Wood shear walls and diaphragms

Wind and earthquake loads push sideways on buildings, and in a wood-frame building the lateral load path runs through sheathed floors, roofs and walls. The roof and floors act as diaphragms, deep horizontal beams that collect the lateral load and deliver it to the walls. The walls parallel to the load act as shear walls, vertical cantilevers that carry it down to the foundation. Both are made of ordinary wood structural panels, plywood or oriented strand board (OSB), nailed to the framing, and their strength comes almost entirely from the nails. This lesson designs the lateral system of the two-storey office annex.

The load path

Wind on the long face of the annex pushes on the wall studs, which span from floor to floor and deliver half of their load to each diaphragm. The roof and second floor diaphragms span between the end walls, like simply supported beams lying flat. Each diaphragm delivers its end reaction to the end walls as a shear along their tops. The end walls carry the shear down through each storey, overturning tries to lift one end of each wall segment, and hold-downs at the ends of the segments carry that uplift into the foundation. Every link in the chain, from the wall studs to the anchor bolts, must be designed.

Diaphragms

A diaphragm behaves like a deep I-beam. The sheathing is the web and carries shear; the boundary members at the edges perpendicular to the load, usually the double top plates of the walls or a rim joist, are the flanges or chords, and carry the bending moment as tension and compression. For a simply supported diaphragm of span \(L\) and depth \(b\) under a uniform line load \(w\):

Here \(v\) is the unit shear along the supported edges, in force per unit length, and \(T\) and \(C\) are the chord forces. The chord must be continuous over the full length, so splices in the top plates are nailed or strapped to carry \(T\). Diaphragms are designed as blocked or unblocked: blocking under every panel edge lets the nails at those edges carry shear and roughly doubles the capacity. Openings for stairs and skylights interrupt the web and need collectors and extra chords around them.

Shear walls

A shear wall is a vertical cantilever. The sheathing nailed to studs and plates carries the shear, the end studs (chords) carry the overturning tension and compression, and the hold-downs anchor the tension chord. Only full-height segments, without openings, are counted in the simple segmented method, and each segment must have an aspect ratio of height to length within the limits of the standard, typically 3.5 to 1 for wind with a reduction above 2 to 1. Other methods, such as the perforated shear wall method and force transfer around openings, count more of the wall with extra detailing.

In O86, the factored shear resistance of a nailed shear wall comes from the nails. For a wall sheathed on one side, the unit resistance is \(v_r = \phi\,J_D\,n_u/s\,J_{us}J_{hd}\), where \(n_u\) is the unit lateral resistance of one nail from the yield equations of lesson 5, \(s\) the nail spacing along the panel edges, \(J_D = 1.3\) a factor for nailed sheathing in shear walls and diaphragms, \(J_{us}\) a factor for unblocked walls and \(J_{hd}\) a factor for hold-down restraint, with \(\phi = 0.8\). The panels must also be checked for buckling, which can govern thin panels on tall walls. Sheathing both faces roughly doubles the resistance.

The unit shear in a wall line is the shear delivered by the diaphragm divided by the total length of full-height segments. A segment's overturning moment at its base is the sum of each storey shear times its height above the base, and the hold-down force is

where \(l_s\) is the segment length and \(D_s\) the dead load on the segment. Strictly the moment arm is the distance between the chord centrelines, slightly less than the segment length, and designers allow for it.

Wind on the office annex

The annex is 16 m long, 8 m wide and two storeys of 3.0 m. With wind on the 16 m face, the factored line loads delivered to the diaphragms are 4.2 kN/m at the roof and 6.0 kN/m at the second floor, from the wind pressure on the wall area tributary to each level. Each end wall is 8 m long. In the second storey it has no full-height openings; in the first storey, a 1.6 m door in the middle leaves two 3.2 m full-height segments. The sheathing is 11 mm OSB with 3.25 mm common nails.

# Lesson 6: wind on the two-storey office annex, 16 m x 8 m, storey height 3.0 m (CSA O86 format)
import math
L, B, h = 16.0, 8.0, 3.0
w_roof, w_floor = 4.2, 6.0            # factored wind line loads on the diaphragms (kN/m)
# Diaphragms span 16 m between the 8 m end walls
for name, w in [("roof", w_roof), ("second floor", w_floor)]:
    R = w * L / 2
    v = R / B
    T = w * L**2 / 8 / B
    print(f"{name:12s}: reaction {R:.1f} kN, unit shear {v:.2f} kN/m, chord force {T:.1f} kN")

V2 = w_roof * L / 2                    # shear in each end wall, second storey
V1 = V2 + w_floor * L / 2              # first storey
seg2, seg1 = [8.0], [3.2, 3.2]         # full-height segments (first storey has a 1.6 m door)
v2, v1 = V2 / sum(seg2), V1 / sum(seg1)
print(f"\nEnd wall shear: second storey {V2:.1f} kN -> {v2:.2f} kN/m; first storey {V1:.1f} kN -> {v1:.2f} kN/m")

# Single-sided 11 mm OSB, 3.25 mm common nails: resistance from the nail, vd = nu / s
nu = 1.10                              # kN, unit lateral resistance of one nail (approximate, yield model)
JD = 1.3                               # shearwall factor for nailed sheathing
for name, v in [("second storey", v2), ("first storey", v1)]:
    for s in (150, 100, 75, 50):
        vr = 0.8 * JD * nu / (s / 1e3)
        if vr >= v:
            print(f"{name}: v = {v:.2f} kN/m, one side, nails at {s} mm: vr = 0.8 x {JD} x {nu}/{s/1e3} = {vr:.2f} kN/m")
            break

# Hold-down at the end of a 3.2 m first-storey segment
lseg = 3.2
Vseg1 = V1 * lseg / sum(seg1)
Vseg2 = V2 * lseg / sum(seg2)
M = Vseg2 * 2 * h + (Vseg1 - Vseg2) * h        # overturning at the base of the segment
Dres = 0.9 * 4.5 * lseg                         # 0.9 x dead load on the segment (4.5 kN/m)
T = M / lseg - Dres / 2
print(f"\nSegment {lseg} m: overturning {M:.0f} kN.m, hold-down tension = {M/lseg:.1f} - {Dres/2:.1f} = {T:.1f} kN")

roof        : reaction 33.6 kN, unit shear 4.20 kN/m, chord force 16.8 kN
second floor: reaction 48.0 kN, unit shear 6.00 kN/m, chord force 24.0 kN

End wall shear: second storey 33.6 kN -> 4.20 kN/m; first storey 81.6 kN -> 12.75 kN/m
second storey: v = 4.20 kN/m, one side, nails at 150 mm: vr = 0.8 x 1.3 x 1.1/0.15 = 7.63 kN/m
first storey: v = 12.75 kN/m, one side, nails at 75 mm: vr = 0.8 x 1.3 x 1.1/0.075 = 15.25 kN/m

Segment 3.2 m: overturning 163 kN.m, hold-down tension = 50.8 - 6.5 = 44.4 kN

The door in the first storey is what drives the design: it removes a fifth of the wall length where the shear is largest, so the first-storey unit shear is three times that of the second storey. Moving the door to the end of the wall would leave one longer segment and reduce both the unit shear and the hold-down force, a good example of how architecture and structure interact in wood buildings.

Anchorage and sliding

The shear at the base of each wall must pass into the foundation. Anchor bolts through the sill plate carry it in bearing on the wood, so they are designed as bolted connections loaded parallel to grain, with plate washers that keep the sill from splitting and that hold the plate down against the uplift of the sheathing. Their spacing follows from the unit shear and the capacity of one bolt, and the first and last bolts sit close to the ends of each sill piece. At the second floor, the shear passes from the upper wall into the floor framing through nails in the bottom plate and from the floor into the wall below through blocking or rim joists. Each transfer is checked, because a wall that is strong in itself but poorly attached to what is below it does nothing.

Deflection of shear walls and diaphragms

Shear walls deflect through four mechanisms: bending of the wall as a cantilever, shear deformation of the panels, slip of the nails, and stretching and slip of the hold-down. For typical walls the nail slip and hold-down slip dominate, which is why the standards include deflection equations with a nail slip term and why tight-fitting hold-downs and shrinkage compensating devices matter in multi-storey buildings. Storey drift limits under wind protect cladding and partitions; under earthquake they protect the structure itself.

Earthquake design

Thunder Bay and Duluth have low seismic hazard, and wind governs the annex. Where earthquake governs, wood shear walls are among the most ductile lateral systems available, because the many nails yield progressively and dissipate energy. The NBC assigns nailed wood shear walls a ductility-related force modification factor \(R_d = 3.0\) and an overstrength factor \(R_o = 1.7\), and O86 adds capacity design requirements so that the nails, not the hold-downs or the anchorage, are the weak link.

Mass timber lateral systems

The pavilion has no wood-frame walls. Its CLT roof is the diaphragm, with screwed splines at the panel joints carrying shear and the edge glulam beams acting as chords, and the lateral load goes to steel rod X-bracing in two end bays and to the concrete block wall at the back of the pavilion, which joins the wash bay. For taller mass timber buildings, CLT shear walls, rocking walls with hold-downs, braced frames and concrete cores are all used, each with its own design rules.

Details that make the system work

Lateral systems in wood fail at their weakest link, and the weakest link is rarely the sheathing. Common problems are missing or under-nailed blocking at panel edges, top plate splices that cannot carry the chord force, hold-downs installed loosely or omitted, anchor bolts too close to the ends of sill plates, and penetrations cut through shear walls by other trades. Inspection during construction, especially of nail spacing and hold-down installation, is part of the design. Over-driven nails, which break the surface of the sheathing, reduce capacity markedly, so pneumatic nailers must be adjusted.