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I was trying to calculate the horizontal deflection of the free end of vertical clamped beam. The beam would be loaded at the free end with a horizontal force [itex]H[/itex] and a vertical force [itex]P[/itex]. My idea was to calculate an initial deflection due to the force [itex]H[/itex]. Then calculate the additional deflection due to the previous deflection and the force [itex]P[/itex]. I'd expect that when the force [itex]P[/itex] is bigger than the Euler buckling load that the deflection would diverge but that's not happening when I try to calculate this.

I tried it on a beam with a length [itex]L[/itex] of 6 m, stiffness [itex]EI = 1476600 Nm^2[/itex] ([itex]E=69 GPa[/itex], [itex]I=2140 *10^4 mm^4[/itex], [itex]H=1 kN[/itex]. I calculated that the Euler buckling load [itex]P_{cr}=(Pi)^2EI/(2L)^2=101,20 kN[/itex] and used a way bigger [itex]P=5000 kN[/itex].

For the initial deflection I used [itex]v_0=(1/3EI)HL^3=4,87607 *10^{-5} m[/itex]. For the next iteration steps I used [itex]v_i=v_0 + (1/3EI)L^2P*v_{i-1}[/itex] which eventually converges to [itex]v=5,08259 * 10^{-5} m[/itex] instead of diverging.

I know 5000 kN isn't a realistic value and that the beam would probably yield with such a high load but shouldn't this diverge?

Also for loads smaller than the Euler buckling load, is this the right way to calculate the deflection? If not what would be a good way then?

Thanks in advance