Modulus Of Elasticity Given Strain Energy Stored In Shaft Subjected To Bending Moment Calculator

Formula Used:

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

Bending Moment in Shaft or Beam (M_b):

N·m

Length of Rod or Shaft (L):

Strain Energy in Rod or Shaft (U):

Area Moment of Inertia of rod or shaft (I):

m⁴

Modulus of Elasticity (E):

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1. What Is The Modulus Of Elasticity Given Strain Energy Stored In Shaft Subjected To Bending Moment?

The modulus of elasticity, also known as Young's modulus, is a measure of a material's stiffness or resistance to elastic deformation under stress. This calculator determines the modulus of elasticity based on the strain energy stored in a shaft subjected to a bending moment.

2. How Does The Calculator Work?

The calculator uses the formula:

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

Where:

\( E \) — Modulus of elasticity (Pa)
\( M_b \) — Bending moment in shaft or beam (N·m)
\( L \) — Length of rod or shaft (m)
\( U \) — Strain energy in rod or shaft (J)
\( I \) — Area moment of inertia of rod or shaft (m⁴)

Explanation: This formula calculates the modulus of elasticity by relating the bending moment, length, strain energy, and moment of inertia of the shaft.

3. Importance Of Modulus Of Elasticity Calculation

Details: The modulus of elasticity is a fundamental material property that indicates how much a material will deform under a given load. It's crucial for structural design, material selection, and predicting how materials will behave under various loading conditions.

4. Using The Calculator

Tips: Enter the bending moment in N·m, length in meters, strain energy in joules, and area moment of inertia in m⁴. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is modulus of elasticity?
A: Modulus of elasticity (Young's modulus) is a measure of a material's stiffness, defined as the ratio of stress to strain in the elastic deformation region.

Q2: What are typical values of modulus of elasticity?
A: Steel: ~200 GPa, Aluminum: ~70 GPa, Concrete: ~20-30 GPa, Wood: ~10 GPa (varies by species and direction).

Q3: How does bending moment affect strain energy?
A: Strain energy stored in a shaft increases with the square of the bending moment, meaning higher bending moments result in significantly more stored energy.

Q4: What is area moment of inertia?
A: Area moment of inertia is a geometric property that reflects how a cross-section's area is distributed relative to a specific axis, affecting its resistance to bending.

Q5: When is this calculation particularly useful?
A: This calculation is valuable in mechanical engineering applications where shafts are subjected to bending loads, such as in automotive axles, machine shafts, and structural beams.