Basic Mechanical Concepts

Owned by Min Qian Lu (Deactivated)
Jan 08, 2021
3 min read

Here, you can study up on stress, strain, yield strength, and other important concepts! There are some good video links as well.

Stress

 

Stress is defined as the applied force (p) per area unit (A)! This is measured in N/m^2 which are pressure units! Typically we use Pascals, MPa, GPa etc.

 

Strain

Strain is defined as a ratio between the change in length over the original length. This is unitless as it is length divided by another length. 

Stress-Strain Curve

A stress-strain curve describes the relation of stress and strain as a part is loaded with more and more applied force! There are a few important points on the graph to note:

 

  • Yield Strength: the maximum stress a part can endure while still maintaining the original geometry

  • Ultimate Strength (UTS): the maximum stress a part can endure

  • Fracture: the part ruptures, this is logically what failure means

 

Elastic Deformation: when a part deforms under loading and is still able to return to its original shape

Plastic Deformation: when a part deforms under loading and is no longer able to return to its original shape

Outstanding video: https://youtu.be/aQf6Q8t1FQE

 

Young’s Modulus and Hooke’s Law

Ah yes, good old Hooke's law. This law states that the stretch length of a spring and the force required to attain said length are proportional!

This blew my mind back in first year but almost all materials act like springs! We can substitute Force with stress and the Extension with strain! 

This kind of makes sense! If we keep the stress under the yield strength, then the material will always return to its original dimensions. This is equivalent to a spring!

Another great video: https://youtu.be/DLE-ieOVFjI 

 

What is considered a failure?

When considering failure point, we use Yield Strength as the standard for several reasons

 

  1. UTS is the maximum stress a part can endure. Beyond it, the force needed to further strain the part drastically decreases.

    1. This means in general, once you reach UTS, the part will fracture shortly thereafter. 

  2. When building parts, we give them dimensions that we would like to keep. Imagine if one of the legs on your table suddenly became shorter!

For these two reasons, yield strength is the most appropriate. Oftentimes we use a safety factor. 

 

Safety Factor

We use safety factors as a buffer zone. Designing a part to handle exactly the maximum load is a dangerous approach. This is assuming that nothing will ever go wrong!

A good example is an elevator. Most elevators have their support cables built with a safety factor of 4! This means that, in theory, ¾ cables could snap and the remaining cable can still support the entire elevator!