What resistance factors does LRFD use?

Tension yielding phi = 0.90 (phi-Pn = 0.90 sigma_y A_g). Tension rupture phi = 0.75 (phi-Pn = 0.75 sigma_u A_e). Compression phi = 0.90. Flexure phi_b = 0.90. The lower 0.75 on rupture reflects the lower ductility of a net-section fracture.

How do LRFD and ASD relate?

AISC 360 unified them in 2005. Same nominal strength Rn; LRFD applies phi (resistance factor) to Rn and compares against factored loads (1.2D + 1.6L etc.), while ASD divides Rn by Omega and compares against service loads. The pair satisfies phi x Omega approximately 1.5.

What load combinations go with LRFD?

ASCE 7 strength combinations, e.g. 1.4D; 1.2D + 1.6L + 0.5(Lr or S or R); 1.2D + 1.6(Lr or S or R) + (L or 0.5W); 1.2D + 1.0W + L + 0.5(Lr or S or R); 0.9D + 1.0W. Required strength Pu or Mu is the envelope of these, compared against phi-Pn or phi-Mn.

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AISC LRFD Steel Design

Load and Resistance Factor Design (LRFD) for steel members per AISC 360-22. Design tensile strength (yielding + rupture, Chapter D), compression with the column curve (Chapter E), and flexural yielding (Chapter F) — each reported as the design strength φR_n to compare against factored demand P_u / M_u.

Units

Steel grade σ_y

Tensile strength σ_uksi (A992: 65; A36: 58)

Modulus, Eksi (steel: 29000)

Gross area, A_gin²

Effective net area, A_ein² (after holes)

Section modulus, S_xin³

Plastic modulus, Z_xin³

Slenderness, KL/r— (compression members)

Design tension φP_n (yield)—kips

Design tension φP_n (rupture)—kips

Design tension φP_n (governing)—kips

Design compression φ_cP_n—kips

Design moment φ_bM_n (yielding)—kip·in

Defaults: A992 wide-flange (σ_y = 50 ksi), A_g = 10 in², KL/r = 80. Output is design strength φR_n — your factored demand (P_u, M_u) must not exceed it. Compactness, LTB, and shear are separately governed by AISC F2–F11 and G.

Tension yielding (AISC D2-1): φ_t = 0.90

$$ P_n = \sigma_y \, A_g, \qquad \phi_t P_n = 0.90 \, \sigma_y \, A_g $$

Tension rupture (AISC D2-2): φ_t = 0.75

$$ P_n = \sigma_u \, A_e, \qquad \phi_t P_n = 0.75 \, \sigma_u \, A_e $$

Compression (AISC E3): elastic σ_e = π²E/(KL/r)²

$$ \sigma_{cr} = \begin{cases} (0.658^{\sigma_y/\sigma_e}) \sigma_y & \sigma_e \ge 0.44\sigma_y \\ 0.877\, \sigma_e & \text{otherwise} \end{cases}, \qquad \phi_c P_n = 0.90 \, \sigma_{cr} A_g $$

Flexural yielding (compact, AISC F2): M_n = M_p = σ_y Z_x; φ_b = 0.90

$$ \phi_b M_n = 0.90 \, \sigma_y \, Z_x $$

φ resistance factor in LRFD (0.90 tension yield / compression / flexure; 0.75 rupture) · P_n, M_n nominal strength · φP_n, φM_n design strength · A_g gross area · A_e effective net area = U × A_n where U is the shear-lag reduction factor.

LRFD vs ASD — they're equivalent now

AISC 360 unified ASD and LRFD in 2005. Both methods use the same nominal strength equations; they differ only in how safety is applied:

LRFD: φP_n ≥ ΣγQ, demand = factored loads (1.2D + 1.6L etc.)
ASD: P_a = P_n / Ω, demand = service-level loads (D + L etc.)

The relationship: φ × Ω ≈ 1.5. For tension yielding, φ = 0.90 and Ω = 1.67 → φΩ = 1.50. LRFD matches reliability theory more directly because the load and resistance uncertainties are factored separately; ASD bundles them into a single Ω.

Compression — the column equation

For KL/r < 4.71 √(E/σ_y) ≈ 113 for A36, the section yields before Euler buckling fully manifests — use the inelastic curve (0.658 raised to the σ_y/σ_e ratio). For KL/r above that, use Euler with a 0.877 reduction for residual stress and initial out-of-straightness. In LRFD, multiply the resulting φ_cP_n = 0.90 σ_cr A_g.

Flexure — beyond yielding

For compact, laterally-braced beams, M_n = M_p = σ_y Z. For non-compact beams, plastic capacity reduces (F2.2). For long unbraced lengths, lateral-torsional buckling (LTB, F2.3) reduces capacity further. The full Chapter F has 11 sub-sections covering different failure modes. This tool returns the compact, fully-braced φ_bM_n = 0.90 σ_y Z_x.

What this calculator doesn't check

Compactness (web/flange λ ratios per Table B4.1b)
Lateral-torsional buckling (need L_b, L_p, L_r, C_b)
Shear (Chapter G — usually not critical for typical W-shapes)
Block shear / coped beam ends (J4.3)
Bolted connection design
Local buckling of slender sections

Combined-force interaction (H1.1)

For members with axial + flexure: P_r/P_c + (8/9)(M_rx/M_cx + M_ry/M_cy) ≤ 1.0 when P_r/P_c ≥ 0.2; else P_r/(2P_c) + M_rx/M_cx + M_ry/M_cy ≤ 1.0. In LRFD, P_r = P_u (factored) and P_c = φ_cP_n. Second-order (P-Δ / P-δ) effects require a direct analysis or B₁/B₂ amplification per AISC C2.

Reference: AISC 360-22 (2022). Specification for Structural Steel Buildings. AISC Steel Construction Manual, 16th ed. ASCE 7-22, load combinations §2.3. Salmon, C.G., Johnson, J.E. (2009). Steel Structures: Design and Behavior, 5th ed., Pearson.

Related tools

AISC Allowable Stress (ASD) — same checks, service-load method
Beam deflection
Euler buckling
Section properties