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__STRENGTH OF MATERIALS__

Elasticity = when an external
force acts on a body, the body tends to undergo some deformation. If the
external force is removed and the body returns to its original shape and size,
then the body is known as elastic body. If the body comes in its original shape
then it is called completely elastic body. Elastic limit marks
the partial break down of elasticity beyond which removal of load
result in a degree of permanent deformation. Steel, aluminum, and copper,
concrete can be considered completely elastic within a certain range.

Plasticity = when an external force acts on a body,
the body tends to undergo some deformation. If the external force is
removed and the body does not return to its original shape and size, then the
body is known as elastic body points to remember. This is useful in
forging operations. Ductility = It is the material can be drawn into thin
wire is called as ductility. And material having the property of
ductility is called as ductile material. Points to remember: Ductile material must
have low degree of elasticity. It is useful in wire drawing. A
ductile material should have a high level of plastic and power.

Brittleness = It is a property of material by virtue
of which material can be break into number of part without any deformation. Points
to remember: cast iron, concrete, Glass and ceramic material are brittle
material. In brittle material failure take place under
load without significant deformation. Malleability = It is the
property of material by virtue of which it can be drawn into thin sheets
without cracking by pressing , rolling, and hammering etc .points to remember: Toughness = It is the property of the material that
enables it to absorb the energy of the fracture without it. Points to remember:
Bend test used for common comparative test. Desirable in material which is
subject to cyclic or shock loading.

Hardness = It has the ability to resist indentation or
surface friction. Strength = It is defined as the maximum or limiting
value of stress that material can withstand without a failure or fracture. It
is property of material for mild steel {M.S.} Yield strength tension
= 250 mpa Ultimate strength tension = 400 mpa Yield = permanent deformation
ultimate = maximum points to remember: load required to cause
fracture, divided by area of test specimen, is a ultimate strength.

STRESS = Force per unit area Where, 6= stress (also
called intensity of stress) P= External force or load A= Cross -
sectional area SI unit N/ Metre square. TYPES of stress:-Tensile stress
Compressive stress Bending stress Tensile stress = It is the internal
resisting force setup per unit cross sectional area under the action of axial
pull. Compressive stress= It is internal resisting force setup per unit
cross sectional area under the action of axial push. Shear stress
= It is the internal resisting force setup per unit cross sectional area
under the action of two tangential force.

Strain = it is dimension less ratio of change in
length to its original length. It is denoted by 'e' TYPES of
strain:-Tensile strain Compressive strain Volumetric strain Shear strain
Tensile strain Increase in length / original length Compressive
strain Decrease in length / original length Shear strain Strain
produced by shear stress is known as shear strain Volumetric
strain Change in volume to original volume.

Hooks law its state that when the material is loaded
within elastic limit then stress is directly proportional to the strain and the
proportionality constant is called as modulus of elasticity, modulus of
rigidity or Elastic Modules. Modulus of rigidity or shear modulus Shear
stress to shear strain Factor of safety Ultimate stress to permissible
stress Bulk or volume modulus of elasticity Normal stress to volumetric
strain Direct stress to volumetric strain Longitudinal strain =
Increase in the length of the body in the direction of p. To length of
body Lateral strain = increase in length to length Decrease in
breath to original breath Decrease in depth to original depth Poisson’s
ratio: - Lateral train to longitudinal strain

Analysis of bars of varying section. P= Axial load
acting on the bar, L1= Length of section 1, A1= cross- sectional area of
section 1, L2, A2 = Length and cross- sectional area if section 2, L3,
A3 = Length and cross sectional area of section 3, E= Young’s modulus for
the bar. Analysis of uniformly tearing circular bars A bar uniformly
tapering from a diameter D1 at one end to a diameter D2 at the other end shown
in Figure. P= axial Tensile load on the bar, L= total length of bar, E=
young's modulus. Analysis of uniformly tapering Rectangular Bar A bar of
constant thickness and uniformly tapering in width from one end to the other
end. P= Axial load on the bar, L= Length of bar, a = width at bigger end=
width at smaller end, E= Young’s modulus, t= Thickness of
bar.

Engineering curve for mild steel for tension under static
loading OA= straight line (proportional region, Hooks law is
valid), OB =
Elastic region, BC= Elasto plastic region, CD= perfectly
plastic region, DE=Strain hardening, EF= Necking region, A=
Limit of proportionality, B= Elastic limit, C= Lower yield point, D= Strain
hardening starts, E= Ultimate stress, F= Fracture point. Equivalent young
modulus of parallel composite bar P= Load, A1= Area of first bar, A2=
Area of second bar, E1= young modulus of first bar, E2= young modulus
of second bar, L= Length of bar . Volumetric strain under
tri-axial loading Here, 6x= Stress in X- direction, 6y= Stress in
y-direction, 6z = volumetric strain. Volumetric strain of cylindrical
bar Ev= Longitudinal strain + (2 x Diametral strain ). Volumetric
strain of sphere Ev= 3 x Diametrically strain .Relation between E, G, K, u
E= Youngs modulus, G= shear modulus, K= Bulk modulus, U= position
ratio,Thermal stress and strain 6= Thermal stress, a= coefficient of
thermal expansion, T= Temperature change, ^ = change in length.

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