Strain Energy
Energy stored in an elastically deformed body.
Formula
Variables
Example
Springs store strain energy
How it works
Strain energy is the work stored inside a body when it is loaded elastically, meaning it returns to its original shape after the force is removed. The factor of 1/2 appears because, in a linear elastic system, the force typically rises from zero to the final value as the deflection increases, so the average force during loading is F/2. Multiplying this average force by the total deflection gives the energy stored.
When to use it
Use this formula when a component behaves elastically and you know the force applied and the corresponding deflection, such as in axially loaded bars, beams under small deflection, or simple spring-like systems. It is useful for finding how much energy is stored or for checking whether a design can safely absorb load energy.
Worked example, step by step
A steel bracket deflects by 3 mm under a load of 800 N. Find the strain energy stored. Step 1: Write the formula: U = 1/2 Fδ Step 2: Convert the deflection to metres: 3 mm = 0.003 m Step 3: Substitute the values: U = 1/2 × 800 × 0.003 Step 4: Calculate: U = 0.5 × 2.4 = 1.2 J Final answer: The strain energy stored is 1.2 joules.
Common mistakes to avoid
- Using the formula for a material that has already yielded or is no longer behaving elastically
- Forgetting to convert deflection into metres when using SI units
- Using the full force instead of the average force concept that leads to the 1/2 factor
Did You Know?
Strain energy stored in a stretched material is released with a snap when it finally breaks.
Share this formula
More in Engineering
View allStress
BasicInternal force per unit area in a material.
Strain
BasicRelative deformation of a material.
Young's Modulus
IntermediateStiffness of a material (stress over strain).
Bernoulli's Equation
AdvancedConservation of energy in fluid flow.
Reynolds Number
AdvancedPredicts laminar vs turbulent flow.
Electrical Power
BasicPower in an electrical circuit.