C:\whit_class\214\LinearMomentum_c3\LM_1.doc 09/03/99 Page 6 of 8
TRACTION VECTOR
Macro View Micro View
Traction “vector”
The forces acting on a surface can act in directions . . . therefore the notion of a vector
Definition
Where “(n)” is used to define the surface DA.
In particular subscript outward normal to the surface
· Which causes the largest traction? woman in spike heels or elephant (barefoot)
Assume:
§ elephant: 9000-13000 lbs. 1ft2/foot
§ woman: 120 lbs ; assume she is walking, so momentarily all weight is on one heel; heel = 1/2 inch x 1/2 inch
assume heel is
Often we need to examine what is happening in the interior of a body. Technique used now (and in 211) is to cut the body with a cutting plane and draw FBD’s.
Observations
From definition of traction vector we obtain
Traction vector depends on orientation of the plane [already seen … since ]
Examples
· Horizontal cut
· Inclined cut
What is
What is traction on right face?
What is on left face?
What is A on left face?
What is on left face?
Do everything in terms of components in directions.
*Although the plane is inclined, the traction vector is defined in the original coordinate system.
Activity: What are the components of the traction vector
· Normal to the left face
· Tangent to the left face
· Assume positive tangent is upward and to the left
General
Note the pattern
Define (This is to simplify notation later & to introduce new concept!)
1-D Stress Tensor vs. Traction Vector
Comments
· property of a point. It is not related to orientation of any boundary or cutting plane
· The traction vector at a point is dependent on the orientation of the surface on which it acts and the particular points
General statement for 1-D:
Two Dimensions
In terms of stress components
See Fig. 3.25 for 3D version.
Note that properties of a point and depends on the coordinate system chosen.
What about tractions on the other faces …