By destructive testing of the different kinds of joints under different kinds and magnitudes of loads.
This means that joints of various kinds are constructed, then loaded in a particular fashion until they break, taking measurements of the forces needed to deform the joint and/or separate the parts. Then, some sort of analysis of the results is used to produce structural ratings for the different joints in specified conditions; and if a consensus can be reached for some application, a committee is likely to draft a standard to make it easier to specify requirements for a certain design. An example of such a specification is (in the USA) the National Design Specification for Wood Construction.
Here, for example, is an excerpt from a technical handbook referencing empirical methods:
Maximum lateral resistance and safe design load values for small-diameter (nails, spikes, and wood screws) and largediameter dowel-type fasteners
bolts, lag screws, and drift pins) were based on an empirical method prior to 1991. Research conducted during the 1980s resulted in lateral resistance values that are currently based on a yield model theory. This theoretical method was adapted for the 1991 edition of the National Design Specification for Wood Construction (NDS). Because literature and design procedures exist
that are related to both the empirical and theoretical methods, we refer to the empirical method as pre-1991 and the theoretical method as post-1991 throughout this chapter. Withdrawal resistance methods have not changed,
so the pre- and post-1991 refer only to lateral resistance. Wood Handbook, Forest Products Laboratory. 1999. Ch. 7
Not just engineers use this method: carpenters often consider themselves, with varying degrees of justification, as engineers of sorts.
Most woodworking joints have evolved over thousands of years. Woodworkers learned to make them based on their own experience, and the experience of the people who taught them. To make successful joints you need a little experience, a basic knowledge of the workings of wood and glue, and a bit of common sense. But in the 21st century we want a definitive answer. We want numbers and we want proof. We want something in writing we can point to when we’re not sure of ourselves.
Like other magazines, we have tested joints to destruction. Popular Woodworking