Local plate buckling

Calculator Voalare Locală — Plăci Metalice

Teoria clasică de voalare elastică · EN 1993-1-5

Material & Steel

Steel grade

f_y [MPa] — from grade

E — modulus of elasticity [MPa]

ν — Poisson's ratio

Plate geometry

b — plate width [mm]

t — plate thickness [mm]

a — plate length [mm] (optional)

c/t — slenderness ratio (computed automatically)

Boundary conditions

Marginea comprimată · selectați tipul plăcii

Pinned

← σ

σ →

Pinned

kσ = 4.00 — setat automat din tipul selectat

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Calculation results

σcr — critical stress

1898.00 MPa

fy = 355 MPa

λp — non-dimensional slenderness

0.4325

limit: 0.673 (internal)

ε — epsilon factor

0.8136

√(235/fy)

c/t — ratio

20.00

b/t = 200/10.0

Cross-section class

Clasa 1

EN 1993-1-1 Tab. 5.2

Governing mechanism

Yielding governs

Comparație σcr / fy

▏ fy = 355 MPa ▏ σcr = 1898.00 MPa

Limite clasificare (element intern — Tab. 5.2 foaia 1) — c/t actual = 20.00

Class 1: c/t ≤ 33·ε = 26.85 ✓

Class 2: c/t ≤ 38·ε = 30.92 ✓

Class 3: c/t ≤ 42·ε = 34.17 ✓

Clasa 4: c/t > 42·ε (placă suplă — necesită beff) —

Plate diagram

Calculation formulae

1 · Elastic critical stress

\[ \sigma_{cr} = k_\sigma \cdot \frac{\pi^2 \cdot E}{12 \cdot (1-\nu^2)} \cdot \left(\frac{t}{b}\right)^2 \]

σ_cr = 4.00 × π² × 210000 / (12 × (1 − 0.30²)) × (10.0 / 200.0)² = 1898.00 MPa

2 · Epsilon factor

\[ \varepsilon = \sqrt{\frac{235}{f_y}} = \sqrt{\frac{235}{355}} = 0.8136 \]

3 · Non-dimensional slenderness

\[ \bar{\lambda}_p = \sqrt{\frac{f_y}{\sigma_{cr}}} = \sqrt{\frac{355}{1898.00}} = 0.4325 \]

Engineering interpretation

The plate reaches yielding before elastic buckling. (σcr = 1898.00 MPa ≥ fy = 355 MPa)

Non-slender plate. (λp = 0.4325)

Class 1 — element plastic ductil; rotație completă posibilă.

Tool information

What this calculator checks

The calculator determines the local buckling resistance of a compressed plate — a flat wall of the section (flange or web) — according to EN 1993-1-5. A thin, compressed wall can buckle locally before the steel reaches yield, and this calculation tells whether and when that happens.

The central quantity is the critical buckling stress \(\sigma_{cr}\):

\(\sigma_{cr} = k_\sigma \cdot \frac{\pi^2 E}{12(1-\nu^2)} \left(\frac{t}{\bar b}\right)^2\)

and the normalised plate slenderness \(\bar\lambda_p = \sqrt{f_y / \sigma_{cr}}\), which decides whether the wall yields or buckles first.

What governs the resistance

If \(\sigma_{cr} \ge f_y\) (small \(\bar\lambda_p\)), the wall yields before it buckles — full behaviour, no reduction.
If \(\sigma_{cr} < f_y\), the wall buckles before yielding, and a reduced effective width is used in design.

The slenderness factor \(\varepsilon = \sqrt{235/f_y}\) ties everything to the steel grade: a stronger steel is, paradoxically, more prone to buckling, because it can reach higher stresses before yielding.

The buckling factor \(k_\sigma\)

\(k_\sigma\) depends on the support of the wall and on the stress distribution across its width:

Internal wall (supported on both edges — the web of an I-profile): uniform compression \(k_\sigma = 4.0\); other distributions (from bending) have values tabulated in EN 1993-1-5 Table 4.1.
Outstand wall (supported on one edge only — the flange of an I-profile): a much smaller \(k_\sigma\), hence less resistant to buckling — Table 4.2.

This distinction also appears in the cross-section classification (EN 1993-1-1 Table 5.2): the \(c/t\) limits differ between internal walls (33/38/42·ε) and outstands (9/10/14·ε) precisely because \(k_\sigma\) differs. The calculator also returns the wall class.

Input data

\(\bar b\) (or \(c\)) and \(t\) — the width and thickness of the flat wall, in mm.
Wall type — internal or outstand; sets the \(k_\sigma\) family.
\(k_\sigma\) — may be left at the default (4.0 for uniform compression on an internal wall) or entered manually for other distributions.
Steel grade — \(f_y\) and, through it, \(\varepsilon\).
\(E\), \(\nu\) — the modulus of elasticity and Poisson's ratio (default 210 000 N/mm² and 0.3).

Assumptions and limitations

A single flat wall is analysed, in isolation, with idealised edge supports. The real interaction between flanges and web (distortional buckling) is not covered.
The plate method applies to hot-rolled and welded profiles. For cold-formed sections, where distortional modes also arise, use cold-formed section stability.
Shear buckling of the web (EN 1993-1-5 §5) is not treated — see shear force.
The effect of longitudinal stiffeners is not treated.

Cross-section class — wall classification by the same \(c/t\) limits
Cold-formed sections — local and distortional buckling by the finite strip method
Shear force — shear buckling of the web
Bending moment — where Class 4 uses the effective modulus