How Does IPE500's Bending Resistance Influence IPE400's Buckling Coefficient?

[Dell]

in a question i have been asked to assess a steel structure made of two IPE beams given the attached schematic

my question is regarding the buckling of the IPE400, to find the coefficient "K" i have used the julian-lawrence nomogram.

as far as buckling about the Z axis goes, the picture is very clear to me, i need to use the sums of the inertia/length of the beams and collumns (using their weak inertia in this case), and need to divide the IPE400 into 2 separate components

my problem comes when i am asked to address the buckling about the "X" axis, ie perpendicular tho the pages plane. initially i thought i could do the same as in the previous case, using the other inertia (about the cross sections strong axis). then after some thought i realized that the case os not that simple since it is not their bending that resists buckling here but rather their torsion. i then thought that since the torsion has a minimum resitance (I beams) i can not take their effect into account and consider the column a cantilever with a length of 10m.
BUT i now think that since the IPE500 is lying with their STRONG direction resists their bending about the y axis, which resists movement of the IPE400, this must have some effect on the IPE400's buckling,. af far as i can see the IPE500 acts as a support preventing movement of the IPE400 in the y direction since they resist their own bending. so i think i need to somehow consider this and like before divide the IPE400 into 2 sections and calculate for each seperately.


how do i take this effect into consideration when calculating the coefficient of buckling "K",
do i need to take this effect into consideration is this really a 10m cantilever?

 

[LightHero]

In order to assess the buckling of the IPE400, it is necessary to consider both the bending and torsional resistance of the beam. First, you should calculate the bending resistance by dividing the IPE400 into two sections and calculating the coefficient of buckling "K" for each section using the Julian-Lawrence nomogram. Then, you should take into account the torsional resistance of the IPE400 by considering the effect of the IPE500 on the IPE400's ability to resist buckling. In particular, you should consider the IPE500's resistance to its own bending, which will prevent movement of the IPE400 in the y direction. This should be taken into account when calculating the coefficient of buckling "K" for the IPE400.