Butted tubing, stress and fatigue.
A good place to start is to ask, why was the design innovation of "butting" of bicycle frame tubing developed? How does it relate to good frame design, when constructing a frame of any material?
In my opinion, THE single most important innovation in bicycle frame design is the technology and understanding connected with butted frame tubing. It is little understood or appreciated. It's not designed to save weight. The only reference on the internet that spells out in basic terms the reason butted tubing was developed is here in the second paragraph. A frame designed without butting is not advanced design. With this in mind, I cannot achieve what a steel frame offers for anywhere near the same price with any other material. I am not prepared to sacrifice frame comfort or robustness for the sake of a few hundred grams of weight saving. At the moment nothing beats steel as a material for a custom made bike frame.
In any structure, joints are the location where stress is concentrated. This is Engineering Stress. Engineering stress is the applied load divided by the original cross-sectional area of a material. Also known as nominal stress. When the joints are at corners, stress is intensified. The point of localised stress concentration, sometimes referred to as a "stress riser'. At welded joints, there is further stress at the edge of any lumpiness (any rapid change to the wall thickness). Heating also diminishes a material's ability to resist high levels of stress. This is why bike frames frames made of aircraft tubing break at the edge of the weld where all this converges. To combat this inherent weak spot in frame tubes, designers specify a heavy wall thickness. Thicker tubing walls at the joints enable thinner walls elsewhere. Known as butting. Reynolds invented it over 100 years ago. Carbon-fibre frames also have extra layers at the joints. Besides saving weight and improving comfort, double-butted tubing principally offers improved fatigue resistance. A smooth section of tubing adjacent to a joint, with a wall that smoothly tapers down to a thin-walled center section can absorb stress that would otherwise concentrate at the joints. This is the bit that messes most with people's heads; the ends of properly designed butted tubing can be thinner than a unbutted tube doing the same job, in resisting premature fatigue-failure. Stiffness and "strength" are a secondary issue to this. This explains how 8/5/8 tubes (.8mm at the ends and .5mm in the middle section) can dissipate stress better (and last longer) than frames built from much heavier 0.9mm wall "aircraft" tubing.
Butted bicycle spokes are a useful way to look at the behaviour of a lightweight structure that is dynamically loaded. A fatigue crack is more likely to start if the material is repeatedly loaded. In a standard spoke, the most highly stressed material is at the ends where there are two great places for a fatigue crack to start, being the bend in the spoke that's under tension and the series of notches at the thread. The shaping employed in butted spokes re-positions the point at which the material is most highly stressed away from the ends. Instead of the bend and thread detail, the adjacent smooth, uncomplicated gradually tapering section of the spoke becomes the point at which the material is the most highly stressed. The end result is that butted spokes are more durable AND happen to be reduced in weight. There is less potential for a fatigue crack to start in a smooth, tapering butt transition. Spokes fail principally by fatigue and not "strength". Another way of putting this is that a plain-gauge spoke is more prone to premature fatigue-failure than a well-designed butted one. The benefits of optimising the location of the material relative to the joints apply to bicycle frames too.
It's interesting to think that a progressive layup of carbon-fibre at the joints, which we've come to expect on many carbon-fibre frames, mimics the anti-stress-riser design feature used for butted bicycle spokes. Butted bicycle frame tubing employs a similar re-distribution of material, adding more to the ends where the joint will be located, reinforcing the joint.
The main way a bicycle frame fails in normal use is by the development and spread of fatigue cracks. That is the main behaviour of all lightweight structures that are flexed repeatedly, from aircraft to bicycle frames. So the key thing to focus on with lightweight dynamically-loaded structures is to design for fatigue rather than "strength" which is far less important but commonly discussed. If you have a structure that is rigid enough for its purpose and has a reasonable lifespan then there is no need to design for strength. Equally, it is more important to focus on dynamic repeating loads than to test the frame by loading it to failure, deforming it permanently.
The best way to lessen the likelihood of fatigue cracks developing is to minimise points of stress concentration. As is done for spokes and aircraft structures where the aim is to design for "an even distribution of stress throughout the structure" at whatever rigidity the design requires. Nature does it with the tapering shape of trees. By this approach, no one piece of a structure is more likely to fail than the rest and in theory every bit is close to failure during use. This approach uses as little material as necessary, reducing weight to a minimum and so is just robust enough for the task and no more.
All the various materials used to make bike frames can experience failure at stress-risers. With this in mind it is worthwhile developing an understanding of the true meaning of Stress, which is the load per unit-chunk of material. Every material has a characteristic properties (expressed in units of stress), for Yield (load at which there is a permanent change of shape when the material is put under tension) and Fatigue-limit (the repeatedly applied load above which fatigue cracks will start to develop when flexed). This is the fundamental behaviour of lightweight structures. Observing what happens around us has led to these theories being developed to explain it. Fatigue-limit is known by several other names; Endurance limit, and Fatigue strength.
If you bend a tube, the material on the underside of the tube will be under compression. The material at the sides will at very low levels of tension and the highest tension will be experienced by the material at the very top of the tube. If the material at the top experiences a level of stress greater than the Yield stress, then it will permanently deform and lengthen. The tube will have permanently bent a small amount. Ultimate tensile strength is another measure of material in units of stress, but it is a far less practical value because to reach it, enormous permanent deformation of the material occurs.
It's important to understand that the Fatigue-limit of steel (and similarly for titanium I think) is a fraction of, a bit more than half the Yield value. So design for fatigue is FAR more important than focusing on Yield strength. While a structure may never reach its Yield limit, if poorly designed it may exceed its Fatigue limit in normal use. This is what has occurred in many "unexplainable" frame cracks. I've inspected dozens fo frames with fatigue cracks and far more of these are made of plain-gauge tubing than butted.
The implication of this understanding is huge. Butting reinforces the known weak spots at the joints. For any material it improves the robustness-to-weight ratio. The resulting structure weighs less. It's counter-intuitive but you can make the structure more robust AND reduce its weight at the same time by dealing with stress risers. Slightly irregular welds can be used without a problem because they are not as highly stressed being in an area with a slightly thicker wall. This is all achieved by adding a few grams of material to the area of the structure that is the known weak spot, and that gives you the option to remove some material where it is not so highly stressed (in units of Stress, load per unit chunk of material).
With steel being eclipsed in some people's perception as an option for a custom bike frame by titanium, I'd like to explain my choice of material and present my take on the value of a steel. If you see a crack in a titanium frame and there are plenty I've seen in person, and far more again on the internet, then the first question HAS TO BE, "has this crack occurred along with the use of butted tubing"? In almost every case, the answer is no, and so the crack could have been made far far less likely to have occurred had the design called for butted tubing. The use of butted tubing is THE number one solution to this design issue. Argon purging, weld sequence, heat-affected zone welder skill ALL pale in importance compared to the benefit that butting offers here. And so it's worth pointing out that for a very good price, you get this ultimate design feature with high-end steel frames. When considering a custom-sized frame, the price is far higher, close to or more than double with titanium and carbon-fibre material. Now while there are also lots of examples of frames made from alloyed-steel with cracks, but I can tell you, that every one of those can be addressed by better design.
By eliminating known weak spots, a more supple, flexible frame can be designed with more confidence. Amounts of flex that would destroy a less advanced design can be considered. I have successfully built a frame from spindly main tubes with 1 inch toptube with the thinnest walls available and a 1-1/8" downtube with similarly thin tubing walls. The bike was loaded with 18kg in front low-rider bags and a handlebar bag and ridden around Japan for 3 weeks and from Adelaide to Melbourne.
There is more advanced design in a frame made with butted tubing than in a frame designed to use non-butted tubing employing precise, uniform welds to hold it together. It's all about advanced design.
Ferrous alloys and titanium alloys have a distinct Fatigue-limit, an amplitude below which there appears to be no number of cycles that will cause failure. Aluminium does not have a distinct limit and will eventually fail even from small stress amplitudes. This lack of a distinct fatigue-limit of aluminium will see many develop fatigue cracks. In the absence of a "service life" which is a control-measure adopted by the aircraft industry, bicycle frames made of aluminium will develop fatigue cracks if used long enough at enough flex cycles. The solution the designers took was to limit flex by making the frame incredibly stiff which is not ideal for a bike frame. That measure lowered the levels of stress occurring in the material. It is common to describe aluminium frames as being stiff and harsh in how they ride. Many mistakenly attribute this to the material itself, but that is not correct. It is a result of the decision the designer made about how stiff to make the frame. The designer must do this in order to make an aluminium frame last long enough. Supple riding aluminium bike frames were made early on but they did not last long enough for customers to accept the "service life".
Many describe titanium frames as having a characteristic ride feel, however that is incorrect. What you feel when you ride a bike frame is the stiffness of the frame. You could make identically stiff frames of steel, aluminium, titanium and carbon fibre and they would all feel basically the same. They would differ in weight and the inherent dampening characteristic of each material. The process by which energy is lost to dampening is called hysteresis, and some movement is converted to heat when an object is deformed and allowed to spring back to shape. Steel is the springiest, with virtually no hysteresis, then the amount increases slightly moving to titanium, aluminium, then carbon-fibre. I reckon, (and there are no measurements I'm aware of that can quantify this), that 90-95% of what you feel is the stiffness of the structure. So think about all the times you've read about a bike made of 953 or whatever material having a particular feel. What's actually happening is that it is the frame designer that decides what diameter and wall thickness to use and hence determines the stiffness. I refer to this as the ride-feel of the frame and bike. For a given stiffness a frame made of carbon-fibre will weigh the least and titanium perhaps 15% less than steel. Efforts solely focused on reducing weight can have a significant impact on other important features; robustness, behaviour at the point of failure, stiffness, comfort, ease of repair.
When a frame made of plain-gauge constant wall-thickness titanium weighing 0.85 units is compared to a frame made from butted alloyed-steel tubing that weighs 1.0 units, it is worth to examining all the subtle differences. The titanium frame costs 35% to 50% more. It requires more advanced equipment, care and skill to process. It is an amazing achievement to get a reasonable service life out of it given that the joints have a significant stress-riser.
It is difficult to put an exact number on this, but for two equally stiff frames the one made of butted tubing is far more resistant to premature fatigue failure than the one made of plain-gauge tubing. The properties of titanium cannot overcome the consequences of where the peak stresses occur. Really precise tig welds on a frame made with plain-gauge tubing can reduce slightly the incidence of premature fatigue failures. It seems earlier titanium frames that were similar in stiffness to the benchmark steel frames of the day had an unacceptably high rate of fatigue failure at or close to the joints. A response was to design with larger diameter frame tubes in the critical areas to reduce flex and this reduced the rate of fatigue failures to acceptable levels. As with aluminium, a stiffer frame was adopted to increase service life. Several designers of titanium frames now offer butting as an option to reduce weight with no mention of durability. A butted frame made of titanium compared to an equally stiff butted steel frame would be equal in robustness and at approximately double the price achieve a reduction in weight of several hundred grams.
The main techniques employed with titanium to get a reasonable service life from a frame is making it with slightly larger diameter tubes, using incredibly precise welds and employing two-pass welds to make the resulting welds even more uniform. The uniform weld eliminates the stress-riser that a slightly more irregular weld creates. When a titanium frame cracks, it is common to see the crack originate from a slight lump on a tig weld bead so it's understandable that these amazing welding skills are employed in an effort to eliminate irregular lumpy welds. It is however not particularly advanced structural design. It is less common in my experience for cracks in butted steel frames to originate from a lumpy weld but rather they can be traced back to other mediocre design decisions.
Titanium tubing is available in butted form off-the-shelf in a very limited range of tube diameters at very high prices. Chainstays are the first of these off-the-shelf tubes that I have seen used in custom-made frames and I'd agree that this is a good move because they have good anti-stress-riser features; taper and butting. Some titanium framebuilders have also set up to linish (abrade) material from the outside of the titanium tubes away from the ends where the joints will be formed. This adds expense to an already expensive product. It is described by the all that I know of (except one), as a weight saving measure which is true but not entirely correct.
Because of all these issues, and despite having the necessary equipment, I prefer to build with steel bicycle frame tubes rather than titanium. When balancing all aspects of a frame, I believe my frames are the better.
There are frames from several sources made with very advanced complex lugs by laser-sintering titanium. That is a huge technical achievement. Gluing them together with constant wall-thickness carbon-fibre tubes is not so advanced. The fatigue performance of carbon-fibre may be very good, but in a design that uses this method there are clear, obvious stress-risers at those joints so I'd not call this advanced design.
The correct term for all the metal material used in bike frames is an "alloy-of". You wouldn't want a frame made of the pure form of that metal. So aluminium is alloyed to improve its properties, principally strength compared to pure aluminium. Similarly the titanium used in bike frames is not pure titanium but alloyed-titanium with a far higher strength than pure titanium. Compared to pure steel, known as "mild steel", the steel used in premium bicycle frame tubing is alloyed-steel with a yield strength 3 to 4 times greater. That enables it to be formed with super-thin walls and yet still perform the same as but at a far lower weight than a similarly stiff tube made of mild-steel.
Articles about bike frames often state another source of confusion, that one type of steel bicycle frame tubing feels different to another. I'd be very surprised if they can actually feel that because the main thing that determines the stiffness of a frame is diameter and wall thickness which I've covered above. How does higher strength steel affect how a bike feels to ride? Despite all that has been written...... the fact is, not much. This fact is contrary to what nearly every article I've ever read says when discussing the various types of frame tubing used by custom framebuilders.
Steel has its own inherent stiffness. if you alloy it, with 1% chromium, and 0.2% molybdenum which are the main elements of 4130, then you will triple it's yield strength. But it will still be 98.8% steel so if you made two tubes with identical diameters and wall thicknesses, one from 4130, the other from mild-steel, then both would be EQUALLY as stiff. Yes. This myth about tubing grades has not been helped by tubing manufacturers implying that higher strength material will somehow behave differently.
The walls of the premium butted bicycle frame tubing these days are super-thin, from typically 0.8 down to 0.65mm at the thick end of the butts, and 0.5 down to 0.45mm in between the butts. At those wall thicknesses, you're well into (in engineering terms) coke-can territory where behaviour is unpredictable once the shape goes out of round. You can experience this yourself when you stand on a coke can and tap the sides making it crush. In normal use you will not me able to detect the higher-strength steel because the key mechanism that occurs is Critical Buckling. You might gain some benefit from the higher strength when you take the tubing to the limits of its strength, but that should only occur in a well-designed bike frame, when you crash! As I mentioned above, resistance to fatigue is what's most important during normal use.
So perhaps a frame made of a higher strength material will a resist buckling failure during a crash? Probably not, because the higher strength material is typically reserved for higher grade tubing which is made with thinner walls, which are more prone to buckling instability. So all the comparisons that have been made about tubing, 853, 653, 531 etc, have in fact without them knowing it, been a discussion about how one combination of tubing diameters and walls thicknesses might feel compared to another combination. However frame size has a significant effect on the stiffness of a frame too and so comparing one butted steel frame to another made with a different set of frame tubes without mentioning frame size makes that comparison one that is pretty much impossible to make. I rarely read frame size mentioned in these discussions. I don't discuss frames in this way.
It's interesting to calibrate yourself with a known "energy loss" and then consider claims made about frames being "stiff and efficient" and ceramic bearings offering astounding savings in drag. You can do this by riding a bike with a modern dynamo hub. At no load, they have a drag of a little over 1 watt under load, they have a drag of 3 watts. Both are so small as to be almost insignificant. Competitive riders doing endurance events such as Paris-Brest-Paris and Tour Divide gladly accept this tiny drag for unlimited lighting and power for their electronic gadgets. Terms such as stiff and efficient when applied to bike frames are meaningless. If you insist it is, then measure it. No one has yet.
A stiffer frame offers the rider a more immediate sense of a response to their high-effort pedalling input. A more flexible frame gives a less immediate response. To state that a flexible frame is less efficient, and by implication that energy is lost is flat out wrong. You can't measure the difference. The frame will not heat up by any measureable amount. It demonstrates a lack of understanding of the common use of the term "efficient" if using the term "stiff and efficient". In my opinion, it is lazy journalism to repeat in a bike review what has become a meaningless figure of speech. It is far more correct to say that more energy is lost in the tyres. It is apparently around the order of 20-30 watts (and by the way a test on a drum is only an approximation of riding on a flat irregularly surfaced road.... ) Rubber has high levels of hysteresis and heats up when repeatedly flexed. Steel has an extremely low level of hysteresis. That's why they make springs out of it. Springs don't heat up much. That's why they add dampers to spring suspension when they have a need to control the motion.
Butted tubing, if invented today, in the form of off-the-shelf steel bicycle frame tubing available to would be a revelation. At a very low cost, extra material is added to the ends of the tube to reinforce it when formed into a joint. By addressing the known weakness at the joint, a slightly lighter-weight tube design can be used than if a constant wall-thickness tube was used. Lighter and "stronger" This tube is also more robust. That's Genius! This is the single most significant aspect of lightweight bicycle frame design, and yet the reason for it, and the benefit it brings is little understood. In my opinion, if looking for a design that is sophisticated and addresses directly the key design challenges which includes price then steel wins. Even better results can be achieved by a skilled knowledgeable framebuilder.
With an understanding of fatigue and its importance to design of a lightweight bike frame, you can effectively reverse-engineer what is known as the Bontrager gusset, which is a reinforcement that is welded only on the side of the tube. That detail optimises a gusset in terms of dynamic loading, flex and fatigue. The weld along the side is curved rather than stretched when the main loading is applied and the frame tube flexes. The gusset is not welded to the most highly stressed part of the tube, the underside because that would create a stress-riser. The downtube joint to the headtube is the most highly loaded and is sometimes fitted with a gusset of this style. Using a Bontrager gusset on a butted frame tube makes no sense and I have examined damaged frames with this combination. A tube butt does far more elegantly what a Bontrager gusset does. In my opinion, a Bontrager gusset works well for plain-gauge tubing, reinforcing the known weak spot at the joint, reducing levels of stress similarly effectively but less elegantly than tube butting.
Gussets where a flat plate is welded between the underside of the toptube and top of the downtube are just dumb. They have forever resulted in frames breaking prematurely with a high failure rate. They clearly create a massive stress riser. The only place for this design disaster is on a show bike to be ridden to the cafe. Laser-cutting patterns and reliefs in this type of plate gusset does nothing to resolve the fundamental design flaw. They are more a can-opener than an improvement to a frame.
Heat effected zones are only of importance if using plain-gauge tubing, where the drop in strength and perhaps a slight increase in brittleness of the material effectively increases the stress-riser located at or close-to the joint. American-english uses the spelling "affected", hence HAZ is the common abbreviation. A butted tube very neatly deals with any HAZ. This is where an overload test of a frame joint is useful in indicating where the point of highest levels of stress in the material is. Load a joint to failure that is constructed of tig-welded plain-gauge Cro-Mo tubing, and it fails just adjacent to but not right at the tig weld at the HAZ. The material, slightly weakened by the welding plays a role in where the tube fails when overloaded. In dynamic loading, that same tube will likely fail at the stress-riser right on the tig weld, just next to the heat-affected material. A butted tube on the other hand, will permanently deform and buckle at the butt transition, where the tubing is thinnest right next to the butt. The butt reinforces the tube more than enough to deal with the heat-effected material at the weld. Brazed joints behave similarly. I've done all these tests and it is well worth doing yourself. It's a distraction to discuss HAZ when the subject is advanced bicycle frame design. Butting trumps all other details for advanced design. HAZ is a discussion best reserved for the welding of pipelines and cooling pipes of nuclear power stations.
I will expand in the future on distortion that occurs during welding and brazing and its potential to impact on the fatigue-limit of a frame. Oh yeah! But rest assured that I manage it well in my process to optimise my frames. That topic really defines a master framebuilder and their understanding of their profession. Using smoothed shapely braze-ons is NOT in itself an anti stress-riser feature. What is far more important is at what stage of your process you install your braze-ons to the frame. You might actually be creating a massive stress-riser. Rushing the process and cutting corners is not smart and can significantly lessen the durability of premium frame tubing.
The really advanced steel bicycle frame tubing in the hands of an inexperienced framebuilder can be made fragile with an unacceptably short fatigue-life. It takes a very well developed knowledge of what has lasted and what has not to be able to create a bike frame that is both lightweight and robust. This also applies to mass-production of frames made with these tubes. There are plenty of examples where efforts to mass-produce frames with the really minimalist, delicate ultra-thinwall tubing have met with failure.
A master framebuilder applies knowledge and observation of the distortion that occurs during brazing and or welding to their process. Astute framebuilders will realise that even in frames with butted tubing, fatigue cracks can develop in places where heat was applied. The way the framebuilder develops an understanding of this improves their process to minimise its effects is the difference between a novice builder and an expert. To quote a master, it's not lego.
The master framebuilder will endure and be capable of making custom-made frames with a very long lifespan and successfully employ the most delicate, thinwall tubing available. They will achieve a very refined balance of frame weight, lifespan and ride characteristics, and not sacrifice these simply in order to try and achieve a weight saving of a few hundred grams. A custom-made steel frame is the best choice by far for the enthusiast cyclist who isn't prepared to smash themselves up on a stiff harsh-riding, fragile bike for the sake of getting perhaps a few seconds advantage in order to place higher in a bicycle race.
I haven't even got into the subject of how Bending Moments explain why it is that joints are the most highly loaded in terms of Stress, because it's quite a difficult concept to explain.
If you made it this far, well done. Simply put, a bicycle frame is a structure of a stiffness as specified by the designer, made as lightweight as possible, with every measure possible employed to ward off premature fatigue-failure to give it a reasonable lifespan. Just like you'd like an aeroplane structure to be designed. Me, I'd like my frame to behave nicely when damaged or I when crash, so steel continues to be my material of choice.