Simply supported elastic plate
Plate-buckling stress
Inputs
User-entered linear-elastic Young’s modulus for the stated plate material and condition.
User-entered isotropic elastic ratio strictly between −1 and 1; it is not looked up.
Uniform unstiffened plate thickness in the stated elastic model.
Width matched to the user-entered buckling coefficient definition; this workspace does not select it.
User-entered dimensionless coefficient from a geometry/loading/boundary-specific source; no chart lookup is performed.
Results
Elastic critical buckling stress
104.12
Declared thickness / reference-width ratio
0.012
—Elastic plate stiffness term
180,762
σcr = kπ²E/[12(1−ν²)](t/b)²
A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.
Nearby: Axial response · Beam deflection & reactions · Elastic stability · Solid-shaft torsion
Method
Formula, when it applies, and when it does not
Calculate simply supported isotropic plate elastic critical stress from material properties, dimensions, and a user-supplied buckling coefficient.
σcr = kπ²E/[12(1−ν²)](t/b)²
When
- Isotropic linear-elastic plate
- Simply supported model selected outside this workspace
- User-entered buckling coefficient
- Elastic bifurcation stress only
Don’t
- This calculates only the declared simply supported isotropic elastic plate-buckling relation using a user-entered coefficient. It does not select boundary conditions, load case, reference width, or buckling coefficient; and excludes plasticity, residual stress, geometric imperfections, post-buckling, stiffeners, connections, code requirements, safety factors, adequacy, and approval.
Timoshenko & Gere, Theory of Elastic Stability