Simple Stress and Strain

Simple Stress and Strain are fundamental concepts in engineering.
All mechanisms and components used in engineering are exposed to external forces that either try to displace or deform the component.
These may be actual forces from surrounding components or processes but they could also be from the physical environment that the component is operating in.

Newton’s First Law states that an object will remain at rest or uniform motion unless acted on by an external force

The object will resist the external force though to keep its current state, this is where Newtons Third Law comes in.

Newtons Third Law states that when two bodies interact the forces in each will have the same magnitude but be in opposite directions

This resistance by the object sets up an internal force in the material which tries to counteract the external force.
This action produces the stress in the object.

Simple Stress

Now that we know what triggers stress in our components we require a formula to be able to determine its value.
The importance of knowing the amount of stress applied to an object is ultimately to prevent its untimely failure……because every object has a lifespan.
How we prevent early failure of components is primarily by checking the following

Making sure that the stress induced does not exceed the material strength
Preventing early fatigue failure

The formula we use to calculate stress contains the following components

And the formula

There are a few considerations when using the formula above that must be noted

The cross sectional area must be uniform throughout its entire length
The cross section used is always the area perpendicular to the longitudinal axis on which the force acts
Weight of the object loaded is typically ignored
It is assumed that that the Force acts through the centroid of the cross sectional area
It is also assumed that the Force is uniformly distributed over the cross sectional area
Can be tensile or compressive

The unit of measure for stress is the Pascal, this however is typically too small for most engineering problems so the following multipliers are used

Tensile and Compressive Stress

Stress can be tensile or compressive in nature.
Its important to be able to distinguish between the two, especially when dealing with multiple forces.

Tensile Stresses are considered to be pulling, such as the stress induced in a towing rope

Compressive Stresses are considered to be pushing, such as columns in buildings

The sign convention for tensile stresses is positive and negative for compression.
This is important when dealing with multiple stresses that need to be added or subtracted to find resultant stress.

Simple Strain

Strain simply refers to the elongation or shortening of an object that is under external forces. Its a Measure of Deformation.
Tensile stresses cause an elongation
and
Compressive stresses cause a shortening of the member or object
The formula for strain contains the following components

The formula

Strain is a ratio of the change in length over the original length, hence its dimensionless (no units).
Its also typically very small, thus it gets measured in microstrain