平行弦ラチス構造物の個材の曲げ座屈で定まる座屈荷重に及ぼす境界部材の効果について

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This paper is concerned on the effect of boundary members on the elastic member buckling of parallel chord rigid-jointed trusses and on the required rigidity of boundary members to hold the effective strength of the truss determined by the elastic member buckling. To treat the problem simply and analytically, an approximate method is presented by using a mathematical model where the nodal translation is ignored. The bifurcation buckling from the uniform original shape of pre-buckling state is only treated. Then, the buckling modes are expressed in the form of the linear combination of the homogeneous solutions of difference equation. The types of the solutions are determined from the roots of the characteristic equation in the periodic or decreasing forms depending on the structure and stress state. The main conclusions obtained are as follows. 1) The validity of the presented method is verified by the comparison between the value obtained by this method and that by the exact method for the elastic member buckling bifurcated from the original configuration. 2) Within the presented approximate method, the effect of boundary members on the elastic member buckling of parallel chord rigid-jointed trusses is cleared by the introduction of the concept of critical rigidity of the boundary member. If the rigidity of the boundary member is larger than the value depending on the combination of sectional forces, the elastic member buckling strength in terms of sectional forces of the truss is not smaller than the value of the effective strength. The effective strength is defined as the lowest buckling strength of repetitive modes without macro-deformation, and has the mode of repetition of two structural units. So in this paper, the minimum rate of the rigidity of boundary web members mentioned above to that of non-boundary web members is defined as the critical value. Then, the effect of the boundary member on the elastic member buckling is classified and explained as follows. a) In case the rotational restraint rigidity of boundary joints is not smaller than that of critical value, the value of macroscopical sectional forces at buckling state is not smaller than that of the effective strength. The buckling mode is constituted with repetitive and decreasing type terms of the homogeneous solutions, and is repetitive type in the middle portion of the truss. b) In case the rotational restraint rigidity of boundary joints is smaller than that of critical value, the value of the sectional forces at buckling state is smaller than that of the effective strength. The buckling mode is decreasing from boundary and is constituted with decreasing type terms of the homogeneous solutions. From a view point of material efficiency, it is better for the truss to buckle in repetitive mode all over the whole structure than to buckle in narrow boundary portions at the lower load. In case the boundary portions are stiffened enough, the effective strength for continuum analogy method is applicable to the calculation of the elastic buckling load. In case the strength is determined by elastic buckling at boundary portions, the elastic buckling load can be calculated by the present method.
社団法人日本建築学会の論文
1988-07-30

平行弦ラチス構造物の個材の曲げ座屈で定まる座屈荷重に及ぼす境界部材の効果について

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