Engineering equations
The following describes the design based on equations that would allow the engineer to be free of constraints and set all parameters as required for the project at hand. For STS loaded in shear, perpendicular to the length axis, it can be done with the yield equations given in CSA O86. For screws loaded in withdrawal, parallel to the axis of the screw, the main direction of loading in most cases uses the EC5 equation in Figure 2.

When using this EC5 equation, special consideration has to be given to the characteristic (5^th percentile) density. The densities for local wood species are given in CSA O86 as relative specific gravity (G) at a wood moisture content (MOC) of oven-dry. However, the densities used in EC5 are given as 5^th percentile values at an MOC of 12 per cent.

To use the CSA densities, some statistical ‘soft’ conversions implying certain assumptions have to be done. The conversion of relative gravity (a value relative to water with 1000 kg/m³ density) to density is straightforward, and the value can simply be multiplied by 1000. To convert the mean value to a 5^th percentile value, the former is multiplied by 0.84, as shown in the equation. As a last step, the MOC has to be taken into consideration. The Wood Handbook by the Forest Products Laboratory of the U.S. Department of Agriculture (USDA) Forest Service gives great information of the effect of moisture content on the density and offers the following formula for conversion:

ρ_k,0% = ρ_{k,0% *} (1+M/100) with M = 12%

Putting it all together the following equation can be used to convert the CSA gravities (G) to EC5-compliant densities:

ρ_k = ([G *1000] * 0.84)* (1+M/100)

When it comes to establishing the factored design capacity, the provisions given in CSA O86 can be used or the EC5 provisions applied, since both codes are semi-probabilistic and use load resistance factor design with similar factors. The material safety factor for connections in EC5 (Ƴ_M) is 1.3 whereas a common factor φ of 0.7 can be used for connections utilizing self-tapping wood screws.

When looking at 1/Ƴ_M = 0.769, it is slightly higher than the 0.7 used in CSA, but when looking at load duration factors and how they are established (which is beyond this article’s scope), the 1/ Ƴ_M can be normalized to φ = 0.7 in combination with the use of the common Canadian load duration factors (K_D).

The engineering design of standardized connection systems from Europe using STS can be done the same way, but most manufacturer provide characteristic (5^th percentile) values for their systems in their ETA as the number of screws per connector is fixed. In that case, only the safety factors have to be applied to the tabulated values.

It is worth noting the tabulated values are, in almost all cases, tabulated solely for the reference density and the standard connection with screws at a set angle to the grain. With a system connector used in connections that are inclined or oblique, the designer has to calculate the capacity as the angle between screw axis and wood grain can differ from the standard situation and impact its capacity.

This also means competing connection systems have to be checked separately as comparison of the standard situation capacity difference between systems may not be linear; it could also be different for inclined or oblique connections. For example, if System A is 10 per cent stronger than System B in a standard situation, it may in fact be weaker in other scenarios.