Understanding Effective Length in Buckling Equations for Columns

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Discussion Overview

The discussion revolves around the concept of effective length in buckling equations for columns, particularly focusing on its definition and the implications of boundary conditions on this measurement. Participants explore the relationship between actual length and effective length, as well as the significance of points of zero moment in the deflected shape of a column.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • Some participants inquire about the meaning of effective length and how it differs from actual length, particularly in the context of fixed, unfixed, or supported ends.
  • One participant explains that effective length is defined as the distance between points of zero moment on the deflected shape or points where curvature changes, emphasizing that this depends on boundary conditions.
  • Another participant seeks clarification on why certain points on a diagram have zero moment and how to determine this.
  • Some participants assert that at a pinned joint or point of counter flexure, the moment is zero, linking this to changes in curvature.
  • There is a discussion about the definition of a point of inflection, described as the point where the curve changes from positive to negative curvature or where the rate of change is zero.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the definitions and implications of effective length and points of zero moment. There is no consensus on the clarity of these concepts, and some questions remain unresolved.

Contextual Notes

Participants reference boundary conditions and the shape of the deflected curve, but there are limitations in the discussion regarding the specific mathematical relationships and assumptions underlying these concepts.

chetzread
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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]
 
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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.
 
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PhanthomJay said:
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.

oP0iDq6.jpg

taking the figure above as example , why the circled part has zero moment ? how to knw that it has 0 moment ?
 
At a pinned joint or at a point of counter flexure where the curvature changes from positive to negative, the moment is zero.
 
PhanthomJay said:
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
 
inflection.jpg
 
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point of inflection = point where curve changes from positive to negative, or the rate of change = 0
 
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