IQ-CAL-PLBREV 2.2NOT A CERTIFICATE

IQEG ENGINEERING REFERENCE LAB · IQ-CAL-PLB · ENGINE 1.0.0 · DATA 1.0.0

Plate and panel buckling.

WORKED EXAMPLE (PDF)

Geometry

The solver stays in millimetres, newtons and MPa. Changing a unit rescales the numbers so the physical plate does not change.

Material

Enter E, ν, fy and fu. No steel-grade table is embedded.

Edges

Rotational stiffness per unit length of an edge set to Elastic rotation. Example: 1e5 N·mm/rad per mm is a stiff restraint; 0 adds no moment. Each node receives kθ times its tributary length. An end node takes half the end element.

Rotational stiffness per unit length of an edge set to Elastic rotation. Example: 1e5 N·mm/rad per mm is a stiff restraint; 0 adds no moment. Each node receives kθ times its tributary length. An end node takes half the end element.

Stress

Positive is compression. y = 0 is the top edge. ψ is calculated and is not edited.

σ1 is the top edge, y = 0. σ2 is the bottom edge, y = b. The figure draws y = 0 at the top. Positive is compression. ψ = σ2/σ1 is calculated and is not edited.

Positive τxy is the value you enter.

Positive τxy is the value you enter. The solver treats it as −txy from a tension-positive shear. With x to the right and y down the web, that positive τ acts +x (to the right) on the top edge and upward, towards y = 0, on the right-hand edge. Reversing the sign does not change a pure-shear τcr. With an off-centre wheel it changes λ by about 15%.

ψ = σ2/σ1 = 1. Read only. y = 0 is the top edge on the figure and in the solver.

Patch load

No patch. The membrane field is the σx, σy and τxy you enter. NOT IMPLEMENTED: eccentric patch, point force, non-uniform patch distribution, GMNIA.

No patch. The membrane field is the σx, σy and τxy you enter. ECCENTRIC PATCH — NOT IMPLEMENTED. POINT FORCE — NOT IMPLEMENTED. NON-UNIFORM PATCH DISTRIBUTION — NOT IMPLEMENTED. GMNIA — NOT IMPLEMENTED.

Stiffeners

No stiffener. The plate is one panel.

x ALONG a · y = 0 AT THE TOP EDGE · y INCREASES DOWN THE WEB · z NORMALGEOMETRYx ALONG a · y = 0 AT THE TOP EDGEy INCREASES DOWN THE WEB · z NORMALGEOMETRYx = 0SSx = aSSy = 0 topSSy = b bottomSSa = 2000 mmb = 1000 mmTHICKNESSt = 10xyzCLICK AN EDGE TO CYCLE ITS RESTRAINTHEAVY ARROW = STRESS · THIN ARROW = DIMENSION · ROLLERS AND HATCHES SIT OUTSIDE THE EDGE

Governing

α = a/b2
CLASSICAL COMPRESSION BUCKLING σcr75.92 MPa
CLASSICAL SHEAR BUCKLING τcr120.33 MPa
Half-waves m × n2 × 1
FEM λ1Not run
FEM σ1 at y = 0—
FEM σy,cr—
FEM τcr—
FEM patch Fcr—
Plate mass157 kg
Stiffener mass0 kg

Classical τcr is the simply-supported plate property. Applied τxy is zero, so that number is not this load case. APPROXIMATE / FIT — not an exact series.

Mesh12 × 12
DOF—
Eigenpair residual—
Solver tolerance1e-8
Iterations—
Element aspect2
Last mesh change—
Mesh statusNOT CHECKED
Solver statusNOT RUN

ANALYTICAL — EXACT FOR IMPLEMENTED IDEALISATION. FEM — NOT RUN. AS 4100 plate check not started. Elastic σcr is not a design resistance. This sheet is not a design certificate.

MESH CONVERGENCE NOT RUN. An FEM result is not verified until the last two meshes agree within 1%.

Combined check

Applied σ1100 MPa
Applied σ2100 MPa
Applied τxy0 MPa
Applied patch F—
Bending σcr75.92 MPa
λσ = σcr/σ10.759
Shear τcr—
λτ = τcr/|τ|—
Patch Fcr—
λF = Fcr/F—
FEM combined λ—
Dunkerley λ (assumption)—

Separate load factors are λσ = σcr/σ1, λτ = τcr/|τxy| and λF = Fcr/F, each with the other actions absent. λFEM is the eigenvalue of the full stress state (every entered direct stress, shear and patch together). It is not an interaction formula. The Dunkerley sum 1/λ = Σ 1/λi is an assumption and is not λFEM.

Calculation record

IQEG · IQ-CAL-PLB REV 2.2 · 2026-11-10 · Printed 2026-11-11

ToolIQ-CAL-PLB REV 2.2 · 2026-11-10
Elastic engineIQ-PLB-E1.0
a2000 mm
b1000 mm
t10 mm
E210000 MPa
ν0.3
fy350 MPa
fu480 MPa
σ1 top edge, y = 0100 MPa
σ2 bottom edge, y = b100 MPa
ψ = σ2/σ11
τxy0 MPa
σy0 MPa
SignPositive is compression
Edgesx=0 ss, x=a ss, y=0 ss, y=b ss
kθ0 N·mm/rad per mm
Patchoff
τxy signPositive τxy enters Kg directly. Patch membrane shear is −txy from the tension-positive plane-stress solve.
Stiffenersnone
Mesh requested12 × 12
Mesh solvednot run
σ2,cr at y = b—
Classical σcr75.92 MPa
Classical τcr120.33 MPa
Classical kσ4
Aspect ratio a/b2
FEM λnot run
FEM patch Fcr—
Patch load pathno patch
λσ0.759
λτ—
λF—
FEM combined λ—
Dunkerley λ (assumption)—
InteractionSeparate load factors are λσ = σcr/σ1, λτ = τcr/|τxy| and λF = Fcr/F, each with the other actions absent. λFEM is the eigenvalue of the full stress state (every entered direct stress, shear and patch together). It is not an interaction formula. The Dunkerley sum 1/λ = Σ 1/λi is an assumption and is not λFEM.
Warningsnone

Mesh

144 elements · 169 nodes · 507 DOF

StepEquationSubstitutionResult
Aspect ratioα = a / ba = 2000 mm, b = 1000 mm2 —
Flexural rigidityD = E t³ / [12 (1 − ν²)]E = 210000 MPa, t = 10 mm, ν = 0.31.923e+7 N·mm
Buckling coefficient kσkσ(m) = (m/α + α/m)², minimum over mα = 2, ψ = 1, m = 2, n = 1. Candidates: m=1 k=6.250; m=2 k=4.000; m=3 k=4.694; m=4 k=6.250; m=5 k=8.410; m=6 k=11.111; m=7 k=14.332; m=8 k=18.0634
Elastic critical direct stressσcr = kσ π² E / [12 (1 − ν²)] (t/b)²kσ = 4, E = 210000 MPa, ν = 0.3, t = 10 mm, b = 1000 mm75.92 MPa
Shear coefficient kτkτ = 5.34 + 4/α²α = 2. Timoshenko fit, not an exact series.6.34
Shear coefficient from a Navier seriesStationary Navier–Galerkin energy for constant τ. Sine terms 1…12 in each direction.α = 2, terms 12×12. Energy upper bound. Orders 12 and 16 differ by less than 0.02% on α = 0.5, 1, 2 and 4. The Timoshenko fit is not this series.6.5464
Elastic critical shear stressτcr = kτ π² E / [12 (1 − ν²)] (t/b)²kτ = 6.34, t = 10 mm, b = 1000 mm120.3333 MPa
How this works
  1. Define the plate or panel above.
  2. Choose the AS 4100 check: plate element or web.
  3. Link or enter the design dimensions. Panel sizes are not copied until you link them.
  4. Enter the design action.
  5. Read the governing result.
  6. Open the full calculation when you need the substitution.

Examples load the AS 4100 design inputs only. The plate model geometry is unchanged.

AS 4100 plate / panel check

Design incomplete. Required before a utilisation can be given:

  • Element slenderness. Plate role is not selected, so b is not taken from the panel model.
  • Axial section capacity. Axial action is not stated. Choose none, compression or tension. A tensile force is not checked as compression.

NOT A COMPLETE PASS — omitted, failed or out-of-scope checks are listed and are not implied to have passed

Elastic σcr is not this resistance. IQ-PLB-AS4100-D1.0.

FEM has not been run. Classical σcr on the sheet above is elastic, not an AS 4100 resistance.

Outside this plate check: Member buckling Nc (6.3).

Not run: Stiffened web combined actions. These do not govern.

Checks not applicable to this configuration: 6
  • Minimum web thickness. The plate is not identified as a web.
  • Web shear. Clause 5.11 is a web shear check. An element that is not a web does not receive it. Elastic τcr is not φVv.
  • Shear and bending. Clause 5.12 is for a web with bending. It is not applied to a plate element.
  • Web bearing. The elastic patch load is not a Clause 5.13 bearing check, and this plate is not identified as a web.
  • Stiffener design. Stiffener clauses 5.14 to 5.16 are web clauses. FEM EI is not an AS 4100 stiffener capacity.
  • Openings. Not a web.
Technical details

Engine v1.0.0. Fastener DB v1.0.0.