Calculating Euler Buckling of Open I Beam in 3 Point Bending

[THE 1]

Homework Statement

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.

Homework Equations

Pcr=(PI^2)EI/L I am 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

The Attempt at a Solution

Don't want a solution can put numbers in myself

 

[PhanthomJay]

Homework Statement

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.

Homework Equations

Pcr=(PI^2)EI/L I am 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

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:
$$f_a/F_a + f_b/F_b <= 1.0$$ , where
$$f_a$$ = actual design axial compressive stress
$$F_a$$ = 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)
$$f_b$$ = actual design compressive bending stress
$$F_b$$ = 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).

 

[Mene]

Hello,

Calculating the Euler buckling of an open I beam in 3 point bending involves using the Euler equation for buckling, which is Pcr = (PI^2)EI/L, where Pcr is the critical buckling load, E is the elastic modulus of the material, I is the moment of inertia of the beam's cross-section, and L is the length of the beam.

To apply this equation to an open I beam in 3 point bending, you would need to determine the effective length of the beam, which takes into account the support conditions and the loading configuration. This effective length can be calculated using various methods, such as the effective length factor or the effective length ratio, depending on the specific beam and loading conditions.

Once the effective length is determined, you can plug in the appropriate values into the Euler equation to calculate the critical buckling load for your open I beam. This will give you an indication of the maximum load that the beam can withstand before buckling occurs.

I hope this explanation helps in understanding how to work out the Euler buckling for an open I beam in 3 point bending. Remember, it is important to properly consider the support conditions and loading configuration in order to accurately determine the effective length of the beam. Let me know if you have any further questions.