地震による各基礎の動きの相違を考慮した細長い平面形を有する建築物の応答に関する基礎的研究

抄録

This paper treats theoretical derivation ofa numerical procedure and its accuracy concerning nonlinear response analysis of buiding subjected to spacially variant ground motion. And furthermore dynamic characteristics of simplified parallel 3-mass system connected by horizontal slab springs that represents the building of long and huge configuration in plan are described. When solving problem concerning response of above building to spatially variant ground motion, it is indispensable to consider not only flexibility of slab but also the effect caused by the time phase delay which occured in the velocity and the displacement of the motion as well as that in the acceleration. However, it is not easy to obtain directly velocity and displacement records. So this method is to calculate response based upon only accelerogram and its numerically integrated velocity. Next step of integration, which gives displacement of the ground motion, is involved in total response calculation. Numerical error in above integration is neglegible when calculating response using time increment less than 0.005 sec. Before proceeding dynamic analysis, difference between original framework and its vibratory model is discussed through comparing the results obtained by 3-D frame analysis to those by simplified method. According to this comparison, the most simplified vibratory model that gives good approximation to 3-D frame analysis is thought to be parallel 3-mass system connected by horizontal slab springs of bending and shearing. Therefore the basic vibratory characteristics of this 3-mass system with uniform mass and stiffness are pursued. Especially to treat above characteristics generally, mathmatical approach is tried concerning the following items ; 1) forming slab matrix [numerical formula] where K_s=(9EI_Y)/(L^3)・(1+Φ_Z)/1・{3/2-(2(1+Φ_z/4))/1}, Φ=12EI_Y/GA_ZL^2, A_Z=A/k., 2) eigen values vectors, 3) participation factors, In this model, fundamental period is equal to 2nd natural period and these two are independent of slab stiffness and shown as follows, ω_1=ω_2 =√<K_F/m> . Here m denotes mass concentrated to each nodal point and K_F denotes stiffness of each frame. According to modal solution concerning this 3-mass system subjected to propagating sinusoidal ground motion and its vibratory chracteristics obtained here, the maximum displacements of the system when the motion resonates with the 1st vibration mode are thoght to be independent of natural period of the system. Using this characteristics, authors describe general tendency of the variation of the maximum displacements against time phase delay which occurs in one end of the structure to the other end. And the results are also compared to those obtained when earthquake ground motion attacks. In this case above values are dependent of the natural period of the system. As conclusion, the following items are presented. 1) A numerical procedure treated here requires time increment less than 0.005 sec when calculating response so that numerical error in integration may be neglegible. 2) The most simplified model that represents building of long and huge configuration in plan with uniform masses and stiffnesses is parallel 3-mass system connected by horizontal slab springs of bending and shearing. 3) In the above model, eigen vectors and participation factors are constant and independent of mass and stiffness. 4) Maximum displacement of 3-mass system subjected to sinusoidal ground motion are independent of natural period of the system and affected remarkably by time phase delay of the motion. At the both side of the structure, the value ranges from 0.36 to 1.18 times, comparing it to the value obtained under the condition of uniform ground shaking. Similarly, at the center of the structure, the values ranges from 0.13 to 1.0 times. Related to the above conclusion, authors describe that higher mode excitation caused by spatially

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