任意方向地震動を受ける直線推動型HPラチスシェルの下部構造との固有周期比および質量比を考慮した応答評価

<p> A hyperbolic paraboloidal (HP) shell with straight edge lines is generated by translating a straight line with varying the tilt of line. On the dynamic response behavior of the HP shells, there are few studies about the steel structure differently from the RC structure. In this paper, the effects of natural period ratios, mass ratios and input directions on the natural vibration characteristics and the seismic response behavior of HP lattice shells are made clear by the Complete Quadratic Combination (CQC) method. In addition, the evaluation methods for maximum seismic response accelerations of HP lattice shells taking natural period ratio, mass ratio and input direction into consideration are proposed. Furthermore, improvement of versatility of the response evaluation method is attempted by proposing the natural period estimation formula for HP lattice shells based on that for lattice shells on the previous study.</p><p> It is concluded as follows, from the above results.</p><p> 1) When the depth span ratio d/L_x of shell roof exceeds 1/20 (the magnification of out of plane stiffness of roof=50 times), the effective mass ratio of antisymmetric one wave (O1) mode becomes the maximum in the vibration modes of model with only a roof structure. In the vibration modes of the model with a supporting substructure, higher-order modes appear when the natural period ratio R_T is less than about 0.2. However, as R_T becomes more than 0.2, the modes which O1 mode and the sway mode of supporting substructures are combined (O1±) appear. The sum of effective mass ratios of those modes becomes more than 94%. Even when the mass ratio R_M changes, O1± modes appear in the top 2 modes.</p><p> 2) In the distributions of maximum response accelerations magnification factor of the model with only a roof structure, the distribution shapes are influenced by O1 mode. The distribution shapes are influenced by O1± modes also in the model with a supporting substructure, when R_T is less than about 5.0. While as R_T is 5.0 or more, the response accelerations are uniform in horizontal direction and do not occur in vertical direction. The maximum vertical response accelerations increase in the near of R_T=1.0. In addition, those increase following an increase of R_M.</p><p> 3) The maximum response accelerations on roof structure of HP lattice shell with supporting substructure can be evaluated regardless of d/L_x by the response evaluation formulae considering the amplification factors expressed as a function of R_T calculated by the natural period of O1 mode and that of equivalent single mass system.</p><p> 4) The maximum response accelerations subjected to earthquake motions with arbitrary direction can be evaluated by the square root of sum of squares for the response accelerations by the response evaluation formulae in the arch and suspension directions multiplied by cos²φ and sin²φ, respectively.</p><p> 5) The response displacements and member stresses under the static seismic loads by response evaluation formulae considering R_T, R_M and input direction agree with those calculated by CQC method though the errors at some nodes and members are up to about 60%.</p><p> 6) The natural periods can be calculated by the proposed natural period estimation formula for HP lattice shell with straight edge lines. By using the obtained natural period, the response values can be evaluated without executing the eigenvalue analyses.</p>