liminfoPlate Bending Calculator
Free web tool: Plate Bending Calculator
About Plate Bending Calculator
The Plate Bending Calculator performs structural analysis of flat plates under applied loads, computing maximum bending stress and maximum deflection. It supports both rectangular and circular plate geometries, with a choice between simply supported edges (free to rotate) and fixed (clamped) edges. Load types include uniform pressure loads (MPa) distributed over the entire plate surface and center point loads (N) applied at a single location.
This tool is used by mechanical engineers, structural designers, product developers, and students working with pressure vessels, machine bases, covers, panels, and enclosures. Understanding plate bending is critical for ensuring structural integrity, preventing fatigue failure, and meeting deflection limits in precision equipment. The calculator also outputs flexural rigidity D, which characterizes how resistant the plate cross-section is to bending.
The calculator uses classical thin-plate theory formulas from Roark's Formulas for Stress and Strain. For circular plates, closed-form analytical solutions are applied. For rectangular plates, Roark approximate coefficients α (deflection) and β (stress) are used as functions of the plate aspect ratio (a/b), clamped to a maximum ratio of 3 to match standard table limits. Flexural rigidity is D = E × t³ / (12 × (1 − ν²)), where E is Young's modulus, t is plate thickness, and ν is Poisson's ratio.
Key Features
- Supports rectangular and circular plate geometries with dedicated input fields
- Two edge conditions: simply supported (SS) and fixed/clamped edges
- Two load types: uniform pressure load (MPa) and center point load (N)
- Maximum bending stress output in MPa for direct comparison with material yield strength
- Maximum deflection output in mm for checking serviceability and stiffness requirements
- Flexural rigidity D (N·mm) calculated and displayed for further analysis
- Roark approximate coefficients for rectangular plates scaled by aspect ratio up to 3
- Real-time calculation with instant updates as you change any input parameter
Frequently Asked Questions
What formulas does this plate bending calculator use?
For circular plates, it uses closed-form thin-plate theory solutions. For rectangular plates, it applies Roark's approximate coefficients α and β, which are tabulated functions of the aspect ratio a/b. Flexural rigidity D = E × t³ / (12 × (1 − ν²)) is used throughout. These are standard formulas from Roark's Formulas for Stress and Strain, a widely used reference in mechanical engineering.
What is the difference between simply supported and fixed edge conditions?
A simply supported edge is free to rotate but cannot translate vertically — it behaves like a pin or roller support. A fixed (clamped) edge cannot rotate or translate, like a plate welded into a rigid frame. Fixed edges produce lower maximum deflection and lower center stress than simply supported edges, but introduce high bending moments and stresses at the edges themselves.
What is flexural rigidity D?
Flexural rigidity D = E × t³ / (12 × (1 − ν²)) represents a plate's resistance to bending. It increases with the cube of thickness, so doubling the plate thickness multiplies D by 8 and reduces deflection eightfold. D has units of N·mm (or N·m in SI). It is the plate equivalent of EI (modulus × moment of inertia) used in beam bending calculations.
What is the aspect ratio limit of 3 in the rectangular plate formulas?
Roark's tabulated coefficients for rectangular plates are given for aspect ratios (longer side / shorter side) from 1 to about 3. Beyond a ratio of 3, the plate behaves increasingly like a long beam supported along two edges, and the standard plate coefficients no longer improve significantly with increasing ratio. The calculator caps the ratio at 3 to stay within the valid range of the Roark coefficients.
How do I check if my plate will yield?
Compare the calculated maximum stress (MPa) against the yield strength of your plate material. For structural steel, yield strength is typically 250–355 MPa. For aluminum alloys, it ranges from 70 to 500 MPa depending on grade. Apply a safety factor of 1.5–3.0 depending on application criticality. If max stress exceeds yield strength divided by your safety factor, increase plate thickness or change the edge condition.
What plate thickness should I use for a given load?
Start with an initial estimate, enter it into the calculator, and check both stress and deflection. Deflection limits vary by application — typically L/200 to L/400 of the span for structural panels, or a fixed maximum for precision equipment. Iterate by increasing thickness until both stress and deflection satisfy your design requirements.
Can I use this for pressure vessel flat end caps?
Yes. For a circular plate with fixed edges and uniform load (pressure in MPa), this calculator gives the maximum stress at the edge and maximum deflection at the center. Compare the stress against the allowable stress for your material and design code (ASME, EN 13445, etc.). Note that for thick plates (thickness > span/10), thin-plate theory underestimates stress, and thick-plate or finite element analysis is more appropriate.
What is Poisson's ratio and what value should I use?
Poisson's ratio ν is the ratio of lateral strain to axial strain when a material is stretched. For steel, ν ≈ 0.3; for aluminum, ν ≈ 0.33; for rubber, ν ≈ 0.5. For most structural metals, ν = 0.3 is a reasonable default. Poisson's ratio affects flexural rigidity D and the stress distribution in plate bending — higher ν increases the effective stiffness of the plate.