Circular Plate Deflection Calculator

Circular Plate Deflection Formula:

\[ \delta = \frac{3 \cdot W \cdot R^4 \cdot (1 - \nu^2)}{16 \cdot E \cdot t^3} \]

Load (W):

Radius (R):

Poisson's Ratio (ν):

unitless

Modulus of Elasticity (E):

Thickness (t):

Deflection (δ):

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1. What is the Circular Plate Deflection Formula?

The circular plate deflection formula calculates the maximum deflection at the center of a circular plate under a uniformly distributed load. This formula is derived from plate theory and is widely used in mechanical and civil engineering for designing plates and diaphragms.

2. How Does the Calculator Work?

The calculator uses the circular plate deflection formula:

\[ \delta = \frac{3 \cdot W \cdot R^4 \cdot (1 - \nu^2)}{16 \cdot E \cdot t^3} \]

Where:

\( \delta \) — Deflection at center (m)
\( W \) — Uniformly distributed load (N)
\( R \) — Radius of the plate (m)
\( \nu \) — Poisson's ratio (unitless)
\( E \) — Modulus of elasticity (Pa)
\( t \) — Thickness of the plate (m)

Explanation: The formula shows that deflection is proportional to the load and the fourth power of radius, and inversely proportional to the cube of thickness and modulus of elasticity.

3. Importance of Deflection Calculation

Details: Accurate deflection calculation is crucial for structural design to ensure plates can withstand applied loads without excessive deformation that could lead to failure or impaired functionality.

4. Using the Calculator

Tips: Enter all values in consistent SI units. Load in Newtons, radius and thickness in meters, modulus in Pascals. Poisson's ratio is dimensionless (typically between 0-0.5).

5. Frequently Asked Questions (FAQ)

Q1: What are typical Poisson's ratio values?
A: For most metals, ν ranges from 0.25 to 0.35. For rubber-like materials, it approaches 0.5.

Q2: Does this formula work for all boundary conditions?
A: This specific formula is for simply supported circular plates with uniformly distributed load. Different boundary conditions require different formulas.

Q3: What is the significance of R⁴ in the formula?
A: The fourth power relationship means deflection increases dramatically with larger plate radii, making larger plates much more susceptible to bending.

Q4: How does thickness affect deflection?
A: Deflection is inversely proportional to the cube of thickness, so doubling the thickness reduces deflection by a factor of 8.

Q5: What are common applications of this calculation?
A: This calculation is used in designing pressure vessel heads, optical mirror supports, diaphragm seals, and various mechanical components.