Wood connections

Connections are where timber structures succeed or fail. A wood member is easy to size, but its strength means little unless the load can be passed into it and out again through nails, screws, bolts, dowels, timber rivets, split rings or proprietary hardware. Wood is weak across the grain and in shear, so a careless connection can split a member long before the member itself is stressed. This lesson explains how dowel-type fasteners carry load, applies the yield model to the knife-plate connection at the pavilion beam ends, and covers the spacing, edge distance and splitting rules that keep connections ductile.

Types of fasteners

Nails are the most common fasteners in light-frame construction, used by the thousands in every shear wall, floor and roof. Wood screws and modern self-tapping screws, now available up to 600 mm (24 in.) long, can be driven without pre-drilling and carry both lateral load and withdrawal; long screws installed at an angle make stiff, strong connections in mass timber. Bolts and drift pins (dowels) carry large loads through steel side plates or knife plates. Timber rivets, split rings and shear plates are older, high-capacity connectors. Proprietary hangers and concealed connectors, tested by their manufacturers, are now the usual way to connect mass timber beams to columns.

Fasteners load wood in two ways: laterally, with the fastener bending and bearing on the wood around it, and in withdrawal, with the fastener being pulled out along its axis. Smooth nails are poor in withdrawal and should not be used to resist sustained pull-out; threaded screws and ring-shank nails are much better.

The yield model

When a dowel-type fastener is loaded laterally, the wood under it crushes and the fastener bends. The European yield model, developed by Johansen in 1949 and the basis of both the Canadian and the American standards, predicts the capacity by assuming that both the wood and the fastener behave as rigid-plastic materials. The wood has an embedment (dowel bearing) strength, and the fastener forms plastic hinges at its yield moment. Each possible combination of crushing and hinging is a yield mode, and the lowest one governs.

For a connection with a steel main plate, the knife plate, and two wood side members, three modes matter. In the first, the bolt stays straight and crushes the wood along the full thickness of each side member. In the second, the bolt forms one plastic hinge in each side member, and the wood crushes only near the plate. In the third, two hinges form in each side member, and very little wood crushes. Thick wood and slender bolts favor the hinge modes, which are ductile; thin wood and stiff bolts favor pure embedment.

The dowel bearing strength depends on the specific gravity \(G\) of the wood, the fastener diameter and the angle between the load and the grain. For dowels 1/4 in. and larger, the NDS gives \(F_{e\parallel} = 11{,}200G\) psi parallel to grain and \(F_{e\perp} = 6100G^{1.45}/\sqrt D\) psi perpendicular to grain. For Douglas fir-larch (\(G = 0.50\)) and a 3/4 in. bolt, these are 5600 and 2578 psi; the perpendicular value is less than half the parallel value, which matters at the pavilion beam ends, where the beam reaction acts across the grain.

The NDS yield limit equations give a reference lateral design value \(Z\) for each mode, each divided by a reduction term \(R_d\) that depends on the mode and the angle to grain: \(4K_\theta\) for the embedment modes, \(3.6K_\theta\) for one hinge and \(3.2K_\theta\) for two hinges, with \(K_\theta = 1 + 0.25(\theta/90)\). The adjusted value is \(Z' = Z\,C_D\,C_M\,C_t\,C_g\,C_\Delta\), where \(C_g\) is the group action factor and \(C_\Delta\) the geometry factor for spacing and edge distances. The bolt bending yield strength is taken as 45,000 psi.

The pavilion beam-to-column connection

At each column, the two beam ends sit on a steel saddle, and a 3/8 in. knife plate welded to the saddle projects up into a slot cut in the end of each beam. Bolts of 3/4 in. diameter pass through the beam and the plate. The bolts carry the beam reaction of 10.6 kips down into the plate, so the load on each bolt acts perpendicular to the grain of the beam. Each wood side member is \((6.75 - 0.375 - 0.125)/2 = 3.125\) in. thick, allowing 1/8 in. for slot tolerance.

# Lesson 5: bolted knife-plate connection at the pavilion beam ends (NDS yield limit equations, ASD)
import math
D = 0.75                        # bolt diameter (in.)
Fyb = 45000.0                   # bolt bending yield strength (psi)
G = 0.50                        # specific gravity, Douglas fir-larch glulam
Fe_par = 11200 * G              # dowel bearing strength parallel to grain (psi)
Fe_perp = 6100 * G**1.45 / math.sqrt(D)   # perpendicular to grain (psi)
Fes_steel = 87000.0             # A36 knife plate, 1.5 Fu
tm = 0.375                      # knife plate thickness (in.)
ts = (6.75 - tm - 0.125) / 2    # each wood side member, with a 1/8 in. slot tolerance

def Z_double(Fes, theta):
    """Reference lateral design value, double shear, wood side members, steel main member."""
    Kt = 1 + 0.25 * theta / 90
    Fem = Fes_steel
    Re = Fem / Fes
    k3 = -1 + math.sqrt(2 * (1 + Re) / Re + 2 * Fyb * (2 + Re) * D**2 / (3 * Fem * ts**2))
    modes = {
        "Im (plate bearing)": D * tm * Fem / (4 * Kt),
        "Is (side embedment)": 2 * D * ts * Fes / (4 * Kt),
        "IIIs (one hinge)": 2 * k3 * D * ts * Fem / ((2 + Re) * 3.6 * Kt),
        "IV (two hinges)": 2 * D**2 / (3.2 * Kt) * math.sqrt(2 * Fem * Fyb / (3 * (1 + Re))),
    }
    return min(modes.items(), key=lambda kv: kv[1]), modes

V = 10.6                        # kips, D + S reaction
print(f"ts = {ts:.3f} in., Fe par = {Fe_par:.0f} psi, Fe perp = {Fe_perp:.0f} psi")
for label, Fe, th in [("load parallel to grain (column)", Fe_par, 0), ("load perpendicular to grain (beam)", Fe_perp, 90)]:
    (mode, Z), modes = Z_double(Fe, th)
    print(f"{label}: governing {mode}, Z = {Z:.0f} lb per bolt")
    for k, v in modes.items():
        print(f"     {k:20s} {v:6.0f} lb")
    Zp = Z * 1.15                # CD = 1.15 for snow; Cg and C_delta taken as 1.0
    n = math.ceil(V * 1000 / Zp)
    print(f"     Z' = {Zp:.0f} lb, bolts needed for {V} kips: {n}")

# Splitting check for bolts loaded perpendicular to grain: V <= (2/3) Fv' b de (de/d)^2
Fv_, b, d = 265 * 1.15, 6.75, 21.0
for de in (10.5, 16.5):
    Vs = 2 / 3 * Fv_ * b * de * (de / d)**2 / 1000
    print(f"  de = {de} in.: splitting limit = {Vs:.1f} kips vs {V} kips")

# Uplift on the CLT roof: self-tapping screws from panel to beam
wnet = 0.6 * 40.0 - 0.6 * 25.0      # psf: ASD 0.6W suction (W = 40 psf) less 0.6D
print(f"\nUplift: net ASD suction {wnet:.1f} psf, force per screw at 24 in. = {wnet*10*2:.0f} lb")

ts = 3.125 in., Fe par = 5600 psi, Fe perp = 2578 psi
load parallel to grain (column): governing IIIs (one hinge), Z = 3707 lb per bolt
     Im (plate bearing)     6117 lb
     Is (side embedment)    6562 lb
     IIIs (one hinge)       3707 lb
     IV (two hinges)        4417 lb
     Z' = 4263 lb, bolts needed for 10.6 kips: 3
load perpendicular to grain (beam): governing IIIs (one hinge), Z = 1684 lb per bolt
     Im (plate bearing)     4894 lb
     Is (side embedment)    2417 lb
     IIIs (one hinge)       1684 lb
     IV (two hinges)        2438 lb
     Z' = 1936 lb, bolts needed for 10.6 kips: 6
  de = 10.5 in.: splitting limit = 3.6 kips vs 10.6 kips
  de = 16.5 in.: splitting limit = 14.0 kips vs 10.6 kips

Uplift: net ASD suction 9.0 psf, force per screw at 24 in. = 180 lb

Splitting perpendicular to grain

A force applied across the grain through fasteners must be carried from the fasteners into the rest of the member. The wood on the side of the fasteners away from the direction of the force, toward the unloaded edge, has to hang from them in tension perpendicular to grain. Wood is very weak in that direction, so the member can split along the fastener line, suddenly and without warning. The protection is to place the fasteners far from the loaded edge, the edge toward which the fastener forces push, so that most of the depth lies between them and that edge, and to check splitting explicitly. For a load hung from a beam, the loaded edge is the bottom and the bolts go high. At a beam support, the bolts push the beam upward, the loaded edge is the top, and the bolts go low, near the seat.

The NDS checks it by limiting the shear force on the beam to \(V \le \frac{2}{3}F_v'b\,d_e\big(\frac{d_e}{d}\big)^2\), where \(d_e\) is the depth of the member less the distance from the unloaded edge to the nearest fastener. At the beam support the bolts push upward, so the top is the loaded edge. With the bolt group centered in the 21 in. beam, \(d_e\) is about 10.5 in. and the limit is only 3.6 kips, well below 10.6 kips. With the lowest bolt 4-1/2 in. above the bottom of the beam, \(d_e = 16.5\) in. and the limit rises to 14.0 kips. The square of \(d_e/d\) makes the bolt position decisive.

An alternative that many designers prefer is to let the beam bear directly on the saddle, so the vertical reaction passes in bearing and the bolts only keep the beam in place. The pavilion detail does both: the beam bears on the saddle seat, and the bolts, sized for the full reaction as a second load path, hold the beam against uplift and lateral load. The design is robust if either path is imperfect.

Spacing, end and edge distances

Fasteners too close to each other or to the ends and edges of a member split the wood before the yield modes develop. Both standards give minimum spacings along and across the grain, end distances and edge distances, all in multiples of the diameter, with larger values for loaded ends in tension. For bolts loaded parallel to grain, typical values are four diameters between bolts in a row, a seven-diameter end distance in tension and one and a half diameters to an unloaded edge. For loads perpendicular to grain, the loaded edge needs four diameters or more.

Rows of bolts parallel to the grain also share load unevenly: the bolts at the ends of a long row take more than their share, and a row of ten bolts does not carry ten times the load of one. The standards reduce the capacity of long rows through row and group action factors, and brittle failure modes, such as row tear-out and group tear-out, where a block of wood shears out along the rows, must be checked for groups with many fasteners. Using fewer, larger groups of shorter rows, or self-tapping screws that reinforce the wood, avoids the problem.

Nails and screws

Nailed connections use the same yield limit equations with nail bearing strengths, and the many small nails in a shear wall act together as a ductile system. An 8d common nail in Spruce-Pine-Fir has a reference lateral value in the order of 70 to 100 lb, depending on the side member, so a shear wall with nails at 6 in. resists a few hundred pounds per foot; lesson 6 uses this. Withdrawal resistance of smooth nails is low and drops further if the wood dries after driving, so nails are not used to resist sustained withdrawal.

Self-tapping screws have changed mass timber design. Installed at 45 degrees across a joint, they load the wood along the screw axis, in withdrawal, where wood is stiff and strong, rather than in lateral bearing. They also reinforce wood against splitting near notches and at beam supports. Their design values come from evaluation reports for each product. At the pavilion, screws fix the CLT deck to the glulam beams, resisting the uplift from wind suction on the roof: Sofia's script shows a small net uplift per screw, which a single screw at 600 mm (24 in.) carries easily, though the spacing is set closer to make the deck act as a diaphragm.

Moisture and connections

Connections are sensitive to moisture changes. A steel plate bolted across the width of a deep glulam beam restrains the wood from shrinking as it dries; if the bolts are far apart across the grain, the shrinking wood splits between them. Good details use bolts in a single column or short groups across the grain, slotted holes in the steel, or several separate plates, so the wood can move. Wet service reduces fastener capacity and corrodes ordinary steel, which is why the salt shed uses hot-dip galvanized or stainless fasteners throughout.