Maximum Deflection in Columns: Fixed & Free End

In summary, the column can buckle but remain elastic if the loading and support points are pinned or free.
  • #1
Gurasees
50
1
How can I find maximum deflection in a column with one end fixed and other free?
 
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  • #4
Gurasees said:
But the column is vertical and it has axial load on it.
Isn't that the same thing, just rotated 90 degrees? Can you post a diagram?
 
  • #7
Gurasees said:
How can I find maximum deflection in a column with one end fixed and other free?

Keywords:
deflection,
column,
axial,
loaded

so I looked up "deflection axial loaded column"
and received a bunch of hits to look through.
Perhaps one discussion can be found that is acceptable, as the mathematics is most likely something you are not yet acquainted with. ( Maybe you are. )

Such as,
http://ocw.nthu.edu.tw/ocw/upload/8/258/Chapter_9-98.pdf --> for a cantilever beam
https://ocw.mit.edu/courses/aeronau...ng-2006/materials-structures/gm12_13notes.pdf
http://www.engr.mun.ca/~katna/5931/Buckling2.pdf --> discusses pin-support
( But also a discussion on EXTENSION OF EULER'S FORMULA TO COLUMNS WITH OTHER END CONDITIONS )

You will notice that the equation for bending

d2w/dx2 = M / EI

applies to either transverse or axial loading. ( As far as I remember from beam loading )

Boundary conditions are what makes the difference.
the support and loading points can be either fixed or pinned or free, and that makes a difference on how much load the column can support safely.
 
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  • #8
russ_watters said:
Oh, right - axial. I don't think there is a specific deflection, since the column is either stable - and returns to center - or unstable - and catastrophically fails

Often this is correct, but not in all cases. With the necessary material properties, a column can buckle but remain elastic. This has been studied extensively in the classical literature under the title "theory of the elastica." In such cases, the mode of deformation shifts from axial compression to bending. It can remain stable in bending just as well.. Long ago, I built a spring using columns in the post-buckled state and it worked beautifully.
 
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1. What is maximum deflection in columns?

Maximum deflection in columns refers to the maximum amount of bending or displacement that a column can experience under a given load. It is an important factor to consider in structural design as excessive deflection can lead to structural failure.

2. How is maximum deflection calculated in fixed end columns?

In fixed end columns, maximum deflection is calculated using the Euler's formula: Δ = PL^3/(48EI), where Δ is the deflection, P is the applied load, L is the length of the column, E is the modulus of elasticity, and I is the moment of inertia of the column cross-section.

3. What about maximum deflection in free end columns?

In free end columns, maximum deflection is calculated using the Rankine-Gordon formula: Δ = PL^4/(8EI), where Δ is the deflection, P is the applied load, L is the length of the column, E is the modulus of elasticity, and I is the moment of inertia of the column cross-section.

4. How does the material of the column affect maximum deflection?

The material of the column, specifically its modulus of elasticity, has a significant impact on maximum deflection. A material with a higher modulus of elasticity will have a lower deflection under the same load compared to a material with a lower modulus of elasticity.

5. Can the maximum deflection in columns be reduced?

Yes, maximum deflection in columns can be reduced by increasing the column's cross-sectional area, using a material with a higher modulus of elasticity, or increasing the column's length. Additionally, proper bracing and reinforcement can also help reduce deflection in columns.

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