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Euler Critical Buckling Load

Buckling is a mathematical instability that leads to a failure mode. The critical load is the point when the load on a column forces a bifurcation of the states of equilibrium: a purely compressed state (with no lateral deviation) or a laterally deformed or buckled state.

The critical load equals the product of \[Pi] squared, the Young's modulus and the second moment of area divided by the length of the column squared.

Formula

QuantityVariable[Subscript["F", "cr"], "Force"] == (Pi^2*QuantityVariable["E", "YoungsModulus"]*QuantityVariable["J", "SecondMomentOfArea"])/QuantityVariable["L", "Height"]^2

symbol description physical quantity
Fcr critical load "Force"
E Young's modulus "YoungsModulus"
J second moment of area "SecondMomentOfArea"
L length of column "Height"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Euler Critical Buckling Load"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Euler Critical Buckling Load"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Euler Critical Buckling Load"], {QuantityVariable[ "E","YoungsModulus"] -> Quantity[211, "Gigapascals"]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1757

Publisher Information