The following formula is an example of the type used to determine the maximum allowable withdrawal loading on the wood when using a lag screw:
p = 1800 D0.75 G1.5
Here p is the allowable load, in pounds per inch of embedment of the threaded portion of the screw. D is the shank diameter, in inches of the screw. G is the specific gravity of oven-dried lumber of the particular species. The screw is assumed to be fastened into the side grain of the wood member.
The ability of the wood to resist side loading must also be checked, using formulas similar to these from Mark’s Standard Handbook for Mechanical Engineers:
P = 2280 D2 (for softwoods)
P = 2640 D2 (for hardwoods)
Here P is the total allowable shear load on the screw, in pounds parallel to the grain. D is the shank diameter, in inches of the screw. There is assumed to be a distance of at least 3 degrees times the screw diameter to the edge of the wood. Also it is assumed that the screw threads are embedded a minimum distance into the wood of seven times the shank diameter of the screw for hardwoods, 11 times for softwoods.