Conservative systems showing instability in tension

Within the framework of a second-order theory, the stability of a straight beam, hinged at one end and supported at an intermediate point, is studied. Two different tensile loading conditions are applied to the beam, causing bifurcation and instability. A new analogy is shown between one of these stability problems and the elastic circular arch problem on spring soil with negative stiffness. The relationship between the results presented here and those presented in Gajewski and Palej (1974), in Zaccaria et al. (2011), and in Feriani and Carini (2017) is shown.