KEVOS® MAKEOS · Strength
Square and Rectangular Flat Plates
What stress and deflection does this square or rectangular plate have under load?
Maximum stress and deflection of square and rectangular flat plates with supported or fixed edges under uniform pressure or a central load, by the handbook’s plate formulas.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Plate and loading | choice | Plate shape, edge support and load. |
| Length (long side) | mm | Distance between supports (long side for rectangles). |
| Width (short side, rectangular) | mm | Short side of a rectangular plate. |
| Thickness | mm | Plate thickness. |
| Uniform pressure | kPa | Uniform pressure (1 kPa = 0.001 MPa; water depth 1 m ≈ 9.8 kPa). |
| Central load (central-load cases) | N | Concentrated load at the centre. |
| Radius of loaded area (central load) | mm | Radius of the area the central load is applied over. |
| Elastic modulus | GPa | Elastic modulus from the material data sheet (steel is typically about 200 GPa). |
| Allowable stress | MPa | Allowable stress from your design code. |
Method and formulas
- Square, uniform (W = p × area): supported S = 0.29W/t² (0.28 bottom only), d = 0.0443WL²/Et³; fixed S = 0.31W/t², d = 0.0138WL²/Et³.
- Square, central load: fixed S = 0.62W/t² ln(L/2r₀), d = 0.0568WL²/Et³; supported S = 0.62W/t² (ln(L/2r₀) + 0.577), d = 0.1266WL²/Et³ (r₀ replaced by √(1.6r₀² + t²) − 0.675t when r₀ < 1.7t).
- Rectangular supported: S = 0.75W ÷ t²(L/l + 1.61 l²/L²), d = 0.1422W ÷ Et³(L/l³ + 2.21/L²). Fixed: S = 0.5W ÷ t²(L/l + 0.623 l⁵/L⁵), d = 0.0284W ÷ Et³(L/l³ + 1.056 l²/L⁴).
- Example: a 1000 × 600 × 8 mm supported plate at 10 kPa reaches 31.302 MPa and deflects 1.2182 mm.
Limitations
- Small-deflection formulas based on ν = 0.3 (within about 3% for other metals).
- Deflections over about half the thickness need large-deflection (membrane) analysis.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check tank sides, access covers and floor plates
- Size a plate for a pressure or point load
- Compare supported and fixed edges
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Maximum stress
- Maximum deflection
- Total load
Interpreting the result
- Stiffeners usually save more weight than a thicker plate.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 288–290. Topic reference; no source tables or recommended settings are reproduced.
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