Span of Spring given Maximum Bending Stress Calculator

Formula Used:

\[ l = \sqrt{\frac{4 \times E \times t_p \times \delta}{\sigma}} \]

Modulus of Elasticity Leaf Spring (E):

Thickness of Plate (t_p):

Deflection of Centre of Leaf Spring (δ):

Maximum Bending Stress in Plates (σ):

Span of Spring (l):

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1. What is Span of Spring given Maximum Bending Stress?

The span of spring calculation determines the length of a leaf spring based on material properties, thickness, deflection, and maximum allowable bending stress. This is crucial for designing springs that can withstand specific loads without failure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l = \sqrt{\frac{4 \times E \times t_p \times \delta}{\sigma}} \]

Where:

\( l \) — Span of spring (m)
\( E \) — Modulus of Elasticity (Pa)
\( t_p \) — Thickness of plate (m)
\( \delta \) — Deflection of centre of leaf spring (m)
\( \sigma \) — Maximum bending stress in plates (Pa)

Explanation: This formula calculates the required span length to ensure the spring operates within safe stress limits while achieving the desired deflection.

3. Importance of Span Calculation

Details: Accurate span calculation is essential for spring design to prevent mechanical failure, ensure proper load distribution, and maintain structural integrity under operating conditions.

4. Using the Calculator

Tips: Enter all values in consistent SI units. Ensure all inputs are positive values. The calculator will compute the span length needed for the given parameters.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of modulus of elasticity in this calculation?
A: The modulus of elasticity represents the material's stiffness and its ability to return to original shape after deformation, directly affecting the spring's performance.

Q2: How does plate thickness affect the span calculation?
A: Thicker plates generally require shorter spans to achieve the same deflection while maintaining safe stress levels, as they provide greater resistance to bending.

Q3: What happens if the maximum bending stress is exceeded?
A: Exceeding the maximum bending stress can lead to permanent deformation or failure of the spring, compromising its functionality and safety.

Q4: Can this formula be used for all types of springs?
A: This formula is specifically designed for leaf springs. Different types of springs (coil, torsion, etc.) require different calculation methods.

Q5: How accurate is this calculation for real-world applications?
A: While this provides a good theoretical basis, real-world factors like material imperfections, environmental conditions, and manufacturing tolerances should be considered with appropriate safety factors.