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STRESS
STRAIN
ELASTIC LIMIT
NORMAL STRAIN
SHEAR STRESS
SHEAR STRAIN
GAUGE LENGTH
MODULUS OF ELASTICITY
MODULUS OF RIGIDITY
BULK MODULUS
PROOF STRESS
FACTOR OF SAFETY
FREE BODY DIAGRAM
STRESS-STRAIN DIAGRAM
BRITTLE MATERIALS
PROOF RESILIENCE
MODULUS OF RESILIENCE
BENDING MOMENTS AND SHEAR FORCE DIAGRAM
SHEARING FORCE
BENDING MOMENT
CANTILEVERS
CONTINUOUS BEAMS
FIXED BEAMS
MOMENT OF INERTIA
PARALLEL AND PERPENDICULAR AXIS THEOREMS
TRUSS ANALYSIS
STRAIN ENERGY

STRESS

When some external forces are applied to a body, then the body offers internal resistance to these forces. The magnitude of the internal resisting force is numerically equal to the applied forces. These internal resisting force per unit area is called “stress”.

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STRAIN

It is defined as change in length per unit length. The strain may be tensile or compressive depending upon whether the length increases (under tensile load) or decreases (under compressive load). It is a dimensionless quantity.

EQUATIONS OF STATIC EQUILIBRIUM

Whenever a solid body under the action of various forces is in static equilibrium or in the state of rest then the algebraic sum of the components of these forces along any chosen three perpendicular axes reference are separately zero. In addition, the algebraic sum of the moments of these forces about any point is also zero. It is not rotating. Mathematically, these results are expressed in the form of following four equations:

UNITS OF STRESS AND STRAIN:

Stress: The stress is defined as the internal force which is resisting to the applied force of deformation per unit area. Therefore, the stress is usually measured in Newtons/Metre Square (N/m²). It is also called Pascal (Pa). Since Pascal is a very small unit, it is not uncommon to use Mega Pascal (MPa) or Giga Pascal (GPa) as unit of stress, where 1 MPa = 10⁶ Pa and 1 GPa = 10⁹ Pa.

Strain: It is defined as the change in length (or elongation in length) per unit length. Mathematically it is defined as strain = change in length/unit length = l/L

ELASTIC LIMIT

Considering a tension test of a specimen of round section being stretched in a UTM. The load recorded by the universal testing machine is the reaction of the test specimen. At room temperature, the load extension diagram in general, at strain rate less than 2 × 10^–3/sec will tend to follow the curve of the adjacent in the below figure. Which is typical for an annealed metal like aluminium or copper.

Initially, the relation between the load and extension is essentially linear–that is, portion OA of the curve, where A defines the limit of proportionality. On further straining the relation between load and extension linear–that is portion OA of the curve, where A defines the limit of proportionality. On further straining, the relation between the load and extension no longer remains linear but the material is still elastic. That is if the load is released the specimen will revert back to its original length. The maximum load which can be applied without causing permanent deformation is known as ‘‘Elastic Limit’’ represented by point B in the Fig-I attached. Usually the points A and B are very near to each other and the real difference can be achieved only by using highly sensitive measuring device. At the point B ends the elastic straining and the inelastic or plastic deformation ensues. Beyond the point B there is a general permanent extension of the test piece until the load attains a maximum value, point D.

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FREE BODY DIAGRAM

The free body diagram of an element of a member in equilibrium is the diagram of only that member or element, as if made from the rest, with all the internal and external force.