Euler Buckling

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1. The problem statement, all variables and given/known data

I want to find the euler buckling for a open I beam( middle section like a box) that is subjected to three point bending with a point load on top.
I am not so interest in a solution but explanation on how this could be worked out using the euler equation for buckling.



2. Relevant equations
Pcr=(PI^2)EI/L im pretty sure this is for a column with pinned ends but don't know how to work out one for an i beam in 3 point bending


3. The attempt at a solution
Don't want a solution can put numbers in myself
 

PhanthomJay

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1. The problem statement, all variables and given/known data

I want to find the euler buckling for a open I beam( middle section like a box) that is subjected to three point bending with a point load on top.
I am not so interest in a solution but explanation on how this could be worked out using the euler equation for buckling.



2. Relevant equations
Pcr=(PI^2)EI/L im pretty sure this is for a column with pinned ends but don't know how to work out one for an i beam in 3 point bending


3. The attempt at a solution
Don't want a solution can put numbers in myself
If you are talking about an I beam subject to both bending stresses and axial compressive stresses, then the beam-column design would be governed by the applicable Steel Code. Now mind you I haven't kept up with the latest Code revisions, but generally speaking, especially when the actual axial stress is small compared to the allowable axial stress, stresses would have to satisfy the following formula:
[tex]f_a/F_a + f_b/F_b <= 1.0[/tex] , where
[tex]f_a[/tex] = actual design axial compressive stress
[tex]F_a[/tex] = Allowable axial compressive stress as if there were no bending (this is generally the Euler buckling stress pi^2EI/KL^2(A) for K=1, with appropriate safety factors)
[tex]f_b[/tex] = actual design compressive bending stress
[tex]F_b[/tex] = Allowable compressive bending stress as if there were no axial load (this allowable stress must take into account lateral torsional buckling of the flange due to the compressive bending stresses, with appropriate safety factors).
 

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