Week 3: Complex stress Flashcards
What is meant by complex stress?
Stress due to loading that is applied in more than one direction at the same time
Book 1 page 74
How do you refer to loading which is in a single axial direction?
Uniaxial
Book 1 page 76
What are the transformation equations?
σθ = σ cos2 θ
τθ = σ sin θ cos θ
Book 1 page 83
At which angle is the maximum normal stress and minimum shear stress experienced (between 0° and 90°)?
θ = 0
Book 1 page 85
At which angle is the minimum normal and shear stress experienced (between 0° and 90°)?
θ = 90°
Book 1 page 85
At which angle is the maximum shear stress experienced (between 0° and 90°)?
θ = 45°
Book 1 page 85
What should be noted when the angle θ is greater than 90°, in terms of shear and normal stresses?
The value of cos θ becomes negative and the direction of the shear stress on the section reverses
Book 1 page 85 & 86
What is ‘stress at a point’?
Describing stress at chosen points of interest in the component
Book 1 page 87
What is the difference between a stress element and a finite element?
Stress element - Infinitesimally small block of material that describes stress at a point
Finite element - Small finite region that is part of a larger mesh used to numerically analyse a complex part
Book 1 page 87
What is meant by complementary shear stresses?
Shear stresses on perpendicular planes which must always be equal in magnitude for the shear element to be in equilibrium
Book 1 page 88
What type of stress is not considered when talking about plane stress?
Shear or normal stresses acting in the out of plane (z-axis) direction
Book 1 page 89
When is a shear stress considered to be positive?
When it is positive facing on the positive face of the element
When it is negative facing on the negative face of the element
Book 1 page 90
What are the two subscripts used in shear stress notation?
First indicates the plane (i.e. the element face)
Second indicates the direction of the shear stress
Book 1 page 90
What is biaxial stress and give an example?
The element experiences axial stress in two directions and no shear stress
Pressurised bottle or can where all the stress acts tangentially to the walls
Book 1 page 93
What is pure shear stress and give an example?
The element experiences shear stress but no axial stress
Shaft under torsion with no other loading
Book 1 page 93
What expression is used to find the angle at which the principal stresses occur?
What expressions are used to find the minimum and maximum principal stresses?
Book 1 page 102
What expressions are used to calculate the maximum shear stress and the angle at which this occurs?
Book 1 page 105
