Strain Energy Stored In Rod Subjected To Bending Moment Calculator

Strain Energy Formula:

\[ U = \frac{M_b^2 \times L}{2 \times E \times I} \]

Bending Moment (M_b):

N·m

Length (L):

Modulus of Elasticity (E):

Area Moment of Inertia (I):

m⁴

Strain Energy (U):

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1. What is Strain Energy in Rod or Shaft?

Strain Energy in Rod or Shaft is defined as the energy stored in a rod or a shaft due to deformation when subjected to bending moment. It represents the work done by external forces that is stored as elastic potential energy in the material.

2. How Does the Calculator Work?

The calculator uses the strain energy formula:

\[ U = \frac{M_b^2 \times L}{2 \times E \times I} \]

Where:

\( U \) — Strain Energy (Joules)
\( M_b \) — Bending Moment (Newton Meter)
\( L \) — Length of Rod or Shaft (Meter)
\( E \) — Modulus of Elasticity (Pascal)
\( I \) — Area Moment of Inertia (Meter⁴)

Explanation: The formula calculates the elastic strain energy stored in a rod or shaft when subjected to pure bending. The energy is proportional to the square of the bending moment and length, and inversely proportional to both the modulus of elasticity and area moment of inertia.

3. Importance of Strain Energy Calculation

Details: Strain energy calculation is crucial for structural analysis, design optimization, and understanding the energy absorption capacity of materials. It helps engineers design structures that can withstand bending loads while storing energy elastically.

4. Using the Calculator

Tips: Enter bending moment in N·m, length in meters, modulus of elasticity in Pascals, and area moment of inertia in m⁴. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between strain energy and stress?
A: Strain energy is the energy stored in a deformed material, while stress is the internal force per unit area. Strain energy depends on both stress and strain.

Q2: When is this formula applicable?
A: This formula applies to rods or shafts subjected to pure bending with constant cross-section and material properties along the length.

Q3: What are typical values for modulus of elasticity?
A: Steel: ~200 GPa, Aluminum: ~70 GPa, Concrete: ~20-30 GPa, Wood: ~10-15 GPa (varies with grain direction).

Q4: How does area moment of inertia affect strain energy?
A: Higher area moment of inertia reduces strain energy for the same bending moment, as the structure becomes stiffer and deforms less.

Q5: Can this formula be used for composite materials?
A: For homogeneous materials with linear elastic behavior only. Composite materials require more complex analysis due to varying material properties.