Moment Of Inertia Of Shaft When Strain Energy Stored In Shaft Subjected To Bending Moment Calculator

Formula Used:

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

Bending Moment in Shaft or Beam (M_b):

N·m

Length of Rod or Shaft (L):

Modulus of Elasticity of Rod or Shaft (E):

Strain Energy in Rod or Shaft (U):

Area Moment of Inertia of Rod or Shaft (I):

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1. What is the Moment of Inertia Formula?

The formula calculates the area moment of inertia of a rod or shaft when strain energy is stored in a shaft subjected to bending moment. It provides a measure of the resistance of a rod's or shaft's to angular acceleration about a given axis without considering mass.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( I \) — Area Moment of Inertia of rod or shaft (m⁴)
\( M_b \) — Bending Moment in Shaft or Beam (N·m)
\( L \) — Length of Rod or Shaft (m)
\( E \) — Modulus of Elasticity of Rod or Shaft (Pa)
\( U \) — Strain Energy in Rod or Shaft (J)

Explanation: The formula calculates the moment of inertia based on the bending moment, length, modulus of elasticity, and strain energy stored in the shaft.

3. Importance of Moment of Inertia Calculation

Details: Accurate moment of inertia calculation is crucial for analyzing the structural behavior of shafts and beams under bending loads, determining deflection characteristics, and ensuring structural integrity in mechanical and civil engineering applications.

4. Using the Calculator

Tips: Enter bending moment in N·m, length in meters, modulus of elasticity in Pascals, and strain energy in Joules. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is area moment of inertia?
A: Area moment of inertia is a geometrical property that reflects how an area is distributed relative to a particular axis. It measures the resistance to bending and deflection.

Q2: How does bending moment affect moment of inertia?
A: Bending moment is squared in the formula, meaning it has a significant impact on the calculated moment of inertia. Higher bending moments result in larger moment of inertia values.

Q3: What is strain energy in this context?
A: Strain energy is the energy stored in a deformed elastic object (like a shaft) due to applied loads. It represents the work done by external forces in deforming the object.

Q4: Why is modulus of elasticity important?
A: Modulus of elasticity measures the material's stiffness and its ability to deform elastically under stress. Different materials have different moduli of elasticity.

Q5: What are typical units for moment of inertia?
A: The SI unit for area moment of inertia is meters to the fourth power (m⁴). Other common units include mm⁴ and in⁴ depending on the application.