Calculate the traction vector on a surface with unit normal
n=(0.400,0.600,0.693)
n = ( 0.400 , 0.600 , 0.693 ) . So T=46.79i+74.86j+34.40kMPa T = 46.79 i + 74.86 j + 34.40 k MPa .
What is the unit of traction?
units, tractions are measured in
Pascals (Pa)
. r r Page 2 Since tractions are vectors, they can be decomposed into normal and tangential vector components. σn and τ denote the magnitude of these components.
How do you find the stress vector from a stress tensor?
The stress vector is the force
per unit surface
. The stress tensor is the matrix {σij(x,t)} and its (i,j)-component is the i-component of the force per unit surface that is exerted at an element of the surface perpendiculart to the direction j.
What is traction and stress?
According to Chapter 8 of Twiss and Moore's Structural Geology,
traction is
.
Force per unit area on a surface of a specified orientation
(Twiss, 129) while stress is. A pair of equal and opposite tractions acting across a surface of specified orientation (Twiss, 129)
What is the concept of stress vector?
The stress vector is
the force per unit surface
. The stress tensor is the matrix {σij(x,t)} and its (i,j)-component is the i-component of the force per unit surface that is exerted at an element of the surface perpendiculart to the direction j.
What is the difference between a tensor and a vector?
Tensors are simply mathematical objects that can be used to describe physical properties, just like scalars and vectors. In fact tensors are merely a generalisation of scalars and vectors; a scalar is a zero rank tensor, and a vector is a
first rank tensor
.
Is stress a vector or scalar?
Stress has both magnitude and direction but it does not follow the vector law of addition thus, it is
not a vector quantity
. Instead, stress follows the coordinate transformation law of addition, and hence, stress is considered as a tensor quantity.
How do you calculate traction?
The coefficient of traction is defined as the usable force for traction divided by the weight on the running gear (wheels, tracks etc.) i.e.:
usable traction = coefficient of traction x normal force
.
What is the difference between traction and friction?
While friction is a general physical expression, vehicle traction can be defined as the friction
between a drive wheel and the road surface
. “traction is the friction between a drive wheel and the road surface. If you lose traction, you lose road grip.”
Is normal stress a vector?
Stresses are internal forces per unit area, whereas tractions are external forces per unit area. However, this is just a matter of terminology, and other disciplines may use different terminologies. Stress can be expressed as a
vector
or a tensor.
Is shearing stress a vector?
The normal stress (vector) is the component of in the direction perpendicular to the surface , and the shear stress (vector) is
the component of in the direction of the unit vector
.
How many components of stress vector are there?
Any arbitrary stress state can be decomposed into
9 components
(labeled σ
ij
). These components form a second rank tensor; the stress tensor (Figure 1).
What is normal stress?
When a force acts perpendicular (or “normal”) to the surface of an object
, it exerts a normal stress. When a force acts parallel to the surface of an object, it exerts a shear stress.
Are tensors just matrices?
All matrices are not tensors
, although all tensors of rank 2 are matrices.
Are all tensors vectors?
All tensors are not vectors
. This is to say, tensors are a more general object that a vector (strictly speaking though, mathematicians construct tensors through vectors). Tensors are technically defined through two different objects: 1.)
What is scalar vs vector?
A quantity that has magnitude but no particular direction is described as scalar
. A quantity that has magnitude and acts in a particular direction is described as vector.
