2. Contents
1. Simple Stress
2. Normal Stress
3. Tensile Stress
4. Compressive Stress
5. Strain
6. Stress-Strain Diagram
7. Elastic Constant
8. Elasticity & Hooks Law
9. Relation Between Elastic Constant
10. Simple theory of Bending
11. Bending Equation
12. Neutral Surface & Neutral Axis
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3. Simple Stress
When some external force or load is applied on a body, then the
body offers resistance to these forces. to make the equilibrium
condition this resistance force(which is developed in the
material against the applied load).This internal resistance force
per unit cross-sectional area is called stress. Unit of stress
N/mm2 or Pascal.
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4. Normal Stress or Direct Stress
If the applying force is normal to the surface then the
developed stress is known direct stress. Direct stress mainly
depends upon the direction of force. Basically its of two
types-
Tensile Stress
Compressive stress
The normal stress (σ) in a material is defined as σ ≡ F/A
where F is the force (either tension or compression) acting
perpendicular to an imaginary plane surface passing through
a piece of material and A is the cross section area.
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5. Tensile Stress
When force is applied in such a way, due to this the length of the
body increases, this force is called tensile force and stress
developed by this force is known as tensile stress.
FF
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6. Compressive Stress
The force is applied in such a way, due to this length of the
body decreases. This type of force is known as compressive
force & the stress which is developed by using compressive
force is known as compressive stress.
FF
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7. Strain
After applying load on body, the body gets deformed. This
deformation is measured in terms of a dimensionless quantity
which is known as unit strain or called strain. This is of three
types-
1. Tensile strain
2. Compressive strain
3. Shear Strain
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8. Stress-Strain Diagram
If we apply load on a specimen of certain material which
causes stress and measure corresponding strain, we get strain
corresponding to the applied stress .Similarly ,if we go on
increasing the load on the specimen and measure
corresponding strain values and plot stresses and strains, we
get stress-strain curve or Stress-Strain diagram.
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11. Elasticity & Hook’s Law
The property of material by virtue of which it returns to its
original shape and size upon removal of load is known as
elasticity. And according to Hooks law-
It states that within elastic limit stress is proportional to strain.
Mathematically E= Stress/Strain
Where E = Young’s Modulus
Hooks law holds good equally for tension and compression.
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12. Poisson’s Ratio
The ratio lateral strain to longitudinal strain produced by a single stress is
known as Poisson’s ratio. Symbol used for poison's ratio is or 1/ m .
Modulus of Rigidity
For elastic materials it is found that shear stress is proportional to the shear
strain within elastic limit. The ratio is called modulus rigidity. It is denoted
by the symbol ‘G’ or ‘C’. G= shear stress 2 N/mm shear strain
Bulk modulus (K)
It is defined as the ratio of uniform stress intensity to the volumetric strain. It is
denoted by the symbol K.
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vstrainvolumetric
nsityStressInte
13. Relation between elastic constants
Elastic constants:
These are the relations which determine the deformations
produced by a given stress system acting on a particular
material. These factors are constant within elastic limit, and
known as modulus of elasticity E, modulus of rigidity G, Bulk
modulus K and Poisson’s ratio μ.
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14. Relationship between modulus of elasticity (E) and bulk modulus (K):
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213
Relationship between modulus of elasticity (E) and modulus of rigidity (G):
212 G
Relation among three elastic constants:
KG
KG
3
9
15. Simple Theory of Bending
Assumptions for bending theory-
• The material of the beam is homogenous and isotropic.
• Young modulus of elasticity is same in tension & compression
and stresses are within elastic limit.
• Beam is initially straight and all longitudinal filaments bend
into circular arcs within a common center of curvature.
• Radius of curvature of the beam is large compared with the
dimensions of the cross section.
• Each layer of the beam is free to expand or contract
independent of the layer above or below it.
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17. Neutral Surface & Neutral Axis
When a beam is subjected to external loads the bending effect
may cause it to sag or hog. The bending moment causing sagging
of the beam are called sagging bending moment in which fibers at
the bottom portion of the beam get stretched and the lower side of
the beam is in tension. There is one longitudinal section of the
beam which is neither in tension nor compression .this section is
called neutral axis.
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