Dynamic Eccentricities in Pushover Analysis of Asymmetric Single-Storey Buildings

Abstract

Α new version about a method of documented application of pushover analysis on asymmetric single-storey buildings has been presented, recently. The main target of this new method was to rationally consider the coupling between torsional (about vertical axis) and translational vibrations of asymmetric singlestorey building diaphragm under translational seismic excitation of its base. For this reason, the equivalent lateral static floor force according to the new method is applied using suitable dynamic eccentricities, eccentric to building Mass Centre, which are added with the accidental eccentricities, in such a way that the final design eccentricities move the application point of floor, external, lateral, static force away from the diaphragm Mass Centre. The origin point for measuring the dynamic eccentricities is called "Capable Near Collapse Centre of Stiffness ". Also, the floor lateral static force must be oriented along the building principal axes which are called "Capable Near Collapse Principal Axes" and , respectively. The appropriate dynamic eccentricities for the stiff-side and the flexible-one of the floor plan derive from extensive parametric analysis and are calculated by graphs and suitable equations. In the present work, a numerical example of an asymmetric single-storey building is presented to illustrate clearly and in detail the step by step application of the proposed pushover analysis method. It is a torsional sensitive reinforced concrete building designed in accordance with Eurocodes EN 1992-1 and 1998-1 for ductility class high (DCH). The proposed method is evaluated relative to the results of non-linear response history analysis (ΤΗ). The final results show that the proposed method of pushover analysis predicts with safety the displacement of the stiff side of the building as well as that of the flexible side.

Seismic Assessment of Asymmetric Single-storey R/C Buildings by Two New Methodologies: Enforced Displacement-Based and Forced-Based Pushover Procedures

“…Then, the following have been calculated: (a) the in-plan location of the "Capable Near Collapse Centre of Stiffness" CR sec , (b) the orientation of the horizontal "Capable Near Collapse Principal Axes" sec and sec , (c) the "Capable Near Collapse Torsional Radii" Ι,sec and ΙI,sec relative to the horizontal axes sec and sec as well as the radius of gyration m of the diaphragm, and (d) the torsional sensitivity of the model according to the relationship Ι,sec or ΙI,sec ≤ 1.10 m . Finally, using the previous data, the inelastic dynamic eccentricities plus the accidental ones, namely the inelastic design eccentricities of the Forced-Based pushover procedure, have been calculated from Equations (1-4) and (5)(6)(7)(8), respectively. Also, the floor enforced displacements of the Displacement-Based procedure are determined using Figures 1 and 3.…”

“…First, by applying the floor lateral static force on the location of the Centre of Mass (CM) that is shifted by the accidental eccentricity, the phenomenon of the development of floor-diaphragm torsional vibration about vertical axis coupled to translational ones cannot be rationally considered. With other words, this phenomenon, occurring both in linear and in non-linear areas, is seriously underestimated, especially in torsionally-flexible buildings, because of the inability to obtain the actual inertial torsional moment of the floordiaphragm [3][4][5][6][7][8][9][10]. Second, EN 1998-1 does not provide any detailed information about the building principal axes and refers to the international literature (although it is emphasized at various points that the lateral loads should be applied along the principal axes of the building) and thus it is unclear which is the appropriate orientation of the lateral static forces in the framework of pushover analysis.…”

“…The seismic resultant force from the composition of these forces/moment always passes eccentric to CM, at a distance which is called as the dynamic eccentricity. According to the proposed Forced-Based procedure, both in recent work [3][4][5][6][7] and the current one, where a numerical example is presented, the abovementioned dynamic eccentricity is treated in a direct way, as in other proposed methods [8][9][10]. Both proposed pushovers are applied with reference to the "Capable Near Collapse Principal system CR sec ( sec , sec , sec )", which is an ideal 3D inelastic principal system at the NC state, where its origin coincides with the inelastic centre of stiffness CR sec and the two orthogonal horizontal axes coincide with the inelastic principal axes sec and sec of the single-storey building, where all its structural members have been provided with their secant stiffness sec at yield.…”

Αντισεισμική Μη-Γραμμική Στατική Ανάλυση Ασύμμετρων Κτιρίων Οπλισμένου Σκυροδέματος Στη Μέγιστη Δυνατή Κατάσταση Επικείμενης Κατάρρευσης Με Χρήση Καταναγκασμένων Μετακινήσεων Ορόφων Ή Ανελαστικών Δυναμικών Εκκεντροτήτων

“…2.18 και 2. 19). Αυτό έχει ως συνέπεια η σχέση δύναμης-μετακίνησης του MDoF συστήματος (διάγραμμα V-Dn) να ισχύει επίσης και για το ισοδύναμο SDoF σύστημα (διάγραμμα F * -D * ), αφού πρώτα και η δύναμη και η μετακίνηση διαιρεθούν με το Γ. H απεικόνιση της τελευταίας σχέσης μπορεί να επιτευχθεί αλλάζοντας την κλίμακα και στους δύο άξονες του διαγράμματος δύναμης-μετακίνησης.…”

“…Η προτεινόμενη διαδικασία αναπτύσσεται αρχικά για τα μονώροφα ασύμμετρα κτίρια ο/σ και κατόπιν επεκτείνεται στα πολυώροφα ασύμμετρα κτίρια ο/σ. Στοιχεία της προτεινόμενης διαδικασίας έχουν ήδη προδημοσιευτεί στις εργασίες Bakalis & Makarios [2017, 2019 Όσον αφορά το τέταρτο ερώτημα, ο ΕΝ 1998-1 στην παράγραφο 4.3.3.5 γενικά επιβάλλει την θεώρηση της χωρικής δράσης των δύο οριζόντιων συνιστωσών της σεισμικής δράσης και προτείνει αυτή να λαμβάνεται με επαλληλίες, εντός της μη-γραμμικής περιοχής, δια μέσω συνδυασμών SRSS (τετραγωνική ρίζα του αθροίσματος των τετραγώνων) ή γραμμικών συνδυασμών των μεγεθών έντασης/παραμόρφωσης που προκύπτουν από τις χωριστές σε κάθε εξεταζόμενη διεύθυνση μη-γραμμικές στατικές αναλύσεις. Εδώ το πρόβλημα εντοπίζεται στο γεγονός ότι γενικά οι επαλληλίες απαγορεύονται αυστηρά στη μη-γραμμική περιοχή συμπεριφοράς.…”