Springs - Strength of Materials

Introduction to Springs:

A Spring is a device whose function is to distort when loaded and to recover its original shape when the load is removed. 
Springs are energy absorbing units whose function is to store energy and restore it slowly or rapidly depending upon the particular application.
Springs are broadly classified into two types bending springs and torsion springs.
1. Bending springs: The spring which is subjected to only bending and the resilience is also due to the same is called bending spring. The leaf, laminated or plate springs fall under this category. These springs are made out of plates and arranged in a particular pattern so as to attain the spring effect.
Carriage spring or Leaf spring:
Leaf spring is made up of a number of leaves of equal width but varying length placed in laminations and loaded as a beam. They are two types of  semi elliptic type and quarter elliptic type.
Semi elliptic type is simply supported at both ends and loaded at its centre. Quarter type spring is arranged as a cantilever i.e fixed at only one end.
Leaf springs are universally used in cars, lorries, railway trucks, vehicle suspensions, electrical switches and bows.
The maximum bending stress developed in the spring is given by
σ = 3Wl / 2nbt2
δ = 3Wl3 / 8Enbt3 
where  W = load on the spring
             l   = span of the spring
             t   = Thickness of the plates
             b  = Width of the plates
             n = Number of plates and 

             E = Young's modules for the material of the plates.

2. Torsion springs: A spring which is subjected to twisting moment or torsion and the resilience is only due to the same is called torsion spring. Closely coiled helical springs are torsion springs. Let us know helical spring in detail.
Closed coil helical Springs:
Helical springs are made of wire coiled into a helical form, the load being applied along the axis of the helix. In these type of springs the major stresses is torsional shear stress due to twisting. They are both used in tension and compression.
When a closely coiled helical spring of mean diameter D is subjected to an axial load W, then the twisting moment due to the load W is given by 
T = W . R = W x D/2 = π/16 x τ x d3
Deflection of the spring is given by 
δ = 64WR3n / Cd4  = 8WD3n/Cd4
Energy stored in the spring 
U = 1/2 . W. δ 
The load required to produce a unit deflection in a spring is called stiffness of a spring and is given by 
s = W/δ  = Cd64R3n = Cd8D3n
where R = Mean radius of the spring coil = D / 2
           d = Diameter of the spring wire,
           n = Number of turns or coils
           C = Modulus of rigidity for the spring material 
           τ  = Maximum shear stress induced in the wire due to twisting

Springs in series and parallel:

When two springs having stiffness k1 and k2 are connected in series then the combined stiffness k is given by 

k = 1/ k + 1/ k2  = k1.k2 / k1 +  k2

JabberWok [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons
When the two springs are connected in parallel then
k = k1 +  k2

Some of the applications of Springs are as follows:

  • To cushion, absorb or control energy due to either shock or vibration as in car springs, railway buffers, shock absorbers and vibration dampers.
  • To apply forces as in brakes, clutches and spring loaded valves.
  • To control motion by maintaining contact between two elements as in cams and followers.
  • To measure forces as in spring balances and engine indicators.
  • To store energy as in watches, toys etc.

Some of the uses of springs:

  • For vehicle suspension in vehicles.
  • Pens
  • Spring mattresses
  • Pop open devices like Cd- players, Tape reorders
  • Cars
  • Lock mechanism
  • Jewellery clasp mechanisms
  • Mini drill
  • Watches Balance springs in mechanical timepieces and spring loaded bars for attaching bands and the clasps.