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14. Strain Energy Method

Theory at a Glance (for IES, GATE, PSU)1. Resilience (U) Resilience is an ability of a material to absorb energy when

elastically deformed and to return it when unloaded.

The strain energy stored in a specimen when stained within

the elastic limit is known as resilience.

2

U = U =2 2

2

E V o lu m e o r V o lu m e

E

2. Proof Resilience Maximum strain energy stored at elastic limit. i.e. the strain energy stored in the body upto

elastic limit.

This is the property of the material that enables it to resist shock and impact by storing

energy. The measure of proof resilience is the strain energy absorbed per unit volume.

3. Modulus of Resilience (u)The proof resilience per unit volume is known as modulus of resilience. If is the stress due to

gradually applied load, then

2

u = u =2 2

2 E o r

E

4. Application

2 22

22

3P .

4 4= 2 2 (2 ) 2.4 4

L L P

P LU d AE d E E

= +

Strain energy becomes smaller & smaller as the cross sectional area of bar

is increased over more & more of its length i.e. A , U

5. Toughness This is the property which enables a material to be twisted, bent or stretched under impact

load or high stress before rupture. It may be considered to be the ability of the material to

LL/4

2d

P

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Chapter

7. Strai

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S

o r

C

I

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s = L

hin walle

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n energy

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rain energ

=

=

0

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2

L

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M

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ases

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o Simpl

portant

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U P

,

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theorem

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0

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oad 'p' at e

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5

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.

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Mondals

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Chapter-14 Strain Energy Method S K Mondals1 =

x x

M U M dx

p EI p

Note:

o Strain energy, stored due to direct stress in 3 coordinates

21 ( ) 2 2

= x x y

U E

o = =If ,in case of equal stress in 3 direction thenx y z

2 23 U= [1 2 ] (volume strain energy)

2 2E k =

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