Wood Column (LRFD, NDS 2018)

How it calculates

Design method

This calculator implements Load and Resistance Factor Design (LRFD) per the 2018 National Design Specification for Wood Construction (NDS 2018). In LRFD, tabulated reference design values are first multiplied by a format conversion factor K_F to express them in LRFD terms, then adjusted by the time-effect factor λ and all applicable LRFD adjustment factors. The factored demand must not exceed the adjusted factored resistance at every limit state:

φ × K_F × F_ref × (adjustment factors) ≥ factored demand

For axial compression, φ_c = 0.90. For bending, φ_b = 0.85. For shear, φ_v = 0.75. All utilization ratios must be ≤ 1.0.

Adjustment factors

The calculator applies the following adjustment factors to each reference design value:

• K_F (format conversion factor) - converts ASD reference design values to LRFD reference resistance; K_F = 2.40/φ for compression and bending
• λ (time-effect factor) - parallels the ASD load duration factor; λ = 0.8 for occupancy live load, 1.0 for wind and seismic, 0.6 for permanent dead load
• C_M (wet service factor) - reduces design values when in-service moisture content exceeds 19% for sawn lumber or 16% for glulam and SCL
• C_t (temperature factor) - reduces values for sustained temperatures above 100°F
• C_F (size factor) - adjusts F_c and F_b for sawn lumber based on cross-section dimensions
• C_i (incising factor) - applied when preservative treatment requires incising, reducing most reference values by a fixed fraction
• C_P (column stability factor) - the primary buckling reduction factor for compression, computed per NDS 2018 Eq. 3.7-1

Column stability factor and buckling

The column stability factor C_P is the central calculation for compression capacity. It is derived from the ratio of the Euler critical buckling stress F_cE to the adjusted reference compression stress F*_c:

F_cE = 0.822 × E'_min / (L_e / d)²

where L_e is the effective unbraced length on the axis being checked and d is the cross-section dimension resisting buckling on that axis. E'_min is the adjusted LRFD modulus of elasticity for stability, incorporating φ_s = 0.85 and the applicable wet service and temperature factors.

The stability factor C_P is then computed from NDS 2018 Eq. 3.7-1:

C_P = [1 + (F_cE / F_c)] / (2c) - √{[(1 + (F_cE / F_c)) / (2c)]² - (F_cE / F*_c) / c}

where c = 0.8 for sawn lumber and 0.9 for glulam and structural composite lumber (SCL). A separate C_P is computed for each principal axis using the corresponding effective slenderness ratio. The governing axis - the one yielding the lower C_P - controls the factored compression resistance.

Compression checks

Two independent factored compression checks are performed, one for each principal axis:

φ_c P'_n,x = φ_c × K_F,c × F_c × λ × C_M × C_t × C_F × C_i × C_P,x × A

Utilization (X-axis): P_u / φ_c P'_n,x ≤ 1.0

Utilization (Y-axis): P_u / φ_c P'_n,y ≤ 1.0

Combined axial compression and biaxial bending

For columns subject to simultaneous axial compression and bending about one or both axes, the calculator evaluates the NDS 2018 LRFD combined interaction equation per §3.9. The denominator amplification terms account for the P-delta effect: axial load increases effective bending demand as the column deflects laterally. P_cE,x and P_cE,y are the Euler buckling loads on each axis. The interaction utilization must be ≤ 1.0 across both combined equations.

Bending and shear

Adjusted factored bending resistance for each axis uses the beam stability factor C_L per NDS 2018 Appendix E. For columns fully braced on both faces, C_L = 1.0. The adjusted factored shear resistance is computed with φ_v = 0.75 and the applicable wet service and temperature factors. Utilization Vu / φVn must be ≤ 1.0.

Bearing

Bearing is checked at the top and base of the column per compression perpendicular to grain. The bearing area factor C_b may exceed 1.0 for bearing lengths under 6 inches located at least 3 inches from the member end. The utilization R_u / φ_c P'_n,⊥ must be ≤ 1.0.

Built-up columns

For nailed or bolted built-up (multi-ply) columns, the effective column stability factor C_P is reduced relative to an equivalent solid section of the same cross-section area. The calculator applies the built-up column reduction to C_P to account for reduced composite action between plies, consistent with NDS 2018 provisions for multi-ply assemblies such as doubled or tripled studs.