توزيع احتمالاتي تغييرمكان نسبي دو سيستم يكدرجه آزاد مجاور هم

Probability distribution of relative displacement of two adjacent single degree of freedom systems

بررسي احتمال برخورد سازه‌هاي مجاور تحت اثر زلزله، اساس تدوين ضوابط آيين نامه‌اي براي تعيين كمينه ابعاد درز انقطاع است. در پژوهش‌هاي پيشين از قانون تركيب تفاضلي دوگانه براي تعيين اين فاصله استفاده شده است و تنها تفاوت بين روش‌ها در تعيين ضريب وابستگي پاسخ لرزه‌اي دو سيستم مجاور هم است. اين ضريب كه وابسته به پريود و ميرايي دو سيستم است، با فرض رفتار خطي سازه‌ها به دست آمده است، و در محدوده غيرخطي، با معادل سازي رفتار سازه با حالت خطي و معرفي مقدار پريود و ميرايي موثر به دست آمده است. مقادير پريود و ميرايي موثر وابسته به مقدار نياز شكل پذيري سيستم و تنها براي يك مدل رفتاري مشخص حاصل شده است. در اين پژوهش يك الگوريتم جامع براي تعيين ضريب وابستگي بين دو سيستم با استفاده از تيوري ارتعاشات تصادفي براي سيستم با مدل رفتاري بوك- ون با رفتار هاي هيسترزيس مختلف، ارايه شده است. علاوه بر اين، روش پيشنهادي براي انواع تحريك ورودي با چگالي طيفي‌هاي مشخص قابل كاربرد است و جامعيت بيشتري نسبت به روابط قبلي دارد. نياز شكل پذيري سيستم متناظر با چگالي طيفي ورودي با استفاده از روابط ارتعاشات تصادفي تعيين و توزيع احتمالاتي تغييرمكان نسبي بين دو سيستم حاصل از روابط ارايه شده با روابط موجود مقايسه مي‌شود. براي صحت سنجي روابط ارايه شده، از آناليز مونت كارلو براي دو سيستم غيرخطي مجاور، تحت ركوردهايي كه براي يك چگالي طيفي به صورت ايستا و غيرايستا شبيه‌سازي شده اند، استفاده شده است.

Seismic pounding between adjacent buildings is an undesirable phenomenon. Depending on the characteristics of the colliding buildings, pounding might cause severe structural damage in some cases, and even collapse is possible in some extreme situations. In order to mitigate the risk of seismic pounding between new buildings, current seismic design codes prescribe a minimum separation distance between adjacent structures. The value of the minimum separation distance is assumed equal to the peak relative displacement computed at the most likely pounding location and corresponding to a site-specific seismic intensity. Examining the collision possibility of adjacent structures as a result of earthquake is the basis of formulating regulations for determining minimum dimensions of separation distances. This distance can be calculated in different ways. In previous studies, double difference combination has been generally used to determine this distance and their only difference is in determining correlation coefficient of seismic response in two adjacent systems. This coefficient which depends on period and damping of the two systems has been obtained in previous works with the assumption of a linear behavior of structures. In the nonlinear range, the same correlation coefficient obtained from the linear mode is used by making structure behavior equivalent to linear mode and introducing values of effective damping and period. Modified values of period and damping depend on the requirement of system ductility under the applied record, which has been obtained for a specific behavioral model and from numerous numerical studies. In this study, the correlation coefficient of the two systems was presented using random vibration equations for the systems by Bouc - Wen different hysteresis behavior model. Moreover, the proposed relation could be applied for different input stimulation with specific spectral density and is more comprehensive than previous relations. Ductility demand of the system corresponding to the input spectral density was determined by random vibration relations and the probability distribution of relative displacement between the two systems which was obtained from the presented relations was compared with the existing ones. This study evaluates the accuracy of two different criteria to calculate the separation necessary to prevent seismic pounding between nonlinear hysteretic structural systems. All of the criteria considered in this paper make use of the same basic equation of the Double Difference Combination rule, but they adopt different procedures to estimate the correlation between displacement responses of nonlinear hysteretic systems. Monte Carlo analysis used to verify the Probability distribution of relative displacement of two adjacent single degree of freedom systems relations presented for two adjacent nonlinear systems under the applied record which were simulated by a specified spectral density in stationary and non-stationary forms. Results obtained through Monte Carlo simulations indicate that the relation presented in this study is completely satisfactory and none of the two criteria evaluated in this study is exact.