#round 3 "Plate Buckling Analysis 'This calculator determines the elastic critical buckling stress of a flat rectangular plate under uniform compression. "References 'Ref 1: Timoshenko, S.P. and Gere, J.M., 1961, Theory of Elastic Stability, 2nd Edition, McGraw-Hill "Inputs '

Plate Geometry

' Plate width (perpendicular to load) -'b = ? {300}mm ' Plate thickness -'t = ? {6}mm ' Plate length (parallel to load) -'a = ? {600}mm '

Material Properties

' Youngs modulus -'E = ? {200000}MPa ' Poissons ratio -'ν = ? {0.3} ' Yield strength -'f_y = ? {250}MPa '

Buckling Coefficient

' Buckling coefficient -'k = ? {4} '

Common values of k:

k = 4.0 — All edges simply supported
k = 6.97 — Loaded edges simply supported, unloaded edges clamped
k = 0.425 — One unloaded edge free, other three simply supported
k = 1.277 — One unloaded edge free, loaded edges clamped

Applied Loading

' Applied compressive stress -'σ_applied = ? {100}MPa "Calculations '

'Click to expand/collapse detailed calculations '

Aspect Ratio

α = a/b ' Aspect ratio -'α '

[Ref 1, Ch. 9]

Plate Flexural Rigidity

D = E*t^3/(12*(1 - ν^2)) ' Plate flexural rigidity -'D|N*mm '

[Ref 1, Eq. 9.1]

Elastic Critical Buckling Stress

σ_cr = k*π^2*E*(t/b)^2/(12*(1 - ν^2))|MPa ' Elastic critical buckling stress -'σ_cr '

[Ref 1, Eq. 9.2]

Governing Capacity

#if σ_cr ≤ f_y σ_gov = σ_cr 'Elastic buckling governs - plate is slender #else σ_gov = f_y 'Yielding governs - plate is stocky #end if ' Governing stress capacity -'σ_gov|MPa '

Utilization

util = σ_applied/σ_gov ' Utilization ratio -'util '

"Results 'Aspect Ratio (a/b): α 'Plate Flexural Rigidity: D|N*mm 'Elastic Critical Buckling Stress: σ_cr|MPa 'Yield Strength: f_y 'Governing Stress Capacity: σ_gov|MPa 'Applied Compressive Stress: σ_applied 'Utilization: util '

Assessment

#if util ≤ 1 '

PASS - Plate Buckling Check

Utilization = 'util' is less than or equal to 1.0

Applied stress of 'σ_applied' is within the governing capacity of 'σ_gov'

#else '

FAIL - Plate Buckling Check

Utilization = 'util' is greater than 1.0

Applied stress of 'σ_applied' exceeds the governing capacity of 'σ_gov'

Increase plate thickness, reduce plate width, or reduce applied stress.

#end if "Conclusion 'The plate with width 'b', thickness 't', and length 'a' has an aspect ratio of 'α'. Using a buckling coefficient k = 'k', the elastic critical buckling stress is 'σ_cr'. The governing stress capacity is 'σ_gov' giving a utilization of 'util'.

Plate Buckling Analysis

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