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.

Lugged Bicycle 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.

Drawing of lugged steel bicycle frame construction

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:

Forces on a rod

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.

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4 comments on “Triaxial tension in a lugged steel bicycle frame.
  1. Paula says:

    I have an old Classic….with lugs and it does ‘look’ better.
    Though metal strength is over my hed, thanks for the article.
    You can never know too much about your bike.

  2. Matt Penney says:

    One advantage of a low temp braze like silver 56% might be that it’s working temp is below the annealing temp of a hardened and tempered tube.
    Lower percent silver rod and brass braze has a working temperature range that is in the annealing range of the parent metal, leaving a “heat effected” zone that has different physical properties than the non effected portion of the tube.
    Who’s to say if this is a plus or minus in ride quality?

  3. Matt P says:

    …great info, by the way, I found it very helpful. thanks 🙂

  4. You are welcome to publicise, if you wish. The lightest strongest bicycle frames would be 4130 chrome vanadium steel, typically used for race cars and light airplanes. The outside diameters of thin wall tube and the next size up are made so that they just slide into each other.
    In order for ‘lugs’ to be as strong as the tube, the lugs need to be welded, because the inside bores of the lugs can be cleaned with a rotating buffer. The lug holds the larger tube against expansion because the lug material surrounds the outer tube. The inner tube needs a short length of tube inside to withstand the squeezing effect of the larger tube. Differences in shear strength of different brazing spelter or glues in principle should be compensated by the length of the joint, because overall strength depends on strength per unit length multiplied by the length of the joint. Welding 4130 is liable to anneal and chill crack 4130. Brass spelter contains zinc, which reacts adversely with chromium, causing embrittlement and cracking. Low temperature nickel silver spelter would appear to be best, the melting point is lower than the annealing temperature of 4130 – but I have not tried it yet. Another way to ensure that a frame joint is adequate in tensile strength is to put in diagonal ties as in the airframe of the WW2 Hurricane fighter, which keeps the frame joints in compression – the compreesive forces are taken by tube, if steel the ratio of length to fradius of gyration needs to be not less than 180, according to the Perry-Robertson formula as derived from Euler strut theory. What needs testing are sleeve joints in a tensile test rig of glue v brazing v welding, compensating by length of joint. Over to you, Georgena. Allan

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