Triaxial tension in a lugged steel bicycle frame

It’s an unexpected marvel of nature: the weakest chain in the link can hold its own with the stronger links. But this blog isn’t about chains; it’s about a lugged steel bicycle frame. In an earlier blog, I described the difference between a lugged frame and a TIG welded frame.

This frame is primed and ready for painting. This photo shows the seat tube lug.

When lugs are used as sleeves to join the tubes of a bicycle, everything is joined with a metal filler, usually brass or silver. When I built frames, I used a silver alloy metal. Silver will flow into the very small gap (from 1 to 5 thousandths of an inch) between the lug and the tube and, like glue, hold everything together.

One way of measuring the strength of a material is its tensile strength. Very loosely speaking, tensile strength refers to how much force can be applied to a material before it starts to deform and “break”. All you need to know for this blog is that higher numbers mean stronger materials. An investment cast lug and steel tubing have a tensile strength of about 120,000 psi (pounds per square inch) and the silver alloy (the “glue”) has a tensile strength of about 70,000 psi.

When the tensile strength of steel joints properly brazed with silver were tested, the joint was able to withstand a stress of 120,000 psi … even though the silver “glue” holding the joint together had a tensile strength of only 70,000 psi.[1] How is this possible?

The science behind this still isn’t completely understood, but it’s been hypothesized that the brazing filler material is so constrained by the lug and tubing around it that it can’t “slip” along the tiny, tiny little planes in its atomic structure.

Another theory has to do with the area of the filler material. Think about pulling on either end of a metal rod. As you pull with more force, the rod stretches before it finally breaks. If you measured the area of the rod before and after stretching, you’ll find it becomes smaller. Perhaps a drawing will help:

Because the brazing material is constrained by the lug and tube around it and has nowhere to go, its area can’t change. Materials engineers refer to it as being in a state of “triaxial tension”. Simply put, the effect of this state is to make the brazing material stronger.

This is one of the many things that makes engineering and bicycles so fascinating.

1 Handy and Harman Brazing Technical Bulletin No. T-3, “Strength of Silver Brazed Alloy Joints”, pp. 1- 2.