Strain energy examples ,What is strain energy in structural analysis , what is strain energy in strength of materials , elastic strain energy 2021
These topics cover in this page (strain energy से related सब टॉपिक के लिए भी इसे ही लीख सकते हैं )
- Strain energy for Axial loading ,
- Strain energy for Bending moment
- Strain energy for castiglious theorem
What is strain energy:-
When a gradual load is applied on an elastic body , then the body is strained and work is done on the body which is stored in the form of internal energy. This internal work done by the body in resisting the straining is called strain energy.
Strain energy For Axial loading :-
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| Strain energy For Axial loading diagram |
U = P× ΔL/2
According to hook's law.
̈̇ P = Aσ
σ = ∈E
U = (σA) × (∈L)/2
= σA∈L/2
= σA/2 × σL/E.
̈̇ A×L = volume
= σ²A/2E × volume
U = PδL/2
V U = p²L/2AE
̈̇ δL = PL/AE
For non uniform body
U = ∫ P²/2AE dx
(used for trusses)
Strain energy For Bwnding moment:-
w.k.t.
U = σ²ɓ/2E × volume.
= ∫ (My/i)² / 2E × dA × dx.
M/i = E/R = σ / y
M/i = σ / y
σ = My/i
̈̇ y² × dA = second moment of inertia(I)
= ∫ m² y² / 2Ei² × dA × dx
= ∫ M² /2Ei² × i × dx
U = ∫M² / 2Ei dx.
( used for frames )
U = ∫ T² / 2GJ dx.
( used for tilting moment )
From castiglious theorem:-
∂u/∂p = Δ , ∂u/∂m = θ
Δ = ∂/∂p{ ∫ M²/2Ei dx }
Δ = ∫ M (∂M/∂p)/Ei dx
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