Stress at a point

2. Load/Force
•Two kind of external load/forces which
may act on a body i.e
•Surface force: Force distributed over the
surface of the body e.g hydrostatic
pressure.
•Body force: Force distributed over the
volume of the body. e.g. Gravitational
force, Magnetic force, inertia force.

4. Force
•The action on a body which tends to make
it move, such as push or pull is called
force.
•Magnitude, direction, point of application
fully describe a force. B
•Graphically: A
•A, point of application, and arrow
indicates the direction and AB denotes
magnitude

5. Force
Force F can be written as the vector sum of
three independent component.
Fx, Fy, Fz,
I,j,k are the unit vector associated with the
coordinates x, y, z
F= Fxi+ Fyj+ Fzk
F

6. Stress
•Stress is a measure of force per unit area within
a body. (Intensity of such a force)
•It is a body's internal distribution of force per
area that reacts to external applied loads.
• Stress is often broken down into its shear and
normal components as these have unique
physical significance.
•In short, stress is to force as strain is to
elongation.

7. Force
Force F can be written as the vector sum of
three independent component.
Fx, Fy, Fz,
I,j,k are the unit vector associated with the
coordinates x, y, z
F= Fxi+ Fyj+ Fzk
F

9. Intensity of a force (stress)
If a solid sustaining forces were to be cut ,a
force F would have to act on the exposed
face to maintain equilibrium..
For a cut perpendicular to the x-axis.
The resultant contribution of these internal
forces on the area element
A to be F
Component of F along x,y, z axis are
the intensities of these force component are
termed as stress
Component.

10. Normal and Shear stress
•
Normal Stress: Intensity of force
perpendicular to a cut.
•
Normal stress that pull away from the cut
are tensile stress
•
Normal stress that push against the face
are compresive stress
•
Shear stress Parellel to the plane of the
element
•
The first subscript denotes the axis
prependicular to plane on which the stress
acts
•
The second designates the direction of the
stress

13. Torsion

16. where shear stresses across the
diagonal are identical
(i.e. sxy = syx, syz = szy, and szx =
sxz) as a result of static equilibrium
(no net moment).
This grouping of the nine stress
components is known as the stress
tensor (or stress matrix).

17. Normal and Shear stress

19. Sign convention