Theory of plastic mechanism control for MRF–CBF dual systems and its validation

In this paper the theory of plastic mechanism control is presented for moment resisting frame–concentrically braced frames dual systems, i.e. for structural systems combined by moment resisting frames and concentrically braced frames. It is aimed at the design of structures failing in global mode, i.e. whose collapse mechanism is characterised by the yielding of all the tensile diagonals and the occurrence of buckling in the compressed ones, and by plastic hinge formation at all the beam ends and at the base of first storey columns. The proposed methodology is based on the application of the kinematic theorem of plastic collapse, by imposing that the global mechanism equilibrium curve has to lie below all the other equilibrium curves corresponding to undesired mechanisms. The practical application of the design methodology is illustrated by means of a worked example. In addition, the results of a non-linear static pushover and dynamic analyses of the designed structure are also discussed in order to demonstrate the effectiveness of the proposed design procedure.     

Seismic design of space steel frames using advanced methods of analysis

A rational and efficient seismic design methodology for regular space steel frames using an advanced time domain finite element method of analysis that takes into account geometrical and material nonlinearities is presented. Seismic loads are applied in the form of Eurocode 8 spectrum compatible real accelerograms along the two horizontal directions of the frame. The iterative design procedure starts with assumed member sections, continues with the response checks for the damage, ultimate and service limit states and ends with the adjustment of member sizes so as all the response checks to be satisfied for all limit states. Thus, the proposed design method deals with nonlinearities and member interactions at the global level and consequently separate member capacity checks through the interaction equations of Eurocode 3 or the usage of the conservative and crude q-factor of Eurocode 8 are not required. Two numerical examples dealing with the design of (a) a space three storey steel frame with one bay in both horizontal directions and (b) a space seven storey steel frame with two and three bays along its two horizontal directions are presented to illustrate the method and demonstrate its advantages.     

Seismic evaluation of an existing complex RC building

The seismic evaluation of existing buildings is a more difficult task than the seismic design of new buildings. Non-linear methods are needed if realistic results are to be obtained. However, the application to real complex structures of various evaluation procedures, which have usually been tested on highly idealized structural models, is by no means straightforward. In the paper, a practice-oriented procedure for the seismic evaluation of building structures, based on the N2 method, is presented, together with the application of this method to an existing multi-storey reinforced concrete building. This building, which is asymmetric in plan and irregular in elevation, consists of structural walls and frames. It was designed in 1962 for gravity loads and a minimum horizontal loading (2% of the total weight). The main results presented in terms of the global and local seismic demands are compared with the results of non-linear dynamic response-history analyses. As expected, the structure would fail if subjected to the design seismic action according to Eurocode 8. The shear capacity of the structural walls is the most critical. If the shear capacity of these elements was adequate, the structure would be able to survive the design ground motion according to Eurocode 8, in spite of the very low level of design horizontal forces. The applied approach proved to be a feasible tool for the seismic evaluation of complex structures. However, due to the large randomness and uncertainty which are involved in the determination of both the seismic demand and the seismic capacity, only rough estimates of the seismic behaviour of such structures can be obtained.     

Higher-mode force response in multi-story strongback-braced frames

Strongback-braced frames employ an essentially elastic steel truss, or strongback, that distributes demands more uniformly to delay or prevent story mechanisms. Because inertial forces are no longer limited by the formation of a story mechanism, strongback-braced frames can exhibit large elastic force demands, particularly in the higher modes. This paper characterizes the higher-mode force response of strongback-braced frames. Four-story archetypes were designed using nonlinear dynamic analyses to incorporate higher-mode force demands into the design process. The response of the archetypes was compared with that of reference buckling-restrained braced frames that were allowed to form story mechanisms. The force demands in the strongback were then described using equivalent-static forces to represent the inertial forces induced by the higher modes. Force demands in the strongback arise from a yielding first-mode ‘pivoting’ and elastic higher-mode ‘bending’ response. These higher-mode force demands are elastic, ill-constrained by the strength of the yield mechanism, and depend significantly on the choice of ground motion record used for the analysis. In remaining elastic in the higher modes, the strongback distributes demands more uniformly and mitigates the formation of story mechanisms. Consequently, design and analysis methods for strongback-braced frames need to include estimates for these near-elastic higher-mode force demands.     

Fragility functions and floor spectra of RC masonry infilled frames: influence of mechanical properties of masonry infills

A wide number of experimental studies conducted in latest years pointed out the high influence of the mechanical properties of masonry units and mortar bed joints on lateral strength and stiffness of masonry panels. This feature significantly modifies the global response of infilled frames under seismic actions as well as the local interaction phenomena. Despite a wide investigation on the influence of the infills on global behaviour of reinforced concrete (RC) frames has already been provided, different features characterizing the seismic performances of buildings suggest the need of accurately evaluating local interaction phenomena as well as the influence of the panel on specific and relevant aspects, as the accelerations transferred to non-structural components. This study provides a parametrical analysis of the influence of shear strength and elastic modulus of masonry infills on the seismic behaviour of RC frames originally designed for gravity loads. Regular buildings with different height were analysed using the Incremental Dynamic Analysis in order to provide fragility curves, investigate on the collapse mechanisms and define the floor spectra depending on the properties of the infills. Results obtained pointed out the high influence of the considered parameters on the fragility of existing RC frames, often characterized by inadequate transversal reinforcement of columns, which may lead to brittle failure due to the interaction with the infills. Floor response spectra are also significantly affected by the influence of masonry infills both in terms of shape and maximum spectral accelerations. Lastly, on the basis of the observed failure mechanisms, a parameter defining the ductility of the frames depending on the properties of the infills was also provided (Capacity Design Factor). The correlation between the mechanical properties of the infills and this parameter suggests its reliability in the simplified vulnerability analysis of existing buildings as well as for the design of new buildings.     

Vulnerability of reinforced concrete frames in low seismic region,when designed according to BS 8110

The overstrength and ductility due to redistribution of internal forces are being investigated for three bay multi-storey reinforced concrete plane frames, using non-linear push-over analysis. These frames are designed to resist gravity loads, wind loads and a notional horizontal load in accordance with the British code BS 8110, which does not have any special provision for seismic loads. The results show that the overstrength factors for the three-, six- and ten-storey frames are respectively, 7·5, 5·6 and 2·2 times the design lateral loads, whereas, the ductility factors for the three frames are similar, and slightly greater than 2. These values yield a response modification factor of 18·0, 12·2 and 4·7 for the three-, six- and ten-storey frames, respectively. The effect of infill walls on the response modification factor is also being investigated, and a suitable response modification factor for assessing the vulnerability of reinforced concrete frames of about 10 storeys high is recommended. Copyright © 1999 John Wiley & Sons, Ltd.     

Modeling of the composite action in fully restrained beam‐to‐column connections: implications in the seismic design and collapse capacity of steel special moment frames

This paper investigates the effect of the composite action on the seismic performance of steel special moment frames (SMFs) through collapse. A rational approach is first proposed to model the hysteretic behavior of fully restrained composite beam‐to‐column connections, with reduced beam sections. Using the proposed modeling recommendations, a system‐level analytical study is performed on archetype steel buildings that utilize perimeter steel SMFs, with different heights, designed in the West‐Coast of the USA. It is shown that in average, the composite action may enhance the seismic performance of steel SMFs. However, bottom story collapse mechanisms may be triggered leading to rapid deterioration of the global strength of steel SMFs. Because of composite action, excessive panel zone shear distortion is also observed in interior joints of steel SMFs designed with strong‐column/weak‐beam ratios larger than 1.0. It is demonstrated that when steel SMFs are designed with strong‐column/weak‐beam ratios larger than 1.5, (i) bottom story collapse mechanisms are typically avoided; (ii) a tolerable probability of collapse is achieved in a return period of 50 years; and (iii) controlled panel zone yielding is achieved while reducing the required number of welded doubler plates in interior beam‐to‐column joints. Copyright © 2014 John Wiley & Sons, Ltd.     

Seismic performance and probabilistic collapse resistance assessment of steel moment resisting frames with fluid viscous dampers

This paper evaluates the seismic resistance of steel moment resisting frames (MRFs) with supplemental fluid viscous dampers against collapse. A simplified design procedure is used to design four different steel MRFs with fluid viscous dampers where the strength of the steel MRF and supplemental damping are varied. The combined systems are designed to achieve performance that is similar to or higher than that of conventional steel MRFs designed according to current seismic design codes. Based on the results of nonlinear time history analyses and incremental dynamic analyses, statistics of structural and non‐structural response as well as probabilities of collapse of the steel MRFs with dampers are determined and compared with those of conventional steel MRFs. The analytical frame models used in this study are reliably capable to simulate global frame collapse by considering full geometric nonlinearities as well as the cyclic strength and stiffness deterioration in the plastic hinge regions of structural steel members. The results show that, with the aid of supplemental damping, the performance of a steel MRF with reduced design base shear can be improved and become similar to that of a conventional steel MRF with full design base shear. Incremental dynamic analyses show that supplemental damping reduces the probability of collapse of a steel MRF with a given strength. However, the paper highlights that a design base shear equal to 75% of the minimum design base shear along with supplemental damping to control story drift at 2% (i.e., design drift of a conventional steel MRF) would not guarantee a higher collapse resistance than that of a conventional MRF. At 75% design base shear, a tighter design drift (e.g., 1.5% as shown in this study) is needed to guarantee a higher collapse resistance than that of a conventional MRF. Copyright © 2014 John Wiley & Sons, Ltd.     

Seismic response of unbraced steel frames

In the analysis and design of unbraced steel frames various models are employed to represent the behaviour of beam-to-column connections. In one such model, termed here as ‘Simple Construction’, pinned connections are assumed when resisting gravity loads, whereas the same connections are assumed to be moment-resistant rigid connections when resisting lateral loads due to an earthquake or wind. Such connections are designed for moments due to lateral loads only; thus, they are not only flexible but may yield when the gravity and lateral loads act concurrently. This paper establishes the seismic performance of two (one 5-storey and the other 10-storey) unbraced steel building frames designed based on the ‘Simple Construction’ technique and on limit state principles. The first part of the paper describes briefly the design of such frames and compares their static responses with the corresponding responses of frames designed based on the ‘Continuous Construction’ assumption. Using realistic moment-rotation behaviour for flexible beam-to-column connections and realistic member behaviour, the non-linear dynamic responses of such frames for the 1940 El Centro record and 2 times the 1952 Taft record have been established using step-by-step time-history analyses. Floor lateral displacement envelopes, storey shear envelopes and cumulative inelastic rotations of beams, columns and connections are presented. The results indicate that the ‘Simple Construction’ frames experience larger lateral deflections while attracting lesser storey shears. During a major earthquake, the columns and connections of the ‘Simple Construction’ frames experience yielding, whereas in ‘Continuous Construction’ frames the beams and columns experience yielding. The cyclic plastic rotations in the connections and in the columns associated with ‘Simple Construction’ frames are found to be considerably higher.     

Collapse risk of controlled rocking steel braced frames with different post‐tensioning and energy dissipation designs

Controlled rocking steel braced frames (CRSBFs) are low‐damage self‐centring lateral force resisting systems. Previous studies have shown that designing the energy dissipation (ED) and post‐tensioning (PT) in CRSBFs using a response modification factor of R=8 can prevent collapse of structures during earthquakes beyond the design level. However, designers have unique control over the hysteretic behaviour of the system, even after the response modification factor is selected. Additionally, recent studies have suggested that CRSBFs could also be designed using R>8 while still satisfying performance limits. This paper examines how the response modification factor and the design of the ED and PT influence the collapse performance of CRSBFs with three and six storeys where collapse occurs because of over‐rotation of the base rocking joint. In addition, the influence of using an additional rocking joint above the base to mitigate higher‐mode forces is evaluated for a 12‐storey frame. A total of 18 different designs are considered for the three buildings using different ED and PT design parameters, including different response modification factors. A suite of 44 ground motions is scaled until at least 50% of the records cause collapse, and fragility curves are generated using the truncated incremental dynamic analysis curves. The results from two different assessment methodologies show that the parameters selected have a marked influence on the collapse performance of a CRSBF. Nevertheless, even CRSBFs designed using R>8 or without supplemental ED can have acceptably low probabilities of collapse, provided that the frame members are designed to remain elastic. Copyright © 2017 John Wiley & Sons, Ltd.     

Quantitative investigation on collapse margin of steel high-rise buildings subjected to extremely severe earthquakes

Reponses of structures subjected to severe earthquakes sometimes significantly surpass what was considered in the design. It is important to investigate the failure mechanism and collapse margin of structures beyond design, especially for high-rise buildings. In this study, steel high-rise buildings using either square concrete-filled-tube (CFT) columns or steel tube columns are designed. A detailed three-dimensional (3D) structural model is developed to analyze the seismic behavior of a steel high-rise towards a complete collapse. The effectiveness is verified by both component tests and a full-scale shaking table test. The collapse margin, which is defined as the ratio of PGA between the collapse level to the design major earthquake level (Level 2), is quantified by a series of numerical simulations using incremental dynamic analyses (IDA). The baseline building using CFT columns collapsed with a weak first story mechanism and presented a collapse margin ranging from 10 to 20. The significant variation in the collapse margin was caused by the different characteristics of the input ground motions. The building using equivalent steel columns collapsed earlier due to the significant shortening of the locally buckled columns, exhibiting only 57% of the collapse margin of the baseline building. The influence of reducing the height of the first story was quite significant. The shortened first story not only enlarged the collapse margin by 20%, but also changed the collapse mode.     

空间半刚性连接钢框架有限元分析和研究

对带双腹板顶底角钢连接以及外伸端板连接空间钢框架进行了非线性有限元分析，研究了空间钢框架的静力承载性能与节点刚度的关系，得到了不同节点刚度对空间钢框架位移和内力的影响结果，对工程应用具有一定的参考价值。     

Advances in theory of plastic mechanism control: closed form solution for MR‐Frames

In this paper new advances in the application of ‘Theory of Plastic Mechanism Control’ (TPMC) are presented. TPMC is aimed at the design of structures assuring a collapse mechanism of global type. The theory has been developed in the nineties with reference to moment‐resisting frames (MRFs) and progressively extended to all the main structural typologies commonly adopted as seismic‐resistant structural systems. In particular, the outcome of the theory is the sum of the plastic moments of the columns required, at each storey, to prevent undesired failure modes, i.e. partial mechanisms and soft‐storey mechanisms. The theory is used to provide the design conditions to be satisfied, in the form of a set of inequalities where the unknowns are constituted by the column plastic moments. This set of inequalities was originally solved by means of an algorithm requiring an iterative procedure. The advances presented in this paper are constituted by the identification of a ‘closed form solution’ and by the use of TPMC in a more systematic design approach. This result is very important, because the practical application of TPMC can now be carried out even with very simple hand calculations. The practical application of TPMC is herein presented with reference to the design of a multi‐storey frame whose pattern of yielding is validated by means of both push‐over analysis and incremental dynamic analyses. Copyright © 2014 John Wiley & Sons, Ltd.     

Influence of deterioration modelling on the seismic response of steel moment frames designed to Eurocode 8

This paper assesses the influence of cyclic and in‐cycle degradation on seismic drift demands in moment‐resisting steel frames (MRF) designed to Eurocode 8. The structural characteristics, ground motion frequency content, and level of inelasticity are the primary parameters considered. A set of single‐degree‐of‐freedom (SDOF) systems, subjected to varying levels of inelastic demands, is initially investigated followed by an extensive study on multi‐storey frames. The latter comprises a large number of incremental dynamic analyses (IDA) on 12 frames modelled with or without consideration of degradation effects. A suite of 56 far‐field ground motion records, appropriately scaled to simulate 4 levels of inelastic demand, is employed for the IDA. Characteristic results from a detailed parametric investigation show that maximum response in terms of global and inter‐storey drifts is notably affected by degradation phenomena, in addition to the earthquake frequency content and the scaled inelastic demands. Consistently, both SDOF and frame systems with fundamental periods shorter than the mean period of ground motion can experience higher lateral strength demands and seismic drifts than those of non‐degrading counterparts in the same period range. Also, degrading multi‐storey frames can exhibit distinctly different plastic mechanisms with concentration of drifts at lower levels. Importantly, degrading systems might reach a “near‐collapse” limit state at ductility demand levels comparable to or lower than the assumed design behaviour factor, a result with direct consequences on optimised design situations where over‐strength would be minimal. Finally, the implications of the findings with respect to design‐level limit states are discussed.     

Probabilistic seismic performance evaluation of SMA-braced steel frames considering SMA brace failure

This study explores seismic performance of steel frame buildings with SMA-based self-centering bracing systems using a probabilistic approach. The self-centering bracing system described in this study relies on superelastic response of large-diameter cables. The bracing systems is designed such that the SMA cables are always stressed in tension. A four-story steel frame building characterized until collapse in previous research is selected as a case-study building. The selected steel frame building is designed with SMA bracing systems considering various design parameters for SMA braces. Numerical models of these buildings are developed by taking into account the ultimate state of structural components and SMA braces as well as the effect of gravity frames on lateral load resistance. Nonlinear static analyses are conducted to assess the seismic characteristics of each frame and to examine the effect of SMA brace failure on the seismic load carrying capacity of SMA-braced frames. Incremental dynamic analyses (IDA) are performed to compute seismic response of the designed frames at various seismic intensity levels. The results of IDA are used to develop probabilistic seismic demand models for peak inter-story and residual inter-story drifts. Seismic demand hazard curves of peak and residual inter-story drifts are generated by convolving the ground motion hazard with the probabilistic seismic demand models. Results show that steel frames designed with SMA bracing systems provide considerably lower probability of reaching at a damage state level associated with residual drifts compared to a similarly designed steel moment resisting frame, especially for seismic events with high return periods. This indicates reduced risks for the demolition and collapse due to excessive residual drifts for SMA braced steel frames.     

Modified capacity design rule for columns in tall steel MRFs with linear viscous dampers within the framework of Eurocode 8

Seismic design codes enforce a set of capacity design rules for steel moment-resisting frames (MRFs) to promote a ductile sway plastic mechanism that involves plastic hinges in beams and column bases. Previous research showed that these capacity design rules may not be effective for tall steel MRFs with viscous dampers under strong earthquakes due to high axial forces in columns. To address this issue, steel MRFs with linear viscous dampers of different stories are designed according to Eurocode 8 along with using a slightly modified conservative capacity design rule. According to this rule, the axial force for the capacity design of a column in the force path of viscous dampers is calculated as the envelope of the axial force from the peak drift state, and, the axial force from the peak velocity state times a scale factor. This envelope axial force value along with the bending moment and shear force from the peak drift state are used to carry out the capacity design of the column by using the formulae of Eurocode 8, i.e. in the same way with a column of a steel MRF without dampers. Incremental dynamic analyses for 44 earthquake ground motions show that the modified conservative capacity design rule results in steel MRFs with viscous dampers that have plastic mechanisms similar to those of steel MRFs without dampers. Moreover, the proposed capacity design rule becomes stricter for buildings with more than 10 stories to address that available analysis methods for structures with dampers underestimate the peak damper forces in the lower stories of yielding tall steel MRFs. More work is needed to extend the findings of this work to the case of steel MRFs with nonlinear viscous dampers.     

A design procedure for tied braced frames

The paper deals with the analysis of the seismic behaviour and design of tied braced frames (TBFs). The behavioural properties of TBFs are described and a comparison drawn with standard eccentrically braced frames. A design procedure is then proposed that aims to achieve optimal collapse seismic behaviour, i.e. a global collapse mechanism characterized by uniform plastic rotations of links. The procedure is based on the displacement‐based approach so as to achieve direct and efficient control of the peak ground acceleration of collapse. Applications are carried out on systems with different numbers of storeys and lengths of links to obtain confirmation of the accuracy of the design hypotheses and methodologies. Copyright © 2007 John Wiley & Sons, Ltd.     

Design objectives and collapse prevention for building structures in mega-earthquake

A "mega-earthquake" is one with an intensity larger than the most severe earthquake intensity category currently considered in design codes. For a "mega-earthquake," the design objective of a given structure is to "preserve living spaces for people in the buildings." In this paper,factors that may influence the collapse resistance of RC frames in a mega-earthquake are analyzed based on seismic damage observed in the 2008 Wenchuan earthquake. Methodologies to improve structural collapse resistance focus on three aspects:global strength margin,global redundancy and global integration of the structural system. Fundamental principles and design concepts for collapse prevention under a mega-earthquake are proposed,and issues that need further research are identified.     

Seismic behaviour of steel plate shear wall systems with staggered web configurations

Unstiffened steel plate shear walls (SPSWs) are used as lateral load‐resisting systems in building structures. The energy dissipation mechanism of SPSWs consists of the tension yielding of web plates and the formation of plastic hinges at the ends of horizontal boundary elements. However, vertical boundary elements (VBEs) of high‐rise SPSWs may experience high axial forces under lateral loading. This study explores the effectiveness of staggering of web plates on the reduction of VBE forces and drift response of SPSWs during an earthquake event. An analytical study has been conducted to determine the base shear reduction factor so as to match the overstrength of staggered systems with conventional SPSWs. A design methodology has been proposed for staggered SPSWs. Six‐, 9‐, and 20‐storey staggered and conventional SPSWs with varying aspect ratios are considered in this study to compare their seismic response. These study frames are modelled and analysed in OpenSEES platform. Nonlinear static and dynamic analyses are performed to compare the drift response, hinge mechanisms, and steel tonnage. Staggered SPSWs showed uniform drift distribution and reduction in interstorey drift and axial force demand on the VBEs.