Lag screws in the Ogopogo joints, checked against the NDS

Hibbeler Chapter 8 asked when a lag-bolted Ogopogo joint is enough and when it should switch to integral joinery. It used rough per-screw numbers and said to verify them against the NDS lag screw tables. This chapter does that: it gets each number from the NDS, shows where it comes from, and checks the joint's count, spacing and grain direction.

How the NDS finds what one lag screw holds

A laterally loaded lag screw in a wood-to-wood joint can fail six ways: the wood crushes under the screw in the main member (Im) or the side member (Is), the screw rotates as a rigid pin and crushes the wood at both ends (II), or the screw bends with one hinge, in the main member (IIIm) or the side member (IIIs), or with a hinge in each (IV). The NDS yield limit equations give a load for each way, and the reference value, Z, is the smallest of the six. For these small lags it is usually IV (or IIIs when the load is across the grain), the screw itself bending, which is why the value changes so little with how thick the side board is.

Inputs: the wood's dowel bearing strength (a table value from its specific gravity, G, and different along and across the grain), the screw's bending yield strength (45,000 psi for the 3/8 and 1/2 inch sizes), and the screw's thread root diameter, because the NDS table values are for the common reduced-body lag screw (3/8 inch: 0.265 in root; 1/2 inch: 0.371 in). The calculator below runs those equations and reproduces all 200 published NDS 2018 Table 12J values it was checked against (3/8 and 1/2 inch lags, four wood groups, every side-member thickness), the largest difference being 5 lb of rounding.

The published numbers

• Southern Pine (G = 0.55), 1-1/2 in side member, 8 diameters of penetration: 3/8 in lag, 210 lb along the grain, 140 lb across it. 1/2 in lag, 410 lb along the grain, 230 lb across it.
• Hibbeler Chapter 8's quick figures were 300 lb and 550 lb, so they ran 1.3 to 2.4 times high depending on grain direction. These are reference values before any adjustment factor.
• Lighter woods carry less: the same 1/2 in lag along the grain is 390 lb in Douglas Fir-Larch and 350 lb in Hem-Fir or Spruce-Pine-Fir.

The adjustments for a connection

• Load duration, CD: the same factors as for lumber, up to 1.6 for wind (the 2.0 impact factor does not apply to connections). Snow 1.15, occupancy live load 1.0, dead load 0.9.
• Wet service, CM: dowel-type fasteners loaded sideways get 0.7 if the wood stays above 19% moisture in service. A joint that is dry in service and was dry when built gets 1.0.
• Group action, Cg: several screws in a row do not share perfectly, because the first and last take more. The NDS formula (Equation 11.3-1) was checked here against its published Table 11.3.6A (44 entries). For 1/2 in lags at 4 diameters of spacing, three in a row cost about 1% and five cost about 4%.
• Penetration: the table assumes the screw goes 8 diameters into the main member, not counting the tapered tip, and the minimum is 4 diameters. With less than 8, the NDS allows multiplying the table value by p/8D or calculating at the real penetration. A half-inch lag only 2 inches into the main member (4D) is about 207 lb along the grain with the safe shortcut, half of 413.
• Geometry, CΔ: if the end distance, edge distance or spacing is under the minimum, the value drops in proportion (below).

Worked case: the half-inch joint, three ways

• Three 1/2 in lags in Southern Pine, loaded along the grain, no load factor: 3 × 410 × 0.99 ≈ 1,225 lb. That matches Chapter 8's "about 1,000 to 1,200 lb for two or three half-inch lags," and two lags carry about 820 lb.
• The same three lags loaded across the grain: about 680 lb. Five carry about 1,090 lb.
• Three 3/8 in lags carry about 630 lb along the grain and about 415 lb across it. It takes five to reach 1,000 lb along the grain and eight across it.
• Load duration helps short loads: the first case under snow (1.15) is about 1,410 lb and under wind (1.6) about 1,960 lb. Wet service cuts it to about 860 lb.

So the Chapter 8 rule of thumb holds for loading along the grain and overstates a joint loaded across it. Which one an Ogopogo moon-eye or melon-head joint sees depends on how the parts are oriented, so the real joint detail decides.

How far apart and how close to the edge

• End distance: 7 diameters where the screw bears toward the end of the board (tension), 4 diameters where it bears away from the end or the load is across the grain. For a half-inch lag that is 3.5 in and 2 in. Half those numbers give a 50% capacity, with a sliding scale between.
• Spacing along a row: 4 diameters for full value, 3 at the least with a reduction (2 in and 1.5 in for 1/2 in lags).
• Edge distance: 1.5 diameters when loaded along the grain (0.75 in for 1/2 in lags; a long screw in a wide pattern needs half the row spacing if that is more). Across the grain, 4 diameters on the edge being pushed toward and 1.5 on the other.
• Rows: 1.5 diameters apart along the grain; across the grain it depends on the screw's length against its diameter. No more than 5 inches between the outermost rows across the grain in solid sawn wood, so a wide board can shrink and swell without splitting.

When the wood tears out instead of the lag

A line of lags along the grain can also fail through the wood: the strip of board beside and between the screws shears out along its length, or the board pulls apart across the line of holes. NDS Appendix E gives one method for checking this for loads along the grain. Row tear-out: each row can shear along two lines, one on each side of the screws, over the distance between screws, so the capacity is n × Fv′ × t × s, where t is the board's thickness and s is the smaller of the end distance and the spacing between screws. Net section: the board's tension capacity across the line of holes, Ft′ × t × (width − holes × hole diameter). Group tear-out, for two or more rows: half of each outer row's tear-out plus the tension strip between the rows. The joint holds the smallest of the lag screws and each of these, for both boards. The calculator reproduces all eight numbers in the NDS's own worked examples for this method (the staggered-bolt and single-row examples).

• Half-inch lags in Southern Pine, 2× side board, 4× main board, boards 5.5 in wide, 2 in between screws, one row, load along the grain. Three lags: 1,225 lb on the lags against 1,575 lb for row tear-out of the side board, so the lags govern. Five lags: 1,975 lb against 2,625 lb. The wood stays about a third stronger than the lags all the way up.
• Shorten the end distance to 1 in (2 diameters) and three lags fall to 788 lb, because the strip of board past the last screw is what tears out. The full-value end distance for a screw pulling toward the end of the board is 7 diameters, 3.5 in.
• A thin side board is closer: three 3/8 in lags through a 3/4 in board carry 532 lb on the lags and 591 lb on the wood, an 11% margin.
• Two rows of three half-inch lags, rows 3 diameters (1.5 in) apart: 2,450 lb on the lags against 2,475 lb for group tear-out, essentially a tie. Squeeze the rows to the 1.5-diameter minimum and group tear-out falls to 1,800 lb, a 27% loss. Three rows at 3 diameters give 3,375 lb on the wood against 3,674 lb on the lags, so the wood governs.

Does the math forbid a fifth lag in an 8 ft 2×6? Neither the minimum distances nor the Appendix E check does. A row of four half-inch lags needs about 9.5 inches of board from the loaded end and five needs about 11.5, group action costs about 4% at five, and the wood limit stays about a third above the lags' own capacity. So the NDS method does not explain Hibbeler Chapter 8's field result, five lags splitting a board. Things these numbers do not capture and that could: a lead hole left out or too small, a screw driven with a hammer instead of turned, a load across the grain (which splits a board along its length), a 2× main board that gives only 1.5 inches of penetration (3 diameters, under the 4-diameter minimum), or a board shrinking against a tight row of screws. That is a list of suspects, not a finding. Keep four as the working limit and add a second board or an integral joint beyond it.

Pulling straight out

For a lag screw loaded in withdrawal, the NDS (Equation 12.2-1) gives W = 1800 × G^1.5 × D^0.75 pounds per inch of thread in the main member, tapered tip not counted. For Southern Pine that is about 352 lb per inch for a 3/8 in lag and 437 lb per inch for a 1/2 in lag: 3 inches of thread in a 3/8 lag is about 1,055 lb, and 4 inches in a 1/2 lag about 1,746 lb, before adjustment factors. Into end grain, multiply by 0.75. The screw's own tensile strength at the thread root can also govern, and that limit is not computed here.

Where to be cautious

• Drill lead holes: the shank gets a clearance hole the same diameter as the shank, and the threaded part a lead hole of 60 to 75% of the shank diameter in wood with G between 0.5 and 0.6 (65 to 85% above 0.6, 40 to 70% at or below 0.5). Turn the screw in with a wrench; never drive it with a hammer. Soap or other lubricant is fine.
• Respect the minimums above. A screw too close to an end or edge splits the board before it reaches the number on this page. The geometry factor reduces capacity if a distance is short, but the calculator does not compute it, so meet every minimum.
• The values are for a single fastener type, sideways load, wood to wood. A steel plate, a screw loaded at an angle, double shear or a screw loaded both sideways and in withdrawal each change the math.
• Across-the-grain loading can split the board along its length where it carries the load. Heavy loads hung below the middle of a single beam need reinforcing against that (NDS Table 12.5.1C note).
• A joint that carries people, a roof or anything that falls on someone is for a structural engineer to design and stamp. This is a worked example.

Open items for a later pass

The real moon-eye and melon-head geometry (load direction, member sizes, distances) once a drawing exists. The 5/8 in lag, because its thread root diameter was not confirmed from the NDS. Metal side plates and double shear. Staggered rows and uneven spacing in the tear-out check (the NDS notes several definitions for the critical group area), tear-out values for woods other than Southern Pine, and tear-out for loads across the grain. The geometry factor when a distance is short, and the full-body lag screw's higher values with a long unthreaded shank (AWC Design Aid No. 1 shows the method).

Sources

• American Wood Council, NDS 2018 with Commentary (free at awc.org): Chapter 12, Table 12J (lag screw values), Table 12.3.3 (bearing strengths), 12.1.4 (lead holes and minimum penetration), Equation 12.2-1 (withdrawal), 12.5.1 and Tables 12.5.1A to 12.5.1D (distances); Chapter 11, Equation 11.3-1 and Table 11.3.6A (group action), Table 11.3.3 (wet service), 11.1.2 (local stresses); Appendix E, sections E.2 to E.4 and samples E.6 and E.7 (net section, row and group tear-out).
• Southern Forest Products Association, Southern Pine Use Guide, 2013, Table 1: No. 2 Southern Pine Fv 175 psi and Ft 675 / 600 / 550 / 475 / 450 psi by board width, used for the tear-out check.
• AWC Technical Report 12 (dowel bearing strength and bending yield, Appendix A) and Design Aid No. 1 (lag screw examples, including the 3/8 in root diameter of 0.265 in).
• The 1/2 in lag's 0.371 in root diameter is from a standard lag screw dimension table (ASME B18.2.1, as listed by Portland Bolt); it reproduces the NDS Table 12J values exactly.
• Written from these public documents, not from the Breyer textbook itself. If the book disagrees, the book and the current NDS win.