Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering Notes | EduRev

Mechanical Engineering SSC JE (Technical)

Mechanical Engineering : Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering Notes | EduRev

The document Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering Notes | EduRev is a part of the Mechanical Engineering Course Mechanical 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 dis given by,

Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering Notes | EduRev
Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering Notes | EduRev
Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering Notes | EduRev
Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering 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,
 Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering Notes | EduRev
Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering Notes | EduRev
• Stiffness of the spring,
 Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering 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,
Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering Notes | EduRev
Closely coiled helical spring subjected to axial twist

Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering Notes | EduRev
• Total angle of bend =  
Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering Notes | EduRev
where l = 2pRn = 2pR 'n '
Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering Notes | EduRev
constant
Thus, the change in curvature or angle of bend per unit length, is constant, throughout the spring.
• Energy stored =
Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering 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.
Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering Notes | EduRev
• Deflection of the spring as a result as a result of axial load,
Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering 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 v
W = axial load on the spring
a = angle of helix
E = Young's modulus
Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering Notes | EduRev
= deflection of closed coiled spring.
SPRINGS IN SERIES AND PARALLEL
(i) Springs in series
Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering 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
Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering Notes | EduRev
where K1 & K2 are individual stiffness of the springs.
(ii) Springs in parallel

Chapter 9 Springs - Strength of Material, Mechanical Engineering Mechanical Engineering Notes | EduRev
• Both the springs have same extension.
d = d1 = d2
• Load applied (W) is shared by the springs.
W = W1 + W2
• The equivalent stiffness is given by,
eq.  K = K1 + K2
 

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