] When KL/r > 4.71√(E/F_y): Fcr = 0.877 × F_e [elastic Euler; F_e = π²E/(KL/r)²] Euler elastic: F_e = π² × E / (KL/r)² [E = 200 GPa = 29,000 ksi]

Nominal compressive strength: P_n = F_cr × A_g [φ_c = 0.90; LRFD: φ_c P_n ≥ P_u]

Example: W8×31, A992 (A_g = 58.9 cm² = 9.13 in², r_y = 2.02 in), KL = 12 ft, K = 1.0 KL/r = 12×12/2.02 = 71.3; 4.71√(29000/50) = 113.4 > 71.3 → inelastic F_e = π²×29000/71.3² = 56.4 ksi; F_cr = 0.658^(50/56.4) × 50 = 0.658^0.887 × 50 = 0.723 × 50 = 36.2 ksi P_n = 36.2 × 9.13 = 330 kips; φP_n = 0.90 × 330 = 297 kips

Beam Design (AISC Chapter F)

Lateral-Torsional Buckling

Three zones based on unbraced length L_b: L_b ≤ L_p (plastic zone): M_n = M_p = F_y × Z_x [fully plastic; no LTB] L_p < L_b ≤ L_r (inelastic LTB): M_n = linear interpolation between M_p and M_r L_b > L_r (elastic LTB): M_n = F_cr × S_x ≤ M_p

Limiting lengths L_p and L_r: L_p = 1.76 × r_y × √(E/F_y) [onset of LTB; plastic moment maintained] L_r = 1.95 × r_ts × (E/(0.7F_y)) × √(J×c/(S_x×h_0) + √((Jc/(S_x×h_0))² + 6.76 × (0.7F_y/E)²)) [r_ts = effective radius of gyration; J = torsional constant; h_0 = distance between flange centroids] For compact doubly symmetric I: r_ts ≈ √(√(I_y × C_w) / S_x) [C_w = warping constant]

Cb — moment gradient factor: Cb = 12.5 × M_max / (2.5M_max + 3M_A + 4M_B + 3M_C) [AISC C1; M_max, M_A, M_B, M_C = moments at critical quarter-points] Cb = 1.0 for uniform moment; Cb > 1.0 for non-uniform (reduces LTB severity; increases M_n) Cb = 1.67 for simply supported beam with midpoint load; Cb = 1.14 for uniform load with equal end moments

Nominal moment (inelastic LTB zone): M_n = Cb × [M_p - (M_p - 0.7F_y S_x) × (L_b - L_p)/(L_r - L_p)] ≤ M_p

Shear strength: V_n = 0.6 × F_y × A_w [A_w = d × t_w; no reduction for stocky webs; φ_v = 1.00] Compact web: h/t_w ≤ 2.24√(E/F_y) → no shear buckling; applies to most standard W-shapes

Combined Loading (AISC Chapter H)

Interaction equations:

For P_r/P_c ≥ 0.2 (H1-1a): P_r/P_c + (8/9) × (M_rx/M_cx + M_ry/M_cy) ≤ 1.0

For P_r/P_c < 0.2 (H1-1b): P_r/(2P_c) + (M_rx/M_cx + M_ry/M_cy) ≤ 1.0

[P_r = required axial; P_c = available axial (φP_n); M_rx, M_ry = required moments; M_cx, M_cy = available moments]

Connection Design

Bolt Design (AISC Chapter J)

ASTM A325 bolts (F_y = 635 MPa; F_u = 825 MPa): Nominal shear strength per bolt: r_n = F_nv × A_b [F_nv = 372 MPa (A325, threads excluded from shear plane)] r_n = 372 × π/4 × (3/4)² × 645 = 372 × 0.4418 in² = 164 kips (for 3/4" A325) → 728 kN

Bearing strength (plate): r_n_bearing = 2.4 × F_u × d_bolt × t_plate [φ_b = 0.75]

Block shear (AISC J4.3): R_n = 0.6F_u×A_nv + U_bs×F_u×A_nt [≤ 0.6F_y×A_gv + U_bs×F_u×A_nt]

ASTM A490 bolts: F_nv = 457 MPa; F_u = 1,040 MPa; used for high-strength connections

Bolt pretension (AISC J3.8): A325, 3/4" bolt: T_b = 28 kips = 124 kN; A490, 3/4" bolt: T_b = 35 kips = 155 kN Slip-critical connections: design for slip resistance in serviceability

Weld Design (AISC Chapter J)

Fillet weld strength: φr_n = φ × 0.6 × F_EXX × (0.707 × w) × L_weld [per inch or mm of weld] φ = 0.75; F_EXX = 482 MPa (E70XX electrode); 0.707 × w = throat dimension; w = weld size Per mm of weld length: φr_n = 0.75 × 0.6 × 482 × 0.707 × w × 1 = 154 × w [N/mm; w in mm]

Minimum weld size (AISC Table J2.4): t_thicker_part = 10 mm → min. w = 5 mm; 20 mm → min. w = 8 mm; ≥ 38 mm → min. w = 10 mm

CJP (Complete Joint Penetration) groove weld: Matches base metal strength; no reduction factor (efficient; requires more inspection)

Seismic Design (AISC 341)

Seismic Force-Resisting Systems

Special Moment Frame (SMF — AISC 341 Chapter E): φ_b × M_p ≥ 1.0 × M_u; strong column-weak beam: ΣM_pc / ΣM_pb ≥ 1.0 Beam compactness: b_f/2t_f ≤ 0.30√(E/F_y); h/t_w ≤ 2.45√(E/F_y) (highly ductile) R = 8 (ductile; SDC D/E/F allowed); Ω₀ = 3; C_d = 5.5

Intermediate Moment Frame (IMF): R = 4.5; moderate ductility; SDC D/E/F with limitations

Ordinary Moment Frame (OMF): R = 3.5; SDC A/B/C; simpler connection details

Strong column-weak beam check: ΣM_pc = Σ Z_c × (F_yc - P_uc/A_gc) ≥ 1.0 × ΣM_pb = Σ 1.1 × R_y × F_yb × Z_b [R_y = expected yield/specified yield ratio; R_y = 1.1 for ASTM A992]

Drift and Serviceability

Seismic drift limits (ASCE 7 Table 12.12-1): Ordinary: Δ_a = 0.025 × h_sx (story height); 0.020 × h_sx (most buildings); 0.010 × h_sx (risk category IV) Δ_designed = C_d × Δ_elastic / I_e ≤ Δ_a

Wind drift (serviceability — not code-mandated; engineer judgment): H/400 to H/500 for office buildings (serviceability); H/600 for sensitive buildings

Standards and References

Standard	Scope
AISC 360-22	Specification for structural steel buildings
AISC 341-22	Seismic provisions for structural steel buildings
ASCE 7-22	Minimum design loads for buildings and structures
ASTM A992	Standard shapes (W-shapes)
AISC Steel Construction Manual (16th Ed.)	Design tables, properties, examples
AWS D1.1	Structural Welding Code — Steel

Output

Provide: structural system (frames: SMF/IMF/OMF/braced; location; building height; seismic/wind zone), load demands (P_u [kN]; V_u [kN]; M_u [kN·m]; load combination controlling), member selection (W-shape or HSS; A_g [cm²]; Z_x [cm³]; I_x [cm⁴]; r_y [cm]), tension check (A_e; U; φT_ny; φT_nu; minimum governs; DCR = T_u/φT_n), compression check (K; L [m]; KL/r; F_e [MPa]; F_cr [MPa]; φP_n [kN]; DCR), beam bending (L_b [m]; C_b; L_p [m]; L_r [m]; zone; M_n [kN·m]; φM_n [kN·m]; DCR), shear check (V_n [kN]; φV_n [kN]; DCR), combined loading (H1-1a or H1-1b interaction value ≤ 1.0), connection (bolt type/quantity; weld size [mm] and length [mm]; block shear check), seismic (if SMF: SCW-WB check ≥ 1.0; compactness: highly ductile criteria; R; Ω₀; C_d), drift (δ_x [mm]; Δ/h_sx; limit), and applicable standard (AISC 360-22 Chapters; AISC 341 if seismic; ASCE 7 load combinations).