Applications of Elastic Behaviour of Materials Video Lecture | Physics for JEE Main & Advanced

applications of elasticity most
materials used by us in our daily life
undergo some kind of stress it is
therefore important to design things in
a way that they are not affected by the
stress principle of elasticity is used
while designing bridges and the ropes of
cranes a crane used for lifting and
moving heavy loads from one place to
another has a thick metallic row to
which the load is attached the Rope is
pulled up or down with the help of
pulleys and motors the required diameter
of the robe is decided by the elastic
limit of the material of the robe and
the load to be lifted suppose the Rope
is made of steel and the crane has to
lift a load of 10 metric tons that is 10
to the power 4 kgs the stress
corresponding to the elastic limit of
steel is 3 into 10 to the power 8 newton
meter to the power minus 2 obviously the
stress produced in the rope should not
exceed the elastic limit that is stress
is less than or equal to elastic limit
stress is equal to load to be lifted by
area of cross section of the rope
therefore load to be lifted by area of
cross section of the rope is less than
or equal to the elastic limit from this
relation we can calculate the area of
the cross section of the rope
it means that the area of the cross
section of the rope should not be less
than three point three into ten to the
power minus 4 meter square this
corresponds to a diameter of about two
centimeters for a rope off circular
cross section in order to provide for a
safety factor of ten so that the rope
can lift a load of 10 to the power 4
into 10 is equal to 10 to the power 5 kg
the diameter of the rope is kept more
than two centimeters further for the
purpose of flexibility the rope is made
of a number of relatively thin wires
braided together
designing of bridges a bridge should be
designed in such a way that it does not
Bend too much
or break under the load of traffic its
own load and the force of winds it is
known from the theory of elasticity that
when a load W is placed at the midpoint
of a bar of length L prep B and
thickness D then the bar sags at the
midpoint by an amount delta given by
Delta is equal to W into L to the power
three by four Y into B into D cube where
Y is Young's modulus of the material of
the bar this expression shows that to
reduce the bending Delta of the bar for
a given load we should use a material of
large Young's modulus and we should
increase the thickness of the bar rather
than the breadth because Delta is
proportional to 1 by d cube
but on increasing the thickness
the power may bend as shown in the
figure this is called buckling to avoid
the sparkling a compromise between
breadth and thicknesses made by using I
shaped steel girders having a large load
bearing surface for the construction of
bridges after many years the bridge
loses its elastic strength due to the
continuous stress and strain and such
bridges are declared unsafe