Buckling and stability

 and from diagram we can say that total rotation is 2θ then the restoring moment 

iii) Taking Moment equilibrium at point B

From above equation we will get one trivial solution  and second solution gives us the critical load

At the critical value of the load the structure is in equilibrium regardless of the magnitude of the angle 

If  the structure is stable

If  the structure is unstable                                                       

If  the structure is neutral equilibrium