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.

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

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

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.

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

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.

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

Torsion

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).

Normal and Shear stress

Sign convention