抄録
This paper focuses on the elasto-plastic behavior on static responses and dynamic responses for plane lattice structures, which are considered as a beam type structure. The purpose is to make clear the relationship between seismic responses and static responses such as load displacement relationships, and to estimate allowable seismic levels with the information of static elasto-plastic behaviors. Two portal frames and column or beam models are treated, as shown in Fig. 1. The energy equilibrium is expressed as Eqn. 2 in static elasto-plastic behaviors. The right term EF is equal to the energy done by load and may be defined as a static absorbed energy of structures. In this paper, each energy is expressed as an equivalent velocity as Eqn. 3. The maximum value of EF may be an allowable amount of input energy, for instances, by seismic loads. The relationships between each energy and displacements are shown in Fig. 5. The equivalent velocity of EF is expressed as a dash and dotted line. The response curves are almost equal although the loading shapes are different as shown in Fig. 3. The fact may show that the differences between static uniform load and quasi-static seismic load do not affect the energy responses, and that the estimation with input energy may not be affected by the shape of loading.
Secondly, the elasto-plastic behavior on dynamic responses is investigated under seismic loads. The relationships between maximum input acceleration and strain energy of each model are shown in Figs. 11, 16 and 21. The curves of 3 parameters are drawn in each figure. The effect of static safety coefficients v is made clear with the curves, to confirm the effect of vertical oscillations is larger than that of horizontal oscillations. In the three figures, the each curve shows the relationship of bi-linear type. In the range after yielding, the maximum input energies at the limit state are compared as shown in Figs. 22 - 24, which show the ratio of dynamic responses against static ones. The static safety coefficient v is smaller, and then the increasing ratio of dynamic responses is larger than static ones.
In order to estimate allowable maximum input accelerations, the comparisons between elasto-plastic behavior of dynamic responses as Fig. 25 and that of static response as Fig. 26 are shown in Fig. 27. The dynamic elasto-plastic property q represents the decreasing properties of plastic range against elastic range in the relationships between maximum earthquake input acceleration and input strain energy. The static elasto-plastic property j represents the relationship of two slopes in the static elasto-plastic behavior. The dynamic property q is smaller than the static property j under vertical oscillations and is almost equal to each other under horizontal oscillations. The preceding considerations are carried out under additional seismic waves of Table 6 and the additional models10). The obtained results are shown in Fig. 28. The results show the same tendency at each seismic loads. The dash and dotted line in Fig. 28 could be presented to estimate the allowable maximum earthquake input acceleration.
The conclusions are follows in the present study.
(1) The relationships between the static absorbed energy and displacements are not affected by the loading shape. It may be able to estimate the response of structures with an index of potential energy.
(2) The fact is confirmed that the allowable maximum earthquake input accelerations are affected with the self-weight under vertical oscillations more than horizontal oscillations.
(3) In comparing the dynamic property q and the static property j, the dash and dotted line in Fig. 28 could be presented to estimate the allowable maximum earthquake acceleration with the static elasto-plastic behaviors for beam type structures.
