The dynamical behaviour of a strut in a truss framework

Abstract

The relation between axial load and axial deformation for a strut generally involves an increase of deformation w ith decreasing load after the m aximum load is reached. Assuming a relation of this form, and assuming also that the tension members obey H ooke’s law, the behaviour of a particular redundant pin-jointed truss which contains a single compression member and is subjected to dead load is examined in detail. It is shown that when the applied load is such that the load in the strut has reached its m aximum value, equilibrium m ay be lost temporarily, and the structure then undergoes what is termed a dynamic jump to a new position of equilibrium. The phenomenon of the dynamic jump is first examined by postulating a rigid-plastic m odel for the strut, which is supposed to consist of two straight halves w ith a small initial eccentricity at the centre. The rigid-plastic model is chosen for analysis because the equations of m otion then take on a reasonably simple form, and the eccentricity m ust be assumed, as an initially straight rigid-plastic strut would have an infinite buckling load. The value of the resulting analysis is that it reveals m ost of the significant features of the dynamical behaviour. In particular, it is shown that the dynamic jump is governed by interchanges between the strain energy stored in the tension members, the work absorbed at the plastic hinge in the strut and the kinetic and potential energies of the applied load. The kinetic energy of m otion of the members of the structure is shown to be negligible, from which it is concluded that in a practical structure the amount of energy involved in both transverse and longitudinal vibrations of the members would also be negligible. The results of the rigid-plastic analysis suggest an energy m ethod for analysing the magnitude of the deformations involved in dynamic jumps in practical cases. This m ethod requires a knowledge of the relationship between axial load and axial deformation for the strut, which can be determined experim entally under quasi-static conditions. It appears that in practice the duration of the dynamic jump will be of the order of m agnitude of 0*1 s, and that the jump will be followed by oscillations which will eventually be damped out primarily by the action of the joints and supports. The amplitude of the oscillations will be fairly small as compared w ith the magnitude of the dynamic jump.