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STRENGTH OF MATERIALS
By,
Dr.S.SURESH,
Assistant Professor,
Department of Mechanical Engineering.
UNIT-III-TORSION
1
SPRINGS
SPRINGS
 Elastic member whose primary function is to deflect
or distort under the action of applied load; it recovers
its original shape when load is released.
 Quality of a spring is judged from the energy it can
absorb.
2
NOTABLE APPLICATION OF SPRINGS
 To apply forces and to control motions as in brakes
and clutches
 To measure forces as in spring balance.
 To store as in clock springs.
 To reduce the effect of shock or impact loading as in
carriage springs.
 To change the vibrating characteristics of a
members as inflexible mounting of motors.
3
The springs are of the following two types depending upon the type
of resilience.
4
(HELICAL SPRINGS)
•A springs made up of a wire coiled into a helix.
•A spring, which is subjected to torsion or twisting
moment only and the resilience is also due to it, is known
as a torsion spring.
5
NOMENCLATURE OF HELICAL SPRING
6
W
S = Spring Stiffness (N/m)
The load required to produce a unite deflection is called Spring
Stiffness (N/m)
7
EXPRESSION FOR MAX. SHEAR STRESS INDUCED IN WIRE
8
(Expression for Max. Shear Stress induced in wire)
9
EXPRESS FOR DEFLECTION OF SPRING
10
(Express for deflection of spring)
11
Example 1: A closed-coiled helical spring is required to carry a
load of 150 N. If the mean diameter is to be 8 times that of the
wire, calculate these diameter. Take maximum shear stress as
100 Mpa.
Given:
Solution:
12
Given:
Solution:
EXAMPLE 2: A closed-coiled helical spring of round steel wire 5 mm in
diameter having 12 complete coils of 50 mm diameter is subjected to an axial
load of 100 N. Find the deflection of the spring and the maximum shearing
stress in the material. Modulus of rigidity (C) = 80 Gpa.
13
Example 3: A closed coiled helical spring of round steel wire
10 mm in diameter having 10 complete turns with a mean
diameter of 12 cm is subjected to an axial load of 200 N.
Determine: (i) The deflection of the spring (ii) Maximum shear
stress in the wire, (iii) stiffness of the spring.
Take C=8x104 N/mm2.
Given:
14
 Deflection
 Shear Stress
 Stiffness
15
 These are also called laminated springs.
 The leaf springs are widely used in Railway wagons, Coaches
and Road vehicles.
 These are used to absorb shocks, which give an unpleasant
feeling to the passengers.
 The energy observed by a laminated spring, during a shock,
is released immediately without doing any useful work.
 Types are (i) Semi-elliptical (ii) Quarter-elliptical
16
EXPRESSION FOR MAX. BENDING STRESS AND DEFLECTION
17
18
Central Deflection of the Spring = δ
19
EXAMPLE 1: A laminated spring 1m long is made up of plates each 50 mm wide
and 10 mm thick. If the bending stress in the plates is limited to
100 MPa, how many plates are required to enable the spring to carry a central
point load of 2 KN. If modulus of elasticity for the spring material is 200 GPa,
What is the deflection under the load?
20
EXAMPLE 2: A leaf spring to be made of seven plates 65 mm wide and
6.5 mm thick. Calculate the length of the spring, so that it may carry a central load
of 2.75 KN, the bending stress being limited to 160 MPa. Also calculate the
deflection at the centre of the spring. Take E for the spring material as 200 GPa.
21

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Torsion (Springs)-Strength of Materials.pdf

  • 1. STRENGTH OF MATERIALS By, Dr.S.SURESH, Assistant Professor, Department of Mechanical Engineering. UNIT-III-TORSION 1 SPRINGS
  • 2. SPRINGS  Elastic member whose primary function is to deflect or distort under the action of applied load; it recovers its original shape when load is released.  Quality of a spring is judged from the energy it can absorb. 2
  • 3. NOTABLE APPLICATION OF SPRINGS  To apply forces and to control motions as in brakes and clutches  To measure forces as in spring balance.  To store as in clock springs.  To reduce the effect of shock or impact loading as in carriage springs.  To change the vibrating characteristics of a members as inflexible mounting of motors. 3
  • 4. The springs are of the following two types depending upon the type of resilience. 4
  • 5. (HELICAL SPRINGS) •A springs made up of a wire coiled into a helix. •A spring, which is subjected to torsion or twisting moment only and the resilience is also due to it, is known as a torsion spring. 5
  • 7. W S = Spring Stiffness (N/m) The load required to produce a unite deflection is called Spring Stiffness (N/m) 7
  • 8. EXPRESSION FOR MAX. SHEAR STRESS INDUCED IN WIRE 8
  • 9. (Expression for Max. Shear Stress induced in wire) 9
  • 10. EXPRESS FOR DEFLECTION OF SPRING 10
  • 11. (Express for deflection of spring) 11
  • 12. Example 1: A closed-coiled helical spring is required to carry a load of 150 N. If the mean diameter is to be 8 times that of the wire, calculate these diameter. Take maximum shear stress as 100 Mpa. Given: Solution: 12
  • 13. Given: Solution: EXAMPLE 2: A closed-coiled helical spring of round steel wire 5 mm in diameter having 12 complete coils of 50 mm diameter is subjected to an axial load of 100 N. Find the deflection of the spring and the maximum shearing stress in the material. Modulus of rigidity (C) = 80 Gpa. 13
  • 14. Example 3: A closed coiled helical spring of round steel wire 10 mm in diameter having 10 complete turns with a mean diameter of 12 cm is subjected to an axial load of 200 N. Determine: (i) The deflection of the spring (ii) Maximum shear stress in the wire, (iii) stiffness of the spring. Take C=8x104 N/mm2. Given: 14
  • 15.  Deflection  Shear Stress  Stiffness 15
  • 16.  These are also called laminated springs.  The leaf springs are widely used in Railway wagons, Coaches and Road vehicles.  These are used to absorb shocks, which give an unpleasant feeling to the passengers.  The energy observed by a laminated spring, during a shock, is released immediately without doing any useful work.  Types are (i) Semi-elliptical (ii) Quarter-elliptical 16
  • 17. EXPRESSION FOR MAX. BENDING STRESS AND DEFLECTION 17
  • 18. 18
  • 19. Central Deflection of the Spring = δ 19
  • 20. EXAMPLE 1: A laminated spring 1m long is made up of plates each 50 mm wide and 10 mm thick. If the bending stress in the plates is limited to 100 MPa, how many plates are required to enable the spring to carry a central point load of 2 KN. If modulus of elasticity for the spring material is 200 GPa, What is the deflection under the load? 20
  • 21. EXAMPLE 2: A leaf spring to be made of seven plates 65 mm wide and 6.5 mm thick. Calculate the length of the spring, so that it may carry a central load of 2.75 KN, the bending stress being limited to 160 MPa. Also calculate the deflection at the centre of the spring. Take E for the spring material as 200 GPa. 21