Bending Moment Due To Force Given Deflection Of One End Of Spring Calculator

Formula Used:

\[ M = \frac{\delta \times E \times b \times t^3}{12 \times l \times r} \]

Deflection of Spiral Spring (δ):

Modulus of Elasticity of Spiral Spring (E):

Width of Strip of Spiral Spring (b):

Thickness of Strip of Spring (t):

Length of Spiral Spring Strip (l):

Distance of CG of Spiral Spring (r):

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.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M = \frac{\delta \times E \times b \times t^3}{12 \times l \times r} \]

Where:

\( M \) — Bending moment in spiral spring (N·m)
\( \delta \) — Deflection of spiral spring (m)
\( E \) — Modulus of elasticity of spiral spring (Pa)
\( b \) — Width of strip of spiral spring (m)
\( t \) — Thickness of strip of spring (m)
\( l \) — Length of spiral spring strip (m)
\( r \) — Distance of CG of spiral spring from outer end (m)

Explanation: This formula calculates the bending moment based on the deflection and material properties of the spiral spring, considering the geometric parameters of the spring strip.

3. Importance of Bending Moment Calculation

Details: Accurate calculation of bending moment is crucial for designing spiral springs, determining their load-bearing capacity, and ensuring they function properly within their elastic limits without permanent deformation.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure deflection, modulus of elasticity, width, thickness, length, and distance are all positive values greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the thickness term being cubed in the formula?
A: The thickness cubed (t³) term indicates that bending moment is highly sensitive to changes in spring thickness. Small increases in thickness result in significant increases in bending moment capacity.

Q2: How does modulus of elasticity affect the bending moment?
A: Higher modulus of elasticity materials (stiffer materials) will produce higher bending moments for the same deflection, as they resist deformation more strongly.

Q3: What is the typical range of values for spiral spring deflection?
A: Deflection values vary widely based on application, but typically range from millimeters to several centimeters, depending on spring design and material properties.

Q4: How does the distance from CG affect the bending moment?
A: The bending moment is inversely proportional to the distance from the center of gravity. Larger distances result in smaller bending moments for the same deflection.

Q5: Can this formula be used for all types of spiral springs?
A: This formula is specifically designed for spiral springs with uniform cross-section strips. Specialized formulas may be needed for springs with varying cross-sections or complex geometries.