Wood Column (LRFD)

How it calculates

The Wood Column (LRFD, NDS 2024) calculator checks sawn lumber, glulam, LVL, and multi-ply solid sawn columns against the Load and Resistance Factor Design provisions of the 2024 National Design Specification for Wood Construction. For each ASCE 7 load combination, the calculator resolves factored demands and compares them against factored resistances derived through the NDS 2024 LRFD adjustment framework.

LRFD adjustment framework

NDS LRFD converts reference design values - tabulated on an ASD basis in the NDS Supplement - into the LRFD resistance space using the format conversion factor KF. Each adjusted resistance is then multiplied by the applicable resistance factor φ and the time effect factor λ, which accounts for the duration of the governing load:

• λ = 0.8 for occupancy live loads
• λ = 1.0 for snow (short duration) and impact
• λ = 1.25 for wind and seismic

For axial compression, the format conversion factor is KF,c = 2.40 and the compression resistance factor is φc = 0.90. The full adjusted compressive resistance per unit area is:

F'c = KF,c × φc × λ × CM × Ct × CF × Ci × Cp × Fc

Adjustment factors applied per the 2024 NDS Supplement include: wet service (CM), temperature (Ct), size (CF), and incising (Ci). The column stability factor Cp is computed separately as described below and applied as the final reduction to the reference compression design value.

Column stability factor Cp (NDS 2024, Cl. 3.7)

The column stability factor accounts for buckling in the critical (weak) axis and governs columns where the slenderness ratio exceeds a practical threshold. It is computed as:

Cp = (1 + FcE/Fc) / (2c) - sqrt[((1 + FcE/Fc) / (2c))² - FcE / (F*c × c)]

Where:

• F*c is the reference compression design value multiplied by all adjustment factors except Cp (i.e. KF,c × φc × λ × CM × Ct × CF × Ci × Fc)
• c = 0.8 for sawn lumber, c = 0.9 for glulam and LVL
• FcE is the critical buckling design value (see below)

The calculator evaluates both axes independently and uses the axis producing the lower Cp.

Critical buckling design value FcE

The Euler critical buckling stress is:

FcE = 0.822 × E'min / (Le/d)²

Where:

• E'min is the adjusted modulus of elasticity for stability, applying the LRFD format conversion factor KF,E = 1.76, φs = 0.85, and all applicable service condition factors (CM, Ct, Ci)
• Le is the effective column length = Ke × L, with Ke set per NDS Appendix G based on end conditions
• d is the cross-section dimension in the buckling axis

Slenderness ratio Le/d is capped at 50 per NDS 2024 Cl. 3.7.1.4.

Axial compression check

utilization = Pu / (F'c × A) ≤ 1.0

The calculator evaluates all ASCE 7 LRFD load combinations, identifies the one producing the maximum factored compressive demand Pu, and compares it against the factored compressive resistance F'c × A. The resistance already incorporates Cp so the check directly accounts for stability effects.

Combined bending and axial check (NDS 2024, Cl. 3.9)

For columns subject to simultaneous axial compression and biaxial bending, the NDS interaction equation is:

(fc / F'c)² + (fbx / F'bx) / (1 - fc / FcEx) + (fby / F'by) / (1 - fc / FcEy - (fbx / FbEx)²) ≤ 1.0

Where:

• fc is the factored compressive stress = Pu / A
• F'c is the adjusted LRFD compressive resistance including Cp
• fbx, fby are factored bending stresses about the strong and weak axes respectively
• F'bx, F'by are the adjusted LRFD bending resistances per the applicable KF,b, φb = 0.85, λ, and all applicable adjustment factors including CL (beam stability factor) for the strong axis
• FcEx, FcEy are the critical buckling design values for each axis

The denominator amplification terms (1 - fc / FcE) capture the P-delta moment magnification that arises when axial compression acts simultaneously with lateral deflection from bending.

Bearing check

Where a bearing length is specified, the calculator checks the factored bearing demand Ru against the factored bearing resistance:

utilization = Ru / (φb × KF,b × λ × F'c⊥ × Ab) ≤ 1.0

Where F'c⊥ is the reference compression design value perpendicular to grain adjusted for wet service, temperature, and incising, φb = 0.90, and Ab is the bearing area.

Reactions and load linking

At the column base, the calculator outputs the maximum factored axial reaction Pu and any shear demands. These can be linked directly to a connected footing or foundation calculation in the same project. Factored reactions from upstream LRFD beam calculations can be linked into the column top, so that when beam geometry or loading changes, the column check updates automatically.