Wood Beam-Column Interaction (NDS 3.9.2)
A stud carrying wind on a bearing wall is a beam and a column at once.
Example
You enter
- Axial compression P (lb) 3000
- Bending moment M (in-lb) 3000
- Area A (in²) 12.25
- Section modulus S (in³) 7.15
- Adjusted Fc' (with Cp, psi) 538.8
- Adjusted Fb' (with CL, psi) 1350
- Adjusted Emin' (psi) 580000
- Effective length le (in) 96
- Depth d, bending axis (in) 3.5
You get
- Fc (psi) 244.9
- Fb (psi) 419.6
- Euler stress FcE 634 psi
- Interaction 0.7132
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
ScopeNDS 3.9.2 combines them as (fc/Fc')^2 + fb/[Fb'(1 - fc/FcE)] <= 1.0, where FcE = 0.822 Emin'/(le/d)^2 and the 1 - fc/FcE denominator is the P-delta magnifier. A 4x4 stud at 3,000 lb + 3,000 in-lb passes at 0.71 with the bending term already amplified 1.6x; double the axial load and the amplifier climbs to 4.4x for a 2.19 fail - the effect a designer must not drop. Enter Fc' with Cp and Fb' with CL already applied. A design aid, not the engineer of record's stamped design.
Formula or tablefc = P/A; fb = M/S; FcE = 0.822 Emin'/(le/d)^2; interaction = (fc/Fc')^2 + fb/[Fb'(1 - fc/FcE)] <= 1.0.
Source and editionThe NDS 2018 3.9.2 combined bending and axial compression interaction with the Euler stress FcE = 0.822 Emin'/(le/d)^2 and the 1 - fc/FcE P-delta moment magnifier, by name.
Free accessThe NDS is free to view at awc.org (ANSI/AWC NDS); the 3.9.2 interaction equation is in the published standard.
What governsEstimate. AHJ and licensed professional govern.
API field namesp_lb, m_inlb, a_in2, s_in3, fc_adj_psi, fb_adj_psi, emin_adj_psi, le_in, d_in, fc_psi, fb_psi, fce_psi, interaction
- Interaction the squared axial term plus the amplified bending term must not exceed 1.0NDS 2018 Eq. 3.9-3
- P-delta amplifier the bending term divides by 1 - fc/FcE, growing without bound as fc approaches the Euler stressNDS 2018 3.9.2
- Adjusted values Fc' enters carrying the column-stability Cp; Fb' carrying the beam-stability CLNDS 2018 3.7 / 3.3.3