Maximum Inter-storey Drift Research Articles

Eurocode-based seismic assessment of modern heritage RC structures: The case of the Tower of the Nations in Naples (Italy)

Given the interest earned recently by modern heritage structures, seismic assessment criteria of Eurocode 8 for ordinary reinforced concrete structures are applied to a modern heritage RC building. This case study, the Tower of the Nations in Naples, was designed at the end of 1930s. Modal dynamic identification, in situ inspections and testing provided the necessary knowledge of the structure in terms of geometry, structural details, and material properties. Two nonlinear models of the structure are built up in both the hypotheses of accounting and not accounting for tuff infills’ stiffness and strength contribution. Lumped plasticity model for reinforced concrete elements and equivalent strut macro-models for tuff and concrete infills are employed. Seismic assessment through nonlinear dynamic analyses is carried out for both limit states of Significant Damage and Damage Limitation. Assessment of bare and infilled models emphasizes a lower demand in terms of maximum interstorey drift of the infilled model with respect to the bare model, for both limit states considered. Record-to-record variability for the sets of seven records becomes larger if infills strength and stiffness contribution is taken into account. Outcome of the assessment is not affected by infills, i.e. the structure can be considered safe (according to EC8 provisions) for both limit states, and in both modeling hypotheses. On the other hand, the ratio demand over capacity, for both the limit states considered, is strictly influenced by infills’ contribution. Assessment tools provided for ordinary RC structures can be addressed to modern heritage buildings as shown in this case study, even if specific care is necessary for nonlinear structural modeling in case of non-conventional structural elements and non-conventional structural materials (e.g., tuff infills in lieu of clay hollow brick infills).

Vector fragility surfaces for reinforced concrete frames in Europe

Traditional approaches to damage estimation in earthquake loss modelling make use of relationships between scalar intensity measures and scalar engineering demand parameters. In this study we present a series of vector-valued fragility surfaces computed for low- and mid-rise reinforced concrete frames typical of those found in Europe. The use of vectors of intensity measures can result in conditional standard deviations of logarithmic engineering demand parameters that are up to 50 % smaller than those from traditional scalar methods. These reductions have significant implications for the shapes of loss curves, particularly for long return periods. The most efficient vector corresponds to a combination of spectral acceleration and a spectral shape parameter, $$\langle \ln S_a, \ln N_p\rangle $$ , when used to predict maximum interstorey drifts. The study also demonstrates that engineering demand parameters have significant heteroskedasticity with respect to various intensity measures and that this feature must be modelled correctly when constructing fragility curves. This feature of the models presented herein has not previously been accounted for during the development of fragility curves or surfaces.

Predicting local seismic damage of RC framed buildings considering the horizontal seismic component

This paper provides a simplified method to define local seismic damage for reinforced concrete frames considering the horizontal seismic component. The proposed method utilises static pushover analysis to evaluate the maximum and residual inter-storey drift limits for each storey. These limits are predicted for five frames and compared to experimental and analytical results by other researchers. Further validation of the method is achieved by conducting incremental dynamic analyses for a concrete frame using five earthquake records. Results have also provided an assessment of the use of residual and maximum inter-storey drifts to define collapse.

THE SEISMIC BEHAVIOUR OF CURTAIN WALLS: AN ANALYSIS BASED ON NUMERICAL MODELLING

Abstract The paper proposes a numerical model to estimate the structural behaviour of a stickbuilt glazed curtain wall system subjected to an imposed displacement of the supports in the plane of the wall. We discuss the role of the parameters that influence on the maximum inter-storey drift corresponding to the service limit state of the wall. The considered parameters are the dimensions of the glazed panel, the gap between the panel and the aluminium frame and the gap between the supports and the mullions. We discuss the problem of remnant deformation of glazed panels, and of misalignment as serviceability criteria. Comparisons are made to laboratory testing results.

Study on Characteristics of Dry Friction Plate-Reset Spring Seismic Isolation System

The seismic dynamic responses on two buildings with the vibration isolation system have been evaluated and the results show that the dry friction plate-reset spring isolation system is apparently effective if the reasonable parameters could be obtained by optimization. The maximum inter-storey drift could be drastically decreased by about 80% at base storey or about 60% at top storey. The elastic coefficient of the reset spring should be larger than the lower limit in order for the effective reposition ability of the system. On the other hand, the influence of the vertical seismic action to the horizontal dynamic response is so small that it could be neglected.

Influence of ground motion characteristics on drift demands in steel moment frames designed to Eurocode 8

This paper investigates the influence of the frequency content of ground motion, as well as the structural characteristics and level of inelasticity, on the global and inter-storey drift demands in frames designed to comply with Eurocode 8 provisions. To represent a wide range of structural characteristics, a suite of 39 steel moment frames is considered by varying the number of storeys, intensity of loading, performance requirements and compliance criteria. Extensive incremental dynamic analyses are carried out on the study frames using 72 far-field ground motion records, which are scaled to simulate four levels of behaviour factor. It is shown that the salient parameters that influence the global drift are the ratio of fundamental period to mean period and the behaviour factor. In addition to these, the relative storey stiffness ratio and the first-mode participation factor have a direct, though less influential, effect on the maximum inter-storey drifts. Based on the parametric assessments, regression models are proposed for predicting the global and storey drifts. Finally, the implications of the findings on the rules incorporated in European and United States design codes are highlighted and discussed.

The Influence of Infill Wall Topology and Seismic Characteristics on the Response and Damage Distribution in Frame Structures

This paper identifies the effects of infill wall existence and arrangement in the seismic response of frame structures utilising the global structural damage index after Park/Ang (<svg style="vertical-align:-3.27605pt;width:44.950001px;" id="M1" height="15.5125" version="1.1" viewBox="0 0 44.950001 15.5125" width="44.950001" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,11.363)"><path id="x47" d="M692 302v-28q-45 -6 -54.5 -17t-9.5 -55v-86q0 -62 7 -95q-7 -2 -32 -7.5l-37 -8l-35.5 -7.5t-40.5 -7t-38.5 -4t-40.5 -2q-165 0 -266 93t-101 243q0 84 32 151t86 108t121.5 63t142.5 22q29 0 62.5 -4t52 -7.5t47.5 -10.5t31 -7l15 -156l-28 -6q-17 87 -66.5 121.5&#xA;t-128.5 34.5q-117 0 -191 -80.5t-74 -216.5q0 -56 17 -110t49.5 -100.5t87.5 -74.5t124 -28q53 0 87 17q17 9 24.5 23t7.5 43v85q0 54 -15.5 67.5t-89.5 18.5v28h254z" /></g><g transform="matrix(.017,-0,0,-.017,12.217,11.363)"><path id="x44" d="M43 650h280q194 0 282 -85q85 -82 85 -215q0 -173 -123 -267q-107 -83 -297 -83h-236v27q65 5 79.5 19.5t14.5 77.5v402q0 45 -6 62.5t-21.5 24t-57.5 9.5v28zM213 547v-416q0 -55 24.5 -75t81.5 -20q133 0 203 86t70 214q0 80 -30 143t-88 97q-66 41 -170 41&#xA;q-62 0 -78 -13q-13 -9 -13 -57z" /></g><g transform="matrix(.017,-0,0,-.017,24.558,11.363)"><path id="x49" d="M303 0h-265v28q62 5 76 19.5t14 77.5v400q0 63 -14 77.5t-76 19.5v28h265v-28q-62 -5 -76 -19.5t-14 -77.5v-400q0 -64 14 -78t76 -19v-28z" /></g> <g transform="matrix(.012,-0,0,-.012,30.35,15.45)"><path id="x50" d="M46 650h247q112 0 169 -41q64 -49 64 -141q0 -91 -56.5 -143t-138.5 -62q-23 -3 -45 -1l-74 19v-157q0 -63 15.5 -77t83.5 -19v-28h-271v28q60 5 74 20t14 77v400q0 65 -12.5 79t-69.5 18v28zM212 559v-245q31 -12 73 -12q59 0 102 38t43 124q0 77 -42.5 115.5&#xA;t-108.5 38.5q-44 0 -56 -12q-11 -8 -11 -47z" /></g><g transform="matrix(.012,-0,0,-.012,36.05,15.45)"><path id="x41" d="M673 0h-245v28q47 6 58 16t1 39l-55 154h-213q-31 -87 -36 -129q-16 -47 -5 -61t68 -19v-28h-226v28q50 7 68.5 23.5t43.5 80.5l214 524l24 9l193 -536q23 -63 41.5 -79.5t68.5 -21.5v-28zM418 280l-81 255h-2q-74 -197 -101 -255h184z" /></g> </svg>) and the maximum interstorey drift ratio (MISDR) to express structural seismic response. Five different infill wall topologies of a 10-storey frame structure have been selected and analysed presenting an improved damage distribution model for infill wall bearing frames, hence promoting the use of nonstructural elements as a means of improving frame structural seismic behaviour and highlighting important aspects of structural response, demonstrating the suitability of such element implementation beyond their intended architectural scope.

Research about Efficiency of Seismic Mitigation for FPS-TMD System

A theoretical analyzing approach about a novel tuned mass damper system, FPS-TMD, was derived according to Lagrange Equation. The solution was presented with Newmark-β method and was programmed with MTALAB software. Computation results show that the maximum storey drift, inter-storey drift, storey velocity and acceleration were significantly decreased with FPS-TMD system. The slide radius, slip friction coefficient and the tuned mass will exert rather large influence upon the efficiency of seismic mitigation and energy dissipation. The system will exhibit the best efficiency with the slide radius being 0.8m, the slip friction factor being 0.4, and the tuned mass M/m=0.5.

Comprehensive Method of Seismic Damage Assessment of Reinforced Concrete Structures Based on CPM

In order to improve the accuracy of earthquake damage assessment of reinforced concrete structure, the earthquake damage assessment mutation model and four-dimensional model of seismic damage analysis are established using catastrophe theory. Firstly, internal damage index, number of inelastic cycles, maximum inter-storey drift and energy-concentrated quotient were taken as evaluation factors. Value assignment and standardization of each evaluation index is conducted. The appropriate mutation model is selected to calculate the total mutation value of seismic damage and comparison with the evaluation criteria of seismic damage of reinforced concrete structure, the extent of structural damage is differentiated. Secondly, comprehensive consideration of people's initiative and non-linear characteristics of the system, a four-dimensional seismic damage analysis model is build based on the mutation assessment of earthquake damage. Finally, four different structures are calculated and the results are compared with the ones of variable fuzzy set theory, set-pair theory to verify the reasonableness and effectiveness of the method.

Probabilistička analiza seizmičkog ponašanja AB okvirnih konstrukcija

The seismic performance of reinforced concrete frame structures of varying numbers of storeys, designed according to EC 8 and EC 2, is analyzed in the paper. The analysis is based on the probabilistic approach in which all identified incidental and indeterminate occurrences are taken into account. Performance of reinforced concrete frame structures is presented through maximum inter-storey drift values, while intensity is defined through spectral response of acceleration. The analysis results show that seismic response values increase by 31 to 54 percent if incidental and indeterminate occurrences are taken into account.

Optimized earthquake response of multi‐storey buildings with seismic isolation at various elevations

SUMMARYThe response of multi‐storey structures can be controlled under earthquake actions by installing seismic isolators at various storey levels. By vertically distributing isolation devices at various elevations, the designer is provided with numerous options to appropriately adjust the seismic performance of a building. However, introducing seismic isolators at various storey levels is not a straightforward task, as it may lead to favourable or unfavourable structural behaviour depending on a large number of factors. As a consequence, a rather chaotic decision space of seismic isolation configurations arises, within which a favourable solution needs to be located. The search for favourable isolators' configurations is formulated in this work as a single‐objective optimization task. The aim of the optimization process is to minimize the maximum floor acceleration of the building under consideration, while constraints are specified to control the maximum interstorey drift, the maximum base displacement and the total seismic isolation cost. A genetic algorithm is implemented to perform this optimization task, which selectively introduces seismic isolators at various elevations, in order to identify the optimal configuration for the isolators satisfying the pre‐specified constraints. This way, optimized earthquake response of multi‐storey buildings can be obtained. The effectiveness of the proposed optimization procedure in the design of a seismically isolated structure is demonstrated in a numerical study using time‐history analyses of a typical six‐storey building. Copyright © 2012 John Wiley &amp; Sons, Ltd.

Seismic performance evaluation of staggered wall system structures with middle corridors

SUMMARYIn this paper, the seismic performance of reinforced concrete (RC) staggered wall structures with middle corridor was evaluated. To this end, 6‐, 12‐ and 18‐storey structural models were designed and were analyzed to investigate the seismic load‐resisting capacity. The response modification factors were computed based on the overstrength and the ductility capacities obtained from pushover curves. The effect of a few retrofit schemes on the enhancement of strength and ductility was also investigated. The pushover analysis results showed that the response modification factors ranged between about 4.0 and 6.0 with the average value around 5.0. When the bending rigidity of the link beams increased up to 100%, the overall overstrength increased by only about 25%. When the rebar ratio of the link beams was increased by 50%, the overstrength increased by about 40%. The replacement of the RC link beams with steel box beams resulted in superior performance of the structures with reduced beam depth. The displacement time histories of the model structures subjected to the earthquake ground motions scaled to the design seismic load showed that the maximum interstorey drifts were well below the limit state specified in the design code. Based on the analysis results, it was concluded that the staggered wall systems with a middle corridor had enough capacity to resist the design seismic load. Copyright © 2012 John Wiley &amp; Sons, Ltd.

Explicit/implicit multi-time step co-computations for blast analyses on a reinforced concrete frame structure

The paper explores the coupling between finite element codes based on implicit and explicit time integration schemes. An external coupling software has been developed based on the multi-time subdomain coupling algorithm, labelled as the GC method in the literature, allowing coupling of any time integration schemes from the Newmark family with the appropriate time step dependent on the features of the subdomain. Explicit/implicit multi-time step co-computations have been carried out for predicting the response of a reinforced concrete frame structure under a blast loading striking its front face. The well known SPEAR structure, pseudo-dynamically tested at the ELSA laboratory, in Ispra, Italy, has been adopted as a testing structure for blast analyses. The structure has been modelled with multi-fibre elements, whose steel and concrete fibres composing the beam and column section, have cyclic and non-linear behaviours. Anticipating that non-linear phenomena will essentially occur in the slender columns of the SPEAR frame structure, a mesh partitioning has been considered, composed of two subdomains: a first subdomain, with linear material behaviour, gathering beam elements handled by an implicit time integration scheme with a large time step and a second subdomain, with non-linear material behaviour, handled by an explicit time integration scheme with a fine time step. Results from co-computations with time step ratio up to 1000 have been checked with respect to full explicit computations. Despite the number of interface nodes involved into the subdomain partitioning, the explicit/implicit multi-time step co-computations provide very accurate global and local response parameters in terms of maximum inter-storey drifts, maximum mid-height column drifts or extreme strains in concrete and reinforcement, while reducing by 60% the computation time.

Recording Inter-Storey Drifts of Structures in Time-History Approach for Seismic Design of Building Frames

The growing trend in the application of direct displacement-based or performance-based design, lays more emphasis on the precise prediction of design parameters such as the inter-storey drift controlling the performance level of the structure. Practising engineers employ different methods to record the inter-storey drifts in time-history approach mainly based on the maximum lateral deformation of the structure. In this study, a 15-storey concrete moment resisting building is designed using time-history analysis. Then reliability and accuracy of each method in predicting the maximum inter-storey drifts under the influence of three earthquake records, namely 1995 Kobe, 1994 Northridge and 1940 El Centro earthquakes, are investigated. Results clearly indicate that to choose the most critical drift to evaluate the performance level of structures, the absolute maximum drift over time should be calculated. Other methods based on the maximum storey deflection may result in unconservative design.

Recording inter-storey drifts of structures in time-history approach for seismic design of building frames

The growing trend in the application of direct displacement-based or performancebased design, lays more emphasis on the precise prediction of design parameters such as the inter-storey drift controlling the performance level of the structure. Practising engineers employ different methods to record the inter-storey drifts in time-history approach mainly based on the maximum lateral deformation of the structure. In this study, a 15-storey concrete moment resisting building is designed using time-history analysis. Then reliability and accuracy of each method in predicting the maximum inter-storey drifts under the influence of three earthquake records, namely 1995 Kobe, 1994 Northridge and 1940 El Centro earthquakes, are investigated. Results clearly indicate that to choose the most critical drift to evaluate the performance level of structures, the absolute maximum drift over time should be calculated. Other methods based on the maximum storey deflection may result in unconservative design.

New scalar intensity measure for near-fault ground motions based on the optimal combination of spectral responses

Intensity Measure (IM), characterizing the strength of an earthquake ground motion, is used to predict the seismic responses of a structure. Recent studies have demonstrated that using Sa(T1) as the seismic scaling index for near-fault ground motions may introduce large variability in the estimated seismic demands. To develop an improved IM, this paper investigates the effectiveness of a large number of combinations of spectral values in reducing scatter in the estimated maximum interstorey drift ratios. For this purpose, Incremental Dynamic Analyses (IDAs) are performed for five generic frames of short-to-relatively long periods, under 40 pulse-like earthquake records. Statistical evaluation of the IDA results reveals that the optimal combination of spectral displacements, compared to that of spectral velocities, leads to less variability for all ranges of the frames. It is concluded that the optimal combination of spectral displacements can be used to predict seismic demands with dispersions less than those of Sa(T1), and which are closer to constant for various intensity levels. Additionally, with respect to the importance of collapse capacity predictions in earthquake engineering, an efficient IM that can considerably improve the accuracy of estimating the probability of collapse is also developed.

EFFECT OF X-BRACING CONFIGURATION ON EARTHQUAKE DAMAGE COST OF STEEL BUILDING / KRYŽMINIŲ RYŠIŲ PAVIDALO POVEIKIS PLIENINIŲ KONSTRUKCIJŲ PASTATO APGADINIMO KAINAI DĖL ŽEMĖS DREBĖJIMO

Seismic structural design of X-braced steel buildings using life cycle cost analysis aims to reveal the most appropriate structural solution for both satisfying economic aspects and earthquake resistant design code requirements among a number of variant solutions accounting architectural concerns. In this study, five storey X-braced steel building with three different X-bracing configurations is designed using various base shear values and the total cost of each design of three configurations is calculated for different earthquake intensities. Initial costs and the cost of the expected damages caused by future earthquakes are determined for each X-bracing configuration. The maximum interstorey drift ratio is selected as seismic performance parameter for satisfying earthquake code demands and evaluated through nonlinear static analysis. The optimum X-bracing configuration is determined by using the balance between the initial cost and the life-time earthquake damage cost. Santrauka Pasitelkus gyvavimo ciklo kainos analizę, plieninių konstrukcijų pastatų su kryžminiais ryšiais seisminio konstrukcijų projektavimo tikslas – rasti tinkamiausią konstrukcinį sprendimą, kuris atitiktų ekonominę pusę, ir žemės drebėjimui atspariųstatinių projektavimo kodekso reikalavimus, kai, atsižvelgiant įarchitektūrines sąsajas, yra daugybė sprendimų variantų . Šiame tyrime, naudojant įvairias pagrindų šlyties jėgų reikšmes, projektuojamas penkiaaukštis plieninių konstrukcijų pastatas su trimis skirtingais kryžminių ryšių pavidalais ir kiekvienam atvejui iš trijų pavidalų apskaičiuojama bendroji kaina, esant skirtingo stiprumo žemės drebėjimui. Pradinė kaina ir numatomos bū simų žemės drebėjimų padaryto apgadinimo kaina nustatoma kiekvienam kryžminių ryšių pavidalui. Siekiant laikytis žemės drebėjimų kodekso reikalavimų, kaip seisminių charakteristikų rodiklis pasirenkamas didžiausias tarpaukštinės slinkties santykis, kuris įvertinamas naudojant netiesinę statinę analizę. Optimalus kryžminių ryšių pavidalas nustatomas subalansuojant pradinę kainą ir per visą gyva-vimo trukmę žemės drebėjimų padarytos žalos kainą.

Performance-based Aeolian risk assessment and reduction for tall buildings

The design of tall buildings subject to wind actions can be developed in the framework of Performance-Based Wind Engineering (PBWE). The structural performances are described by a set of measurable attributes, the decision variables, which are functionally related to proper measures of the structural damage, in turn dependent on proper engineering demand parameters characterizing the structural response, and measures of the intensity of the wind field. In this paper, PBWE is applied to the assessment of the comfort requirement and the structural reliability for a 74 storey building. Probabilistic calculations of the structural response are carried out in frequency and time domains, and the parameters of the wind velocity field are calibrated on the basis of the time-histories of the global floor forces derived by experimental tests on a rigid 1:500 scale model of the building. The occupant comfort is related to the motion perception under moderate winds, and quantified by the probability of exceeding threshold values of the across-wind acceleration at the top of the building. The structural reliability is related to the lateral deformation capacity under strong winds, and quantified by the probability of exceeding threshold values of the maximum inter-storey drift ratio. The results of numerical analyses suggest the use of a tuned mass damper to enhance the building performances.

Five-Element Connection Number Method for Seismic Damage Evaluation on RC Structure

In view of the problem that seismic damage evaluation for reinforced concrete structure are difficult to quantify, a new model for seismic damage evaluation was established by five-element connection number based on set pair analysis in the paper, which took internal damage index, maximum inter-storey drift, number of inelastic cycles and energy-concentrated quotient as evaluation factors. All indexes can be summarized into five-element connection number. Four different types of structure are analyzed on the model with more satisfactory results. Compared with the matter-element analysis evaluation method, this model is perfect, the evaluating result is more reasonable and its resolving power is higher. By this practical example, the model proved to be effective in seismic damage evaluation on reinforced concrete structure.

Seismic response analysis of an irregular base isolated building

This paper assesses the reliability of code-compliant linear and nonlinear dynamic analyses for irregular buildings with base isolation system (BIS). Comprehensive analyses are carried out for a case study comprising a large reinforced concrete multi-storey framed hospital with 327 high-damping rubber bearings. Spectral and time history (linear and nonlinear) analyses were performed on the three-dimensional (3D) finite element model (FEM) of the structure; simplified analyses were also conducted on single-degree-of-freedom (SDOF) systems. It is found that, at damageability limit state, the values of maximum interstorey drifts (d/h) computed with spectral analyses on the three-dimensional FEM range between 1/6 and 1/10 of the code limit (d/h = 0.33%); thus more stringent code limits should be required for buildings with BISs. The maximum floor acceleration is reduced by about 70% with respect to the ground acceleration (free field site); the acceleration profile is uniform along the height of the multi-storey frame. Threshold values of floor accelerations to assess the seismic performance of equipments in buildings with BIS are lacking. At ultimate limit state (ULS), spectral analyses provide values of actions and deformations that are less conservative than those derived through time history analyses. To perform reliable dynamic analyses of base isolated buildings it is crucial to select natural earthquake ground motions compliant with the fundamental period of vibration of the structural system. Nevertheless, it is not straightforward to select adequate natural strong motions in the catalogues available world-wide; buildings incorporating BISs possess periods of vibration which are generally higher than 2.0 s. As a result, distant and high-magnitude earthquakes are effective for base isolated buildings; nevertheless, such earthquakes are scarce in the seismic databases. The outcomes of the present study also demonstrate that simplified linear analyses tend to provide estimates of the response quantities, displacements of base isolators and base shear of the superstructure, which can be reliably employed at preliminary design stage. Spectral analysis results of the 3D model tend to match those of the SDOF systems, even for irregular superstructure, provided that modal mass participating ratios are greater than 85–90%. The results of spectral analyses on both SDOF and three-dimensional FEM envelope the outcomes of linear time histories.