C2.1 Elastic Deformation

In Chapter 1.2 we looked at why deformation is important, and you’re given the deformation magnitude and tasked to determine the strain.

For practical scenarios, we are usually given instead the loading magnitude and the material properties (e.g. Young’s modulus E). So how do we determine the deformation from these given variables? Well, we have the elastic deformation formula:

Elastic Deformation formula

Note:

P is the axial load in member (e.g. road or bar) (units: N)
Lis the length of the member (units: m)
A is the cross-sectional area (units: m²)
E is the Young’s modulus of the material (units: Pa)
Can be +ve or –ve depending on the direction of P

C2.1 Elastic Deformation

In Chapter 1.2 we looked at why deformation is important, and you’re given the deformation magnitude and tasked to determine the strain.

For practical scenarios, we are usually given instead the loading magnitude and the material properties (e.g. Young’s modulus E). So how do we determine the deformation from these given variables? Well, we have the elastic deformation formula:

Elastic Deformation formula

Note:

P is the axial load in member (e.g. road or bar) (units: N)
Lis the length of the member (units: m)
A is the cross-sectional area (units: m²)
E is the Young’s modulus of the material (units: Pa)
Can be +ve or –ve depending on the direction of P

The formula given above is when all parameters are constant. We present the general formula for when any parameter is not constant:

Elastic Deformation general formula

Look’s complicated? Not to worry, you probably wouldn’t use this 99% of the time, since we deal mostly with uniform members (i.e. same cross-sectional area and material properties).

Derivation

Personally I don’t like derivations as its too math-heavy (we’re engineers after all). Nevertheless the derivation for this formula is too easy, that I’ll include it for your reference (you don’t need to know this though):

Elastic Deformation formula derivation

Voila! Easy aye? Let’s look at an example now.

The formula given above is when all parameters are constant. We present the general formula for when any parameter is not constant:

Elastic Deformation general formula

Look’s complicated? Not to worry, you probably wouldn’t use this 99% of the time, since we deal mostly with uniform members (i.e. same cross-sectional area and material properties).

Derivation

Personally I don’t like derivations as its too math-heavy (we’re engineers after all). Nevertheless the derivation for this formula is too easy, that I’ll include it for your reference (you don’t need to know this though):

Elastic Deformation formula derivation

Voila! Easy aye? Let’s look at an example now.