Bending Moment Given Strain Energy Stored In Spring Calculator

Formula Used:

\[ M = \sqrt{\frac{U \times E \times b \times t^3}{6 \times l}} \]

Strain Energy In Spiral Spring (U):

Joule

Modulus of Elasticity of Spiral Spring (E):

Pascal

Width of Strip of Spiral Spring (b):

Meter

Thickness of Strip of Spring (t):

Meter

Length of Spiral Spring Strip (l):

Meter

Bending Moment In Spiral Spring (M):

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1. What is Bending Moment in Spiral Spring?

Bending moment in spiral spring is the reaction induced in a spiral spring when an external force or moment is applied to the element, causing the element to bend. It represents the internal moment that resists the bending deformation in the spring.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M = \sqrt{\frac{U \times E \times b \times t^3}{6 \times l}} \]

Where:

\( M \) — Bending moment in spiral spring (Newton Meter)
\( U \) — Strain energy in spiral spring (Joule)
\( E \) — Modulus of elasticity of spiral spring (Pascal)
\( b \) — Width of strip of spiral spring (Meter)
\( t \) — Thickness of strip of spring (Meter)
\( l \) — Length of spiral spring strip (Meter)

Explanation: This formula calculates the bending moment based on the strain energy stored in the spring and the material and geometric properties of the spring.

3. Importance of Bending Moment Calculation

Details: Calculating bending moment is crucial for designing spiral springs that can withstand specific loads without permanent deformation. It helps engineers determine the spring's capacity to store and release energy efficiently.

4. Using the Calculator

Tips: Enter all values in appropriate units. Strain energy should be in joules, modulus of elasticity in pascals, and all length dimensions in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is strain energy in a spring?
A: Strain energy is the energy stored in a spring when it is deformed elastically. It represents the work done to deform the spring.

Q2: Why is modulus of elasticity important in this calculation?
A: Modulus of elasticity quantifies the material's stiffness and its resistance to elastic deformation, which directly affects how much energy the spring can store.

Q3: How does strip thickness affect bending moment?
A: Bending moment increases with the cube of thickness (t³), making thickness the most significant geometric factor in determining bending moment capacity.

Q4: What are typical applications of spiral springs?
A: Spiral springs are commonly used in mechanical watches, clocks, toys, and various instruments where rotational energy storage is required.

Q5: Can this formula be used for all types of springs?
A: No, this specific formula is designed for spiral springs. Other spring types (helical, leaf, etc.) have different formulas for calculating bending moment and strain energy.