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

Formula Used:

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

Strain Energy in Rod or Shaft (U):

Joule

Modulus of Elasticity of Rod or Shaft (E):

Pascal

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

m⁴

Bending Moment in Shaft or Beam (M₆):

N·m

Length of Rod or Shaft (L):

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1. What is the Length of Shaft Formula?

The formula calculates the length of a rod or shaft based on strain energy stored when subjected to a bending moment. It's derived from Castigliano's theorem and relates material properties and bending moment to the resulting length.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the length by considering the strain energy stored, material elasticity, moment of inertia, and the applied bending moment.

3. Importance of Length Calculation

Details: Accurate length calculation is crucial for structural design, mechanical engineering applications, and ensuring proper load distribution in shafts and beams under bending moments.

4. Using the Calculator

Tips: Enter strain energy in joules, modulus of elasticity in pascals, moment of inertia in m⁴, and bending moment in N·m. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is strain energy in mechanical systems?
A: Strain energy is the energy stored in a material when it is deformed under load, which can be recovered when the load is removed.

Q2: How does modulus of elasticity affect the length calculation?
A: Higher modulus of elasticity (stiffer material) results in shorter calculated length for the same strain energy and bending moment.

Q3: What is area moment of inertia?
A: Area moment of inertia is a geometric property that measures a cross-section's resistance to bending about a particular axis.

Q4: When is this formula most applicable?
A: This formula is most applicable for homogeneous, isotropic materials undergoing elastic deformation under pure bending moments.

Q5: Are there limitations to this calculation?
A: The calculation assumes linear elastic behavior, constant cross-section, and may not account for shear deformation or other complex loading conditions.