# Buckling and column effective length question

• fuofa
In summary, to determine the minimum length at which buckling is likely to occur for a fixed column with outer diameter of 100mm and inner diameter of 60mm, the equations used are K = 0.5 sqrt (R^2 + r^2), ESR = sqrt pi^2 E/ yield stress, and ESR = Le/k, where R is the outer radius, r is the inner radius, E is the Young's modulus, and the yield stress is 180MNm^-2. After solving for K and ESR, the minimum length is found to be 6.84m.
fuofa

## Homework Statement

If I have a column, fixed at both ends, i am aiming to work out the minimum length where buckling is likely to occur.
I know this is a similar question to that asked before, however please bear with me.
Column outer diameter 100mm, inner diameter 60mm
Youngs modulus E=250GNm^-2
Yield stress = 180MNm^-2

## Homework Equations

1. K = 0.5 sqrt (R^2 + r^2)
2. ESR = sqrt pi^2 E/ yield stress
3. ESR = Le/k

## The Attempt at a Solution

To find K using the above equation I have taken the radius 0.5 x sqrt (0.05^2 + 0.03^2) = 0.0292
Then to find the ESR I have sqrt(pi^2 x 250000000000 / 180000000) = 117.080
Changing the third equation from above for Le I have ESR x K = Le (117.080 x 0.0292) = 3.419m
Given that the column is fixed at both ends I have multiplied this by 2 and reach the minimum length of the column at which buckling is likely to occur to be 6.84 m - is that correct please?

fuofa said:

## Homework Statement

If I have a column, fixed at both ends, i am aiming to work out the minimum length where buckling is likely to occur.
I know this is a similar question to that asked before, however please bear with me.
Column outer diameter 100mm, inner diameter 60mm
Youngs modulus E=250GNm^-2
Yield stress = 180MNm^-2

## Homework Equations

1. K = 0.5 sqrt (R^2 + r^2)
2. ESR = sqrt pi^2 E/ yield stress
3. ESR = Le/k

## The Attempt at a Solution

To find K using the above equation I have taken the radius 0.5 x sqrt (0.05^2 + 0.03^2) = 0.0292
Then to find the ESR I have sqrt(pi^2 x 250000000000 / 180000000) = 117.080
Changing the third equation from above for Le I have ESR x K = Le (117.080 x 0.0292) = 3.419m
Given that the column is fixed at both ends I have multiplied this by 2 and reach the minimum length of the column at which buckling is likely to occur to be 6.84 m - is that correct please?

Yes, this looks correct.

Thank you!

## 1. What is meant by buckling in structural engineering?

Buckling is a phenomenon in which a structural member, such as a column or beam, experiences a sudden failure due to compressive forces exceeding its critical load capacity. It typically occurs when the member is long and slender, and the compressive force causes it to buckle or bend instead of remaining straight.

## 2. How is buckling different from other forms of failure?

Unlike other forms of failure, such as yielding or fracture, buckling does not involve the material itself reaching its ultimate strength. Instead, it is a result of the structural member's geometry and the applied load causing instability and loss of stiffness.

## 3. What is the effective length of a column and why is it important?

The effective length of a column is the distance between its fixed or restrained ends. It is an important parameter in buckling analysis because it affects the critical load and failure mode of the column. A shorter effective length results in a higher critical load and a more stable column, while a longer effective length leads to a lower critical load and a more prone to buckling column.

## 4. How is effective length determined for a column?

The effective length of a column depends on its end conditions, such as whether it is fixed, pinned, or free to rotate. It can be determined through theoretical calculations or experimental testing. In general, fixed or restrained ends result in a shorter effective length, while pinned or free ends result in a longer effective length.

## 5. How can the critical load and failure mode of a column be predicted?

The critical load and failure mode of a column can be predicted through buckling analysis, which involves determining the appropriate effective length and applying mathematical equations to calculate the column's critical load. Additionally, physical testing and simulations can also be used to predict the behavior of a column and its potential failure mode.

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