2×4 and 2×6 walls are regularly used in wood framing to hold up whole buildings, but without sheathing, individual sticks tend to buckle at very low axial loads. Just like a ruler, unbraced 2x “columns” tend to kick out to the side way before the material actually crushes.
When it comes to stick-framed walls, bracing 2×4’s and 2×6’s with either structural sheathing or blocking eliminates weak-axis buckling, greatly strengthening the overall wall. Structural sheathing can also turn walls into shear walls, an absolute must for high lateral loads, like strong winds or seismic.
To explore that, we’ll take a quick dive into the Column Buckling strength of braced and unbraced 2×4’s and 2×6’s according to the American Wood Council’s National Design Specification, as well as discuss shear walls in brief.
Bracing & Buckling
Buckling is when a compressive member kicks out to the side at a lower load than the load that would crush the material it’s made of. Think of things like a ruler compressed on its ends, or an aluminum can. Visually, watch about the first twenty seconds of this video from The Efficient Engineer:
There are two ways to fight this kind of buckling: either alter the shape of your column to get something more buckling-resistant (something with a higher Radius of Gyration, covered in-depth in my article here) or add lateral bracing, which prevents the column from kicking out to the side.
You can experience the massive effects of bracing yourself with a thin ruler. Try pushing down on the end and feel how much force it takes to kick out to the side, then try it again with your other hand lightly providing lateral support halfway up the ruler. The ruler should take a lot more force to buckle, and take on an s-shape of double curvature.
If you have a friend around, try one more time, this time bracing at third points, and see how much higher that strength is.
2×4 & 2×6 Compressive Strength – Braced vs Unbraced
In the US, the American Wood Council’s “National Design Specification” governs wood design for structural engineers.
It provides a Supplement filled with reference design values for various sizes and species of wood, and has the engineer apply numerous adjustment factors to these, accounting for things like high temperature in service, use in wet areas, and sustained loading, all of which degrade the strength of wood members.
For column Allowable Stress Design, the adjustment factors are the Load Duration Factor, C.d, Wet Service Factor, C.m, the Temperature Factor, C.t, Size Factor, C.F, Incising Factor (accounts for the loss of strength due to the small blades that slice up the surface for pressure-treated lumber), C.i, and the Column Stability Factor, C.p. This stability factor is what accounts for buckling.
In my area of the country, most construction lumber is Spruce-Pine-Fir, so I’ll use that for our example. The Reference Design Compressive Strength Parallel to the Grain for SPF Studs is 725 psi, from Table 4A in the NDS Supplement.
For adjustment factors, we’ll use a permanent load duration (C.d = 0.9), dry service (C.m = 1.0), normal temperature use (C.t = 1.0), and non-pressure-treated lumber (C.i = 1.0). The Size Factor for a 2x comes from the Supplement and is 1.05 for a stud. The Column Stability Factor is based on the section properties and length of the column, so we’ll save that for the various cases we’re looking at.
For the assumptions above, we get the following allowable axial loads on braced and unbraced 2x4s and 2x6s:
| Nominal Lumber Size | Allowable Axial Load, Unbraced | Allowable Axial Load, Fully-Braced |
|---|---|---|
| 2×4 | 278 lbs | 2013 lbs |
| 2×6 | 437 lbs | 4755 lbs |
Multiplying together what we already have, we get a value known as F.c*:
The 685 psi * C.p will be multiplied by the cross-sectional area of each column. According to NDS Supplement Table 1B, the 2×4 (1.5″x3.5″ true dimensions) has an area of 5.25 in², and the 2×6 (1.5″x5.5″) has an area of 8.25 in².
The equation for the Column Stability Factor is unfortunately ugly, as instability equations tend to be. It depends on the minimum expected Young’s Modulus of the stud, which for our stud-grade SPF is 440,000 psi.
For rectangular columns made from sawn lumber, c = 0.8, and l.e/d shall be taken as the larger of the two ratios l.e1/d.1 or l.e2/d.2, where each ratio is adjusted by the appropriate buckling length coefficient.
2×4 Stud 8′ Long, braced & unbraced
By providing sheathing with an appropriate nailing pattern, we can effectively eliminate buckling in the weak axis of the 2×4, but it’s still possible for the braced column to then buckle in the strong axis.
Checking out the unbraced state, we get l.e1/d1 = 96″ / 1.5″ = 64, which gives us:
For the case with sheathing providing full bracing, we instead look to the 3.5″ dimension of our 2×4, which gives l.e2/d2 = 96″/3.5″ = 27.43, assuming we don’t have any strong-axis bracing. Crunching those numbers, we get F.cE of 481 psi, which gives a Column Stability Factor of 0.5595, and an allowable axial load for the braced 2×4 of 2013 lbs, over 7x the strength of the unbraced 2×4 without sheathing!
2×6 Stud 8′ Long, braced & unbraced
The same process goes for the 2×6, except we’ll be using d.1 = 1.5″, d.2 = 5.5″, and A = 8.25 in².
For the unbraced version, we have the same d.1 as in the unbraced 2×4, so the same l.e1/d1 = 96″ / 1.5″ = 64, which means we get no change to the Column Stability Factor. The only increase we gain over the 2×4 is a greater area, which gives us:
However, the 5.5″ depth gives us an even greater benefit from bracing the column. l.e2 / d.2 = 96″ / 5.5″ = 17.45. This gives F.cE = 1187 psi, and a Column Stability Factor of 0.8412. The bracing supplied by the sheathing and a proper nailing pattern hops the allowable axial load all the way up to 4755 lbs, over 10x the strength of the unbraced 2×6, and 17x the strength of the unbraced 2×4!
Sheathing plays a HUGE role in getting the most strength out of a given 2×4 or 2×6, and should definitely be considered wherever large compressive loads are present. This is why some interior load-bearing walls end up with sheathing and frequent nailing patterns, to take advantage of these huge gains.
Shear Wall Summary
Stick framing is incredibly popular in residential construction across the country, but the simple nailed connections that make it so easy don’t provide much lateral strength. Think of nailing a stud to another, and then pushing on the stud sideways to try to pry out the nail. It’s not that hard to pop the nail loose.
To support large lateral loads, like those from high wind or seismic, builders and engineers have two realistic options, they can either add diagonal strapping help turn the walls into trusses with some lateral strength, or they can add sheathing and proper nailing patterns to create shear walls.
Shear walls are walls that are stiff and strong under lateral loads, and the sheathing and nailing pattern can meet those requirements. Additionally, those same fasteners that help use the rigidity of the sheathing in-plane to make a shear wall can also provide the bracing we discussed above.
For more about the types of loads engineers have to design buildings to resist, check out my article “What Loads do Structural Engineers Design For?“.
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