Drift Concentration Factor Research Articles

Mitigating inter-story drift concentration in seismic-resistant self-centering braced frames by using strong backup systems

Seismic-resistant self-centering concentrically braced frames (SC-CBFs) are susceptible to the concentration of inter-story drifts during earthquakes owing to the relatively low energy dissipation ability of braces. To address this limitation, this study proposed a novel solution by designing a strong backup (SB) system to mitigate inter-story deformation concentration in “weak” stories. The proposed SB system consisting of truss members can be attached to the existing SC-CBF through pin connections, forming a system, termed strong backup SC-CBF (SC-CBF-SB), to promote a more uniform distribution of inter-story drifts along the height of the frame and mitigate the weak story behavior. A six-story chevron-braced frame is adopted to investigate the seismic performance of SC-CBF and SC-CBF-SB. Finite element models of SC-CBF and SC-CBF-SB are built. The mechanical characteristics and dynamic responses of the SC-CBF-SB are examined. To comprehensively evaluate the performance of both SC-CBF and SC-CBF-SB, static pushover analyses and nonlinear time-history analyses are conducted. Additionally, incremental dynamic analysis (IDA) is performed to evaluate the responses (particularly drift concentration) of both frame types subjected to increasing seismic intensity levels. Numerical results show that the maximum value of the drift concentration factor (DCF) is around 1.3 and 1.8 for SC-CBF-SB and SC-CBF, respectively, indicating that SC-CBF-SB can effectively mitigate inter-story drift concentration of SC-CBF. Meanwhile, the proposed SB system has a minimal negative impact on the favorable SC ability of the frame.

Theoretical model to predict the seismic drift concentration effect for self-centering-braced frame

This study is motivated to predict such drift concentration effects for SCB frames with the perfect flag-shape hysteretic behavior. Nonlinear time history analyses are conducted to compare and elucidate different deformation mechanisms between BRB and SCB frames. An elastic-plastic static model is established to predict the static drift concentration factor (DCFS) for the SCB frame under static lateral loads, where influential parameters include the column-to-frame stiffness ratios, α, and the SCB's post-yielding stiffness ratio, βk,2. To capture the dynamic loading effect, a regressive formula is further developed as the dynamic amplification factor by normalizing the dynamic drift concentration factor (DCFD) with the DCFS under static loads. The results show that unlike BRB frames with drift concentrated in the bottom story, SCB frames often feature peak story drifts in the top story. As opposed to BRB frames, the equivalent lateral loads do not feature an inverted triangle distribution but a parabolic distribution along the building height. The drift concentration effect for the SCB frame is reliably predicted by multiplying static DCFS with the corresponding closed-form formula for the dynamic amplification factor. The predicted DCFD is also utilized to identify a design range of βk,2 (i.e., 0.2–0.4) to effectively control the peak story drift and drift concentration for SCB frames.

Post-earthquake functionality assessment of MRFs enhanced by resiliently lateral-resistant and bottom systems

The accumulated stiffness and strength degeneration of rigid bottom joints and uneven lateral deformation mode of the moment-resisting frame (MRF) during earthquakes can result in disastrous structural failures. Damage accumulation, excessive residual inter-story drift, and the lack of self-centering behavior and energy-dissipation capacity in structures are major challenges in controlling losses after earthquakes. This paper aims to propose a self-centering energy-dissipation (SCED) system that enhances the seismic performance of MRFs. This system, called the resilience-enhanced MRF (ReMRF), utilizes a rocking truss as a lateral-resistant structure and incorporates two bottom joints with SCED capabilities into the MRF design. These bottom joints, referred to as the Buckling Restraint Steel Plate (BRSP) bottom joint and the Light Self-Centering (LSC) bottom joint, are composed of key components such as BRSPs and post-tensioned (PT) strands, respectively. Structural design methods and parameters for the rocking truss and bottom joints are discussed to determine optimal values for balancing stiffness demand, SCED capacity, and construction convenience. Special attention is paid to the working stability of the bottom joints during earthquakes and the effectiveness of the SCED system. Results indicate that the performance of the bottom joints and the SCED system is in line with expectations. The findings from both pushover and time history analyses have substantiated that ReMRF outperforms MRF in terms of achieving higher seismic performance objectives. It is intuitively demonstrated by several quantitative metrics derived from static and dynamic analyses, including the overstrength factor, ductility factor, drift concentration factor, peak inter-story drift, and residual inter-story drift.

Improved seismic resilience of existing steel moment frame by built-in continuous columns

A seismic resilience strategy of retrofitting the existing columns of frame structures into built-in continuous columns (BCCs) hinged to the main frame is presented in this paper. The continuous columns provide vertical continuous stiffness to adjust the structural deformation distribution achieving collapse control. This study retrofits three 5-, 7- and 9-story prototype steel moment frames (SMFs) through external continuous columns (ECCs) or BCCs. In addition, effects of strength and stiffness deterioration on the seismic response of the SMFs are also considered. Results from pushover and incremental dynamic analysis show that the ECCs and BCCs can both mitigate structural displacement concentration. With a performance target of plasticity hinge ratio up to 50% for the main frame, when the stiffness demand is satisfied, the inter-story drift concentration factor of the BCC frame is always smaller than that of the ECC one. It indicates that the inter-story deformation distribution of the BCC frame is more uniform under the premise of satisfying the target collapse resistance performance.

Performance-based seismic design method for retrofitting steel moment-resisting frames with self-centering energy-absorbing dual rocking core system

This research intends to propose an upgraded strategy for steel moment-resisting frames (SMRFs) by implementing Self-Centering Energy-absorbing Dual Rocking Core (SEDRC) systems to achieve enhanced seismic performance, improved seismic resilience, and avoid inter-story drift concentration. A performance-based method is developed to design the SEDRC system for upgrading the existing SMRF. The maximum inter-story drift and drift concentration factor are adopted as the design performance objectives. Two prototype SMRFs with three and nine stories are introduced to validate the proposed performance-based design procedure. Nonlinear static analyses were first performed for the original SMRFs and the updated ones (denoted as SEDRC-MRFs) to investigate the efficiency of the proposed retrofit strategy. The pushover curves of the analytical structures confirm that the SEDRC systems can increase the stiffness and strength of SMRFs, and SEDRC-MRFs upgraded through the proposed design procedure show no strength deterioration before the fracture of the brace in the SEDRC system. A set of 18 ground motions were chosen to study the seismic performance of the designed SEDRC-MRFs. The analysis results indicate that SEDRC-MRFs can obtain the desired performance objectives. The SEDRC system could reduce the maximum and residual inter-story drifts of SMRFs and promote uniform inter-story drift distribution. Moreover, the designed SEDRC-MRFs can be used immediately without the need for repairing structural members after the design basis earthquakes and can be repaired economically after the maximum considered earthquakes.

Seismic performance assessment of steel frame structures equipped with buckling-restrained slotted steel plate shear walls

The near-fault ground motion records may impose high seismic energy input to the building structures. The steel plate shear walls (SPSW) are one of the robust and efficient lateral-force resisting and energy-dissipating components and SPSWs are increasingly equipped in steel moment frame to form a dual structural system. A modified type of buckling-restrained SPSW with inclined slots has been proposed and applied in the steel frame. This paper presents the seismic performance of steel frame-SPSW system subjected to near-fault ground motions. Four multi-story (5-, 10-, 15- and 20-story) steel frame-SPSW structures were selected and designed. The accuracy of the SPSW models' predictions was assessed using previous experimental results. Nonlinear time-history analysis assuming two groups of 15 near-fault ground motions and 15 far-fault ground motions was used to predict the structures' interstory drift ratios, floor accelerations, residual interstory drift ratios and drift concentration factor. Incremental dynamic analysis was used to predict collapse probabilities using the same groups of ground motions. The analytical results can provide significant insights to the seismic behavior of steel frame-SPSW structures when subjected to near-fault ground motions.

Parametric study of rocking cores-moment frames with supplemental viscous damping and self-centering devices using a distributed parameter model

A distributed parameter model is proposed for the rocking cores-moment frames (RCMFs) with supplemental viscous damping and self-centering devices. In this model, the moment frame and rocking cores are simplified as a shear beam and a flexural beam, respectively, while viscous damping and self-centering devices are substituted by rotational constraint with linear viscous damping and elastic stiffness. Three nondimensional parameters, frame-core stiffness parameter, base-rotation fixity parameter and damping parameter, are introduced to describe the dynamic behavior of the full physical structural system. Closed-form solutions for complex modal shapes are derived, and then parametric study is conducted to explore the effects of these three parameters on modal damping ratios, eigenvalues, complex modal shapes, and drift concentration factor. Explicit expressions of modal damping ratios with these three parameters are established through curve-fitting technique that can be conveniently used for engineering practice. Frequency responses of base shear forces and moments are obtained using the distributed transfer function method. It is concluded that the modal damping ratios are significantly affected by these three parameters, and their peak values will be remarkably reduced as the increasing of the frame-core stiffness and base-rotation fixity. For design purpose, appropriate ranges of these three parameters are recommended to achieve better drift uniformity control, response reduction, and higher modes effect mitigation. The proposed model and conclusions of the parametric study can be used as a tool for rapidly evaluating seismic performance in a preliminary design phase of the RCMFs.

Dynamic behavior of upgraded rocking wall-moment frames using an extended coupled-two-beam model

Rocking wall-moment frames (RWMFs), which perform well in controlling the soft-story mechanism, can achieve an enhanced performance by substituting their pinned base by a variable base rotational constraint provided by replaceable self-centering and energy dissipation devices. Rather than experiencing damage inside the moment frames, those upgraded RWMFs show a high potential towards seismic resilience by transferring damage to the replaceable base rotational constraint. The effect of this rotational constraint and the stiffness ratio between the moment frame and rocking wall on the dynamic behavior of upgraded RWMFs is investigated with the aid of an extended coupled-two-beam model proposed in this paper. In this model, the rocking wall and moment frame are represented by a linked flexural beam and a shear beam, respectively. The model replaces the fixed base of the flexural beam by a rotational spring to take the variable base rotational constraint into account. Closed-form solutions for modal displacement shapes, modal drifts, modal shear force and modal moment are derived. The model is verified with finite element analysis, and modal contributions to seismic response and drift concentration factor demand under earthquakes are investigated. It is found that within identified ranges of the rotational constraint and the stiffness ratio between the moment frame and rocking wall, a relatively good uniformity of story drift distribution is obtained and the higher modes effect caused by the full releasing of the rocking wall is mitigated. The model, the derived interstory drift spectra and drift concentration factor spectra can serve as useful tools for preliminary resilience oriented design purpose.

Elastic displacement spectrum-based design of damage-controlling BRBFs with rocking walls

This paper investigates the seismic design and performance of buckling-restrained braced frames with rocking walls (BRBF-RWs) for the purpose of using rocking walls (RWs) to mitigate the drift concentration issue of buckling-restrained braced frames (BRBFs). Formulas for calculating the elastic structural lateral displacement and RW internal force under typical lateral loads are derived and validated; then, the stiffness and strength demand of the RW are approximately determined based on the elastic formulas when the BRBF-RW enters the inelastic stage. Combined with the proposed inelastic demand, an elastic displacement spectrum-based design procedure is presented, which can directly determine the sectional area of the buckling-restrained braces (BRBs) and the required stiffness and strength of the RW. A 6-story steel BRBF-RW is designed using the proposed procedure as an example, and a series of nonlinear pushover analyses (NPAs) and nonlinear response history analyses (NRHAs) are performed to validate the design. The example shows that the designed target displacement and the NRHA result are close and that the deviations between the drift concentration factor, RW maximum moment and shear force obtained using formulas and using NPAs and NRHAs are small. Lastly, a brief comparative analysis is performed to illustrate the enhanced seismic performance of the designed BRBF-RW via NPAs and NRHAs.

Research on residual drift response of steel frames under strong earthquakes

Steel frames designed to the current codes will undergo an unrecoverable plastic deformation under strong earthquakes. The structures subjected to excessive deformations after earthquakes cannot be desirably repaired to their serviceable state, and can only be demolished, which brings about a serious direct and indirect economic loss. Thus, it is of great significance to predict the residual drift for the performance evaluation and control of structures after earthquakes. In order to investigate the residual drift response of steel frames under strong earthquakes, steel frames between 2 and 10 stories in height are designed according to Code for seismic design of buildings (GB50011-2010) and Code for design of steel structures (GB50017-2003) in this study. The designed structures are investigated numerically by pushover analysis and elasto-plastic time history analysis. Furthermore, the peak drifts, residual drifts and drift concentration factors are reasonably obtained under the action of moderate earthquakes and major earthquakes. The results indicate that the scatter in the residual drift results is a bit large. On the basis of analysis results, the calculation formulae are proposed to estimate the residual drifts of steel frames as a function of the expected peak drift, the initial recoverable elastic drift, and the drift concentration factor of steel frames.

Modeling on collapse behaviour of high-rise concrete-filled steel composite frames under over-design seismic excitations

This paper presents a numerical study on seismic collapse capacity of high-rise concrete-filled steel tubular moment resisting frames (CFT-MRFs) under extreme ground motions that are beyond the design levels. The ground motions characterised as flat velocity spectral shape were selected to neglect record-to-record uncertainty induced by the changing of the natural periods of structures. A simple numerical approach was developed using fibre element with stiffness and strength degradation accounted in stress–strain models. Then, incremental dynamic analyses with various parameters were performed to evaluate the P-Delta and degradation effects on local and global collapse mechanisms. Results have shown that a drift concentration at the lower stories triggered the side-sway collapse mode that was dominated by the post-buckling strength degradation of CFT columns. The height of drift concentration indicates the range where the collapse mechanism was formed, and a drift concentration factor was proposed to estimate the extent of drift concentration. Last, a factor indicating the safety margin under collapse was computed based on the probability of earthquake occurrence.

Drift Concentration of a Three-Story Special Concentrically Braced Frame with Strongback under Earthquake Loading

In conventional special concentrically braced frame (SCBF) structures, the buckling of the braces leads to severe reduction in system strength and stiffness. Therefore soft story mechanisms followed by large permanent deformation are commonly observed in SCBF structures. The strongback system using additional structural components along the height of the building to resist local deformation is able to improve the distribution of the drift. This research conducted case studies to investigate the effects of strength and stiffness of the strongback system on the behavior of typical three-story SCBF system. The primary variables to be investigated are stiffness factor α (strongback stiffness/SCBF stiffness) and strength factor β (strongback strength/SCBF strength). We conducted nonlinear dynamic analyses to evaluate the effectiveness of α and β on structural demand parameters including maximum drift ratio and drift concentration factor (DCF). Analyses results show that although strongback system with excessively high α and β will reduce maximum drift ratio and DCF of SCBF systems, it is noneconomic. On the other hand, strongback systems with low α and β (α<0.0048 and β<0.054) have only little effects on improving structural behavior. The case studies suggested that 0.0096≤α≤0.0168 and 0.081≤β≤0.134 accounting for both efficiency and economics can be used in the design of the selected SCBF systems.

A distributed parameter model of a frame pin‐supported wall structure

SummaryMany reinforced‐concrete frames collapse via a soft‐story mechanism during severe earthquakes. Such collapses are mainly attributed to concentrated deformation in a soft story. Deformation control is thus important in preventing collapse. The frame pin‐supported wall structure is a type of rocking structure that releases constraints at the bottom of the wall. Previous research has obtained good results for the deformation control of this type of structure. However, the interior forces and strength demands of the pin‐supported wall have not been systematically explored. In this paper, a distributed parameter model is developed to investigate the strength demand of the wall in a frame pin‐supported wall structure. In the model, the pin‐supported wall is simplified as a bending beam and the frame is simplified as a shear beam. The two beams are joined by distributed shear connectors, so that the shear force can be transferred at any location on the interface. The model can be solved using differential equations based on equilibrium and compatibility. The accuracy of the model is verified using SAP2000 (Computers and Structures Inc., Berkeley, CA, USA). Displacement distribution of the structure and distributions of the moment and shear force within the pin‐supported wall are obtained for two typical external force profiles. It is found that the pin‐supported wall can effectively reduce the drift concentration factor. Distributions of the displacement, moment, and shear force are closely correlated with the relative stiffness of the wall and frame. Finally, recommendations on the stiffness and strength of a pin‐supported wall are made. Copyright © 2015 John Wiley & Sons, Ltd.

STORY DRIFT CONCENTRATION AND HYSTERESIS ENERGY FOR TWO STORY BRACED FRAME WITH BUCKLING BRACES SUBJECTED TO STRONG MOTION

In our previous researches, it is shown that story drift concentration is restrained by columns in two braced frames with buckling-restrained braces. For the two story braced frames with buckled braces, it is possible for the column to distribute the shear force on each story over height and the story drift concentration may be restrained, if it keeps elastic. In this paper, the equations of the drift concentration factor for two story braced frames with buckled braces have been developed from the equilibrium conditions of the frames subjected to lateral force. This paper clarifies the mechanism of the two story braced frames and the relationship between the drift concentration factor and the ratio of column flexural stiffness. Finally, the drift concentration with seismic response analysis is estimated with the equation for static drift concentration.

Residual Drift Response of SMRFs and BRB Frames in Steel Buildings Designed according to ASCE 7-05

A recent study has shown that residual drifts after earthquakes that are greater than 0.5% in buildings may represent a complete loss of the structure from an economic perspective. To study the comparative residual drift response of special moment-resisting frames (SMRFs) and buckling-restrained braced (BRB) frames, buildings between 2 and 12 stories in height are designed according to ASCE 7-05 and investigated numerically. This investigation includes pushover analyses as well as two-dimensional nonlinear time-history analyses for two ground motion hazard levels. The two systems show similar peak drifts and drift concentration factors. The BRB frames experience larger residual drifts than the SMRFs; however, the scatter in the residual drift results is large. Expressions are proposed to estimate the residual drifts of these systems as a function of the expected peak drifts, the initial recoverable elastic drift, and the drift concentration factor of each system. When subjected to a second identical earthquake, both framing systems experienced larger-than-expected drifts when an initial drift greater than 0.5% was present.

Erratum: CONTINUOUS COLUMN EFFECTS OF GRAVITY COLUMNS IN U.S. STEEL MOMENT-RESISTING FRAME STRUCTURES [Journal of Structural and Construction Engineering (Transactions of AIJ) Vol. 75 (2010) , No. 650 pp.761-770

Typical steel moment-frame structures in the United States comprise a few seismic frames and many gravity frames, which include “continuous columns” that are pin-connected to beams. These continuous columns, which are often ignored in seismic design, can improve the seismic performance of the structure. This study investigates the effects of continuous columns on the structural stability and seismic response of building frames. Stability coefficients representing the separate and combined effects of geometric and material nonlinearities are used with a simplified modeling technique, which separates the shear-type and flexural-type lateral-force-resisting systems in moment frames. Relationships between continuous column stiffness ratio and the stability coefficients, inter-story drift, and the drift concentration factor are presented. It is shown that for realistic structures, the columns in the seismic frames are generally sufficient to prevent unstable response and large drift concentrations, and the inclusion of gravity continuous column stiffness tends to decrease both the drift concentration and inter-story drift.

CONTINUOUS COLUMN EFFECTS OF GRAVITY COLUMNS IN U.S. STEEL MOMENT-RESISTING FRAME STRUCTURES

Typical steel moment-frame structures in the United States comprise a few seismic frames and many gravity frames, which include “continuous columns” that are pin-connected to beams. These continuous columns, which are often ignored in seismic design, can improve the seismic performance of the structure. This study investigates the effects of continuous columns on the structural stability and seismic response of building frames. Stability coefficients representing the separate and combined effects of geometric and material nonlinearities are used with a simplified modeling technique, which separates the shear-type and flexural-type lateral-force-resisting systems in moment frames. Relationships between continuous column stiffness ratio and the stability coefficients, inter-story drift, and the drift concentration factor are presented. It is shown that for realistic structures, the columns in the seismic frames are generally sufficient to prevent unstable response and large drift concentrations, and the inclusion of gravity continuous column stiffness tends to decrease both the drift concentration and inter-story drift.

Prediction of seismic drifts in multi-storey frames with a new storey capacity factor

Standard procedures exist for the estimation of the total (or roof) displacement of a structure for seismic design, based on the response spectra of single-degree-of-freedom systems. However, for a more realistic prediction of the seismic demands, especially in the context of the performance based design, an appropriate estimation of the storey drift distribution is necessary. A few general approaches are available in the literature, and these often require certain structural modeling analysis. The present paper aims to provide a simple alternative method for the prediction of the storey drift distribution and the critical drift concentration in a RC frame. A new storey capacity factor is introduced, to represent the combined effect of the storey strength and stiffness on the distribution of storey drift along the frame height, while the storey strength and stiffness are evaluated, taking into account different possible plastic mechanisms. The structural regularity is subsequently evaluated based on the storey capacity factor. Nonlinear pushover and dynamic response history analyses are performed on several representative multi-storey frames, to verify the correlation between the storey capacity factor profile and the distribution of the actual storey drifts. Results indicate that the inverse of the storey capacity factor correlates well with the storey drift distributions. An empirical relationship between the critical drift concentration factor and the overall regularity index is derived based on the dynamic analysis results.

EFFECT OF ROTATIONAL SPRING OF ELASTIC CANTILEIVER COLUMN ON MECHANISM OF DAMAGE CONTROL FOR TWO STORY BRACED FRAME WITH RESTRAINT BRACES

In our previous paper, it is shown that story drift concentration is restraint by columns of two braced frames with pinned and fixed column bases. But embedded column bases are nearly fixed and exposed column bases are nearly pinned in the real structures. These column bases is designed as rotational springs. In this paper, the equations of the drift concentration factor for two story braced frames with columns base of rotational springs have been developed from the equilibrium conditions of the frames subjected to lateral force. This paper clarifies the relationship between drift concentration and ratio of column flexural stiffness and column rotational stiffness.