Transcript 111303 – SOLID MECHANICS

111304 – SOLID MECHANICS
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S.ARAVINDAN
Lecturer
Department of Aeronautical Engineering
Rajalakshmi Engineering College
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STRESS
Stress is the ratio of applied force F and cross section A, defined as "force per
area".
Direct Stress or Normal Stress
Stress normal to the plane is usually denoted "normal stress" and can be
expressed as
σ = Fn / A
(1)
where
σ = normal stress ((Pa) N/m2, psi)
Fn = normal component force (N, lbf)
A = area (m2, in2)
Shear Stress
Stress parallel to the plane is usually denoted "shear stress" and can be expressed
as
τ = Fp / A
(2)
where
τ = shear stress ((Pa) N/m2, psi)
Fp = parallel component force (N, lbf)
A = area (m2, in2)
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Strain
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Strain is defined as "deformation of a solid due to stress" and
can be expressed as
ε = dl / lo = σ / E
(3)
where
dl = change of length (m, in)
lo = initial length (m, in)
ε = unitless measure of engineering strain
E = Young's modulus (Modulus of Elasticity) (Pa, psi)
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Hooke's Law - Modulus of Elasticity (Young's Modulus or
Tensile Modulus)
Most metals have deformations that are proportional with the
imposed loads over a range of loads. Stress is proportional to
load and strain is proportional to deformation expressed by the
Hooke's law like
E = stress / strain = (Fn / A) / (dl / lo)
(4)
where
E = Young's modulus (N/m2) (lb/in2, psi)
Modulus of Elasticity or Young's Modulus are commonly used
for metals and metal alloys and expressed in terms 106 lbf/in2,
N/m2 or Pa. Tensile modulus are often used for plastics and
expressed in terms 105 lbf/in2 or GPa.
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Poisson's Ratio
υ = - εt / ε l
where
υ = Poisson's ratio
εt = transverse strain
εl = longitudinal or axial strain
Strain can be expressed as
ε = dl/L
where
dl = change in length
L = initial length
For most common materials the Poisson's ratio is in the
range 0 - 0.5.
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Elasticity
Elasticity is a property of an object or material which will restore it to its original
shape after distortion.
A spring is an example of an elastic object - when stretched, it exerts a restoring force
which tends to bring it back to its original length. This restoring force is in general
proportional to the stretch described by Hooke's Law.
Hooke's Law
One of the properties of elasticity is that it takes about twice as much force to stretch a
spring twice as far. That linear dependence of displacement upon stretching force is
called Hooke's law which can be expressed as
Fs = -k dL
(4)
where
Fs = force in the spring (N)
k = spring constant (N/m)
dL = elongation of the spring (m)
Yield strength
Yield strength, or the yield point, is defined in engineering as the amount of stress that
a material can undergo before moving from elastic deformation into plastic
deformation.
Ultimate Tensile Strength
The Ultimate Tensile Strength - UTS - of a material is the limit stress at which the
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material actually breaks, with sudden release of the stored elastic energy.
Modulus of Rigidity (or Shear Modulus) is the
coefficient of elasticity for a shearing force. It is defined
as "the ratio of shear stress to the displacement per unit
sample length (shear strain)" .
Modulus of Rigidity can be experimentally determined
from the slope of a stress-strain curve created during
tensile tests conducted on a sample of the material.
Definition of Modulus of Rigidity:
The ratio of shear stress to the displacement per unit
sample length (shear strain)
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COMPOSITE BAR
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THERMAL STRESS
Mechanical stress induced in a body when some or all of its parts are not free to expand
or contract in response to changes in temperature. In most continuous bodies, thermal
expansion or contraction cannot occur freely in all directions because of geometry,
external constraints, or the existence of temperature gradients, and so stresses are
produced. Such stresses caused by a temperature change are known as thermal stresses.
Problems of thermal stress arise in many practical design problems, such as those
encountered in the design of steam and gas turbines, diesel engines, jet engines, rocket
motors, and nuclear reactors. The high aerodynamic heating rates associated with high-
speed flight present even more severe thermal-stress problems for the design of
spacecraft and missiles.
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