Issue 40

N. G. Pnevmatikos et alii, Frattura ed Integrità Strutturale, 40 (2017) 129-136; DOI: 10.3221/IGF-ESIS.40.11 131 Finalized design accepted Control system installation Calculation of Elastic and Design forces No Yes Redesign of structure Estimate α>(1/q) Reduced elastic spectrum by α Elastic spectrum New design spectrum a Design initially, accepted Time history control analysis of structure, with saturation and time delay Response satisfies the elastic criteria? No Yes Design of structure, according to Eurocodes Elastic spectrum Design spectrum 1/q Is the difference of elastic to design forces lower than the device capacity? Redesign of structure with higher α Initially, the controlled structure is designed based on a design spectrum provided by the pertinent code (Eurocodes) with a specific level of ductility. The required control forces that will take a portion of earthquake forces are calculated as the difference from forces obtained from the elastic spectrum to those obtained from the design spectrum. The maximum value of capacity of the control devices is compared with the required control force. If the capacity of the control devices is larger than the required control force then the control devices are accepted and installed into the structure. If the capacity is smaller than the required control force then a control device with larger capacity should be chosen or more devices per floor should be installed In case the maximum available control device capacity is smaller than the required control force, or, there is a limitation to the number of control devices, then using an iterative procedure, a scale factor, α, higher than the value 1/q that reduces the elastic response spectrum is calculated. The structure is redesigned based on the new reduced spectrum by scale factor, a, and then the devices are installed into the structure. The flow chart of the procedure is shown in Fig. 2 with a solid line. Figure 2 : The flow chart of the proposed design procedure. Estimation of scale factor, a. From the elastic seismic forces and the maximum capacity of the control device a scale factor α is obtained and applied on the elastic spectrum. Knowing the mass and initial stiffness of the structure the eigenmodes Φ i , eigenperiods T i or eigenfrequencies f i and the corresponding damping ratios ξ i of the uncontrolled system are obtained. The participation factor ψ i , and elastic seismic forces F q,el,i for the i th eigenmode are given as: T i i T i i ψ = , i=1,...,n Φ ME Φ MΦ (1) , , , ( , ), 1,..., q el i i i e i i i S T i n     F MΦ (2) where E is the direction matrix for the earthquake and S e,i (T i , ξ i ) is the elastic spectral acceleration. The maximum elastic seismic forces F q,e for each degree of freedom are obtained combining the Square Root of Sum Squares method (SRSS) the elastic seismic forces from each eigenmode, thus: