eulerian critical load

[reye]

Good evening to all, I have a little doubt about an exercise concerning the critical load of eulero. In the attached case, my prof wrote in lesson that the spring recall force is k*l*senx, with x angle between rod and vertical. on the text there is also the coefficient 1/2. Can you enlighten me? Thank you.

 

[luigi.paiano]

the spring reacts to the shift in vertical direction equal to lsinx (look triangle). factor 1/2 is inserted if you want to consider half structure I suppose