Thickness of each Plate given Total Resisting Moment by n Plates Calculator

Formula Used:

\[ Thickness\ of\ Plate = \sqrt{\frac{6 \times Bending\ Moment\ in\ Spring}{Maximum\ Bending\ Stress\ in\ Plates \times Number\ of\ Plates \times Width\ of\ Full\ Size\ Bearing\ Plate}} \]

Bending Moment in Spring (Mb):

N·m

Maximum Bending Stress in Plates (σ):

Number of Plates (n):

Width of Full Size Bearing Plate (B):

Thickness of Plate (tp):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Thickness of Plate Formula?

The thickness of plate formula calculates the required thickness of plates in a spring assembly based on bending moment, maximum bending stress, number of plates, and plate width. This calculation is essential for designing mechanical springs that can withstand specified loads without failure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ tp = \sqrt{\frac{6 \times Mb}{\sigma \times n \times B}} \]

Where:

\( tp \) — Thickness of Plate (m)
\( Mb \) — Bending Moment in Spring (N·m)
\( \sigma \) — Maximum Bending Stress in Plates (Pa)
\( n \) — Number of Plates
\( B \) — Width of Full Size Bearing Plate (m)

Explanation: The formula calculates the minimum plate thickness required to resist the bending moment while keeping the stress below the maximum allowable limit.

3. Importance of Plate Thickness Calculation

Details: Accurate plate thickness calculation is crucial for spring design to ensure structural integrity, prevent failure under load, and optimize material usage in mechanical systems.

4. Using the Calculator

Tips: Enter bending moment in N·m, maximum bending stress in Pa, number of plates (must be ≥1), and plate width in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the square root in the formula?
A: The square root accounts for the non-linear relationship between plate thickness and bending resistance, as thickness affects the moment of inertia in a squared relationship.

Q2: How does the number of plates affect the thickness calculation?
A: More plates distribute the load, allowing for thinner individual plates while maintaining the same overall strength.

Q3: What are typical values for maximum bending stress?
A: Maximum bending stress depends on the material properties. For spring steel, typical values range from 300-1500 MPa, but always consult material specifications.

Q4: Can this formula be used for other plate applications?
A: While derived for spring design, the formula can be adapted for other plate bending applications with similar boundary conditions.

Q5: What safety factors should be considered?
A: Always apply appropriate safety factors (typically 1.5-3.0) to the calculated thickness to account for material variations, dynamic loads, and unexpected stress concentrations.