Strength & Stiffness: What’s the Difference?

In everyday life, strength and stiffness are two things that are usually found together. For instance, when it comes to utensils, a stainless-steel fork is both stronger and stiffer than a plastic fork. Stiffer means that, compared to a plastic fork, it takes more force to flex a stainless-steel fork. Stronger means that it takes more force to permanently bend or break it.

Because we tend to see high strength accompanied by high stiffness, and low strength accompanied by low stiffness, we often tend to lump strength and stiffness together in our minds. However, they are actually two distinct properties. Even though most engineers know this, the mental habit of lumping these two properties together is very difficult to break. This confusion can lead to serious design mistakes.

The yield strength of a material is the amount of stress (force per unit area) required to permanently deform it. As long as the stress remains below the yield strength, the material will return to its original shape when the stress is removed. However, if the stress exceeds the yield strength, the material will no longer return to its original shape. If the stress is increased even further, the material will eventually reach its breaking point, which is known as the ultimate strength.

For metals, the yield strength and ultimate strength are properties that can be changed, either by heat treatment or cold work. For example, let's take a commonly used steel grade, AISI 4140, which is a chromium-molybdenum steel with 0.45% carbon. In the annealed condition, this steel can have a yield strength as low as 60,000 pounds per square inch. Quenched and tempered, it can have a yield strength as high as 250,000 pounds per square inch. This means that, depending on heat treatment, the yield strength of this steel grade can vary by more than a factor of four. It also means that just specifying the steel grade -- without specifying the heat treatment -- says almost nothing about the strength.

Stiffness depends on both material and geometry. The stiffness of a material depends on a property known as the modulus of elasticity. This property describes the relationship between stress and strain (deflection per unit length). Unlike strength, this is a property that is essentially unchangeable for a given material. The modulus of elasticity of AISI 4140, and nearly all other kinds of steel, is about 29 million pounds per square inch, regardless of heat treatment or cold work.

To understand the design mistakes that can be caused by confusing these properties, let's consider a simple example: a spring that needs to compress to a given height when a given load is applied. Let's suppose that the spring compresses too far when the load is applied. Will heat-treating the spring to a higher strength level solve this problem? No, because the modulus of elasticity will remain the same. The problem could be solved by changing to a material with a higher modulus of elasticity. It could also be solved by forming the spring from a larger diameter wire.

On the other hand, let's consider a different problem. This time, let's suppose that the spring compresses to the correct height when the load is applied, but fails to return to its original height when the load is removed. In this case, increasing the spring's yield strength through heat treatment would be a possible solution.

Understanding the difference between strength and stiffness is also critical for lightweighting of components. For example, let's suppose that a stress analysis of a steel part shows that the maximum stress is well below the yield strength of the steel. Based on the maximum stress, an engineer might conclude that the part can be made out of aluminum in order to save weight. However, it's important to remember that the modulus of elasticity of aluminum is about one third that of steel. This means that, under the same stress, the part will deflect three times more. Therefore, when redesigning a steel part in aluminum, it's often necessary to redesign the part geometry in order to prevent excessive deflection.

The concepts I've described here are extremely basic, and should be familiar to anyone who has taken an introductory mechanics of materials class. However, I've seen many engineers, who should know better, make these mistakes.

This is not necessarily a result of stupidity, ignorance, or failing to pay attention in class. Instead, it's a result of how the human brain works. As Canadian psychologist Donald Hebb famously said, "Neurons that fire together wire together." When two things (such as strength and stiffness) are frequently observed together, they become associated in our brains. This phenomenon is extremely useful in the learning process. However, on occasion, it can also lead our brains to trick us.

The best way to avoid being tricked is to be conscious of this tendency. Asking yourself the simple question, "Is this a strength problem or a stiffness problem?" can prevent many design mistakes.

Related posts: