Theoretical and Experimental Analysis of Buckling of Eccentrically Loaded Rods

Poznato je da se ravni vitki konstrukcijski elementi pri određenoj tlačnoj uzdužnoj sili počinju izvijati. Ta sila se naziva Eulerova kritična sila izvijanja. Dostizanjem te sile element gubi stabilnost, što znači da, osim ako se tlačno osno opterećenje ne ukloni, nepovratno gubi svoj početni ravni položaj i poprima savinuti oblik. Ukoliko je element opterećen ekscentričnom tlačnom silom (čije je hvatište izvan težišta poprečnog presjeka), takva sila dodatno uzrokuje momente savijanja pa izvijanje nastaje prije postizanja Eulerove kritične sile. U ovom radu su izvedeni teorijski izrazi za Eulerovu kritičnu silu štapa zglobno oslonjenog na oba kraja te izrazi za progib, maksimalni moment savijanja i maksimalno naprezanje kada je takav štap opterećen ekscentričnom tlačnom silom. Zatim je laboratorijskim ispitivanjima provjerena njihova točnost. Zaključeno je da teorijski model zadovoljavajuće predviđa ponašanje tlačno opterećenih štapova, ali se u stvarnosti, zbog različitih nesavršenosti, štapovi se pri istoj sili deformiraju više, a Eulerova kritična sila se nikada ne dosegne.It is well known that slender structural elements buckle at a certain compressive axial force. This force is called Euler's critical buckling force. When this force is reached, the element loses its stability, which means that, unless the compressive axial load is removed, it irreversibly loses its initial straight configuration and becomes bent. If an element is loaded by an eccentric compressive force (whose point of application is outside the centroid of the cross section), such a force additionally creates bending moments so that buckling takes place before reaching the Euler’s critical force. In this work theoretical expressions for Euler’s critical force have been derived for a rod with pinned supports at both ends, as well as expressions for the deflections, maximal bending moment and maximum stress in the case where such a rod is loaded by an eccentric compressive force. Subsequently, the accuracy of those expressions has been assessed. It was concluded that the theoretical model’s prediction of the behaviour of the compressive rods is satisfactory, but in reality, due to different imperfections, at the same force, rods deform more and the Euler’s critical load is never reached