Understanding Effective Length in Buckling Equations for Columns

  • Thread starter chetzread
  • Start date
  • Tags
    Buckling
In summary, the conversation discusses the concept of effective length in solid mechanics, particularly in relation to columns. The effective length is the distance between points of zero moment on the deflected shape or between points where the curvature changes. This is dependent on the boundary conditions, and can be simulated by zero moment points. The conversation also touches on how to identify points of zero moment and explains the concept of curvature changing from positive to negative.
  • #1
chetzread
801
1
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]
 
Physics news on Phys.org
  • #2
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.
 
  • Like
Likes chetzread
  • #3
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 ?
 
  • #4
At a pinned joint or at a point of counter flexure where the curvature changes from positive to negative, the moment is zero.
 
  • #5
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
 
  • #6
inflection.jpg
 
  • Like
Likes chetzread
  • #7
point of inflection = point where curve changes from positive to negative, or the rate of change = 0
 
  • Like
Likes chetzread

1. What is effective length in buckling equations for columns?

Effective length in buckling equations for columns is a measure of how easily a column can buckle or fail due to compressive forces. It takes into account the end conditions of the column, such as whether it is fixed or pinned, as well as its physical characteristics.

2. How is effective length calculated for a column?

Effective length is typically calculated using the column's actual length and its end conditions. For example, if a column is fixed at one end and pinned at the other, its effective length would be equal to its actual length. However, if both ends are pinned, the effective length would be twice the actual length.

3. Why is effective length important in column design?

Effective length is important in column design because it affects the column's ability to resist buckling and maintain structural stability. A column with a shorter effective length will have a higher capacity to resist buckling, while a longer effective length will make the column more susceptible to failure.

4. How does the material of the column impact its effective length?

The material of the column can impact its effective length in terms of its stiffness and strength. A stiffer and stronger material will have a shorter effective length, while a more flexible and weaker material will have a longer effective length. This is because the material's properties affect its ability to resist buckling forces.

5. Are there any limitations to the use of effective length in column design?

Yes, there are limitations to the use of effective length in column design. It is important to note that effective length is an approximation and may not accurately reflect the real-world behavior of a column. Additionally, it is typically used for slender columns and may not be suitable for more complex or non-uniform structures.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
3
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
5
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
4
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
2
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
7
Views
9K
  • Engineering and Comp Sci Homework Help
Replies
10
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
1
Views
3K
  • Engineering and Comp Sci Homework Help
2
Replies
47
Views
25K
Back
Top