Som strain energy

Som strain energy

1. STRENGTH OF MATERIALS STRAIN ENERGY:-

2. STRENGTH OF MATERIALS RESILIENCE:- PROOF RESILIENCE:-

3. STRENGTH OF MATERIALS 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.

4. STRENGTH OF MATERIALS 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)

5. STRENGTH OF MATERIALS .............(B) WORK DONE = WORK STORED STRAIN ENERGY DUE TO GRADUAL LOADING WILL BE

6. STRENGTH OF MATERIALS STRAIN ENERGY DUE TO SUDDEN LOADING:-

7. STRENGTH OF MATERIALS 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

8. STRENGTH OF MATERIALS 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.

9. STRENGTH OF MATERIALS 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.