Understanding Effective Length in Buckling Equations for Columns

[chetzread]

1. The problem
http://www.efunda.com/formulae/solid_mechanics/columns/columns.cfm

what is the meaning of effective length here?

Homework Equations

The Attempt at a Solution

When the ends is fixed or unfixed , or supported , the length remain L , am i right ? what's the difference between actual length and effective length ? [/B]

 

[PhanthomJay]

The effective length is the length between points of zero moment on the deflected shape or between points where the curvature changes (reverses) . That depends on the boundary conditions. You should google on another site which more clearly shows the shape of the curve for various boundary conditions and those distances between the zero moment points or extended curve zero moment points. The zero moment points simulate a pinned connection at those points.

 

[chetzread]

The effective length is the length between points of zero moment on the deflected shape or between points where the curvature changes (reverses) . That depends on the boundary conditions. You should google on another site which more clearly shows the shape of the curve for various boundary conditions and those distances between the zero moment points or extended curve zero moment points. The zero moment points simulate a pinned connection at those points.

taking the figure above as example , why the circled part has zero moment ? how to knw that it has 0 moment ?

 

[PhanthomJay]

At a pinned joint or at a point of counter flexure where the curvature changes from positive to negative, the moment is zero.

 

[chetzread]

At a pinned joint or at a point of counter flexure where the curvature changes from positive to negative, the moment is zero.

what do you mean by curvature changes from positive to negative ? i don't understand it

 

[Nidum]

 

[rob grunwald]

point of inflection = point where curve changes from positive to negative, or the rate of change = 0