تعيين پاسخ لرزه اي سازه ها بر مبناي تحليل طيفي با

Determination of Seismic Response of Structures Using Ellipsoid Envelope

در تحليل و طراحي سازه‌ها براي بارهاي لرزه‌اي بايد تاثير نيروهايي كه همزمان به يك عضو وارد مي‌شوند، در نظر گرفته شود. بهترين نمونه قابل اشاره، اندركنش نيروهاي محوري و لنگرهاي خمشي در ستون‌ها مي باشد. روش تحليل طيفي معمولي مقادير بيشينه هر پاسخ را جداگانه تعيين مي‌كند. ليكن، تركيب بحراني اين پاسخ ها در اغلب موارد شامل اين مقادير بيشينه نيست. در اين پژوهش، به كارگيري روشي براي تعيين پوش بيضوي براي تركيب بحراني دو يا چند پاسخ همزمان در سازه‌هايي با رفتار خطي بر مبناي محاسبات طيفي ارايه مي‌شود. در صورتي‌كه امتداد محورهاي اصلي حركت زمين نسبت به محورهاي سازه مشخص باشد، اين پوش يك بيضي است. براي حالتي كه امتداد محورهاي اصلي حركت زمين مشخص نيست، يك پوش جامع به دست مي‌آيد كه شامل امتدادهاي بحراني محورهاي اصلي است. در نرم افزارهاي تجاري، مانند SAP و ETABS طراحي لرزه‌اي سازه‌ها بر اساس پوش مستطيلي است، كه منجر به طرح محافظه كارانه تر سازه‌ها مي‌شود بنابراين، لزوم به كارگيري پوش بيضوي در نرم افزارهاي تجاري براي طراحي اقتصادي سازه‌ها مي‌تواند مد نظر قرار گيرد.

The response spectrum method is usually utilized to estimate the maximum values of responses for linear structures subjected to seismic loads. In this method, peak responses for each mode are calculated using a set of response spectra corresponding to the characteristics of the ground motion and soil type. Then, the maximum values of each mode are combined in an appropriate method to estimate the peak values of the responses. In practical applications, combination rules are usually SRSS and CQC methods. The conventional response spectrum method is suitable for designing or analyzing of structural elements that are controlled by the maximum value of a single response such as a beam for the maximum bending moment. For members that the simultaneous action of multiple responses must be taken into account (e.g., a column subjected to axial load and bending moments), the critical combination of responses may not coincide with the maximum value of any of the individual responses. For such cases, it is desirable to develop an envelope that bounds the vector of seismic responses in the time domain. For deign purposes, this envelope could be superimposed over the capacity surface of the member that known as the interaction diagram to determine the critical combination of the responses. Nowadays, in most of the commercial analyzing and designing softwares (e.g., SAP and ETABS), response-spectrum-based method with rectangular envelope to estimation of the individual response maxima is utilized. The rectangular envelope is usually conservative for many design situations. In this paper, a response-spectrum-based procedure for predicting the envelope that bounds a vector of seismic responses is implemented. Charles Menon and Der Kiureghian (2000) developed the original formulation of this envelope. As shown by the mentioned researchers, for an assumed orientation of the principal axes along which the ground motion components are uncorrelated, this envelope is an ellipsoid. For the case when the orientation of the principal axes is unknown, a ‘‘supreme’’ envelope is obtained, which corresponds to the most critical orientation of the axes. In this research, the accuracy and applicability of the proposed procedures are evaluated and its influence on the design of structural elements subjected to seismic loads is investigated. The accuracy of the applied envelope is re-examined by comparison of the results of the linear time-history analyses and ellipsoid envelop. For this purpose, a two dimensional finite element computer program in MATLAB environment has been developed for skeleton type and plan strain type structures. In the finite-element model, for skeleton structure two-node frame element with three degree of freedom for each node and for the plane strain case four-node solid element with two degree of freedom in each node has been used. Here, two examples are considered. The first example is the 18-story concrete frame and the second case is the two-dimensional concrete dam. The obtained results for ellipsoid envelope and linear time history analysis are compared for Northridge and Loma perieta records. For the commercial softwares such as SAP and ETABS that are usually utilized in the economic seismic designing of buildings, the implementation of the ellipsoid envelope instead of the rectangular envelope is necessary.