Quote of the Day
It's like, at the end, there's this surprise quiz: Am I proud of me? I gave my life to become the person I am right now. Was it worth what I paid?
— Richard Bach
Introduction
Figure 1: Excerpt Lateral Strength Reference Data from the NDS for 1.5 inch Thick Stock. (Source)
I am an amateur carpenter, and I work hard to ensure that I always comply with the applicable building codes. The various codes include requirements for a properly nailed joint (examples). Since I like to understand where these requirements come from, I have been the reading some sections of the National Design Specification for Wood Construction (NDS) that address fastening with nails. During my reading, I saw many interesting formulas associated with determining the NDS design ratings for nail withdrawal force (covered here) and lateral force resistance, which is the subject of this post.
My focus here is on duplicating some of the results in NDS Table 11N, which contains lateral resistance design values for different nails in different species of wood. I did this exercise so that I could confirm that I understood the mechanics associated with the formulas that I read in the NDS. I will not be presenting any tutorial information because the NDS goes into tremendous detail on the subject.
Disclaimer: I am NOT a structural engineer. I am just a guy who finds the subject interesting. If you have structural questions, contact a structural engineer.
Background
Definitions
- Sinker Nail
- A type of nail used in contemporary wood-frame construction; thinner than a common nail, coated with adhesive to enhance holding power, with a funnel-shaped head, and a grid stamped on the top of the head. (Source)
- Common Nail
- A nail with a mostly smooth, uncoated shank less than one third the diameter of its head, used for interior construction, especially framing. (Source)
- Box Nail
- Box nails are made for use in thin dry wood. To reduce a nail's tendency to split such wood, the point is slightly blunted, so that it crushes the wood fibers and punches its way through instead of enlarging a crack. Box nails are thinner than the corresponding penny size in common nails, and about ⅛ inch shorter than their nominal size. Often they are coated with a resin (such as nylon) that is melted by the heat generated in driving the nail and glues the nail in place. (Source)
- Dowel
- Dowel is a generic term used for a fastener that transfers a load between connected members by a combination of flexure and shear in the dowel, and shear and bearing (referred to as embedment) in the timber. (Source)
Modeling Information
Figure 2 shows the yield limit formulas from the NDS that are applied to dowels loaded in shear – a nail is a form of dowel. If you want more background on these formulas, please see the NDS.
Figure 2: Key Formulas in Determining the Lateral Resistance Rating of a Nail. (Source)
The NDS defines a reduction term (Figure 3) that must be applied to the calculations.
Figure 3: Definition of Reduction Term.
I coded these formulas into a Mathcad program (shown below). I assume that both connected members are 1.5 inches thick. For additional verification, I work the case of two 1.75 inch members in Appendix A.
Nail Information
I have summarized the characteristics of various types of nails in Figure 4. I grabbed this data from various sources (example).
Figure 4: Table of Nail Characteristics.
Analysis
Lateral Strength Function
Figure 5 shows my Mathcad implementation of what I thought I read in the NDS, which goes into excruciating detail on this topic. Please refer to the NDS because I cannot do the subject justice here. The key point is that the variable Ζ contains the formulas for the four dowel failure modes, and the program returns the minimum of these four values n units of pounds-force.
Figure 5: My Realization of the NDS Dowel Lateral Strength Function.
Solution Setup
Figure 6 shows how I used Mathcad to generate the same results as are in Table 11N, which I confirm by taking the difference between my results and the Table 11N and getting a result of all Øs.
Figure 6: Checking My Function Output Against the Reference.
Conclusion
I was able to duplicate some of the results in Table 11N from the NDS. This gives me good confidence that I understand how the table was generated.
Appendix A: Analysis Repeated for 1.75 inch Thick Stock.
In Figure 7, I repeated my analysis of 1.5 inch thick stock for 1.75 inch thick stock and also duplicated the results in Table 11N.
Figure 7: Example Using 1.75 inch Thick Wood.