Wood Member (Design Only - ASD, NDS 2024)

How it calculates

Design methodology

The calculator implements Allowable Stress Design (ASD) as defined in the 2024 National Design Specification for Wood Construction (NDS 2024). In ASD, actual stresses are compared to adjusted allowable stresses derived from tabulated reference design values multiplied by a chain of applicable adjustment factors. Each limit state passes when the demand-to-capacity ratio does not exceed 1.0:

utilization = actual stress / adjusted allowable stress ≤ 1.0

Reference design values reflect the NDS 2024 Supplement, which supersedes NDS 2018 for species and grade combinations where tabulated values have been updated.

Adjusted allowable stresses

Each adjusted allowable stress is formed by multiplying the applicable reference design value by every required adjustment factor for the specified service conditions.

Adjusted allowable bending stress:

F'b = Fb × CD × CM × Ct × CF × Cfu × Ci × Cr × min(CL, CV)

Adjusted allowable compression stress (parallel to grain):

F'c = Fc × CD × CM × Ct × CF × Ci × Cp

Adjusted allowable tension stress (parallel to grain):

F't = Ft × CD × CM × Ct × CF × Ci

Adjusted allowable shear stress:

F'v = Fv × CD × CM × Ct × Ci

The key adjustment factors are:

• CD (load duration): amplifies allowable stress for short-duration loads - 1.6 for wind or seismic, 1.25 for construction, 1.15 for snow, 1.0 for occupancy live load, 0.9 for permanent dead load. The governing value is the highest CD among all loads applied simultaneously.
• CM (wet service): reduces capacity when in-service moisture content exceeds 19% for sawn lumber.
• Ct (temperature): reduces capacity for sustained service temperatures above 100°F.
• CF (size factor): adjusts reference design values for member depth and width; applied to visually graded sawn lumber per NDS Supplement Tables 4A and 4B.
• Cfu (flat use): applies when a rectangular member is loaded on its wide face rather than its narrow face.
• Ci (incising): reduces design values for preservative-treated members that have been incised to improve penetration depth.
• Cr (repetitive member): allows a 15% increase to F'b when three or more members spaced 24 in. or less apart share a load-distributing element such as structural sheathing.
• CL (beam stability factor): accounts for lateral-torsional buckling of members not continuously braced on the compression face; computed from the slenderness ratio RB per NDS 2024 §3.3.3.
• CV (volume factor): applies to glulam members; reduces bending capacity for larger volumes per NDS 2024 §5.3.6. For sawn lumber CV = 1.0.

NDS 2024 §3.3.3 requires using the lesser of CL and CV, not both simultaneously.

Column stability factor Cp

For members carrying axial compression, the column stability factor Cp captures the reduction in allowable compressive stress due to buckling. Cp is computed from:

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

Where:

• FcE = 0.822 × E'min / (Le/d)² is the critical buckling stress, with Le/d taken as the larger of the two slenderness ratios about each axis
• F*c = Fc × CD × CM × Ct × CF × Ci (all adjustment factors except Cp)
• c = 0.8 for sawn lumber, 0.85 for round timber poles, 0.9 for glulam and SCL
• E'min = Emin × CM × Ct × Ci × CT, the adjusted modulus of elasticity for stability

The governing (largest) slenderness ratio Le/d must not exceed 50 per NDS 2024 §3.7.1.4.

Individual member checks

Before applying the combined interaction equations, the calculator evaluates each load effect independently:

Bending: fb = M / S ≤ F'b, where S is the section modulus and F'b incorporates all applicable adjustment factors including min(CL, CV).

Shear: fv = 1.5 × V / A ≤ F'v for rectangular sections (NDS 2024 §3.4).

Axial compression: fc = P / A ≤ F'c, where F'c includes Cp.

Axial tension: ft = T / A ≤ F't.

Combined axial and bending - NDS 2024 Eq. 3.9-3 and Eq. 3.9-4

When a member carries both axial load and bending moment simultaneously, the individual stress checks are insufficient and the interaction between the two effects must be evaluated explicitly.

For combined axial compression and biaxial bending (NDS 2024 Eq. 3.9-3):

(fc / F'c)² + fb1 / (F'b1 × (1 - fc / FcE1)) + fb2 / (F'b2 × (1 - fc / FcE2 - (fb1 / FbE)²)) ≤ 1.0

Where:

• fc is the actual compressive stress, F'c is the adjusted allowable compressive stress including Cp
• fb1 and F'b1 are the actual and adjusted allowable bending stresses about the strong axis (axis 1)
• fb2 and F'b2 are the actual and adjusted allowable bending stresses about the weak axis (axis 2)
• FcE1 and FcE2 are the critical buckling stresses for each axis = 0.822 × E'min / (Le/d)²
• FbE = 1.20 × E'min / RB² is the critical buckling stress for lateral-torsional buckling

The denominator amplification terms (1 - fc / FcE1) and (1 - fc / FcE2) capture the P-delta moment magnification that arises when axial compression acts simultaneously with lateral deflection from bending. As fc approaches FcE the denominator approaches zero, which correctly represents the increasing sensitivity to combined loading as the member approaches its elastic buckling load.

For combined axial tension and bending (NDS 2024 Eq. 3.9-4):

ft / F't + fb / F'b ≤ 1.0

For members carrying axial tension, the interaction is linear and CL = 1.0 is used in F'b because tension braces the compression face against lateral-torsional buckling. The calculator evaluates both interaction equations when the sign of the axial force is ambiguous across load combinations and uses the governing (maximum) interaction ratio.

Output and utilization summary

The calculator reports the utilization ratio for each limit state. All ratios must be ≤ 1.0 for the member to satisfy NDS 2024 requirements. The governing interaction ratio from Eq. 3.9-3 or 3.9-4 is highlighted as the controlling check when combined loading governs. Each adjusted allowable value and the numerical value of every contributing adjustment factor are shown, so the full calculation chain can be traced directly to the NDS 2024 code reference.