The document discusses different types of strain energy. It defines modulus of resilience as the maximum amount of energy per unit volume a material can absorb through elastic deformation or recover from after stress is released, with units of Joules per cubic meter. For gradual loading, strain energy is calculated as half the load multiplied by the change in length. For sudden loading, strain energy stored equals the load multiplied by the displacement, which can be determined using stress, length, and Young's modulus from Hooke's law. For impact loading, strain energy equals the load multiplied by the displacement height plus the deformation calculated from stress and material properties.

2. STRAIN ENERGY:-

3. RESILIENCE:-
PROOF RESILIENCE:-

4. Modulus of Resilience:-
 The modulus of resilience is the maximum amount of energy per volume that a material
can absorb while elastically deforming.
OR
 This is the maximum amount of energy per volume that a material can absorb and still
recover after the applied stress is released.
 What are the units for modulus of resilience?
The modulus of resilience has units of energy per unit volume. In the international
system (SI), this is Joules per cubic meter or J/m3. Because a Joule is a Newton-meter,
J/m3 is the same as N/m2.

5. STRAIN ENERGY DUE TO GRADUAL
LOADING:-
 Consider a bar of Length L placed vertically and one end of it is atteched at the ceilling.
Let, P=gradually applied load
L= length of bar
A= Cross section area of bar
dL= change in length of deflection due to loading
= Axial stress induced in Bar.
E=Modulus of Elasticity
work done on the bar= Area of Deformation Diagram
= ................(A)LP
2
1

6. .............(B)
WORK DONE = WORK STORED
STRAIN ENERGY DUE TO GRADUAL LOADING WILL BE

7. STRAIN ENERGY DUE TO SUDDEN
LOADING:-

8. STRAIN ENERGY DUE TO IMPACT LOADING:-
Let us see the following figure, where we can see one vertical bar which is
fixed at the upper end and there is collar at the lower end of the bar. Let us
think that one load is being dropped over the collar of the vertical bar from a
height of h as displayed in following figure

9. Strain energy stored in the vertical bar = Work done by the load in deforming the vertical bar
Strain energy stored in the vertical bar = Load x Displacement
Strain energy stored in the vertical bar = P. (h + x)
U = P. (h + x)
As we know that strain energy stored in the body U will be provided by the following expression as
mentioned here
Now we will secure the value of extension x in terms of Stress,
Length of the body and Young’s modulus of the body by using
the concept of Hook’s Law.
Stress = E. Strain
Where E is Young’s Modulus of elasticity of the material
σ = E. ε
σ = E. (x/L)
x = σ. L/ E
Let use the value of the extension or deformation “x” in
above equation and we will have.

10. Once we will have value of the stress (σ)
induced in the vertical bar due to impact
load, we will easily determine the value of
strain energy stored in the vertical bar due to
an impact load.