Abstract
The instability of von Mises truss and shallow sinusoidal arch is investigated either in symmetric or asymmetric buckling forms. The constitutive equation of the material is assumed to be the general linear hereditary integral equation or the power series presentation of hereditary integrals in which the first considered equation forms the term of the first order. In the linear material equation case the limit load value for asymptotically constant, stable state of equilibrium is analytically established and the relationship between load and critical time is numerically established. In the case of non-linear material equation, only numerical treatment of the problem is outlined and demonstrated by an example.
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