Materials Science of the Barbell

by Andrew Lewis, SSC | October 28, 2020

Anything not directly contributing to the movement of the bar should be as rigid as possible to maximize force transfer in a lift. This is why a trainee should hold their breath when they squat. This is why you clean and snatch with straight arms. This is why you lock out your knees and squeeze your abs in the press. This is also why you squat in hard-soled squat shoes on rigid, hard platforms, and not in tennis shoes on a mattress. The constant talk about the "whip" of a barbell being good is nonsense – a floppy barbell is not desirable.

“Whip” in this context just refers to how much a bar bends under load. Furthermore, there is a serious misunderstanding of what affects the bend of a bar – the ultimate tensile strength (UTS) is usually quoted by manufacturers despite the fact that the UTS is not an indicator of how much the steel will bend. The UTS does not even indicate how practically strong the bar is. The deflection – “whip” – of a bar during a deadlift is a function of five inputs: 1.) the grip width of the lifter, 2.) the distance between the plates on the right and left of the lifter, 3.) the elastic modulus of the bar, 4.) the radius of the bar, and 5.) the weight of the plates themselves. Finally, the relevant factor in understanding the strength of a bar is not the UTS, but the yield strength.

Just to be clear, most reputable barbell manufacturers sell barbells that are fine for training. Just buy a well-reviewed, general purpose 20kg bar from Texas Power Bars or Rogue Fitness, and you'll probably be happy and never even wonder why. However, if you want to actually buy and use barbells and plates intelligently, you will need to understand some metallurgy and physics.

Deformation: Temporary and Permanent

Steel deforms in a predictable manner based on the stress imposed on it. Stress is defined as force applied over a cross-sectional area. Mathematically, this is expressed as Sigma (σ) where F is the force (lb) and A is the area (in²) and Sigma σ is stress (lb/in² or psi). When tension stress pulls apart a piece of steel, it elongates until it breaks. This elongation is expressed as strain (ε). It is defined as the change in length expressed as a decimal of the original length, where L is the instantaneous length and Lo is the original length. The stress of steel can be plotted on a graph as a function of strain – the deformation caused by stress (Figure 1). The resultant curve has some notable features: the mostly-linear portion (elastic deformation), the non-linear increasing portion (plastic deformation), and the non-linear decreasing portion (necking). The curve terminates on the right side with fracture.

A steel rod that is “pulled apart” a small amount will spring back to its original position when the pulling force is removed. Steel has a spring-like quality where, under a small amount of force, it will change shape and stretch, but can return back to its original shape. The elongation of the steel as force is imposed on it is expressed by the steel's elastic modulus (also called Young's modulus), the material characteristic indicating the stiffness (the resistance to deformation) of the material during elastic deformation. A stiffer material will have a higher elastic modulus, so the material will deform less under a given load than a material with a lower elastic modulus.

The rod will not return to its original shape if enough force is pulled on it. It will spring back a little but then remain elongated. This is plastic deformation. The steel has yielded and changed shape permanently. It still has an elastic component, so it springs back a little. The stress required to cause plastic deformation is called the yield strength (leftmost X on Figure 1).

Tensile Strength vs. Yield Strength

Steel in tension will continue to deform until it reaches its ultimate tensile strength (UTS, middle X on Figure 1). The cross section of steel experiencing the highest stress then reduces in area which is called necking (Figure 2). Finally, the material will fracture into two pieces (rightmost X on Figure 1).  

stress-strain curve of a 41xx steel

Figure 1. Stress-strain curve of a 41xx steel

necking leading to fracture in a tensile sample

Figure 2. Necking leading to fracture in a tensile sample

A barbell bending during a lift will have tension imposed on the top half of its diameter. The center of the bar – called the neutral axis – experiences no tension or compression. The bottom half of the diameter of the bar is in compression. Figure 3 shows the tension and compression when a bar is in bending. A bar bends permanently when the top stress exceeds the yield strength in tension and the bottom stress exceeds the yield strength in compression. The yield strength for tension and compression are the same.

tension and compression along the axis of a bar in bending

Figure 3. Tension and compression along the axis of a bar in bending

Hopefully, the deformation most lifters have seen in barbells is all elastic and the barbell returns to its original, straight shape. However, barbells do deform plastically, usually when dropped crooked, and remain bent. The stress is high enough to exceed the yield strength and the steel plastically deforms. It is unlikely any lifter has ever seen a barbell fracture in bending. Steel is extremely tough and can bend a great deal before it fractures even if someone is deliberately trying to break it.

Yield strength, therefore, is clearly more relevant than ultimate tensile strength in the context of barbells. The UTS indicates nothing about the performance of the barbell for strength training. Some argue that the UTS tells you about the bending of the barbell. This is false. The bending of the bar is only a function of the five factors previously listed. Furthermore, the only factors that the barbell manufacturer has any affect on are the dimensions of the bar: the collar-to-collar length and the radius.

A yield strength higher than 90ksi (90,000psi) would be appropriate for most lifting applications. Eleiko sells bars made out of ETD 150 which has a yield strength of 130ksi. This is probably excessive, but if you have the money, you may want one. Most companies advertising UTS will have steel with a UTS between 190ksi and 215ksi. These are primarily the companies making good barbells. The companies making worthless barbells out of hot rolled 1018 non-alloy steel are not even mentioning the UTS.

In case you're interested. I looked at various steels that would actually be used for barbells and independently did some calculations on what kind of force rating I would be comfortable with on a barbell. Based on those two together, I got the 90ksi yield strength value. These kinds of steels are going to be cold worked or quench and tempered.

A load rating would be the most helpful variable to advertise: the amount the bar can be loaded before it plastically deforms. The equation governing the bending of a barbell in the squat would be

equation governing the bending of a barbell in the squat


  • F = Force (lb) required to cause plastic deformation
  • L = Length between centers of plates (in)
  • = Yield strength (psi)
  • r = Radius of bar (in)

Based on the equation, it is clear that the rating would vary based on how the bar is loaded. For example, using steel plates would produce a higher load rating than cast iron or rubber plates, because the mass of the plates is closer to the center. The knurl is also going to affect the bar, because it will reduce the diameter of the shaft. A 28.5mm bar that has knurling with a minor diameter of 27.5mm is going to bend more than a bar with a more shallow knurl. However, a rating could still be provided with standard loading of cast iron plates.

Bend and the Elastic Modulus

The nature of each material characteristic must be understood in order to know why some materials are viable, why others are not, and why changing one characteristic doesn't change another.

The elastic modulus is affected exclusively by atomic bonding. There are bonds between the atoms in the steel which can flex without breaking. This is the elastic deformation we see in the bending of our barbell when the shape returns to its original form after the force is removed. Over time, this can lead to fatigue – the weakening of a material caused by cyclic loading resulting in damage to the bonds if the iterations of bending are numerous enough and the force is high enough. The fatigue limit is the stress level below which an infinite number of bending events will not cause fatigue damage. Steel can be designed for infinite life under small enough forces because of its atomic structure, while metals like aluminum and copper cannot.

The elasticity of these atomic bonds are not affected by the microstructure or post-solidification processing – they are only influenced by the chemistry. Once the steel is melted and refined, the solid steel that comes out of the caster has a fixed elastic modulus. A barbell manufacturer can make a novel barbell out of tungsten or titanium or pasta noodle if they want to affect the elastic modulus, but the current industry standard for high quality barbells is chrome-moly steel (formally designated 41xx, with the last two numbers indicating the alloy recipe, as in 4140). These alloy steels can be cold worked and quench and tempered for increased yield strength. It is also extremely tough, meaning it will absorb a lot of energy in plastic deformation before it fractures. Stainless steel is also used, and although it has a smaller elastic modulus (less stiff), the difference is only about 7%.

Microstructure is the crystalline make-up of the material. At the microscopic scale, the constituents of the alloy come together to create bulk material properties that are continuous throughout the material. For the purposes of the barbell, the steel can be thought of as one bulk material. However, the microstructure matters in that it determines a lot of the material characteristics of the bulk material, like yield strength and UTS. There are a wide variety of processes that can impact the microstructure of the steel: cold working, hot working, control of the cooling process of the melt, and heat treatment can all affect the yield strength and UTS.


Examining the equations that govern barbell bending will illustrate why some bars are “whippier” than others. Consider a deadlift where the hands take a symmetrical grip about the center of the bar and the bar is symmetrically loaded with plates as in Figure 4.  

deadlift a bar supported between two equally-concentrated loads diagramed

Figure 4. A deadlift: a bar supported between two equally-concentrated loads

The maximum deflection is governed by the following equation.

equation governing maximum deflection


  • 𝛿 = max deflection (in)
  • a = distance between force P and grip (in)
  • P = Force (lb)
  • L = Length between (in)
  • E = Elastic modulus (psi)
  • I = Second area moment of inertia (in⁴)

The deadlift grip width will affect the bend, but ideal grip width is determined by anthropometry, so that's largely irrelevant to this analysis. The equation can be simplified by moving the hands closer together until they touch. Then the supporting load can be approximated like a single concentrated load as in the case of a squat. It's not precisely this way, but it's close enough for explanatory purposes. 

simplified deflection equation after moving hands in to touch


  • 𝛿 = Max deflection (in)
  • F = Force (lb) = 2P
  • L = Length between (in)
  • E = Elastic modulus (psi)
  • I = Second area moment of inertia (in⁴)

The second area moment of inertia (I) can be thought of as an object’s tendency to resist rotational change. Think about an ice-skater. If they are spinning on one skate with their arms out, they spin slower (larger moment of inertia). They bring their hands closer to their chest, and they spin faster because they've made their moment of inertia smaller.

rod I value

for a rod which simplifies the max displacement to

equation for maximum displacement for a rod


  • 𝛿 = Max deflection (in)
  • F = Force (lb) = 2P
  • L = Length between (in)
  • E = Elastic modulus (psi)
  • r = Radius of bar (in)

This equation should make it clear that bar bend during the squat is only affected by these four factors. The bend is directly proportional to the load, F, and inversely proportional to the elastic modulus, E. What's important to note is that the bend is proportional to the cube of the distance between the center of mass of the plates, L3 and proportional to the radius to the fourth power, r⁴. The implication being that increasing the radius by 1 inch has a much greater effect on bar deflection than increasing the distance between the center of mass of the plates by 1 inch. However, practically, this isn't feasible. The range of available bars on the market are 25mm to 31.75mm bars with lengths between 65.5" and 96.5" and a collar-to-collar length between 45" and 59.5". The maximum radius increase would be about a quarter of an inch. Whereas, the center of mass of the plates could be changed by 14" simply by ordering a bar with a shorter collar-to-collar length.

Most lifters have experienced this in the form of the "rubber plate PR." Try to set a personal record on the deadlift with all cast iron plates and it's going to be a lot harder than setting a PR with rubber plates. This is because rubber plates move the center of mass of each group of plates away from the center of the bar, increasing the bend in the bar before the plates leave the floor so that the full weight of the load isn't felt until a higher position is obtained. This is why it's always better to lift with the same plates – in addition to the benefit of ignoring manufacturing error in the mass of the plates.

Whip in the Deadlift and the Olympic Lifts

Some deadlifters like a more elastic bar. They'll refer to a bar as having "good whip."

What happens when the bar bends a lot during a deadlift? The elastic deflection is directly proportional to the amount of force on it. A bar with 400lb loaded will deflect about an inch when it's locked out at the top of a deadlift. The bar will deflect about half an inch when only 200lb of force is imposed on it during the set up on the floor. This means that the lift actually starts on the floor when the bar is bending the full inch. The elastic deflection is directly proportional to the amount of force on it. This is easy to see in a 525lb deadlift (Figure 5) when the innermost plates are off the ground and light is reflecting off the ground underneath, but the outermost plates are still touching the ground. At the time, the lifter has not imposed 525lb on the bar, because the normal force of the floor holding up the load is still acting on the outermost plate. The force is between 450lb and 525lb. A 600lb deadlift might deflect a full two inches depending on how it's loaded. This might not seem like a lot, but anyone who has trained deficit deadlifts knows that every inch matters.

The Rogue Elephant Bar was specifically designed for the strongman deadlifts at the 2016 Arnold. Two inch "deep-dish" plates were specifically created for this event as well - this is about ¾" thicker than normal 45 pound plates. The observations of lifters using the bar are that 1) the force required off the ground is lower due to the bending of the bar and 2) the movement of the plates because of the bending and rebound (oscillation) makes the lift more difficult to control. During the 1000 pound deadlifts, the center of the bar deflects about four inches before the outermost plate leaves the ground. A deadlift four inches off the ground is the same height at which some lifters rack pull.

Similarly, Olympic weightlifting bars are marketed as having "good whip" for the purpose of Olympic lifting. Some Olympic lifters claim that they are able to use the whip of the bar to elastically store energy and then redirect the stored energy upwards on the extension of the whip. There is no video of a lifter squatting, cleaning, jerking, snatching, or pushing as fast as the elastic rebound of a bar. There are countless slow-motion videos showing this fact. I see no evidence for the claim that any human is capable of elastically loading the bar and rebounding in time with the elastic rebound. In addition, oscillating the bar at the top of the lift is against the rules. It should seem obvious from this analysis, therefore, that a stiff bar is preferable to a more elastic bar. The Olympic lifters of the 70s, who performed the quick lifts with cast iron plates, showcase that this can be done.

Strength is the ability to produce force against an external resistance. Increasing the force production of a lift with consistent technique over a consistent range of motion is the relevant part of lifting. Not how "hard" we can make a lift by modifying for bar deflection or oscillation.

Deadlifting with a Short Bar - An Anecdote

In February 2020, I bought a custom deadlift bar from Texas Power Bars. It is identical to the Starting Strength 20kg bar except that

  1. the collar-to-collar length is 30.5" instead of the usual 50" and
  2. the sleeves are much longer to retain a 20kg mass.

This bar effectively does not bend even under my personal records loads (555lb). Perhaps it will be perceptible at higher loads, but I have not been able to test it.

It has the feeling of immediate force transmission with no latency. It doesn't oscillate at all during the lift.

Figure 5 shows images of a normal bar (Rogue Fitness B&R 2.0 with 28.5mm radius) in the process of a deadlift. It was loaded to 525lb. The top image was taken before any force was applied to the bar. The middle image was taken just before the outermost plates left the ground. The bottom image shows the images overlaid to show the deflection in a more obvious manner. The bar deforms 35mm (1.38 inches).

deflection of a normal bar loaded with 525 pounds

Figure 5. 35mm deflection of a normal bar (50” collar to collar) loaded with 525lb

Figure 6 shows images from a short bar deadlift loaded to 525lb. The deflection was 37% of the normal bar. Both were loaded with the same plates and collar clips. Finally, Figure 7 displays both overlay images stacked one on the other. The difference in deflection should be obvious.

deflection of a short bar loaded with 525 pounds

Figure 6. 13mm deflection of a short bar (30.5” collar to collar) loaded with 525lb.

visual comparison of the overlaid images

Figure 7. Visual comparison of the overlaid images

I’ve learned a few things about deadlift with an extremely stiff bar over the last eight months. First, a stiffer bar favors ideal mechanics. Jerking the bar off the ground, being forward of the midfoot, and setting up with shoulders directly on top of the bar are going to be immediately punished by the immediate force transmission. This is similar to the deficit and paused deadlifts where ideal mechanics are necessary and anything but ideal mechanics will be immediately perceptible to the lifter. One could argue that this makes the stiffer bar a more “advanced” bar, but I would argue the opposite. Practice correct form right away, and fewer problems will occur later.

Second, an inch of deflection is a lot. Anyone who has done deficit deadlifts knows how brutally hard even half-inch deficit deadlifts can be. By contrast, a long bar that deflects an inch off the ground is easier. This happens over time. The bar doesn’t deflect an inch when the lifter loads 135lb, 225lb, or even 315lb. As the trainee gets stronger, the bar will deflect more and more. The same is true of the short bar, but the deflection is about a third that of the long bar affecting the lift over time less.

Finally, this bar is far stronger than a traditional bar. Refer to the load rating equation in the deformation section. The short bar's length is 61% of the B&R 2.0, and therefore, the strength is significantly higher because the failure force increases as length decreases. This all assumes the plates are loaded the same.

The point of all of this analysis is to illustrate that if you want to intelligently buy a bar for deadlifting, squatting, or Olympic lifting, you need to understand the underlying physics and metallurgy so that you can see through marketing bullshit. I'm not here to convince you to buy a custom bar with a 30.5” collar-to-collar length from Texas Power Bars because it will make your deadlift stronger. I do believe that's the case, and I'm going to continue to deadlift on my short bar, but you don't need one to get stronger.

What you should be convinced of is that when you see a Facebook post or website ad about a new deadlift bar and how it has “sick whip” or “the best whip of any bar on the market,” you should know that is not desirable and that the basic B&R bar or Starting Strength bar you own is just fine. You don't need to pay a premium for marketing nonsense. You need to add 5lb to your deadlift and squat.

And don't deadlift with all rubber plates. Use cast iron or steel plates.

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