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
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0368393100099442/resource/name/S0368393100099442_equ01.gif?pub-status=live)
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).