Courses in ME

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SAMPLE COURSE – 1

FREE BODY DIAGRAMS AND EQUILIBRIUM

What is a Force?

A “Force” is a push or a pull which tends to change the state of a body. This definition is derived from Newton’s First Law.

(“A body continues in a state of rest or uniform motion unless acted upon by an external force”) . If, therefore, there is a change in state of the body, there must have been a “force” which caused it.

Note that the change in state need not always be “visible”.

In the picture below, a man is trying to pull a heavy weight. Assuming that the weight is too heavy,

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he will not be able to move it. Visually, no change can be observed, but a force exists!

The change, actually, is internal and not visible externally.
You must understand this.
If the man keeps on pulling the weight (even if it does not move), he will, at the end of the day, get very tired! The change in state occurs inside the weight, which gets stressed when a force acts on it.

SAMPLE COURSE – 2

 

STRESS AND STRAIN

Basic Definitions
Stress

A loaded body tends to deform. The molecules inside the body resist this deformation. This resistance (a force) per unit area is called stress. Note: To maintain equilibrium, the resistive force must be equal to the applied force.

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Stress = Force / Area or
σ = F or P/A where
F or P = Load or force acting on the body and
A = Cross-sectional area of the body
Units of Stress is N/m2 (Pa), or MPa (106 Pascal) or GPa (109 Pascal)

Strain

The deformation (per unit length) which a loaded body undergoes is called “strain”.

ϵ = δl/l    or  δl = ϵ l  where δl = change in length and l = original length

Strain is a unit less quantity as it is a ratio.

Tensile / Compressive Stress

When a load tends to increase the length of the body, the corresponding stress is called “Tensile” stress. When it tends to decrease the length of the body, the stress is called “Compressive” stress.

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Normal / Shear stress

When the area considered is normal to the load, it is a normal stress. When the area considered is parallel to the load, it is a shear stress.

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Here is another way of looking at Normal Stress

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Here is another way of looking at Shear Stress. The rivet is undergoing shear stress.

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Poisson’s Ratio

When a body deforms in one direction there is a deformation in other directions also. Poisson’s ratio is the ratio of lateral strain to longitudinal strain.

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Poisson’s Ratio = Lateral Strain / Longitudinal Strain

A high Poisson’s Ratio means a large deformation in the lateral direction.

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Normal values of Poisson’s Ratio are:

Cement: – 0.15,

Metals: – 0.25 to 0.33 and

Rubber: – 0.50.

Its symbol is µ, or 1/m

 

Elasticity

The property of a material’s returning to its original position, after removal of a deforming load, is called elasticity.

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Materials can be “perfectly “elastic or “partially” elastic, depending on whether they return fully to their original position or not.

Elastic Limit

It is the stress, beyond which, the deformation is not fully restored on removal of the load. There will be a “residual deformation”. The material would have gone from “elastic” to “plastic” stage.

Hooke’s Law

The law states that, if a material is loaded within its elastic limit, the stress is proportional to the strain.

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Mathematically,

Stress / Strain    = Constant = E    (where “E” is called the Young’s Modulus or the Modulus of Elasticity).

This also defines Young’s Modulus: It is the stress which causes unit strain. (Note: Unit strain means that the material has deformed to double its original length – assuming that it can happen within elastic limits)