Strings Civil Engineering (CE) Notes | EduRev

Civil Engineering SSC JE (Technical)

Civil Engineering (CE) : Strings Civil Engineering (CE) Notes | EduRev

The document Strings Civil Engineering (CE) Notes | EduRev is a part of the Civil Engineering (CE) Course Civil Engineering SSC JE (Technical).
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Chapter 9 

SPRINGS
Spring is a device, in which the material is arranged in such a way that it can undergo a considerable change, without getting permanently distorted.  A spring is used to absorb energy due to resilience which may be restored as and when required.  The quality of a spring is judged form the energy it can absorb. The spring which is capable of absorbing the greatest amount of energy for the given stress is the best one.

Stiffness of a Spring 

  • The load required to produce a unit deflection in spring is called spring stiffness.

Types of Springs There are two types depending upon the type of resilience: 

  • Bending spring (leaf spring) 
  • Torsion spring (helical spring)

Leaf Springs 

Central deflection d is given by,

Strings Civil Engineering (CE) Notes | EduRev 
Strings Civil Engineering (CE) Notes | EduRev
Strings Civil Engineering (CE) Notes | EduRev
Strings Civil Engineering (CE) Notes | EduRev
Where,

l = Span of spring
t = thickness of plates
b = Width of plates
n = Number of plates
W = Load acting on the spring
E = Young's modulus

Closed coiled helical springs subjected to axial loading 

Deflection in the spring due to load W,

 Strings Civil Engineering (CE) Notes | EduRev
Strings Civil Engineering (CE) Notes | EduRev

  • Stiffness of the spring,

Strings Civil Engineering (CE) Notes | EduRev

 

Where, W = axial load n = no. of turns of spring d = diameter of the rod of the spring R = mean radius of the coil  G = modulus of rigidity for the spring material.

  • Energy stored,

 Strings Civil Engineering (CE) Notes | EduRev

Closely coiled helical spring subjected to axial twist
Strings Civil Engineering (CE) Notes | EduRev

  • Total angle of bend = φ

 Strings Civil Engineering (CE) Notes | EduRev

where l = 2 pRn = 2pR ' n '

  • Strings Civil Engineering (CE) Notes | EduRev

Thus, the change in curvature or angle of bend per unit length, is constant, throughout the spring.

  •  Energy stored = Strings Civil Engineering (CE) Notes | EduRev

 Where, R = mean radius of the spring coil
n = no. of turns or coils
M = Moment or axial twist applied on the spring
R = decreased mean radius due to twist
n = increased no of turns due to twist
I = moment of inertia of spring rod section
E = Young's modulus

 Open coiled helical spring subjected to axial load 

  • In  this case load W will cause both twisting and bending of coils.

 Strings Civil Engineering (CE) Notes | EduRev

  • Deflection of the spring as a result as a result of axial load,

 Strings Civil Engineering (CE) Notes | EduRev

Where,
d = Diameter of spring wire
R = Mean radius of spring coil
P = Pitch of the spring coil
n = no. of turns of coils
G = modulus of rigidity for spring material

 W = axial load on the spring
a = angle of helix

E = Young's modulus 

  • If we put µ = o

Strings Civil Engineering (CE) Notes | EduRev

 = deflection of closed coiled spring.


SPRINGS IN SERIES AND PARALLEL
(i) Springs in series

 Strings Civil Engineering (CE) Notes | EduRev

  • Total  extension = å (individual extensions) 

d = d1 + d2 

  • load applied (W) will be same on both the springs. 
  • The equivalent stiffness is given by

 Strings Civil Engineering (CE) Notes | EduRev

where K1 & K2 are individual stiffness of the springs.

(ii) Springs in parallel

 Strings Civil Engineering (CE) Notes | EduRev

Both the springs have same extension.
δ = δ1 = δ2 

Load applied (W) is shared by the springs.
W = W1 + W2
The equivalent stiffness is given by,

 Keq = K+ K2

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