Introduction and Internal Forces: Stress Flashcards
What are the four fundamental quantities?
- Force
- Mass
- Time
- Space
What is the definition of force?
It’s a measure of the interaction between bodies
What are the key factors we need to consider when thinking about how a material reacts to the application of forces?
- Cross-Sectional Area
- Orientation of the Material
- The Material Itself
- The Way the Load is Applied
What are the ways that we can apply a load?
- Bending
- Torsion
- Tension + Compression
- Shear
What will always be present if there is bending present?
A Shear Force
Because of the quantity of internal forces meaning that it would be impossible to calculate each point, how do we model internal forces?
We can instead find the resultant force and moment
How do we model the maximum value of the internal forces that vary across a material?
Introduce the concept of stress
How can we use stress to model the maximum internal force?
We take a small area on the face of the sample, naming it delta A
We then can assume that all of the forces on the small area are equal and act in the same direction which would provide their maximum theoretical values
We can tthen find the average stress over the whole sample by using the assumptions from delta A
Average Stress = Delta F / Delta A
How can we make it easier to define the components of stress?
If we use a cartesian axis, we can then resolve into the individual axis
What is the symbolic representation of the normal (direct) stress?
σn where the n is in subscript
How do we symbolically represent the tangential (shear) stress?
Tau n where the n is in subscript
What is the equation for the tangential (shear) stress?
We use the pythagorean theorem as it’s the component of the stress which runs along the face of the sample. The easiest way of solving is when using thhe other two components that also rest on the face, being tau (xy) and tau (xz)
Where does the direct (normal) stress act?
Perpendicular to the surface
Where does the shear (tangential) stress act?
Tangential to the surface
What is the value of the axial force?
It’s the integral for the perpendicular stress relative to the area of the sample
What are the shear forces?
They are the integrals of the relative shear stresses related to the area of the sample
Vy uses the shear stress xy whereas Vz uses the shear stress xz
In a plane stress case, how do we usually represent stresses?
We represent stresses acting on the sides of a rectangular element
If we have an plane stress case in equilibrium, that means that the sum of forces and the sum of moments equal 0. What is the equation to balance about the centre point of the plane?
2 * (Tau xy) dydz . (dx/2) - 2 * (Tau xy) dxdz . (dy/2) = 0
This equation means that the two shear stresses are equal to each other
On perpendicular planes, what comment can be made about the shear stresses?
The shear stresses are equal and symmetric, meaning they are either convergent or divergent
Are stresses forces?
No
When can we add stresses?
If they are all applied at the same point
When we write the equilibrium of bodies, what must we do?
We have to multiply the stresses with areas first, and then add the resultant forces
What is a good way to think of a direct shear?
Like a pair of scissors
What is the stress at a point?
The limit of the average stress when the area tends to zero
