In cases of tapered struts with hinged or built-in ends where the exact determination of the buckling load is complicated it may be useful to apply a method of successive approximations.

Let us first consider a bar of the length l with hinged ends under the action of the compressive force P. The differential equation of the bending line becomes

where v is the deflection at the section u, v with the moment of inertia I (u) and E is Young's modulus. At the ends of the bar the deflection v is equal to zero (Fig. I).