**There are three methods used to analyze the strength of materials: strength, stiffness, and stability.** In this article I will attempt to explain the meaning of these three physical properties, and outline their importance and roles in materials-selection. A proper balance between properties must be struck in the selection and production-phases, so that the end product has the required physical attributes.

**Strength**

**The term “strength” in regards to materials is its ability to withstand stresses without failing. **Unfortunately, it’s not a matter of “if”, but “when” and “how”. It’s a

measure of a material’s strength in terms of tension, compression, and shear – the three forms of stress. A given material’s strength increases in proportion to its ability to resist these stresses.

**Stiffness and its Relationship with Young’s Modulus**

**Stiffness is an elastic material’s ability to resist deformation along a given degree of freedom. **Although closely related to the elastic or Young’s modulus, stiffness is a measure of a solid body that is dependent on size and mass, an extensive property, whereas Young’s modulus is an intensive property and has nothing to do with size, volume, area, length, etc.

**For example, one could say that the stiffness of a given board** depends not only on material makeup but also on its dimensions, while the Young’s modulus of a given board would depend only on its material makeup.

**Young’s modulus is defined as **“*the ratio of the uniaxial stress over uniaxial strain in the range of stress where Hooke’s law holds*”, expressed in Pascals. This just means that it is equal to the amount of force per square meter of cross-sectional area, that it takes to stretch a sample material to double its length – within its elastic limits (Hooke’s law).

**One can think of stiffness as the overall measure of a given material’s ability to resist deformation**, with its values increasing with any increase in its size and cross section, and Young’s modulus as a measure of that same material’s stiffness, expressed as a ratio and therefore an intensive property, having nothing to do with its size. It would be safe to say that *stiffness* is simply the more general or all-encompassing term.

**In a single degree of freedom, stiffness can be defined as** where *k* is the stiffness, *F* is the force applied to the body, and *δ* is the displacement, or change in length of the elastic body along a single degree of freedom. As you can see, when the applied force is only along a single degree of freedom, or “constrained”, stiffness is equal to the Young’s modulus.

**But this equation or definition won’t work with anything but this “special” case**, as most objects have more than one degree of freedom. For example, the axial stiffness for a non- “special” member in tension or compression is defined by where *A* is the cross sectional area, *E* is the Young’s modulus, and *L* is the length of the member. Stiffness is typically measured in newtons per meter or pound force (lbf) per inch.

**Stability **

**Stability is simply a material’s ability to maintain its original configuration under various loads and stresses.** For example, when a column is loaded axially to its buckling limit, it will experience what is called instability. Any further loading or even the slightest introduction of a lateral force such as wind, will cause it to fail by buckling. Resistance to time-dependent deformation such as creep can be thought of as a result of material stability.