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The Pushover Analysis in its Simplicity

Authors:
Rahul Leslie at Kerala Public Works Department
Rahul Leslie
  • Kerala Public Works Department
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Abstract

One of the emerging fields in seismic design of structures is the Performance Based Design. The subject is still in the realm of research and academics, and is only slowly emerging out into the practitioner’s arena. Seismic design is slowly transforming from a stage where a linear elastic analysis for a structure was sufficient for both its elastic and ductile design, to a stage where a specially dedicated non-linear procedure is to be done, which finally influences the seismic design as a whole. The need for a simple method to predict the non-linear behaviour of a structure under seismic loads saw light in what is now popularly known as the Pushover Analysis (PA). It can help demonstrate how progressive failure in buildings really occurs, and identify the mode of final failure. Here, what the author has intended is to explain the method of Pushover analysis step by step, in terms basic and simple, to be understandable to anyone who is familiar the conventional seismic analysis.
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... In the interest of the application of the linear analysis, seismic action represented by the elastic response spectrum is reduced by the behaviour factor q to the design response spectrum. This means that only 1/q of the total seismic force is captured by the limit state capacity of the structure, while further displacements are accepted by the ductile capacity of the structure [3]. EN 1998-1:2004 gives a set of guidelines for detailing of structural elements and joints to ensure that the full seismic action (beyond its limit state capacity) can be taken by the ductile capacity in order to avoid the collapse. ...
... Pdelta effects, the change in stiffness of members due to cracking and yielding and change in the final estimated seismic force among all are reasons which for linear approach would mislead any inexperienced engineer in his aim to evaluate the behaviour of the structure due to the seismic action. In order to capture these effects and estimate the behaviour of the structure more accurately, a non-linear analysis must be employed [3]. It also provides an overview of the distribution of damage and collapse mechanism, as well as an estimation of the structural performance in the post-elastic range. ...
... In this paper, only flexural hinges were considered, and as such were modelled at the ends of beams and columns, forasmuch as the reinforcement yielding and concrete cracking are more likely to take place in these zones. In the numerical sense, the hinge portrays a localised force-displacement relationship (in the case of bending, the moment-rotation ratio) of an element due to seismic load, the most commonly of elasto-plastic character [3]. ...
The use of pushover analysis for evaluation of behaviour of six-storey RC building designed according to capacity design rules
Conference Paper
Full-text available
  • Oct 2019
Aseismic design of RC structures according to EN 1998-1:2004 allows reaching the limit state during the earthquake action, while ensuring sufficient deformation capacity. Seismic forces represented by the elastic response spectrum, which correspond to the linear response of the structure, are reduced by the application of the behaviour factor. Thus, the required bearing capacity is determined for the lower level of seismic action than the one that would occur due to the elastic response of the structure. Therefore, with a certain degree of damage, a nonlinear response of the structure for a real seismic action is allowed. In order to investigate the post-elastic behaviour of the structure, a non-linear analysis must be employed. This paper deals with the nonlinear static analysis of the six-story L-shaped RC building subjected to the monotonically increasing horizontal load. Since the characteristics of plastic hinges at the opposite ends of the beams differ in certain cases, two directions for each of the main vibration modes had to be examined. Therefore, the horizontal action of the positive and negative directions of the two orthogonal components was studied, as well as the two combinations of the main orthogonal components. The nonlinear behaviour of the structure was observed by the means of the development of plastic hinges throughout the structure, which also provided the insight into the progression of damage of each structural element. The target displacement was calculated using the N2 method, introduced in Eurocode 8. The behaviour of the structure, as well as the values of the target displacement and the base force, are similar for both pairs of opposite directions. The results were given in the form of pushover curves. Furthermore, obtained values of the behaviour factor were compared with the ones provided in the code. It was concluded that the structure fully corresponds to the requirements of the capacity design.
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... As forced-based design is uncapable of predict ductile behavior of the structure, during Earthquake-Resisting System (ERS) design a Modification Response Factor "R" is employed to guarantee seismic energy dissipation through hinges appearance, by designing the element to respond elastically only under 1/R th of the total seismic load and assuming that a ductile behavior will be achieve for larger loads [6]. ...
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... The Acceleration Displacement Response Spectra (ADRS) curve in ATC 40 [19] is described by seismic coe cient Ca (in uences at portion of the RS curve) and Cv (governs the downward sloping portion of RS curve), where the curve just as in IS:1893-2016 [23] has a at intensity part of 2.5*Ca and downwardsloping part which follows Cv/T [11]. ...
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Preprint
Full-text available
  • Mar 2024
Fragility analysis is essential for assessing structural vulnerability during natural hazards like earthquakes and floods. It guides risk mitigation, enhances infrastructure resilience, and informs decision-making, emergency planning, and disaster recovery efforts. This manuscript aims to explore the fragility curves potential in assessing the structural systems performance, particularly those with high irregularity. The study employs a non-linear static analysis of a G+6 storey irregular structural frame designed in accordance with Indian standards using SAP2000. It demonstrates the use of fragility curves in assessing structural performance of a G+6 irregular reinforced concrete structure under earthquake forces. This manuscript underscores the importance of considering discrete damage probabilities and collapse risks in different directions for accurately assessing structural vulnerabilities. It reveals a higher collapse probability within the direction of push-y (44%) in contrast with the push x-direction (5%), indicating a greater susceptibility to damage under specific loading conditions. The study concludes that fragility curves offer a rational and consistent method for seismic performance assessment of structures with high irregularity. It also affirms the adequacy of buildings designed as per Indian standards in withstanding earthquake forces.
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... Plastic hinge forms at a point where the structure undergoes cracking and yielding with higher intensity, resulting in considerable displacement (Leslie, 2012). When plastic hinge occurs, the elastoplastic phase changes to the plastic phase of the structure. ...
Modelling Study of Pile Group Foundation by Including Lateral Load in Clay Soil
Article
Full-text available
  • May 2023
Indonesia’s geographical condition causes earthquakes to occur more frequently. This study aims to investigate pile group response under earthquake loading by performing pushover analysis. Since clay soil is dominant and widespread in Indonesia, the study focused on pile group embedded in single layer of clay. The undrained shear strength (Su) parameters of the clay are varied from 20 kPa, to 100 kPa with 20 kPa intervals. The pile and soil were modelled by Beam-on-Nonlinear-Winkler-Foundation (BNWF), and the soil was presented as a series of Winkler springs using the nonlinear p-y method. The analysis was conducted with a finite element method (FEM) software, OpenSees. The pile was modelled as a fiber section, where the transversal and longitudinal reinforcement can be considered. The research found that the soil’s Su affects the ductility and formation of plastic hinge. Greater Su resulted in higher ductility and occurrence of plastic hinge. Higher Su was also found to increase the internal force experienced in the pile, as well as lead to higher group efficiency factor. There was no shear failure detected in the results, but bending failure happened at the lead pile in Su 100 kPa. The overturning moment phenomenon occurred on the pile group in Su 20 kPa and 100 kPa. For Su = 20 kPa, this phenomenon is caused by the middle pile and rear pile, which did not have optimal performance. Bending failure at the lead pile led to the phenomenonin Su 100 kPa.
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... The response spectrum curve described in ATC-40 has two seismic parameters such as C a and C v , which depends on soil, time period and zone type. The flat and downward slope portion of IS response spectrum curve was matched with the intensity of flat and sloping portion of ATC-40 response spectrum curve [27]. The C a and C v values were found for all the ground motion cases of PGA 0.10-1.70 ...
Effect of Seismicity on the Seismic Resilience of a R.C. Building
Article
Full-text available
  • Dec 2022
This study was carried out to evaluate the functionality of an existing reinforced concrete structure under various ground motions along with its seismic resilience. An existing high-rise G + 10 storey reinforced concrete building which was designed for a specific ground motion with peak ground acceleration (PGA) of 0.36 g was subjected to various seismicity with respect to different ground motions of PGA ranges from 0.10 to 1.70 g. For each case, the performance level and structural damage ratio were estimated by performing nonlinear static pushover analysis. The influences of different ground motions on the structural functionality and seismic resilience were examined using three recovery functions namely, linear, trigonometric and exponential. The result shows that the maximum number of hinges formed with the performance level close to or just exceeding the level of collapse prevention at the maximum considered PGA of 1.50 g and 1.70 g with loss of resilience up to 36.25%. The maximum level of PGA that the existing building would withstand along with likelihood of recovery has been obtained.
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BUILDING STRABLE AND FIXED BASE WITH SAP
Article
Full-text available
  • Oct 2021
Prior conventional building configuration chosen was regular or symmetrical building with fixed base. Practically speaking the building configuration need not be symmetrical always. In reality building rests on the soil. Usually flexible soil condition and nonlinearity of the building is neglected during analysis. In such case, the building is to be analyzed considering soil structure interaction and nonlinear conditions using appropriate software. The 3D model analysed using software should be a replica of realistic structure. In the present study a 10 storey, 3D irregular building is chosen and analysed using SAP 2000 V19.2.1 software. The irregularity chosen is in vertical direction with fixed base and with flexible soil base (continuum method). The irregular building is subjected to linear static analysis and non linear static pushover analysis. The results obtained for vertically irregular building are compared for fixed and flexible base for both linear and nonlinear analysis. The variation in displacement, base force and time period are observed. The building which displays better realistic results can be chosen for future reference.
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Seismic Vulnerability Study on RC Bare Frames Using Non Linear Ststic Analysis
Article
Full-text available
  • Aug 2016
Many buildings in the present have irregular configurations both in plan and elevation. An analysis has been performed to study the lateral forces and base shear of a Multi-storeyed (15-story) building for 4 different models. To perform analysis by equivalent static force method ETABS V.15 is used however, when the buildings are subjected to Non-Linear static analysis method, Comparison of Zone III and IV.
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