Column buckling under axial+transverse combined load

[Vigardo]

Dear experts,

Do you know the buckling load of a column (one end clamped one end free) under axial compressive and transverse lateral forces (applied combined at top free end)?

Does the lateral load reduce the critical load or just reduces the stiffness of the column?

Would you help me?
-Thanks!

 

[Nidum]

What do you think ?

Try drawing some diagrams and see if you can see intuitively what is likely to happen .

 

[Vigardo]

Thanks for the quick reply!

Intuitively, this problem seems related to the eccentrically loaded column buckling problem. Am I right? I tried to follow Timoshenko´s energy method to determine the buckling load but I failed.
${U_{(\delta )}} = {V_{(\delta )}} \\<br /> \frac{{4{P^2}{\delta ^2}L}}{{15EI}} = F\delta + \frac{{2{\delta ^2}P}}{{3L}}$
Where U is the internal bending energy and V the work done by the axial (P) and transverse (F) forces. I´m not sure about the "F" contribution to energy...

Please, find below the diagram of my problem: