Why a stiff material and a strong material are not the same thing
Two independent properties, and the designs that confuse them.
A stiff material and a strong material are not the same thing because stiffness describes how much a material resists changing shape under load, while strength describes how much load it can actually withstand before it breaks, and a material can be extremely stiff and quite weak, or comparatively flexible and remarkably strong, since nothing about resisting deformation says anything at all about how much force is needed to cause outright failure.
Gordon's The New Science of Strong Materials is subtitled, more or less, Why You Don't Fall Through the Floor, which is exactly the right way to introduce the subject, since the floor underfoot is stiff enough not to visibly sag and strong enough not to break, two entirely separate promises that happen to be kept by the same piece of material.
What is really going on
Stiffness is a measure of how much a material deflects under a given applied load, a stiff material barely bending at all, a flexible material bending considerably more for the same push, and this property is captured by what engineers call its elastic modulus, a fixed number describing how firmly the material resists being deformed within the range it can spring straight back from. Strength is a wholly separate measure, describing how much load or stress the material can actually endure before something permanent happens to it, before it yields, cracks, or breaks outright and cannot be trusted again. A material can score highly on one property and poorly on the other, because resisting a small deformation and surviving a large force are simply different physical behaviours, governed by different aspects of how the material's internal structure actually responds to load, and there is no law of nature anywhere requiring the two to move together in step.
The glass-rod comparison
A glass rod and a fibreglass fishing rod make the difference impossible to miss. Press down on the end of the glass rod and it barely deflects at all, holding its shape rigidly right up until, past a certain load, it snaps suddenly and completely with almost no warning bend beforehand at all, a dramatic demonstration of high stiffness paired with comparatively low strength. Press down on the fibreglass fishing rod with the same or even considerably more force and it bends dramatically, curving through a wide arc that would look, on the glass rod, exactly like the final moment before disaster, and yet the fishing rod does not break at all, springing back perfectly straight the instant the load is finally released. The fishing rod is far less stiff than the glass rod, deflecting enormously under a load the glass rod would barely acknowledge, and yet it is, in the sense that actually matters for surviving a load without breaking, considerably stronger.
Why designs confuse the two properties
The confusion between stiffness and strength shows up constantly in casual, everyday language, a material described as strong when what is actually meant is that it feels rigid underhand, or a material dismissed as weak simply because it happens to flex noticeably under load. This loose usage causes real design mistakes when it is carried, unexamined, into an actual engineering decision, choosing a stiffer material in the belief that stiffness alone guarantees safety against breaking, when in fact the stiffer choice may fail at a lower load than a more flexible alternative would have survived without difficulty. A bracket redesigned in a stiffer material purely to stop it flexing under normal handling can end up more prone to snapping outright under a sudden shock load than the original, more flexible bracket ever was, precisely because the flex the redesign eliminated was doing real work absorbing energy that the stiffer replacement now has nowhere left to send except straight into cracking.
The number that matters here
Steel is roughly three times stiffer than aluminium for a given shape, deflecting only about a third as much under the same load, yet a well-chosen aluminium alloy can be nearly as strong as a mild steel in terms of the load it can withstand before failing, a pairing that would look like a straightforward contradiction if stiffness and strength were really the same property measured two different ways, and is simply an ordinary, unremarkable fact once they are correctly understood as two genuinely independent numbers.
Where the two properties genuinely do travel together
None of this means stiffness and strength are entirely unrelated in every material, since within a single family of alloys, different grades of the same base steel, for instance, stiffness usually stays almost identical across every grade while strength varies considerably between them, a pattern covered in more detail in the next article in this set. What varies between genuinely different materials, glass against fibreglass, steel against aluminium, is far less predictable, and it is specifically across that wider comparison, between materials rather than within a single family of them, that stiffness and strength part ways most dramatically and most usefully for a designer choosing between real alternatives.
Why this matters in practice
Recognising stiffness and strength as separate, independently chosen properties changes how a material actually gets picked for a job, since the right question is never simply how rigid or how strong a material feels in general, it is how much deflection a specific application can tolerate and how much load it genuinely needs to survive, two different numbers pulled from a material's Young's modulus and its strength rating respectively, chosen deliberately rather than assumed to travel together simply because a material happens to feel reassuringly solid in the hand. The rest of this set on materials returns to this same distinction repeatedly, since almost every genuine surprise a material springs on a designer traces back to assuming one of these two numbers when the problem actually depended on the other.