Modulus of Elasticity of Rod given Strain Energy Stored Calculator

Formula Used:

\[ E = \frac{P^2 \times L}{2 \times A \times U} \]

Axial Force on Beam (P):

Length of Rod or Shaft (L):

Cross Sectional Area of Rod (A):

m²

Strain Energy in Rod or Shaft (U):

Modulus of Elasticity of Rod or Shaft (E):

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1. What is the Modulus of Elasticity?

The Modulus of Elasticity (Young's Modulus) is a mechanical property that measures the stiffness of a solid material. It defines the relationship between stress (force per unit area) and strain (proportional deformation) in a material in the linear elasticity regime of a uniaxial deformation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E = \frac{P^2 \times L}{2 \times A \times U} \]

Where:

\( E \) — Modulus of Elasticity (Pa)
\( P \) — Axial Force on Beam (N)
\( L \) — Length of Rod or Shaft (m)
\( A \) — Cross Sectional Area of Rod (m²)
\( U \) — Strain Energy in Rod or Shaft (J)

Explanation: This formula calculates the modulus of elasticity based on the strain energy stored in a rod or shaft when subjected to an axial force.

3. Importance of Modulus of Elasticity

Details: The modulus of elasticity is a fundamental property in materials science and engineering. It helps determine how much a material will deform under a given load and is crucial for designing structures and components that can withstand specific loads without excessive deformation.

4. Using the Calculator

Tips: Enter axial force in newtons (N), length in meters (m), cross-sectional area in square meters (m²), and strain energy in joules (J). All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of modulus of elasticity for common materials?
A: For steel: 190-210 GPa, aluminum: 69-79 GPa, concrete: 20-40 GPa, wood: 8-14 GPa (parallel to grain).

Q2: How does temperature affect modulus of elasticity?
A: Generally, modulus of elasticity decreases with increasing temperature as atomic bonds weaken and materials become less stiff.

Q3: What's the difference between modulus of elasticity and modulus of rigidity?
A: Modulus of elasticity relates to tensile/compressive stress and strain, while modulus of rigidity relates to shear stress and strain.

Q4: Can modulus of elasticity be negative?
A: No, modulus of elasticity is always positive as it represents a material's resistance to deformation.

Q5: How is modulus of elasticity determined experimentally?
A: Typically through tensile testing where stress-strain curves are generated, and the slope of the linear elastic region gives the modulus.