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    Estimation of seismic drift and ductility demands in plane regular X-braced steel frames

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    This paper summarizes the results of an extensive study on the inelastic seismic response of X-braced steel buildings. More than 100 regular multi-storey tension-compression X-braced steel frames are subjected to an ensemble of 30 ordinary (i.e. without near fault effects) ground motions. The records are scaled to different intensities in order to drive the structures to different levels of inelastic deformation. The statistical analysis of the created response databank indicates that the number of stories, period of vibration, brace slenderness ratio and column stiffness strongly influence the amplitude and heightwise distribution of inelastic deformation. Nonlinear regression analysis is employed in order to derive simple formulae which reflect the aforementioned influences and offer a direct estimation of drift and ductility demands. The uncertainty of this estimation due to the record-to-record variability is discussed in detail. More specifically, given the strength (or behaviour) reduction factor, the proposed formulae provide reliable estimates of the maximum roof displacement, the maximum interstorey drift ratio and the maximum cyclic ductility of the diagonals along the height of the structure. The strength reduction factor refers to the point of the first buckling of the diagonals in the building and thus, pushover analysis and estimation of the overstrength factor are not required. This design-oriented feature enables both the rapid seismic assessment of existing structures and the direct deformation-controlled seismic design of new ones. A comparison of the proposed method with the procedures adopted in current seismic design codes reveals the accuracy and efficiency of the former

    Maximum displacement profiles for the performance based seismic design of plane steel moment resisting frames

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    New relations to estimate maximum seismic displacement profiles of plane steel moment resisting frames are proposed. These expressions associate maximum floor displacements with local member deformation seismic demands and are based on statistical analysis of the results of several hundred nonlinear dynamic analyses of steel frames. The influence of specific parameters, such as the number of stories, the number of bays, the joint capacity design factor and the level of inelastic deformation induced by the seismic excitation, is studied in detail. It is concluded that the main structural characteristic that affects the shape of the displacement pattern is the number of stories. Furthermore, the present study reveals that a differentiation between the profile of a frame in the elastic and the inelastic range of response is necessary. A comparison between the proposed displacement patterns and other existing ones is also made to demonstrate the merits of the former

    Behaviour factor for performance-based seismic design of plane steel moment resisting frames

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    Simplified expressions to estimate the behavior factor of plane steel moment resisting frames are proposed, based on statistical analysis of the results of thousands of nonlinear dynamic analyses. The influence on this factor of specific structural parameters, such as the number of stories, the number of bays, and the capacity design factor of a steel frame, is studied in detail. The proposed factor describes the seismic strength requirements in order to restrict maximum storey ductility to a predefined value. Interrelation studies between maximum storey ductility and the Park-Ang damage index are also provided for the damage-based interpretation of the performance levels under consideration. Realistic design examples serve to demonstrate the ability of the proposed factor to convert conventional force-based design to a direct performance-based seismic design procedure

    Drift and ductility estimates in regular steel MRF subjected to ordinary ground motions : a design-oriented approach

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    A simple procedure to estimate drift and ductility demands of regular steel frame buildings subjected to ordinary (i.e., without near fault effects) ground motions is described. Given the strength reduction (or behavior) factor, the procedure provides reliable estimates of the maximum roof displacement, the maximum interstorey drift ratio and the maximum rotation ductility along the height of the structure. The strength reduction factor refers to the point of the development of the first plastic hinge in the building and thus, pushover analysis and estimation of the overstrength factor are not required. This important feature enables both the rapid seismic assessment of existing structures and the direct deformation-controlled seismic design of new ones. The derivation of the proposed relations is based on regression analysis of the results of thousands of nonlinear time history analyses of steel frames. A comparison of the proposed method with the procedures adopted in current seismic design codes reveals the efficiency of the former

    Seismic response of plane steel MRF with setbacks: estimation of inelastic deformation demands

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    An extensive parametric study on the inelastic seismic response of plane steel moment resisting frames (MRF) with setbacks is presented. A family of 120 such frames, designed according to the European seismic and structural codes, are subjected to an ensemble of 30 ordinary (i.e. without near-fault effects) earthquake ground motions scaled to different intensities in order to drive the structures to different limit states. The statistical analysis of the created response databank indicates that the number of stories, beam-to-column strength ratio, geometrical irregularity and limit state under consideration strongly influence the heightwise distribution and amplitude of inelastic deformation demands. Nonlinear regression analysis is employed in order to derive simple formulae which reflect the aforementioned influences and offer, for a given strength reduction (or behaviour) factor, three important response quantities, i.e. the maximum roof displacement, the maximum interstorey drift ratio and the maximum rotation ductility along the height of the structure. A comparison of the proposed method with the procedures adopted in current seismic design codes reveals the accuracy and efficiency of the former

    Extension of the hybrid force/displacement (HFD) seismic design method to 3D steel moment-resisting frame buildings

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    The hybrid force/displacement (HFD) seismic design method for planar steel frames developed by the authors is extended to 3D steel buildings using moment-resisting frames. HFD combines the advantages of both the displacement-based and the force-based seismic design methods and reduces or eliminates their disadvantages. An extensive response databank is developed through nonlinear dynamic analyses on 38 steel space frames designed according to Eurocodes 3 and 8 and subjected to 42 pairs of earthquake ground motions. This response databank is then utilized for the development of empirical formulae providing the behavior factor as a function of the geometrical and dynamic characteristics of the building, including its accidental eccentricity, as well as the target maximum interstorey drift ratio and local ductility. Thus, the proposed seismic design method, eventhough works as a force-based design one, controls structural and non-structural damage through the use of a behavior factor, which is a function of seismic deformation demands. Numerical examples are presented to illustrate the proposed method and demonstrate its merits over the force-based seismic design method of Eurocode 8

    Estimation of seismic inelastic deformation demands in plane steel MRF with vertical mass irregularities

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    An extensive parametric study on the inelastic seismic response of plane steel moment-resisting frames with vertical mass irregularity is presented. A family of 135 such frames, designed according to the European seismic and structural codes, are subjected to an ensemble of 30 ordinarily (i.e., without near-fault effects) earthquake ground motions scaled to different intensities in order to drive the structures to different limit states. The statistical analysis of the created response databank indicates that the number of storeys, beam-to-column strength ratio and the location (top, midheight and bottom) of the heavier mass influence the heightwise distribution and amplitude of inelastic deformation demands, while the response does not seem to be influenced by the mass ratio. Nonlinear regression analysis is employed in order to derive simple formulae which reflect the aforementioned influences and offer, for a given strength reduction (or behavior) factor, three important response quantities, i.e., the maximum roof displacement, the maximum interstorey drift ratio and the maximum rotation ductility along the height of the structure

    Dimensional response analysis of multistorey regular steel MRF subjected to pulselike earthquake ground motions

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    An alternative and efficient procedure to estimate the maximum inelastic roof displacement and the maximum inelastic interstorey drift ratio along the height of regular multi-storey steel MRF subjected to pulse-like ground motions is proposed. The method and the normalized response quantities emerge from formal dimensional analysis which makes use of the distinct time scale and length scale that characterize the most energetic component of the ground shaking. Such time and length scales emerge naturally from the distinguishable pulses which dominate a wide class of strong earthquake records and can be formally extracted with validated mathematical models published in literature. The proposed method is liberated from the maximum displacement of the elastic single-degree-of-freedom structure since the self similar master curve which results from dimensional analysis involves solely the shear strength and yield roof displacement of the inelastic multi-degree-of-freedom system in association with the duration and acceleration amplitude of the dominant pulse. The estimated inelastic response quantities are in superior agreement with the results from nonlinear time history analysis than any inelastic response estimation published previously

    A hybrid force/displacement seismic design method for steel building frames

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    This paper proposes a performance-based seismic design methodology for steel building frames which combines the advantages of the well-known force-based and displacement-based seismic design methods in a hybrid force/displacement design scheme. The proposed method controls structural performance by first transforming user-specified values of the interstorey drift ratio (non-structural damage) and local ductility (structural damage) to a target roof displacement and then, calculating the appropriate strength reduction factor for limiting ductility demands associated with the target roof displacement. The main characteristics of the proposed method are: (1) treats both drift and ductility demands as input variables for the initiation of the design process; (2) does not use a substitute single degree of freedom system; (3) makes use of current seismic code approaches as much as possible (e.g., conventional elastic response spectrum analysis and design); (4) includes the influence of the number of stories; (5) recognises the influence of the type of the lateral load resisting system (moment resisting frame or concentrically braced frame); (6) recognises the influence of geometrical (setbacks) or mass irregularities. A realistic design example serves to demonstrate the advantages of the proposed method over the currently used force-based design procedure
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