Buckling and column effective length question

[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?

 

[SteamKing]

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.

 

[fuofa]

Thank you!