Wood Bending Plus Axial Tension (NDS 3.9.1)
A truss bottom chord holding up a ceiling, or a tie loaded off its centerline, carries tension and bending together.
Example
You enter
- Axial tension T (lb) 5640
- Bending moment M (in-lb) 3000
- Area A (in², net at holes) 8.25
- Section modulus S (in³) 7.563
- Adjusted Ft' (psi) 1009
- Fb* = Fb' without CL (psi) 1495
- Fb** = Fb' without CV (psi, blank = Fb*) 1495
You get
- Tension face ft/Ft' + fb/Fb* 0.943
- Compression face (fb - ft)/Fb** -0.192
Checked against published worked examples from: Missouri University of Science and Technology (J. Thomas, CE 5260 Wood Design).
Details, formula, and sources
ScopeNDS 3.9.1 checks both faces: the tension face ft/Ft' + fb/Fb* against 1.0, with Fb* left without the beam stability factor because the tension side cannot buckle, and the compression face (fb - ft)/Fb**, which matters when bending outruns the tension on a slender, unbraced member. A 2x6 No. 1 DF-L chord with 5,640 lb of snow-case tension and 3,000 in-lb of ceiling bending works at 0.943 of its capacity, about 72% of that from the tension. Adjusted design values are entered; the engineer of record governs.
Formula or tableft = T/A; fb = M/S; Eq. 3.9-1 ft/Ft' + fb/Fb* <= 1.0 (Fb* = Fb' excluding CL); Eq. 3.9-2 (fb - ft)/Fb** <= 1.0 (Fb** = Fb' excluding CV).
Source and editionThe NDS 2018 3.9.1 bending-and-axial-tension interaction, Eq. 3.9-1 and 3.9-2, by name.
Free accessThe NDS is free to view at awc.org (ANSI/AWC NDS); the worked check is a free Missouri S&T course solution (CE 5260, Problem 7-5).
What governsEstimate. AHJ and licensed professional govern.
API field namest_lb, m_inlb, a_in2, s_in3, ft_adj_psi, fb_star_psi, fb_dstar_psi, tension_interaction, compression_side_ratio
- Fb* Fb' with every applicable factor except the beam stability factor CLNDS 2018 3.9.1
- Fb** Fb' with every applicable factor except the volume factor CV; blank uses Fb*NDS 2018 3.9.1
- Area the user enters the net area where fastener holes reduce the sectionNDS 2018 3.1.2