P-delta Effects Research Articles

Effects of P-delta and spectral shape of ground motion records on strength reduction factor and inelastic displacement ratio of SDOF systems with deterioration

Force-based design, due to its usefulness and simplicity with reasonable accuracy, is the main core of current seismic design codes. In this method, the behavior factor and deflection amplification factor are major elements that play a key role in linking linear and nonlinear behavior. This article examines the strength reduction factor due to ductility (Rμ) and inelastic displacement ratio (Cμ), which are important parts of the codes coefficients, considering the spectral shape of ground motion records and the P-delta effect. The nonlinear response history analysis (NL-RHA) is conducted for an extensive range of single-degree-of-freedom (SDOF) systems with different periods by categorizing the ground motion records based on ε, SaRatio, and Np. The most important emphasis of the paper, to which attention has not been paid previously, is to study the effect of spectral shape of ground motion records as an input excitation indicator and the P-delta effect as a structural parameter on strength reduction factor and inelastic displacement ratio of SDOF systems. In addition, the effects of some other structural parameters, including the ductility factor, deterioration, post-capping stiffness ratio on strength reduction factor and inelastic displacement ratio are evaluated. The results demonstrate that the values of Rμ and Cμ change by changing ε in the range of short periods than long periods. However, they vary more clearly with the change in SaRatio and Np. Furthermore, with the increase in θ-αs as an index of the P-delta effect, the system requires more design strength, and Cμ increases as well.

EXPEDITIOUS NUMERICAL CAPACITY ASSESSMENT IN PRECAST STRUCTURES VIA INELASTIC PERFORMANCE-BASED SPECTRA

The seismic design of precast structures hinges on unique characteristics intrinsic to precast technology. Emphasis is placed on lightweight structural elements for efficient on-site assembly and cost reduction. This leads to increased slenderness in beams and columns compared to traditional cast-in-situ constructions, accentuating the role of second-order effects. Dry pinned joints, favoured for connecting beams and columns, contribute to the overall efficiency in assemblage. Cast-in-situ concrete is typically reserved for connection to foundations and topping precast floor elements. Pinned joints transform the structure into an ideal isostatic system, with cantilevered columns anchored securely at the base, in designers' mind. However, this transformation reduces the energy dissipation capacity, preventing plastic hinge formation in beams and amplifying P-Delta effects in columns. The simplified approach proposed herein assesses dynamic instability in single and multi-storey precast hinged frames, providing a tool for expeditious numerical capacity assessment, useful at the initial design stage. The goal is to predict dynamic collapse and/or the attainment of specific seismic-oriented limit states based on fundamental structural parameters. Incremental nonlinear dynamic analysis, utilising far-field ground motion records, is employed to evaluate performance of a variety of precast structures modelled as equivalent single-degree-of-freedom systems. The outcomes yield inelastic spectra that provide insights into the structural capacity in terms of response modification factor and could help analysts/designers towards seismic performance-based design as well as the assessment problem. These spectra, which can themselves be taken as metrics for structural performance evaluation (in addition to as a reliable tool/means for design), are generated based on various structural parameters, including building height, column aspect ratios, and floor mass configurations, in relation to different limit states typically deemed crucial in the design of these structures for earthquake-induced actions. Regression analyses of median spectra show that polynomial expressions could fit them with good accuracy, as testified by a coefficient of determination in the 0.76-0.98 range for most of the cases.

The Influence of Variations in Shape and Placement Sliding Walls on The Behavior of Multi-Story Building Structures to Withstand Earthquake Loads (Case Study: Building Pasar Raya Inpres Block)

System the structure of Building a Pasar Raya Inpres Padang Block IV, namely system double that uses wall shift as retainer lateral load and SRPMK as retainer style gravity, but cold sliding on the building the only there is on the 1st floor only if wall shifts No continuously until building roof floor so can influence behavior structure building the like mark style shift basis, displacement, deviation between the floor and p-delta influence. The study this aims to compare mark style shift basis, displacement, and deviation between which floor and p-delta later will compared against 4 variation models shape and placement wall shift. The method used that is method comparative with analysis uses response spectrum using ETABS software. Results of the study show model 2 structure has a mark base shear namely 3658,658 kN. Model 2 has a mark displacement the smallest in the x direction is 3,766 mm and Model 4 has a mark displacement the smallest in the y direction is 2,347 mm. Model 2 has a mark deviation atar floor smallest namely 8,019 mm for the X direction and 4,015 for the Y direction. All models are confirmed safe at the moment checking the P-Delta effect, with model 2 having the mark lowest for the X direction and Y direction.

Optimization of Staging Height of RCC Overhead Water Tank in High Seismic Zones Using P-Delta Analysis

Abstract: This study investigates the P-delta effect, which is a secondary effect or a geometric non-linear effect in the analysis of a circular overhead water tank with a capacity of 100 KL using STAAD software in high seismic zones, i.e., Zone IV & Zone V with a focus on optimization of staging height and to quantify the effect of P-Delta. Initially, a linear static analysis was performed without considering the P-Delta effect to determine the shear forces, bending moments and lateral displacements due to all possible loads including seismic and wind loads acting on RCC overhead water tanks. Subsequently, the P-Delta effect has been considered to assess the structural behaviour of the RCC overhead water tank with varying staging heights. To optimize the staging height, the maximum lateral displacement has been considered as the governing criteria. Based on the analysis, the optimum staging heights can be observed at 30 m. and 33 m. in Seismic Zone V and Zone IV respectively

Eccentrically compressed behavior of UHPC columns considering the P-delta effect

Eccentric compression is a critical behavior observed in arches and columns, particularly in structures constructed with ultra-high performance concrete (UHPC). Compared to normal concrete structures, those made with UHPC exhibit distinct behaviors that need to be clearly investigated. This study comprehensively investigates UHPC columns under eccentric compression load through experimental study and theoretical analysis. Various experimental parameters, including slenderness ratio, eccentricity distance, fiber content, and stirrup ratio, were examined across 26 UHPC columns. Failure modes were evaluated using digital image correlation (DIC) methods. The load-displacement responses indicated that slender columns subjected to significant eccentricity exhibited load decreases during yielding stages, whereas short columns experienced load increases. This discrepancy in yielding stages was attributed to P-delta effects. In addition, theoretical models were developed to determine the ultimate bearing capacity of columns experiencing compression-controlled and tension-controlled failures, considering the P-delta effect caused by the different slenderness ratios. The moment magnifying coefficients for UHPC were calibrated based on theoretical analyses of the limit curvature of eccentric compression members. The proposed theoretical models agreed well with the experimental results, with an average ratio of 1.02. The second-order effect for the case of UHPC short column with a slenderness ratio of 5 can be ignored as per Eurocode 2, which is less than 10 % of the corresponding first-order effect.

DESIGN OF REINFORCED CONCRETE STRUCTURE WITH ORDINARY MOMENT FRAME IN LOW SEISMIC REGION (CASE STUDY: MIDRISE SHOPPING BUILDING IN SINGKAWANG CITY)

This paper focuses on the design of a reinforced concrete structure for an eight-story shopping building in Singkawang City, located in a low to moderate seismic area. The study integrates relevant design considerations in response to the region's seismic conditions. Through structural analysis, the building is categorized as seismic design category B due to moderate seismic risk, leading to the selection of an ordinary moment-resisting frame system compliant with SNI 1726:2019. Emphasis is placed on the importance of using such a system to enhance ductility and prevent brittleness during earthquakes.The research emphasizes the need to design structures capable of withstanding various loads, including dead, superimposed dead, live, wind, and earthquake loads, particularly in West Kalimantan, known for its historically low to moderate seismic activity. Recent earthquake records highlight the necessity of earthquake-resistant design for safety and durability. Structural analysis confirms the building's stability against seismic forces, with a modal participation ratio meeting SNI 1726:2019 requirements, indicating robust response under seismic loads.The study also assesses inter-story drift and P-Delta effects to ensure they meet allowable limits, which is crucial for preserving structural integrity and preventing post-earthquake instability. A detailed reinforcement design following SNI 2847:2019 enhances structural strength and durability, especially when under seismic loading. The foundation design uses tailored hollow spun piles to provide sufficient bearing capacity and stability. This approach demonstrates resilience against potential seismic events in low-to-moderate seismic regions, highlighting the importance of integrating seismic design principles and ductility considerations for effective earthquake hazard mitigation.

The Performance Assessment of the Structural Bracing Model for Multi-Story Building

Earthquakes are a severe issue for construction. The building collapsed due to the earthquake because it could not bear the earthquake load. Even more so, it was constructed using outdated and different building regulations that do not comply with modern building codes that account for seismic loads. As a result, disaster mitigation methods, such as retrofitting, must be implemented. Retrofitting procedures are commonly used in many developed countries. The bracing system is a typical retrofitting method used on building structures. In this study, a retrofitting program was carried out on The State Finance Building II Semarang, which was built in the 1980s, one of the old buildings in Semarang City, using a reinforced portal structure. This study's bracing system is a Concentrically Brace Frame (CBF) with Inverted V Brace and V Brace variations. The structural analysis software ETABS V.18.2.0 analyzes the building's structure. The structural review includes story drift, the P-Delta effect, and horizontal torsion irregularities. According to the results, steel bracing can minimize the period and displacement associated with story drift, making the structure more stable, with a maximum displacement reduction of 59.66% for inverted V-type steel bracing. Aside from that, steel bracing also can minimize the occurrence of torsion in the building. As a result, steel braces can be used to strengthen the structure.

Pushover Analyses of Slender Cantilever Bridge Piers with Strength and Ductility Degradation

Reinforced concrete bridge piers are often subject to spatially non-uniform deterioration which typically produces strength and ductility degradation. When piers are subject to deterioration, the sectional response is no longer uniform and the determination of the pushover curves from sectional response is no longer immediate. This paper proposes a simplified procedure to accomplish this task for RC bridge cantilever piers. The method is simplified only with respect to geometric nonlinearities and yields an accurate estimate of the ultimate displacement, free of numerical issues typical of fiber-based finite elements. The procedure is based on an iterative approach to enforce the element equilibrium under P-Delta effects induced by vertical loads and can consider arbitrary deterioration patterns through the specification of different moment-curvature response along the elevation. After validating the approach with experimental results, a parametric analysis of the influence of sectional strength and ductility degradation is carried out for the case study of a rectangular hollow RC pier. Results show that significant variations of the pier equivalent plastic hinge length can be expected because of the occurrence of deterioration in the lower part of the pier. Moreover, paper provides quantitative measure of the extent of the strength and ductility degradation.

Alternative Design of Menara 17 Structure in Surabaya with Castellated Steel Beam

Assigning structural material is one of critical step in designing, steel material often used because of it high ductility. Menara 17 is a 17 storey multipurpose building with reinforced concrete as an existing material structure. This research analyze Menara 17 alternative design with Special Moment Frame (SMF) steel structure to resist lateral load with high ductility and expected to withstand significant inelastic deformation. Castellated beam is used to increase it capacity to weight ratio and ease MEP installation through the opening. SNI and AISC is used for main design guide. From the analysis result, the alternative design has satisfy criteria of irregularity, P-delta effect, story drift, and Strong Column Weak Beam. Honeycomb castellated beam HCO 520.250.9.14 profile is used as main beam. King-cross column KC 800.400.16.30 profile is used as main column. Circular hollow section CHS 406,4.40 profile is used as diagonal bracing. Wide flange WF 200.200.8.12 profile is used as lateral bracing. Lateral bracing to beam is connected with shear connection. Beam to column is connected with endplate moment connection. Menara 17 design with steel structure is 59,17% less heavy than reinforced concrete structure.

PERFORMANCE ANALYSIS OF HORIZONTAL IRREGULAR BUILDINGS BASED ON RESPONS SPEKCTRUM AND TIME HISTORY METHODE

Indonesia is geographically located in the Pacific Ring of Fire, Especially on Java Island, which has the densest infrastructure and population and is located between the Indo-Australian plate and the Eurasian plate, causing this area to have many active volcanoes and has a high potential for earthquakes. Therefore, it is necessary to pay the planned earthquake load in planning the building structure design to minimize losses due to the earthquake. This study aims to determine the structure's performance against safeguards, deviations between levels, and structural stability limits against earthquake loads and to review horizontal structural irregularities based on SNI 1726: 2019 regulations in existing buildings at the Simpang Temu MRT Dukuh Atas Jakarta Building. The analysis process was carried out by 3D building modeling using the ETABS software program, analysis based on time history and spectrum response. Time History analysis uses recorded earthquakes of Kobe Japan, ChiChi Taiwan, and El Centro which match the earthquake response spectrum, the results of the analysis based on the program were carried out to compare the two methods used. Based on the results of the analysis, the building is classified into horizontal irregularities with excessive torque ratio > 1.4, average displacement value from the 2nd to 12th floor in the horizontal direction X exceeds the drift value limit. The results of the instability limit for structural stability against displacement based on the P-Delta effect still meet the structural stability limits so it can be stated that the structure is stable and safe.

The comparison of X-braced frame and moment frame on structural building (case study: government office of North Toraja, South Sulawesi, Indonesia)

The seismic force can damage the building and harm the occupants. Therefore, its structure needs to be designed seismic-resistant. One of the essential things in seismic-resistant building is the effect of lateral force to its structural rigidity. It can be improved by using the lateral resistant element such as bracing and shear wall. The lateral element used in this study is concentric X-bracing. This study conducted an optional structural model of the office of North Toraja Regent, Panga, South Sulawesi. The building was originally analyzed as a whole unit structure, but it has already rotated in its first mode shape due its irregularity. The comparison analysis is conducted by using the same existing structure configuration, except with the addition of X-bracing. The analysis results of the dynamic response are the fundamental building period, mode shape, base shear, lateral displacement and P-delta effect. The fundamental building period using X-bracing is smaller than moment frame building. It indicates that the use of X-bracing lead to the stiffer building. The use of the X-bracing results in a larger base shear value than the moment-frame building. The difference in base-shear between X-braced frame with moment frame is about 211.77% and 212.10% for seismic force with X-direction and Y-direction respectively.

Assessment of P-Delta Effect in Multistorey Building

Abstract: This research paper focuses on the analysis of the P-delta effect on high-rise structures, which has been the subject of numerous recent studies. The P-delta effect is considered the secondary effect and is deemed more significant. It arises due to an increase in the number of stories in a structure and is particularly relevant when considering lateral loads such as earthquakes and wind loads. The objective of this paper is to incorporate axial load and displacement in the calculation of the P-delta effect in multi-storey buildings. The analysis involves RCC framed structures of different heights, specifically G+15, G+20, and G+25. The load combinations are determined according to IS 456:2000, and the software E-Tabs is utilized for the analysis. The earthquake load is applied to the structure based on IS-1839 (2002), and deflection curves are observed. Both models with and without the P-delta effect are examined in terms of bending moment, shear force, and displacement. The findings clearly demonstrate the necessity of considering the P-delta effect in multi-storey buildings. The analysis is conducted using the linear static method, and the results provide valuable insights into the structural behavior under different loading conditions.

Seismic Fragility Assessment of SMRFs Equipped with TMD Considering Cyclic Deterioration of Members and Nonlinear Geometry

This paper presents seismic fragility curves to assess the effect of far-field ground motions on the behavior of high-rise steel moment resisting frame (SMRF) structures equipped with Tuned Mass Damper, considering the cyclic deterioration of members and P-Delta effect in the nonlinear region. For this purpose, three 8-, 20-, and 30-story SMRF structures are selected, 44 earthquake record sets are extracted from the FEMA P-695, Incremental Dynamic Analysis (IDA) is operated, and four structural damage states are considered through the framework of HAZUS, including slight, moderate, extensive, and complete. Maximum structural inter-story drift and floor acceleration are employed to quantify the damage states, and spectral acceleration is used as the intensity measure. Results show that the Tuned Mass Damper can reduce the probability of damage under earthquake excitation in all damage states for both structural and non-structural elements. The decline varies from 4.0% to 20.0%, depending on the ground motion intensity level, based on engineering demand parameters. Moreover, it is clear that nonlinear properties and component deterioration under cyclic excitation can affect structural response in all damage states, which concerns the obtained curves.

Effects of the Vertical Component of Ground Motion on the Maximum-Inelastic-Horizontal-Response of SDOFs

This study investigates potential effects of the vertical-component-of-ground-motion (VCGM) on the maximum-inelastic-horizontal-response (MIHR) of single-degree-of-freedom (SDOF) systems. The effects of VCGM can be considered in two categories. First, it may initiate some modes of failure, like over-compression, and second, it might adversely influence the horizontal response through altering the P-delta effect. The latter is a result of variation of the gravitational acceleration, and hence, seismic weight, upon action of the VCGM. This study uses time-history analysis to compare the response of SDOFs in presence and absence of the VCGM. In both cases, the P-delta effect is inherent in analyses and period-dependent feature of the stability-coefficient, which is essential for reliable treatment of the P-delta effect, is explicitly reflected. Since available record selection and scaling strategies use uncoupled vibrators in vertical and horizontal directions, this research follows two steps to avoid undesirable bias. The first step, which focuses on examining the influence of some important parameters, adopts an event-based record selection scheme. Results indicate that for certain combinations of the strength reduction factor and initial period of vibration the effect of the VCGM on the MIHR is significant. Specifically, the systems with initial periods between 1.0 and 2.0 s are found most vulnerable. Moreover, the mentioned effect is not limited to near source regions. The second step evaluates capability of the VCGM to initiate dynamic instability. In this step, a set of 26 records, which resembles an assumed target spectrum at a near field site, is used. Results show that under action of some of the examined records, the presence of the VCGM leads to dynamic instability; hence, this study suggests consideration of the VCGM for collapse evaluation.

Analytical Study of Buckling Restrained Braced Frames in Different Seismic Zone Using ETABS

Abstract Tall buildings have unique seismic challenges, particularly the P-delta effect. This can cause an increase in loads on certain parts of the structure, leading to potential instability or collapse. The solution is to use buckling restrained bracing (BRB) systems, which improve the lateral strength of the structure and control the P-delta effect. The present study aimed to determine the effectiveness of various brace configurations in reducing the seismic response of a 50-story reinforced concrete structure, with a focus on P-delta effects. To achieve this, linear dynamic analysis (response spectrum analysis) was conducted using E-TAB software. The selection of bracing configuration, however, depends upon the seismic zone. For this reason, five distinct configurations (X-pattern, inverted V, forward inclined, zig-zag, and bare frame) are considered for the analysis of buildings in different seismic zones. A building model was employed to study the behaviour of a structure with and without BRB to compare the parameters of storey drift, story displacement, diaphragm drift, story shear, story stiffness, and story acceleration using E-TAB software. Results showed that both Type-4 and Type-2 braces perform similarly in several aspects in seismic zones III and V. However, Type-2 braces perform slightly better in terms of storey stiffness-Y, with a lower difference of 39-40 % compared to Type-4 braces with a difference of 49 %.

Sustainable Earthquake-Resistant Mixed Multiple Seismic Systems

Mixed multiple seismic systems (MMSSs) are ideally suited for sustainable seismic design (SSD). MMSSs are combinations of two or more different earthquake-resisting structures (ERSs) that provide lateral support for gravity frameworks. Same-system combinations have been demonstrated to not be suitable for SSD. Regardless of the carbon footprint reduction, unless a structure has been designed for seismic sustainability it would be disposable with greater harm to the environment. Here, design means planning for both seismic resistance as well as post-earthquake realignment and repair (PERR). Earthquakes are random, natural, and dynamic events, whereas PERR is a deliberate, manual, and static process. In SSD the practicality of PERR is as important as the relevance of the theoretical assumptions. In SSD the non-lateral-resisting items are designed not to partake in seismic resistance, nor hinder the realignment process. Additionally, efforts are made to mitigate the P-delta effects that undermine the global strength of the system and oppose the recentering effort. The purpose of this paper is to identify and remedy design flaws and physical issues that prevent MMSSs from achieving seismic sustainability as cost-effectively as possible. Two newly developed technologies, the ladder moment frame (LMF), and the fail-safe (FS) system, as well as a capacity distribution rule together with six simple axioms are introduced. Brief descriptions of LMF and FS are presented in the text.

Improved estimation of P-delta effects on the response of bilinear SDOF systems

P-delta ( PΔ) effects can worsen the seismic performance of building and bridge structures and potentially lead to dynamic instability and collapse. An accurate characterization of PΔ effects is therefore imperative, for both design and assessment of structures. Adopting an earthquake database composed of 7032 ground motions, this article uses the results of a large statistical analysis of amplifications of the displacement demand due to PΔ effects for bilinear single-degree-of-freedom systems to investigate and improve practice-oriented methods to account for PΔ effects. A large range of fundamental periods, ductility levels, and effective heights are investigated, and limits for dynamic instability and negligible PΔ effects are examined in terms of both elastic and inelastic stability coefficients. It is seen that systems with the same stability coefficient present increased PΔ induced displacement amplification with reducing fundamental period and increasing ductility level. New expressions for estimation of the median values of the PΔ displacement amplification ratio are proposed that take into account the combined effect of stability coefficient, ductility level, and fundamental period with improved transition close to dynamic instability. Results of the numerical analyses indicate that the new expressions provide improved accuracy over existing approaches without undue complexity.

Verification of seismic enforced-displacement pushover procedure on torsionally flexible, asymmetric, multi-storey r/c buildings

A recently proposed direct Displacement-based procedure of nonlinear static (pushover) analysis on multi-storey reinforced concrete (r/c) buildings is verified here against the results of Nonlinear Response History Analysis. An asymmetric, regular in elevation, torsionally flexible, multi-storey r/c building designed according to Eurocode EN 1998 is investigated. Taking fully into account the inelastic torsion and the higher mode effects, as well as the P-Delta effects, the proposed procedure applies a pattern of seismic floor enforced-displacements along on the “Capable Near Collapse Principal Axes of the building”, aiming at Near Collapse state.  The envelope of the results of sixteen final non-linear static analyses on the investigated building shows that the main aspects of the spatial seismic action effects can be safely captured by the proposed procedure, especially regarding the inelastic interstorey drift ratios, as well as the plastic mechanism of the building.

Identification and Calibration of Advanced Hysteresis Models for Recycled Rubber–Fiber-Reinforced Bearings

Several studies have investigated the feasibility of reducing the implementation cost of base isolation. In this optic, recycled rubber–fiber-reinforced bearings (RR–FRBs) represent a suitable solution for structures in developing countries. Such devices can be produced using simple manufacturing procedures at a limited cost with respect to conventional isolators. Full-scale tests on RR–FRBs featured energy dissipation values similar to those associated with high-damping natural rubber bearings (HDRBs). Equivalent viscous damping, ranging from 10 to 15%, resulted from testing of RR–FRBs, with poor degradation after cyclic loading. On the other hand, a sensible softening response, associated with the axial–shear interaction, which is much more significant compared to that exhibited by HDRBs, was observed. As a result, the numerical description of the cyclic behavior of the RR–FRBs appears to be more challenging than that of HDRBs. In past studies, simple bilinear hysteresis models were adopted to describe the cyclic behavior of low-cost rubber bearings, thus completely neglecting the P-delta effects which significantly influence the dynamic behavior of such bearings. In this paper, advanced hysteresis numerical models, able to capture the nonlinear response of RR–FRBs, were examined and properly calibrated using a powerful optimization technique, the differential evolution algorithm. Preliminary results of the numerical analyses, performed in OpenSees, were described and compared with those of experimental tests on low-cost rubber bearings. The findings of this study represent the first step of a characterization procedure aimed to provide an accurate representation of the dynamic behavior of these particular bearings. Obviously, additional studies are needed to compare results of response history analyses with those of experimental tests for real structures on RR–FRBs. In this optic, the present paper, along with further studies, could provide a new impulse for the application of low-cost rubber-based devices in current practice.

Appraisement of the P-Delta Effects in Multi-Storey Reinforced Concrete Buildings Influenced by Seismic Load

Population increment encourages engineers to build high-rise structures. However, in high-rise structures lateral load has a more severe impact on the structure than axial loads and this effect is known as the P-Delta effect. The current study aims to evaluate P-Delta effects in a high-rise structure located in Kabul city and to pinpoint the minimum height required for considering P-Delta effects in structural analysis. The analysis is carried out utilizing the response spectrum method performed by ETABS software for a total of five models with a different number of storey and lateral load-resisting systems. It is observed that with the increase in lateral stiffness, P-Delta effects can be minimized to a certain extent. Lateral displacement, storey drift, and stability coefficient are some of the other parameters considered for comparison purposes which are significantly mitigated while a shear wall is provided. Also, an adequate and proper positioning of shear walls has resulted in an appropriate solution for minimizing the P-Delta effects. Keywords: P-Delta effect, Lateral displacement, Lateral stiffness, Stability coefficient.