Nonlinear Static Analysis Research Articles

The Effect of Plan Geometry on Progressive Collapse of Tall Buildings with Diagrid Structure Based on Nonlinear Static and Dynamic Analyses

The Effect of Plan Geometry on Progressive Collapse of Tall Buildings with Diagrid Structure Based on Nonlinear Static and Dynamic Analyses

Experimental and Numerical Investigation on Flexural Strengthening of Precast Concrete Corbel Connections with Fiber-Reinforced Plastic Sheet

This paper presents the results of experimental and numerical investigations aimed at enhancing the flexural capacity of Precast Concrete Corbel Beam–Column Connections (PC-CBCCs) using Fiber-Reinforced Plastic (FRP) sheets. The experimental study primarily focused on assessing the flexural capacity of pinned PC-CBCCs reinforced with FRP layers, comparing them to a moment-resisting connection. A series of half-scale specimens, including three PC-CBCCs with varying FRP configurations, were tested alongside one in situ concrete fixed connection. The first specimen (PC-1) utilized L-shaped and full-wrap FRPs, whereas PC-2 and PC-3 employed both U-shaped and full-wrap layers. The objective is to quantify the ultimate flexural capacity of PC-CBCCs reinforced by FRP sheets. In PC-3, the external anchorage is introduced to assess its influence on delaying the FRP layer debonding under lateral loading. The effects of the FRP layer thickness, locations, and potential debonding are examined under unidirectional static tests while applying a constant axial compressive load to the columns and subjecting the beams to lateral loads until fracture. The test results illustrate that strengthening the corbel connection with L-shaped FRP or spiral U-shaped FRP sheets without mechanical anchorage cannot result in a significant bending capacity due to debonding. However, with the incorporation of mechanical anchors, the connection manages to enhance the moment capacity to 81% of a fixed connection’s flexural capacity. Additionally, a finite element model of the PC-CBCCs and a fixed joint is developed to simulate nonlinear static analyses of the connections using ANSYS 19.2 software. The simulation model is precise in predicting the initial stiffness and ultimate capacity of the beam–column joints, as verified by the experimental results. A comprehensive comparison is conducted to determine their responses by employing various FRP configurations and properties. Moreover, design parameters such as bond length and thickness of the FRP sheets, along with appropriate mechanical anchorage, are identified as effective in preventing debonding, and delamination. However, wrapping the beam far away from the joint interface has a minimal impact on the failure mode, stress reduction, and load-bearing capacity.

Hybrid-self-centring steel frames: Insights and probabilistic seismic assessment

This paper comprehensively discusses the seismic performance of steel moment-resisting frames with hybrid-self-centring connections (SMRF-HSCC) employing energy dissipation sequences by probabilistic seismic assessment. The hysteretic model of the HSCC was first developed based on experimental results, and a simplified nonlinear-spring-based model to simulate the behaviour of the connection was proposed and verified by physical test data. A series of codified prototype structures were developed, considering the fracture behaviour of post-tensioned (PT) steel strands in the connections. The seismic performance of prototype structures was assessed in terms of nonlinear static analyses and nonlinear dynamic analyses. The results indicated that the hysteretic response of SMRF-HSCC exhibited trilinear hysteretic features with the expected energy dissipation sequences. The influence of the high-mode effects on SMRF-HSCC was mitigated with the increase in energy dissipation and post-yield stiffness of the structure. Finally, the fragility analyses of the prototype structures were further performed, and the risk assessment was also made considering a 50-year service period. The collapse probability and the exceedance probability of target residual drift over a 50-year service period of SMRF with conventional self-centring connections showing flag-shaped hysteresis were higher than that of SMRF-HSCCs. The results also confirmed that the collapse probability and exceedance probability of target residual drift over a 50-year service period of SMRF-HSCC can be adjusted by reasonably modulating the arrangement of the HSCCs.

Photogrammetry-aided numerical seismic assessment of historical structures composed of adobe, stone and brick masonry. Application to the San Juan Bautista Church built on the Inca temple of Huaytará, Peru

This research presents a cost-effective surveying methodology to assist the seismic assessment of complex heritage buildings, based on terrestrial structure-from-motion (SfM) photogrammetry. The method was applied to the study of the seismic performance of the church of San Juan Bautista – Inca temple of Huaytará, Peru, an emblematic case study due to its complex architecture and coexistence of different construction materials. The geometrical model for the seismic assessment was developed with an error of less than 2 % using SfM photogrammetry. Non-linear static pushover analyses were performed on 3D FEM models of the nave and the towers to evaluate their individual response under seismic loading. Mechanical properties of different structural materials of the church were evaluated based on laboratory experimental tests on mortar and adobe, contemporary and ancient fired brick, Inca stone, colonial stone and rubble stone units. Non-linear pushover analyses were conducted in four directions perpendicular to the perimeter walls, and the response of the structure was compared with the seismic demand specified in Peruvian Standards. The simulations show that damage-prone areas are the western and eastern facades, with cracking at the connections between orthogonal walls, as well as at the interface of adobe masonry with Inca stone masonry. The towers exhibit similar seismic response, with lower strength capacities compared to the main nave. In this case, flexural overturning mechanisms and cracking at the interface between stone and adobe masonry were observed. The displacement-based seismic assessment using the N2 method shows that a peak ground acceleration of 0.21 g could lead to the collapse of the north and south facades of the main nave. The towers showed a much smaller capacity with PGA leading to collapse of approximately 0.09 g. Overall, this study contributes to the understanding of the seismic performance of the Huaytará-Huancavelica church, highlighting vulnerabilities and providing valuable information for its preservation and future interventions. Future investigations should focus on on-site tests that will allow the estimation of the effect of existing damage on the structural response and their incorporation in the numerical model.

Methodical Investigations on Seismic Retrofitting of Steel Plate Shear Wall Systems

An efficient retrofitting technique is expected to improve the seismic performance of a lateral force-resisting system without increasing the seismic demand on the structure, which can unfavorably lead to irreparable damages during a seismic event. On this basis, the present study aims to introduce an optimal strategy for seismic retrofitting of steel plate shear wall (SPSW) systems using low yield point (LYP) steel material and to demonstrate its effectiveness through systematic investigations. To this end, detailed nonlinear static, cyclic, and dynamic analyses, as well as fragility analyses, have been performed on single- and multi-story, code-designed as well as retrofitted SPSWs. The aim is to identify the most efficient retrofitting approach and to demonstrate its effectiveness in enhancing the seismic performance and lowering the seismic vulnerability of the system. It is shown that replacing the original, conventional steel infill plate in an SPSW system with an LYP steel plate having twice the original thickness can improve not only the buckling capacity and serviceability, but also the structural performance and seismic response of the system, without increasing the demand on the structure and creating overstrength concerns. Fragility analysis also shows that the vulnerability, as well as probability, of damage to system can be considerably lowered as a result of the implementation of such a retrofitting strategy.

A hybrid buckling-restrained brace for enhancing the seismic performance of steel moment resisting frames

Buckling-restrained braces (BRBs) are effective and widely used devices to enhance the seismic performance of steel moment resisting frames (SMRF), but they might fail to prevent significant structural damage or structural collapse under unexpectedly high seismic loads. To address this issue, a novel hybrid BRB (HBRB) composed of a conventional BRB and a friction damper in series is proposed, where the activated force/displacement of the friction damper could be adjusted to protect the HBRB from failure. The paper begins by providing a detailed explanation of the configuration and working principle of the proposed HBRB. The cyclic behavior of the HBRB is thoroughly analyzed both theoretically and numerically. Building on this, a performance-based design approach is developed, focusing on enhancing the seismic response of SMRF using the HBRB. To assess the effectiveness of the proposed HBRB and design method, two typical SMRFs, one with 9 stories and the other with 20 stories, are enhanced with the HBRB. Comprehensive numerical models are established, considering the bare SMRFs, HBRB-enhanced SMRFs, and conventionally BRB-enhanced SMRFs. Nonlinear static and dynamic analyses are conducted to evaluate the seismic performance of these steel frames. Special attention is given to the performance comparison between HBRB-enhanced SMRFs and conventionally BRB-enhanced SMRFs, specifically under the extremely rare earthquake (ERE) scenario. The results highlight that the HBRB can achieve comparable energy dissipation capacity to conventional BRB while displaying superior energy dissipation efficiency. Moreover, the proposed design method achieves the predefined seismic performance objectives for the enhanced SMRFs in a straightforward and time-efficient manner. Furthermore, the HBRB proves effective in eliminating the failure risk associated with conventional BRB under ERE conditions, effectively mitigating structural damage and preventing collapse.

Determining the optimal layout of energy-dissipating mechanisms for hybrid self-centering walls

To eliminate the inherent energy dissipation deficiency of self-centering walls, hybrid self-centering walls (HSWs) have been developed by employing internal or external energy dissipating (ED) mechanisms. Mild steel bars have been extensively used as energy dissipators among ED mechanisms due to their affordability and simplicity. This study investigated the effect of ED bars layout on the damage, response features, collapse probability and collapse risk of HSWs. To this end, five different layout scenarios were defined first, and their response was studied by developing numerical models. Conducting nonlinear static and dynamic analyses (IDA), the scenarios damage, response features, collapse probability and risk were estimated and further examined to determine the optimal ED bars layout. Fragility analysis was performed on global and local scales, using IDA results, to estimate scenarios collapse probability. The results revealed that the wall with ED bars at the boundary elements outperformed other scenarios. Placing ED bars at the boundary elements of HSWs decreases the self-centering capability, fundamental period, collapse probability and the extent and severity of damage (especially in toe regions), while increases the energy dissipation capacity, adjusted collapse margin ratio and structural demand. Increasing ED bars cross-sectional area increases the extent and severity of damage. Using IDA results, the wall with ED bars at the boundary elements achieved the lowest ductility ratio; moreover, the response modification factor 3 was recommended for the strength-based design of HSWs. An optimality index (OI) was proposed herein to interpret the results quantitatively and determine the optimal layout. The calculated OI showed that placing ED bars at the boundary elements or along the wall width can be considered the optimal ED bars layout for achieving better seismic performance and decreasing the collapse probability and seismic risk of HSWs.

A non-linear static analysis for the seismic design of single-span integral abutment bridges

Integral abutment bridges are characterised by a monolithic connection between the deck and the abutments. Because of this connection, the seismic behaviour of the entire structure tends to be controlled by its interaction with the surrounding soil, and especially with the approach embankments. To date, methods for the seismic design of this type of bridges are still characterised by substantial uncertainties, mostly because of insufficient understanding of the dynamic response of the soil–structure system. This paper provides a contribution to the interpretation of the seismic behaviour of integral abutment bridges, focusing on a single-span structural scheme that has been receiving significant attention in recent years. The dynamic interaction between the bridge and the soil is studied with global numerical models of the soil–bridge system developed in OpenSees and subjected to a variety of ground motions. The results of the dynamic simulations, interpreted also with the aid of a modal analysis of the system, are used to develop and finally validate a simplified design procedure. This procedure is based on the capacity spectrum method, aimed at evaluating the maximum deformation and internal forces in the structure produced by the longitudinal component of the seismic motion that typically dominates the design of integral bridges.

Near-Fault Response and Loading Protocols of Box Columns in Steel Frames with Self-Centering Braces to Provide Recentering Capability

The main objective of this study was to establish loading protocols for self-centering braced frames (SCBFs) while taking into account the impact of near-fault ground motions. SCBFs are self-centering frames that have lower residual drift than buckling-restrained braced frames (BRBFs) under near-fault earthquakes; thus, SCBFs can better control damage to buildings. Typically, first-story columns are employed to represent the seismic behavior of a structure; therefore, loading protocols were developed for first-story columns in SCBFs under near-fault earthquakes. Nonlinear static and dynamic analyses of SCBFs designed with various periods were conducted for better understanding the seismic performance of SCBFs. Finally, the loading protocols developed for SCBFs were compared with those for BRBFs under the same near-fault motions.

Seismic performance factors of quarter-elliptic-braced steel moment frames (QEB-MFs) using FEMA P695 methodology

One of the newest lateral load-resisting systems is quarter-elliptic-braced steel moment frames (QEB-MFs). The elliptical geometry of this bracing system not only resolves the shortcomings of conventional concentrically braced frame systems but also leads to greater energy absorption. The QEB-MF system's seismic performance factors (SPFs) are specified in this paper using the FEMA P695 approach. To this end, a three-dimensional group of 2-, 4-, 6-, and 8-story archetypes in two distinct seismic design categories (SDC Cmax and Cmin) were designed according to presumed SPFs. The adjusted collapse margin ratio (ACMR) for each archetype was calculated utilizing the results of non-linear static (pushover) analysis and incremental dynamic analysis (IDA) under far-field ground motion (FFGM) records. In order to confirm presumed SPFs, ACMRs were compared to FEMA P695's acceptable values. The results indicate that the ACMR values for the QEB-MF systems that were designed with a response modification factor of 6.5 are acceptable. In addition, the deflection amplification factor and the over-strength factor have been acquired to be equal to 6.5 and 2.5, respectively.

Performance-based seismic design method for disc spring-based self-centering viscous dissipative braced steel frame

Disc spring-based self-centering viscous damper (SCVD) has emerged as a novel technology, offering velocity-dependent energy dissipation and exceptional self-centering capabilities. Integrating this damper in structural bracing systems can effectively enhance passive control over critical structural demands such as peak deformation, residual displacement, and floor acceleration. Nevertheless, a seismic design method specifically tailored for self-centering viscous dissipative braced steel frames (SCVDFs) needs further refinement. This study proposes a performance-based seismic design (PBSD) method for SCVDFs, which is grounded in the performance-based plastic design (PBPD) approach. The proposed procedure primarily considers the effects of two critical hysteresis parameters: the post-activation stiffness ratio and the viscous damping ratio. To verify the effectiveness of the design method, a set of SCVDFs was designed, each utilizing different combinations of design parameters. Nonlinear static and dynamic analyses were performed on these archetypes to evaluate their seismic performance. The evaluation findings demonstrated that the properly designed SCVDFs can achieve the expected design performance and effectively suppress the peak inter-story drift, residual inter-story drift, and peak absolute floor acceleration of the structure, thereby achieving a favorable trade-off in the design outcome and maximizing the advantages of the SCVDF in seismic resilience.

Simple Nonlinear Numerical Modeling for Unreinforced and FRP-Reinforced Masonry Domes

This paper presents a new method to model the nonlinear behavior of double-curvature masonry structures, possibly reinforced by composite materials, by means of conventional elasto-plastic analyses. The method is meant to be used in professional design, especially for assessment and retrofitting purposes, based on the exploitation of the simplest nonlinear finite elements available in commercial software, namely, trusses with elasto-fragile and elasto-ductile behavior (Cutoff Bars, according for instance to the definition provided by Strand7 R3.1.3a). Numerical static nonlinear analyses are carried out by considering elastic hexahedral elements for bricks and by lumping nonlinearities on joints. These are assumed, in turn, to be elastic–brittle and elastic–plastic by using 1D elements, namely, Point Contacts, under the No-Tension Material hypothesis, and Cutoff Bars, respectively, assigning a small tensile resistance to the material. The reinforcement, realized with FRP hooping strips, is successfully modeled in a similar fashion, i.e., by applying perfectly bonded elastic–plastic Cutoff Bars at the extrados of the dome, where debonding is accounted for in a conventional way, limiting the tensile strength according to Italian Standards’ indications. The procedure is validated against benchmark models with the same geometry, using experimental data and more refined structural model results for comparison. After an in-depth analysis of the obtained results, in terms of capacity curves, the robustness and accuracy of the proposed approach are assessed.

Preferred Seismic Performance Attainment in Important Buildings

In the aftermath of earthquakes, hospital buildings are expected to remain occupiable to treat the injured. For the purpose, firstly, an appropriate structural system that ensures no or limited structural damage should be provided in such buildings; wall-frames are the recommended structural systems in hospital buildings. Secondly, it is also essential to adequately design wall-frames to help meet the preferred Occupiability seismic performance. The work presented in this paper examines the contributing factors for failure of structural elements in hospital buildings and explores structural configuration and design strategies for mitigating these failures. Nonlinear analyses studies of a typical hospital building in high seismic region in India are carried out to help provide quantitative guidelines for: (a) Structural Plan Density (SPD) of structural walls, and (b) design parameters, for achieving the preferred performance. Displacement-based limit state of structural damage adopted from traditional displacement demand estimation rules is proposed. Lateral stiffness, strength, and ductility are evaluated of study buildings, and efficacy of results obtained from nonlinear static analyses confirmed by performing nonlinear time history analyses in commercial software PERFORM 3D. Results demonstrate inadequacy of moment frame structural system in hospital buildings under strong earthquake shaking, identifies optimum overall SPD of structural walls and relative column-to-beam strength ratio of frame members, required to achieve Occupiability. A minimum 3% SPD of structural walls in Wall – Special Moment Resisting Frame (WSMRF), 4% SPD in Wall – Ordinary moment resisting frame (WOMRF) hospital buildings, and a minimum column-to-beam strength ratio (CBSR) of 2 is required in hospital buildings to attain Occupiability performance.

Predição da capacidade última de elementos em concreto armado usando metodologias de análises não linear

Abstract This work aims to investigate the ultimate capacity of reinforced concrete elements in terms of cracking and stiffness loss. Nonlinear finite element analysis (NLFEA) was performed in the ATENA software and compared with a proposed numerical simulation of nonlinear static analysis (NLSA), where material cracking is evaluated based on the loss of tangent stiffness of the elements. The analysis was applied to a low-rise reinforced concrete frame with constant axial loads in the columns, and monotonic lateral load applied at the top beam level. Both methodologies showed good agreement regarding the capacity curve and crack patterns, and the numerical simulation NLSA allowed the identification of the sequence of elements' stiffness loss. The results indicated a substantial similarity between the numerical simulation NLFEA and NLSA and the experimental test, indicating a high potential in predicting the nonlinear behavior of reinforced concrete.

Failure mechanisms of hexagonal-shaped intra-module connections in modular steel building

Modular construction has gained popularity for its cost-effectiveness, time savings, and environmental benefits. This research delves into innovating modular buildings to enhance their aesthetic value in contemporary architectural designs. Traditional rectangular modules have lost architectural significance in the modern era. The study focuses on the failure mechanisms of hexagonal intra-module connections under nonlinear static analysis, aiming for advanced structural design and performance in modular construction. The study tested a control model, a Welded Flange Bolted Web (WFBW) connection, and three variations with different parameters: boundary condition, bolt arrangement, and steel grade. For the boundary condition, the tie constraint between the beam's flanges and the diaphragm was removed. Bolt arrangement was assessed with staggered and non-staggered bolts. Steel grade variations included S275 and S355. Results showed that the WFBW connection outperformed the Bolted Web (BW) connection in load resistance. The most damaged component was the beam, with bearing failure at the upper bolt hole. Non-staggered bolts exhibited larger displacements than staggered bolts. The study emphasized the significance of steel material strength in terms of stress and strain on bolt capacity. It highlights the importance of intra-module connections in modular steel structures and the need to consider design parameters carefully. The findings offer insights into improving modular connections' performance and failure mechanisms, facilitating the creation of aesthetically pleasing and structurally sound modular structures. This nonlinear static analysis aids in developing advanced modular construction designs, enhancing architectural significance in the modern era. By merging structural performance and aesthetics, the study promotes innovative modular construction to meet contemporary architectural demands.

Modelling a reinforced concrete arch bridge by means of the Discrete Macro-Element Model: the case of Giovanni XXIII bridge in Ragusa

Numerical modelling of reinforced concrete structures in the nonlinear field requires the adoption of sophisticated although robust models. When it comes to bridges, to obtain an accurate numerical model uniaxial elements should not be employed due to geometrical inconsistency. Two- or three-dimensional elements are more appropriate even though the explicit modelling of concrete and steel bars can make the simulations too cumbersome for many practical applications. In this study, the Discrete Macro-Element Model (DMEM), implemented in the software HiStrA, initially introduced for the nonlinear modelling of existing masonry structures and also applied in the case of masonry arch bridges, is extended for modelling reinforced concrete structures. The presence of rebars is explicitly accounted for by introducing their contribution in the interface elements. The original modelling strategy is here applied to the Giovanni XXIII bridge in Ragusa (Italy), a road reinforced concrete supported deck arch bridge located in the city centre. The structure is currently a case study identified within an accurate survey and permanent health monitoring installation designed within the MonVia Project funded by the Italian Ministry of Economic Development. The results reported in this paper are relative to numerical simulations where the mechanical parameters of the linear elastic model are calibrated to match the experimental dynamic properties of the structure while the nonlinear parameters are consistent with those reported in the original design of the bridge. Nonlinear static analyses are performed considering both operational and seismic load configurations. The results could be used to define the threshold levels to be considered for the health monitoring of the bridge.

A simplified procedure for the seismic retrofit of bridges by seismic isolation: Part 2 - predimensioning of the isolation system

This study presents a simplified procedure for the seismic retrofit of bridges by means of isolation system (IS), applicable to bridges with an isostatic or continuous deck layout, supported by conventional bearings that can be replaced by seismic isolators. The procedure consists of two steps: (1) the assessment of suitability of the bridges for seismic isolation; (2) the preliminary design of the isolation system. The first part of the procedure is presented in a companion paper. This contribution presents the second step of the procedure. A nonlinear static analysis of the existing bridge is performed, and its capacity curve is determined. This curve is then transformed into that of the equivalent SDOF system. Combining the information of the nonlinear static analysis and the bridge characteristics in the ADRS plane, the minimum characteristics of the isolation system to achieve a preset performance point are derived. Two scenarios are considered: in the first one it is sufficient to shift the period of the deck; in the second one, in addition to period shifting, it is necessary to introduce damping to control the displacement of the deck. Once the minimum characteristics of the isolators have been defined, the type and model can be identified through a search into databases of commercial devices. The application of the procedure to a case-study bridge and the validation of the method are finally shown.

How much code-based shear models affect seismic assessment of pre-code RC buildings?

Existing Reinforced Concrete (RC) building stock have exhibited a significant vulnerability under seismic shaking after the most recent earthquakes worldwide. They were often designed without capacity design principles, even where seismic hazard is very high, such as in Italy. Two-third of Italian existing RC buildings have been designed to sustain gravity loads only (GLD). Almost all of them lack stirrups in beam-column joints and have a minimum amount of transverse reinforcement in columns. These features make such buildings extremely prone to shear failures under seismic actions. Additionally, the same physical phenomenon, i.e., the shear failure of beams/columns or joints, is assessed differently worldwide. As a result, the same building has (even very) different seismic capacity depending on the code adopted for its assessment. The main aim of this work is quantifying such a difference with reference to RC GLD Italian case-study buildings with different number of stories located in sites with different seismic hazard, based on nonlinear static analyses. Code-based safety checks according to European (Eurocode 8-part 3, 2005; Italian DM 2018) and American (ASCE-SEI 41, 2017) approaches are carried out. The results show that capacity at Severe Damage (SD) Limit State (LS) is generally limited by joints failures. Relevant design of seismic strengthening at SD LS, thus, strongly depends on the adopted code approach, leading to generally higher strengthening costs when joints failures are (very conservatively) detected by means of the current European approach.

Seismic Assessment of RC Frame Structure by Nonlinear Static Pushover Analysis.

Seismic Assessment of RC Frame Structure by Nonlinear Static Pushover Analysis.

Response Reduction Factor for Structures Irregularities in Plan and Elevation Taking into Account Soil-Structure Interaction

The structure's ability to release energy through inelastic behaviour is reflected in the response reduction factor (R). It results from a combination of redundancy, ductility, and over strength. Thus, determining R with accurate values plays a critical function in the process of seismic design. This study aims to determine the response factor of structures of reinforced concrete (RC). With different structural irregularities, additionally, determine the impact of the interaction between soil and structure (SSI) using non-linear static pushover analysis was adopted in numerical simulation by using SAP2000. The selected irregularities included elevational and in-plan changes It was determined that, in comparison to regular buildings, buildings with irregular vertical geometries had poorer inelastic seismic capacities. Therefore, R is less than that which is stated in the ECP 2020, so it ought to be reduced by 15–40% before the design stage. The outcomes demonstrated that It isn't concluded that irregularity has a considerable effect on weak soil (C). The reduction in R, considering (SSI), reached 20.3% and 13.1% for fixed and isolated supports, respectively, in case of loose soil. Moreover, it became obvious that for the same structure the stiffer the base soil the greater the R's value.