Multi-storey Frame Research Articles

Exact closed-form dynamic stiffness matrix of damaged frames comprising Timoshenko–Ehrenfest beams

The present work proposes the extension of an exact distributional model for cracked beams to include the local influence on axial deformation on shear deformable beams. Axial, shear and flexural concentrated flexibilities are taken into account to model the damaged sections. Shear deformability is accounted for by adopting the Timoshenko–Ehrenfest model and exact closed-form solution of the mode shapes for multiple cracked beams are derived. On this ground, the final achievement of the work consists in the original formulation of the Dynamic Stiffness Matrix (DSM) with multiple cracked sections in exact closed form. The closed-form expression of the DSM allows the assemblage of the global DSM of a structure to conduct the free vibration analysis of damaged framed structures as well as for the study of frames with semi-rigid joints. This approach has the advantage to avoid any numerical procedure for the construction of the DSM as well as the introduction of further degrees of freedom (dofs) in correspondence of the damaged sections, keeping the size of the problem the same as in the intact configuration. Natural frequencies of the frames are determined by means of the Wittrick–Williams algorithm (W–W), then the mode shapes and modal forces are subsequently obtained in closed form. The proposed approach is validated with results available in literature for two portal frames characterized by the presence of cracks and semi-rigid joints, respectively. Finally, the potentiality of the approach, also in view of practical applications, is demonstrated analysing a multi-storey frame with semi-rigid connections.

Two Stochastic Methods to Model Initial Geometrical Imperfections of Steel Frame Structures

The stochastic modeling of geometrically imperfect steel frame structures requires statistical inputs for imperfection parameters, often with specific mutual correlations. The stochastic input values of geometrical imperfections are derived from European Standard EN 1090-2:2018 tolerance criteria. Two advanced stochastic methods, #RSS (random storey sway) and #RSP (random storey position), are developed based on these criteria. This paper presents a verification study, using random sampling simulations, for these two stochastic methods (#RSS and #RSP) to directly model the initial global geometrical imperfections of steel frame structures. The proposed methods have been verified for structures with equidistant storey heights and for those comprising up to 24 storeys, making them applicable to a wide range standard steel frame structures. It has been found that the performance of the #RSS method is satisfactory. An advantage of #RSS is that the random parameters are statistically independent. On the other hand, the #RSP method requires the definition of these mutual correlations in order to satisfy the criterion that 95 percent of random realizations of initial imperfections fall within the tolerance limits of the corresponding European Standard. The #RSP method, however, might have certain advantages for structures with a larger number of storeys (above 24), as closely discussed in this study. Additionally, this study provides useful provisions for the advanced numerical analyses of multi-storey steel frames of various geometries.

A two-level performance-based plastic design method for multi-story steel frames with double-yielding systems

The performance-based seismic design (PBSD) is usually conducted under design basis earthquakes (DBE), and then, the performance of the designed structures is examined under maximum considered earthquakes (MCE). As a result, it is challenging to simultaneously satisfy the performance targets associated with the DBE and MCE levels. To this end, this study proposes a two-level performance-based plastic design (PBPD) method. The fused steel frames exhibiting trilinear capacity curves are selected as the example structures. The peak interstory drift ratios under the DBE and MCE levels are defined as the performance targets and they are explicitly utilized at the beginning of the design procedure. The expressions of two energy modification factors are first obtained by establishing energy balance equations for single-degree-of-freedom (SDOF) systems under the DBE and MCE levels, respectively. Nonlinear time history analyses (NLTHA) for SDOF systems with various trilinear capacity curves are conducted to derive necessary design parameters. The versatility and flexibility of this design method are achieved by enabling both the primary and secondary yielding systems to yield under the DBE level. To demonstrate and validate the proposed design method, a six-story benchmark steel frame equipped with idealized metallic yielding damping braces is selected and designed with two sets of performance targets. The nonlinear static and NLTHA results proved that the designed structures can simultaneously meet the prescribed performance targets under both DBE and MCE levels.

Survivability of multi-storey building frame with prestressed elements

Survivability of multi-storey building frame with prestressed elements

Seismic response of non-structural components in multi-storey steel frames

This paper investigates the elastic and inelastic seismic response of non-structural components in multi-storey steel moment framed structures and derives predictive relationships for their displacements and spectral accelerations. Within 38 primary structural steel frames, non-structural components characterised by various periods and strength reduction factors, are modelled as single-degree-of-freedom systems which are fixed to individual floors. The primary structures are three, five, and seven-storey steel moment-resisting frames, designed according to the provisions of Eurocode 8. Detailed nonlinear time history analyses are conducted, employing a large set of 100 ground motion records from both far-field and near-field sources. These records are scaled to two distinct levels to simulate the response of primary structures in both elastic and inelastic states. The influence of the ground motion type and the inelasticity level in the non-structural components is examined in detail. The sensitivity to strain hardening and viscous damping considerations is also assessed and discussed. Based on the results, representative relationships for predicting the inelastic displacement ratios are proposed. In addition, various provisions stipulated in European design guidance for determining the spectral accelerations are critically evaluated and improvements are suggested with due consideration for the inelasticity of both the non-structural components and the primary structures.

COMBINED SLAB-PILE FOUNDATION

Solid reinforced concrete slab foundations are commonly employed in the construction of multi-story frame and panel buildings on natural grounds, as well as in industrial structures such assilos, elevators, chimneys, steel reactors, and more.One significant advantage of monolithic foundations is their ability to be used on weak and uneven ground bases. These foundations can distribute uneven loads over a considerable area, redistributingthem to equalize the inevitable differential settlements of individual foundations. On soft and uneven soils, slab foundations are not only used to mitigate deformations but also to protect against highgroundwater, creating what is known as a "floating" foundation.It has been demonstrated that the combined slab pile foundation (CSPF) is an effective development in the field of foundation construction. CSPF constitutes a foundation system comprising a "pile field – slab grillage – soil base," where piles bear a portion of the building load, and the slab grillage functions as a foundation slab. CSPF can be interpreted as a monolithic slab supported by piles of various types arranged in the form of a pile field, strips,clusters, or individual piles. Various types of piles, including "barrette" piles, can be used for CSPF foundations.Considering the soil resistance beneath the slab grillage in the deformation calculations and loadbearing capacity of combined slab-pile foundations provides a reserve for enhancing their economic efficiency. This includes reducing the number ofpiles, lowering the consumption of steel reinforcement, and decreasing the thickness of the grillage.However, the implementation of CSPF in construction is hindered by the limited theoretical research, necessary regulatory framework, and design experience for such structures.The determination of design parameters for CSPF is carried out using the method of successive approximations. By specifying the area of the slab grillage and defining the pile length and spacing, the number of piles in the foundation, the settlement ofan individual pile, and the design load on the pile are calculated (initially assuming that all piles bear 70-80% of the total load).

The impact of infill wall distribution on the mechanical behavior and failure patterns of multi-story RC frame structures: An acceleration–strain coupled testing approach

Historically, earthquakes have caused extensive damage to multi-story buildings, often leading to partial or total collapses. Nevertheless, these severely damaged structures rarely exhibit the "strong column–weak beam" failure pattern, and the performance of their vertical load-bearing components varies notably. Our study reveals that the uneven distribution of infill walls leads to divergent mechanical behaviors in columns located at different positions within the frame structure. To address this issue, an acceleration–strain coupled testing system was developed and implemented in a typical reinforced concrete (RC) frame structure of a veranda-style teaching building. This system, utilizing strong-motion seismographs for trigger acquisition, collected synchronized strain data from both columns adjacent to the veranda and those partially constrained by infill walls. Two sets of records were obtained, preliminarily confirming the internal force concentration due to the infill walls' constraints. Furthermore, the varied mechanical behaviors of components along two axes emerge as the primary factors causing significant structural damage and collapse. Based on these characteristic behaviors, quasi-static tests were conducted on frame columns, both unrestricted and partially restricted by infill walls. Results indicate that the constraining effect of the partial infill walls intensifies with deformation, markedly affecting column behavior. Notably, the load-bearing capacity, ductility, and ultimate displacement exhibited substantial differences between the two column types. The coexistence of these mechanically diverse components within the same structure leads to a sequence of failures, thereby altering the mechanisms of structural damage and collapse.

The effective length factor of columns in steel framed buildings with end restraint effects

The present article presents a practical method to determine the effective length factor of multi-storey frames based on a rigorous analytical approach applied to a basic model judiciously parameterized in terms of geometry and load arrangement. The adopted novel model considers the different interactions and effects of varying the boundary conditions at the ends of the columns and beams that are connected to the column under consideration. Subsequently, parametric studies are presented to evaluate the influence of the boundary conditions at the ends of the columns located above and below the column under consideration on the effective length factor value K. It is worth specifying that these variations are considered for the braced and unbraced frame cases. A comparative study revealed substantial differences between the values of the effective length factors thus obtained and those calculated using the method recommended by Eurocode 3 and CCM97. The proposed charts and relating to the effective length factor value K associated with the double cross model adopted by Eurocode 3 and CCM97, are of practical significance as they are very useful in the conception and design of such frames.

Exploring influence of eccentricities and axis deviations on stress and strain state of reinforced concrete columns in multi-story frame buildings

Exploring influence of eccentricities and axis deviations on stress and strain state of reinforced concrete columns in multi-story frame buildings

Seismic performance of improved multistorey X-braced steel frames

During an earthquake, the brace of a multistorey X-braced steel frame experiences out-of-plane instability. After the brace becomes unstable, the middle span of the brace-intersected beam exhibits a large imbalance force. This force causes a significant vertical displacement in the middle of the brace-intersected beam. To address this issue, an improved multistorey X-braced steel frame is proposed. Adding an arc energy-dissipation structure to the original structure adjusts the bearing capacity of the brace and ensures that the brace does not lose stability. The deformation of the arc energy-dissipation structure reduces the vertical displacement of the brace-intersected beam. A finite element model of the improved multistorey X-braced steel frame is established, and the seismic performance of the structure is analysed. The analysis shows that the brace of the improved multistorey X-braced steel frame does not experience instability, and the lateral bearing capacity is increased by 20%. The vertical displacement in the middle of the brace-intersected beam is small. The improved multistorey X-braced steel frame exhibits good seismic performance.

Behavior of a Multi-Story Steel Structure with Eccentric X-Brace

Eccentrically Braced Frames (EBFs) outperform moment-resisting frames in seismically active regions because of their strength, stiffness, energy dissipation, and ductility. Conventional bracing systems, such as X, Y, V, or K types, are utilized to enhance structural integrity. This study employs computational modelling to analyze multi-story steel buildings featuring an eccentric X-brace system. In this investigation, 120 multi-story steel frame buildings were selected. These multi-story structures comprise six-, nine-, and twelve-story geometries. ETABS built a full-scale FE model of multi-story structures. The study's parametric variables are the X-brace eccentricity, steel X-brace section size, and X-braced placement. Steel X-braces may have an eccentricity of 500, 1000, or 1500 millimeters. The ETABS model was validated when its findings matched experimental data. According to the data, the eccentric X-brace increases top-story displacement more for 6-story multi-story structures than for 9- and 12-story ones. Eccentric X-braces reduced lateral stiffness, allowing more significant floor movement. Eccentric and diagonal braces offer less lateral rigidity than concentrically braced frames due to their flexibility. Eccentricity reduces stiffness, even if the X-braced component has a larger cross-section. EBFs may migrate horizontally. Since the EBF absorbs more energy, changing the X-brace section size and eccentricity affects its ductility.

Design of ultra-lightweight and energy-efficient civil structures through shape morphing

This paper gives a new formulation to synthesize load-responsive structures through shape morphing. The design method is based on the minimization of the whole-life energy, which comprises an embodied share in the material and an operational share for adaptation. Target shapes that counteract the effect of the design loads are obtained through geometry and sizing optimization. Adaptation through shape morphing enables effective stress redistribution so that the design is not dominated by peak loads with long return periods. Material utilization is maximized, and therefore embodied energy is significantly reduced. The geometry is controlled through length changes of optimally-placed linear actuators. The actuator commands are computed through minimization of the operational energy to satisfy safety and serviceability criteria. Minimum energy solutions are obtained through a univariate optimization process in which embodied and operational energy minimization are nested. Numerical benchmarks between adaptive and mass-optimized passive solutions are provided on a truss bridge and multi-story frame configurations. Parametric studies show that mass and energy savings are significant for slender structures and when the live load is dominant over the permanent load. Generally, larger shape bounds result in a greater reduction of mass and embodied energy at the cost of a larger operational energy.

Identification of Damage in Planar Multistory Reinforced Concrete Frames Developing a Beam-Sway Plastic Mechanism Using the “M and P” Technique

The effectiveness of a recently proposed methodology for the identification of damage in planar, multistory, reinforced concrete (RC) moment frames, which develop a plastic yield mechanism on their beams, is showcased here via the examining of a group of such existing multistory frames with three or more unequal spans. According to the methodology, the diagram of the instantaneous eigenfrequencies of the frame in the nonlinear regime is drawn as a function of the inelastic seismic roof displacement by the performance of a sequence of pushover and instantaneous modal analyses with gradually increasing target displacement. Using this key diagram, the locations of severe seismic damage in an existing moment frame can be evaluated if the instantaneous fundamental eigenfrequency of the damaged frame, at an analysis step within the nonlinear area, is known in advance by “the monitoring and the identification of frequencies” using a local network of uniaxial accelerometers. This is a hybrid technique because both procedures, the instrumental monitoring of the structure and the pushover analysis on the frame (M and P technique), are combined. A ductile, five-story, planar RC moment frame with three unequal spans is evaluated in this paper by the M and P technique. The results show that the seismic roof displacement, the lateral stiffness matrix, and, finally, the damage image of this existing frame, are fully compatible with the eigenfrequencies identified by the monitoring and are calculated with high accuracy.

An ANN-based Hong-Lagrange algorithm (ANN-based HLA) for auto design-based building application (ABBA) with prestressed precast piperack frame

ABSTRACT Building optimization using traditional approaches based on explicit objective functions is difficult because of large numbers of variables and constraints. Many studies, thus, developed derivative-free optimizations using evolutionary programming, particle swarm methods, swarm intelligence, etc. Applications of artificial neural networks (ANNs) in frame designs are not common, although ANN is an evolutionary technology in many areas. This study presents novel holistic designs and optimizations of prestressed multi-story frames in general and piperack frames in particular, using the ANN-based Hong-Lagrange Algorithm. The proposed method provides optimized designs in terms of multiple objective functions such as costs, CO2 emissions, weights, and energy consumptions. A software is developed based on MATLAB codes for generating big datasets following American standards. A big data of 120,000 samples is used to train ANNs, formulating objective and constraint functions of 38 input and 69 output parameters. Designs minimizing multiple objective functions are performed by applying sequential quadratic programming to ANN-based functions constrained by equalities and inequalities imposed by architectural and code requirements. Examples show reductions up to 31.81%, 38.63%, 5.06%, and 37.36% in costs, CO2 emissions, weights, and energy consumption, respectively, compared with the minima of those identified from 340,000 samples.

Modelling of non-structural components of an industrial multi-storey frame for seismic risk assessment

Seismic risk assessment of industrial facilities is complex due to the presence of different types of equipment. It represents a research issue that requires further investigation. To this end, some analytical approaches have been developed in the framework of performance-based earthquake engineering. Nonetheless, their accuracy in the case of complex critical facilities, such as nuclear and non-nuclear industrial plants, is still under investigation. Thus, the proposed study intends to research in depth, in a risk assessment framework, some critical aspects related to: (1) modelling of industrial facilities and their secondary equipment with different degrees of accuracy, also taking into account their dynamic interaction; (2) selection of seismic records for fragility analysis, due to the narrow distribution of frequency values for non-structural components; (3) effectiveness of performance-based earthquake engineering applied to this particular class of coupled structure-equipment for risk assessment. In this context, the proper selection of seismic records becomes relevant, and SCoRes, an innovative algorithm for accelerograms selection is worthy of investigation. On these premises, two different configurations of a primary industrial structure, i.e. a moment resisting frame and a braced frame, equipped with non-structural components and subjected to shake table test campaigns are selected as case studies. For the two configurations, a vulnerability assessment of two vertical tanks installed on the first floor was carried out. Along these lines, to establish the effectiveness of the proposed method for both the moment resisting frame and braced frame configurations, the mean annual frequency of exceedance of the bottom-wall strain of the above-mentioned tanks, both at the design basis and safe shutdown earthquake has been evaluated.

The influence of the steel beam‐concrete slab interaction on the robustness capacity of steel frames

AbstractSeismic resistant multistorey steel frames are expected to mitigate progressive collapse even when subjected to extreme loading events. The use of high redundant structural systems and ductile members and connections are key features that provide such structural robustness. The composite action between the steel beam and the concrete slab may also help increasing the robustness, but in practice it is difficult to quantify this contribution if the joint behaviour is not detailed. The paper presents the results of a numerical study that aimed to investigate the contribution of the composite action to the progressive collapse resistance of steel frame structures. The main parameters investigated in the study were the level of the composite action in beams and strength and stiffness properties of beam‐to‐column joints. The numerical model was calibrated using two reference experimental column loss tests, one with steel beams and one with composite beams. The model considers the interaction between the steel beams and concrete slab by means of shear studs and reinforcement detailing. The results showed that the contribution of the slab lessens the demands on the joints when compared with bare steel systems and provides and adequate behaviour at large deformation stage. The progressive collapse resistance may be further controlled by means of joint flexural and axial strengths.

Seismic Performance of Ordinary and Damage-tolerant Concrete Beam-column Joints under Reversed Cyclic Loading

The adoption of the capacity design principle in modern codes of practice allows for multi-storey frame structures to exhibit ductile behaviour in a major earthquake without collapsing. Whilst the risk of shear failure in regions of large inelastic deformation can be largely reduced, the detailing requirements in capacity design often leads to reinforcement congestion that adds difficulty during the construction process, due to the high amount of transverse reinforcement required to provide shear resistance and confinement. The work presented in this paper forms a part of a wider research programme that aims to simplify the detailing requirements of transverse reinforcement in the joint and plastic hinge regions of moment-resisting frame structures. To this end, damage-tolerant concrete known as engineered cementitious composite (ECC) was used to substitute concrete in these critical regions. In this article, the results of reversed cyclic tests on two half-scale exterior beam-column joints, constructed with ordinary concrete and ECC, are presented. Key features of the response such as the reversed cyclic hysteresis loops, stiffness degradation and cumulative energy dissipation are discussed, along with crack development under reversed cyclic loading in the form of digital strain maps.

Artificial Neural Network Technique For Seismic Fragility Analysis Of A Storage Tank Supported By Multi-Storey Frame

Abstract Fragility function, which defines the conditional probability of exceeding a limit state given an intensity measure (IM) of the earthquake, is an essential ingredient of modern approaches like the performance-based earthquake engineering methodology. However, the generation of such curves generally entails a high computational effort to account for epistemic and aleatory uncertainties associated with structural analysis and seismic load. Moreover, a certain probability function, such as the log-normal distribution, is usually assumed in order to carry out the conditional probability of failure of a structure, without any prior information on the correct probability distribution. In this paper, an artificial neural network (ANN) model is proposed to carry out fragility curves in order to avoid the aforementioned problems. In this respect, this paper investigates the following aspects: (i) implementation of an efficient algorithm to select proper seismic intensity measures as inputs for ANN, (ii) derivation of surrogate models by using the ANN techniques, (iii) computation of fragility curves by means Monte Carlo Simulations and (iv) validation phase.

A framework for performance-based assessment in post-earthquake fire: Methodology and case study

Post-earthquake fire (PEF) is a threatening hazard triggered immediately after an earthquake, resulting in extensive destruction and casualties. It is important to evaluate structural performance in this typical cascading hazard to develop mitigation strategies and improve multi-hazard resilience. However, existing research mainly focuses on the structural response in PEF scenarios, while there is still a lack of knowledge on other critical parts of performance evaluation. In contrast, there has been a well-established methodology for performance-based assessment in earthquake engineering (PBEE), which can be regarded as the basis for extension to PEF scenarios. Based on that, a comprehensive framework has been proposed in this study for performance-based assessment in post-earthquake fire engineering (PB-PEF-E). To demonstrate the feasibility of the proposed methodology, an illustrative example of a realistic multi-storey steel frame is presented with specific details. The overall procedure considering the hazard, structure, damage, and loss domains is utilised for step-by-step PEF performance evaluation. Firstly, a dual-cause PEF ignition model is used to capture the probabilistic causation among the earthquake-fire sequence, considering ignition related to utility system damage and ignitable contents overturning. Then, structural demands with respect to both earthquake and fire intensities are obtained by a series of nonlinear analyses via numerical modelling, and uncertainties that significantly influence the responses are included. Finally, the structural capacity in different performance levels is estimated with PEF fragility development, and the consequences are measured using quantitative indicators for decision-making. The proposed methodology provides important benefits in evaluating the performance of alternative solutions thus facilitating robust decision-making in PEF scenarios, and it can be further extended to performance-based assessment in other multi-hazard scenarios with cascading effects.

Comparative Analysis of Steel Structure with Rigid and Semi Rigid Joint using Analysis Tool ETABS

Generally, in steel structure the connection between beam and column are designed as moment connection and pinned connection, but in actual condition the structure behaves between these two conditions, resulted into semi-rigid condition which is intermediate stage between rigid and pinned joints. Effect of semi-rigid connection on multi-story multi-bay frame is accomplished in this Study. The present study introduces the effect of static and dynamic loading on high rise steel structure of G+12 story with 4m, 6m and 8m three bay span length. Structure is analyzed under two different condition of partial release of semi-rigid connections which is derived by fixity factor of values 0.5 and 0.75 in this study. The analysis is done commercially available software ETABS. From the non-linear analysis, the story displacement and story drift are obtained. The overall performance of the structure from the analysis, semirigid joints display more story displacement and story drift compared to rigid joints. To overcome the results, bracing system is introduced at different location of periphery of structure. These brace frame structure consist of X- bracing and diagonal bracing. Again, comparative analysis is to be performed in ETABS on these three-bay span lengths. It is found that braced semi-rigid frame structure perform quite well as compared to unbraced frame structure.