It is important to quantify the deformation of structures under loading to ensure it meets design specifications. For instance, you wouldn’t want the Sydney Harbour Bridge to be sagging by 5 m when cars pass through it! Might seem like an exaggeration, but you get the idea.

Deformation must also be considered *relative to its own length*. A 10 mm deformation in a rod might not seem big but if the rod’s *original length* is 20 mm, then it’s a 50% relative deformation! Similarly a 50 mm deflection in a beam might seem huge but if the beam is 15 m in length, then the deflection is acceptable.

The concept of “relative deformation” is what we call strain. We will consider both normal and shear strains.

It is important to quantify the deformation of structures under loading to ensure it meets design specifications. For instance, you wouldn’t want the Sydney Harbour Bridge to be sagging by 5 m when cars pass through it! Might seem like an exaggeration, but you get the idea.

Deformation must also be considered *relative to its own length*. A 10 mm deformation in a rod might not seem big but if the rod’s *original length* is 20 mm, then it’s a 50% relative deformation! Similarly a 50 mm deflection in a beam might seem huge but if the beam is 15 m in length, then the deflection is acceptable.

The concept of “relative deformation” is what we call strain. We will consider both normal and shear strains.

Consider a stretched rod as follows:

- To prevent confusion with other dimensionless parameters, we use “ε” as the unit to denote that it’s strain
- Some textbooks also use m/m or mm/mm.
- Sign: +ve for tensile strain, -ve for compressive strain

Shear strain is trickier. Rather than considering the change in length, we look at the “tilt” of the body under a shear load:

- Shear strain has the units of rad or radian
- 2 ways of calculating shear strain are presented above, but they are effectively the same
- Sign: +ve or –ve does not matter now, but will be important when we look at strain transformation

Let’s look at an example now.

Consider a stretched rod as follows:

- To prevent confusion with other dimensionless parameters, we use “ε” as the unit to denote that it’s strain
- Some textbooks also use m/m or mm/mm.
- Sign: +ve for tensile strain, -ve for compressive strain

Shear strain is trickier. Rather than considering the change in length, we look at the “tilt” of the body under a shear load:

- Shear strain has the units of rad or radian
- 2 ways of calculating shear strain are presented above, but they are effectively the same
- Sign: +ve or –ve does not matter now, but will be important when we look at strain transformation

Let’s look at an example now.