Pushover Response Research Articles

Simplified Methods for Predicting the Pushover Response of a Hybrid Steel Braced Frame with Concentric and Eccentric Connections

Simplified Methods for Predicting the Pushover Response of a Hybrid Steel Braced Frame with Concentric and Eccentric Connections

Surrogate models for seismic and pushover response prediction of steel special moment resisting frames

For structural engineers, existing surrogate models of buildings present challenges due to inadequate datasets, exclusion of significant input variables impacting nonlinear building response, and failure to consider uncertainties associated with input parameters. Moreover, there are no surrogate models for the prediction of both pushover and nonlinear time history analysis (NLTHA) outputs. To overcome these challenges, the present study proposes a novel framework for surrogate modelling of steel structures, considering crucial structural factors impacting engineering demand parameters (EDPs). The first phase involves the development of a process by which 30,000 random steel special moment resisting frames (SMRFs) for low to high-rise buildings are generated, considering the material and geometrical uncertainties embedded in the design of structures. In the second phase, a surrogate model is developed to predict the seismic EDPs of SMRFs when exposed to various earthquake levels. This is accomplished by leveraging the results obtained from phase one. Moreover, separate surrogate models are developed for the prediction of SMRFs’ essential pushover parameters. Various machine learning (ML) methods are examined, and the outcomes are presented as user-friendly GUI tools. The findings highlighted the substantial influence of pushover parameters as well as beams and columns’ plastic hinges properties on the prediction of NLTHA, factors that have been overlooked in prior studies. Moreover, CatBoost has been acknowledged as the superior ML technique for predicting both pushover and NLTHA parameters for all buildings. This framework offers engineers the ability to estimate building responses without the necessity of conducting NLTHA, pushover, or even modal analysis which is computationally intensive.

Numerical modeling and design sensitivity of seismic behavior of UHPC-NSC bridge piers with the longitudinal grooved contact surface

Normal strength concrete (NSC) has low structural and durability resistance to meet the comprehensive performance requirements of modern construction. The reinforced concrete bridge column quickly degrades, particularly when exposed to environmental compartments, causing the concrete to deteriorate and the reinforcement to corrode. The phenomenon significantly reduced the durability and load-bearing capacity of the column, which impacted the functionality of the bridge and threatened its recovery operation. The superior behavior of advanced cementitious ultra-high-performance concrete (UHPC) has drawn increasing benefits among the construction industries. However, the high cost of UHPC has developed a concern that resulted in its small-scale application. Therefore, incorporating UHPC with NSC has the potential to balance the low performance of NSC and the economic cost of UHPC. Therefore. This study incorporates UHPC and NSC in a large-scale two-column bridge pier and investigates its seismic performance. The study aims to understand the general behavior, failure modes, and effect of design parameters of developed UHPC-NSC bridge columns with longitudinally grooved contact surfaces through finite element analysis. The pushover response of the UHPC-NSC two-column with a typical geometry and gravity load of a representative bridge was investigated. A comprehensive parametric study was carried out to evaluate the effect of interface groove geometry, longitudinal reinforcement ratios, core NSC compressive strength, and reinforcement grade on the characteristic behavior of the columns. The study shows that the capacity of the composite UHPC-NSC bridge column under gravity load is 11 % higher than the conventional NSC concrete. The UHPC-NSC column with 300 × 300 mm interface groove, reinforced with 4 % HRB500 longitudinal rebars, can sustain over 80 % of the peak capacity up to 5 % drift. A higher axial load ratio of up to 14 % can increase the capacity of the UHPC-NSC two-column by 75 %, which has a more significant impact than what is often observed on NSC piers.

Effect of reinforcing and crack width on the vibration damping capacity of rubberized concrete beams

The damping of simply supported rubberized concrete beams was measured and compared against conventional concrete beams in their uncracked and cracked states. The variables controlled were: rubber content (10% and 20% by total volume of aggregates replaced), reinforcing content, axial load, and damage state. Impact hammer-induced free-vibration was used to excite the specimens and quasi-static four-point bending used to damage the beams. Rubberized concrete displayed a measurable increase in damping relative to ordinary concrete in both the uncracked and cracked states. It was found that reinforcing appears to reduce the damping of all beam specimens in their undamaged state compared to unreinforced counterparts. No relationship was found between reinforcing ratio and damping. For crack widths up to 0.1 mm a non-linear monotonic increase in damping was observed. Damping measured throughout the entire pushover response of the beams was found to follow a skewed-shaped bell curve. Compressive axial load was found to reduce the damping of the beams. The shape of the free vibration decay envelopes was examined. Rubber was found to make the damping response more viscous-like. Whilst reinforcing made the shapes of the decay curves more similar between beams made of different concrete types. No clear evidence for friction damping due to cracking was found. For all beams, based on the free-vibration response, it was found that the damping exhibited by both plain and reinforced concrete is not a true exponential decay curve. This means that the damping calculated by the logarithmic decrement method will depend on the choice of interval selected. A method for standardizing the implementation of the logarithmic decay method to avoid arbitrary choices of intervals and allow for fairer cross-study comparison of damping values was therefore proposed.

A simple numerical approach for the pushover analysis of slender cantilever bridge piers taking into account geometric nonlinearity

The response of slender bridge piers to horizontal actions may be significantly influenced by geometric nonlinearities. In such conditions, the use of sophisticated models implemented in complex structural analysis software can be economically disadvantageous, especially in the preliminary design phases. This paper proposes a simple numerical procedure to compute the nonlinear pushover response of cantilever bridge piers subject to horizontal loads. The procedure is based on an iterative approach to enforce the element equilibrium under large displacements, efficiently accounting for P-Delta effects induced by vertical loads. Evaluation of the bending moment–curvature response of the pier base cross section is required and used as basic input data. For fast preliminary analyses, sectional response can be manually computed in simplified linearized form, thus completely eliminating the need to use structural analysis software. Indeed, the entire procedure can be implemented in standard programming codes, such as PythonTM or Matlab®, and used to evaluate the pushover response of piers with arbitrary cross section. Comparison with experimental test results and solutions based on Finite Element models shows that proposed procedure can be used to get a fast, yet accurate, estimate of the entire force–displacement curve and, in particular, of the pier ultimate displacement.

Modelling issues and pushover response of singlestory older steel buildings

AbstractThe paper describes a study concerning the seismic response of some typical non‐residential single‐story older steel buildings. To this end, the design of two archetype buildings was simulated according to structural codes and standards of practice used in Italy in the 1980s‐1990s. The basic structural layout was assumed to be made of trussed portals in the transverse direction and concentric braces in the longitudinal direction. In the direction of the trussed portals, two alternative structural options were considered: (a) a pinned column base with moment action provided by the truss, and (b) a semi‐continuous column base with a pinned connection between the truss and the column top cross section. 3D finite element non‐linear models of the two case study structures were built. The model included the main frame members, some critical connections and explicit representation of fracture propagation for braces. Results from non‐linear static analysis are then presented and discussed. The paper highlights differences in the structural response due to differences in the selected design options, comparing both global and local response results.

Pushover Response of Multi Degree of Freedom Steel Frames

Seismic codes use the behaviour factor to consider the ductility and the structure's non-linearity to improve the system's overall performance. Generally, Steel moment-resisting frames are characterized by a relatively high period showing high deformability and, foreseen that with stringent damageability criteria, the adopted behaviour factor might not optimally be utilized for achieving better performance of the frames. The design is generally governed by stiffness, leaving behind a complex structural system where the capacity design rules are disturbed and therefore necessitates to relax the drift limits for such frames. Given this and with extensive parametric analysis, the current paper aims to examine the behaviour factor of steel Moment Resisting Frames (MRFs). The parametric analysis has been conducted on rigid steel MRFs of 9, 7, and 5 storeys with bay 4 different bay widths of 9.15 m, 7.63 m, 6.54 m, and 5.08 m. Perimeter frame configuration has been designed using 4 different behaviour factors (q = 6.5, 4, 3, and 2) for a total number of 144 cases. Static nonlinear analysis has been conducted, and consequently, the behaviour factors have been examined. It has been observed that compatibility is required while choosing the drift limit for an assumed ductility class of the code. Doi: 10.28991/cej-2020-SP(EMCE)-08 Full Text: PDF

Numerical modeling and design sensitivity of structural and seismic behavior of UHPC bridge piers

Advanced behavior of Ultra-high performance concrete (UHPC) is attracting a growing interest among the construction industry worldwide. Currently, UHPC is commonly used in precast bridge deck joints and connections. As the UHPC market grows, the material will have a great potential to extend to larger structural applications. However, there is no guidance yet on best practices or optimum structural designs that fully utilize the UHPC superior mechanical properties for larger components. The objective of this study is to better understand the overall behavior, failure mechanism, and effect of reinforcement and design details of UHPC bridge columns using detailed finite element modeling. The pushover response of a two-column bridge pier with the typical geometry and gravity loads obtained from a representative California bridge is investigated when UHPC is used instead of conventional concrete for the columns. A detailed sensitivity/parametric analysis is conducted to assess the effect of different steel fiber ratio, longitudinal reinforcement ratio, and steel grades of reinforcement bars on the overall structural behavior of the columns. The total strain crack model, as readily implemented in DIANA FEA, is utilized with user-defined input to model the UHPC constitutive material behavior. The UHPC stress-strain relationships in tension and compression are independently defined using uniaxial curves from the literature. For comparison, the two-column bent of conventional concrete is modeled and used as the reference case to evaluate the relative increase in load capacity of the UHPC bridge columns.

Seismic response assessment of reinforced concrete structures based on displacement, force and energy criteria, considering soil-structure interaction

ABSTRACTSeveral 3D nonlinear models consisting RC moment-frame and dual frame-wall systems were developed using generic structures’ algorithm. A realistic nonlinear modelling of ductile behaviour for RC elements was performed in combination with the sub-structuring method to take into account SSI. Nonlinear pushover and nonlinear response history analyses were conducted to evaluate displacement-based ductility and damage indices of the structure, normalised stories shear forces and overturning moments, normalised story inertial forces and kinetic energy, as well as foundation rocking motion. The effects of different paramters including the foundation flexibility, the seismic force-resisting system, directivity effect of near-filed earthquakes, story strength distribution, uni-directional vs. bi-directional excitation, and number of stories on the structures' seismic respones were considered. The results indicated the seismic response values were noticeably affected by the directionality factor which is itself influenced by the ratio of pulse period to the structure period for near-field earthquakes. Besides, the distributions of the responses along the height of the structure was mainly controlled by both the lateral resisting system type and number of stories. Both of these parameters also had a significant effect on the role of SSI in modifying the ductility factors and the foundation rocking motion.

Vector mechanics-based simulation of large deformation behavior in RC shear walls using planar four-node elements

For the large deformation of shear walls under vertical and horizontal loads, there are difficulties in obtaining accurate simulation results using the response analysis method, even with fine mesh elements. Furthermore, concrete material nonlinearity, stiffness degradation, concrete cracking and crushing, and steel bar damage may occur during the large deformation of reinforced concrete (RC) shear walls. Matrix operations that are involved in nonlinear analysis using the traditional finite-element method (FEM) may also result in flaws, and may thus lead to serious errors. To solve these problems, a planar four-node element was developed based on vector mechanics. Owing to particle-based formulation along the path element, the method does not require repeated constructions of a global stiffness matrix for the nonlinear behavior of the structure. The nonlinear concrete constitutive model and bilinear steel material model are integrated with the developed element, to ensure that large deformation and damage behavior can be addressed. For verification, simulation analyses were performed to obtain experimental results on an RC shear wall subjected to a monotonically increasing lateral load with a constant vertical load. To appropriately evaluate the parameters, investigations were conducted on the loading speed, meshing dimension, and the damping factor, because vector mechanics is based on the equation of motion. The static problem was then verified to obtain a stable solution by employing a balanced equation of motion. Using the parameters obtained, the simulated pushover response, including the bearing capacity, deformation ability, curvature development, and energy dissipation, were found to be in accordance with the experimental observation. This study demonstrated the potential of the developed planar element for simulating the entire process of large deformation and damage behavior in RC shear walls.

Push-Over Analysis of RC Frame with Corroded Rebar

As known, the Italian building heritage largely consists of reinforced concrete frames designed before the ‘80s, which are, in many cases, built in the absence of specific anti-seismic criteria. Moreover, many of them, today, are characterized by bad structural conditions. Moreover, the problem of the structural conditions of the existing buildings, and their residual strength capacity, is often linked to the deterioration induced by the corrosive phenomena, which end up having a big impact on steel rebar mechanical properties. In this work, in order to investigate the influence of corrosion-damage on seismic response of existing reinforced concrete structures, a study has been carried out by analysing the non-linear behaviour of a reinforced concrete frame. The strength deterioration and reduction of the cross-section of steel rebar have been investigated and taken into account in the numerical analysis. This work shows the way in which the corrosion levels affected the push-over response, and the numerical results have been deeply analysed.

Static pushover response of spring anchored unbonded post-tensioned rocking systems

This paper describes the static pushover response of a proposed lateral force resisting system that uses spring anchored post tensioning (PT) tendon to create a rocking system. The spring at the PT tendon anchorage is aimed at facilitating manual post tensioning of the PT tendon which helps to implement rocking systems in developing communities subjected to high seismic hazards without the need for trained workers or specialized equipment. The reduction in the lateral stiffness of this system at high intensity loads causes rocking behavior that is initiated by a gap opening at the base of the system. The PT tendon is unbonded over the length of the system to prevent yielding and the loss of prestressing force. Because the prestress force in the unbonded PT tendon is maintained, the lateral force resisting system exhibits self centering behavior. This paper derives closed form expressions that describe the lateral force deformation behavior of the proposed system. A simple finite element analytical model is presented to verify the closed form expressions and to study the effects of the system parameters on the static pushover response. Results of this study show that the closed form expressions display an excellent agreement with the analytical model including the predictions of the gap opening, clamping of the spring element, yielding and fracture of the PT tendon.

Spatial distribution of seismic responses in tall buildings

Seismic design of tall buildings is mostly achieved by a performance-based approach followed by a series of deformation- and force-based response assessments. This approach does not include explicit quantification of ductility or damage induced to structures. The aim of this study is therefore to propose an alternative seismic design method for tall buildings by introducing the spatial distribution of the ductility and damage index. The method comprises overall response assessment considering seismic directionality effects in the estimation of critical responses polarised along non-principal planar directions. Height-wise response distributions can also be studied if the spatial distribution formulation is extended in terms of inter-storey demand parameters. A case study was done on a 42-storey building with concrete core wall dual system by conducting multi-direction pushover and non-linear response history analyses. Regression analyses indicated up to 35% and 40% increase of the critical responses due to the directionality effects on planar and vertical response distributions.

Probabilistic models of abutment backfills for regional seismic assessment of highway bridges in California

Seismic responses of ordinary highway bridges that feature stiff superstructures have been shown to be strongly affected by abutment-backfill interactions. Seismic risk assessment of these bridges at the regional scale faces the added challenge of having to deal with the large uncertainty in backfill properties. In this regard, the study develops probabilistic backfill models to better quantify the uncertainties in modeling the abutment. First, efforts to establish the validity of the numerical method in predicting the pushover response of backfills are described. Advanced plasticity materials are used in finite element models (FEMs) to simulate sandy and clayey soils that yield consistent backfill force-displacement relationships against full-scale test results. Second, a probabilistic analysis framework is constructed to incorporate soil uncertainties that are identified from field investigations. Statistical moments are extracted from the resultant pushover curves to fully define the probabilistic backfill models, which are verified to bear appropriate uncertainty treatment and reasonable height adjustment factors. Further, statistical analysis tools are used to investigate the influences of different backfill models on the bridge demand estimates of two common bridge classes. The study reveals that backfill models will affect the response estimates of different bridge components in both diaphragm and seat-type abutment bridges. However, probabilistic models shall be especially considered on backfills for the bridge components that are expected to have dominant responses in the longitudinal direction. The proposed backfill models appear to outperform previous deterministic models in predicting realistic bridge responses. The models can be employed in the task of regional seismic assessment of various bridge classes.

Does a Single ANN Properly Predict Pushover Response Parameters of Low-, Medium- and High-Rise Infilled RC Frames?

Artificial neural networks, ANNs, can predict the behavior of systems that have common main features. When the problem under consideration contains groups that involve different main features, different ANNs are needed to predict the behavior of each group separately. In this paper, the efficiency of a single ANN to predict the lateral behavior of two-span structures representing a mix of low-, medium- and high-rise buildings in Egypt was investigated. All buildings were first analyzed using nonlinear pushover analysis to obtain their capacity curves, failure loads and displacements. Obtained data were used for training different ANN models. The results indicated the efficiency of a single ANN to predict the behavior of a mix of all buildings under investigation with a confidence level of 99%. The successful network was further utilized to obtain another set of data that were merged with the original data and used to develop a design neural network. The obtained network showed a very good capability to predict design variables which can be a good tool for engineering practitioners.

Collapse Mechanisms of Controlled Rocking Steel Braced Frames: Base Rocking Joint vs. Capacity-Protected Frame Members

Controlled rocking steel braced frames (CRSBFs) have been proposed as a low-damage seismic force resisting system with reliable self-centering capabilities. The frame members in CRSBFs are selected to remain elastic during design-level earthquakes, so they must be designed to resist the peak forces from at least the first-mode pushover response. However, several researchers have shown that higher mode effects can contribute significantly to the peak member forces. Some collapse assessment studies on CRSBFs have included member yielding and buckling in the numerical models, but the studies have not examined a range of possible design intensities for the higher modes, and have not separated the influence on the collapse risk of the capacity design from that of the design of the base rocking joint. This paper presents the collapse assessment results for 12-story CRSBFs that were designed either excluding the higher-mode forces, or including the higher-mode forces at the DBE level, MCE level 1.5 times the MCE level, and 2.0 times the MCE level. The ground motions were selected conditionally based on the first-mode period of each example frame. The probability of collapse during an MCE-level event was computed for the frames when buckling and yielding of the frame members was modeled, and compared to the probabilities of collapse when the members were modeled as elastic. The results indicate that the base rocking joint design was more conservative than required to provide adequate collapse prevention compared to the design of the frame members. Including the higher-mode forces at the MCE level for capacity design seems appropriate from a collapse prevention perspective.

Use of Ricker motions as an alternative to pushover testing

When undertaking centrifuge studies on seismic soil–structure interaction, it is useful to be able to define the pseudo-static ‘pushover’ response of the structure. Normally, this requires separate centrifuge experiments with horizontal actuators. This paper describes an alternative procedure, using Ricker ground motions to obtain the pushover response, thereby allowing both this and the response to seismic shaking to be determined using a centrifuge-mounted shaker. The paper presents an application of this technique to a 1:50 scale model bridge pier with two different shallow foundations, as part of a study on seismic protection using rocking isolation. The moment–rotation (‘backbone’) behaviour of the footings was accurately determined in the centrifuge to large rotations, as verified through independent three-dimensional dynamic non-linear finite-element modelling. Ricker wavelet ground motions are therefore shown to be a useful tool for the identification of pushover response without requiring additional actuators. Furthermore, a simplified analytical methodology is developed, which allows one to predict the maximum foundation rotation induced by a specific Ricker pulse. This methodology may be useful in predicting the characteristics (frequency and acceleration magnitude) of the Ricker pulse required to describe the pushover response of any (practically) rigid oscillator supported on shallow foundations.

Comparative in-plane pushover response of a typical RC rectangular wall designed by different standards

Structural walls (also known as shear walls) are one of the common lateral load resisting elements in reinforced concrete (RC) buildings in seismic regions. The performance of RC structural walls in recent earthquakes has exposed some problems with the existing design of RC structural walls. The main issues lie around the buckling of bars, out-of plane deformation of the wall (especially the zone deteriorated in compression), reinforcement getting snapped beneath a solitary thin crack etc. This study compares performance of a typical wall designed by different standards. For this purpose, a case study RC shear wall is taken from the Hotel Grand Chancellor in Christchurch which was designed according to the 1982 version of the New Zealand concrete structures standard (NZS3101:1982). The wall is redesigned in this study to comply with the detailing requirements of three standards; ACI-318-11, NZS3101:2006 and Eurocode 8 in such a way that they provide the same flexural and shear capacity. Based on section analysis and pushover analysis, nonlinear responses of the walls are compared in terms of their lateral load capacity and curvature as well as displacement ductilities, and the effect of the code limitations on nonlinear responses of the different walls are evaluated. A parametric study is also carried out to further investigate the effect of confinement length and axial load ratio on the lateral response of shear walls.

Earthquake vulnerability assessment of a mobile jackup platform in the Gulf of Suez

The vulnerability of an existing jackup platform, in the Gulf of Suez region, to earthquake ground loads, is investigated in this paper. A case study for the earthquake response assessment of a typical mobile jackup platform located in the Gulf of Suez area is presented. The seismic performance of the jackup rig is assessed using the finite-element method. A nonlinear finite-element model of the jackup rig is constructed taking into account the effect of structure to soil interaction. The platform is first assessed for environmental loads including waves and currents. Earthquake ground motion is then incrementally applied using a time-domain dynamic pushover response analysis. Member stresses resulting from environmental loads are combined with seismic stresses. Results show that the platform is able to resist low-to-moderate seismic activity up to 0.30g after which the integrity of the platform could be compromised. The Gulf of Suez is a seismically active region. Jackup platforms operating in this area should be assessed for earthquake loads.

Persisting challenges for performance-based building assessment

Intense research and refinement of the tools used in performance-based seismic engineering have been made, but the maturity and accuracy of these methods have not been adequately confirmed with actual data from the field. The gap between the assumed characteristics of actual building systems and their idealized counterparts used for analysis is wide. When the randomly distributed flaws in buildings as they exist in urban areas and the extreme variability of ground motion patterns combine, the conventional procedures used for pushover or dynamic response history analyses seem to fall short of reconciling the differences between calculated and observed damage. For emergency planning and loss modeling purposes, such discrepancies are factors that must be borne in mind. Two relevant examples are provided herein. These examples demonstrate that consensus-based analytical guidelines also require well-idealized building models that do not lend themselves to reasonably manageable representations from field data. As a corollary, loss modeling techniques, e.g., used for insurance purposes, must undergo further development and improvement.