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In SI unit system, the unit of strain energy is the joule (J), and the unit of volume is m³. ∴ u = `\frac{U}{V}` = `\frac{J}{m^{3}}` = J/m³ ∴ The SI unit of strain energy density is J/m³.
- Angle of Twist
Here the angle ‘Φ’ measured over the cylindrical surface...
- Angle of Twist
The strain energy stored in an elastic material upon deformation is calculated below for a number of different geometries and loading conditions. These expressions for stored energy will then be used to solve some elasticity problems using the energy methods mentioned in the previous section.
When a material does obey Hooke's law, the elastic strain energy, E can be calculated with an equation. The equation is the area of a right-angled triangle under the force-extension graph; Where: E = elastic strain energy (or work done) (J) F = average force (N) ΔL = extension (m)
The energy methods provide a powerful tool for deriving exact and approximate solutions to many structural problems. 8.1 The Concept of Potential Energy. From high school physics you must recall two equations. 1. E = Mv2 kinematic energy. 2. W = mgH potential energy. (8.1a) (8.1b)
Strain energy. The area under the \(\sigma_e - \epsilon_e\) curve up to a given value of strain is the total mechanical energy per unit volume consumed by the material in straining it to that value. This is easily shown as follows: \[U^* = \dfrac{1}{V} \int P\ dL = \int_0^L \dfrac{P}{A_0} \dfrac{dL}{L_0} = \int_{0}^{\epsilon} \sigma d\epsilon\]
This equation is a general expression for the internal strain energy of a linear elastic structure of any type. It can be simplified significantly for structures
equation for strain energy can be written as: p2L U = 2AE (13.3) which is often a more usable expression for the strain energy stored in an elastic bar. As the strain energy stored in the bar is equal to the work done to extend the bar, what do you think are the units of strain energy? Joules (Newton.metres)
