P-delta Effects Research Articles

Parametric Study of P-Delta Effect on Irregular RC Structure with Structural Systems Having Different Density of Shear Walls

P-Delta analysis affect the seismic responses of structures. When the structure responds elastically, its importance can be insignificant, but it is relevant when the structure responds to an inelastic set. The P-∆ effect normally raises the structural displacement response. Dynamic instability can also occur when the system is exposed to extreme earthquake motions. Plan irregularities can lead to substantial eccentricity between the centre of mass and the centre of rigidity in the RC framed structure, which can lead to a negative lateral and torsional response. Irregular structures require more careful structural evaluation to reach a suitable behaviour during an earthquake. In this research, a parametric study will be conducted on G+29 RC framed buildings having plan irregularity with consideration of the P-delta effect. Time history analysis, response spectrum analysis and static co-efficient method will be conducted to evaluate results of different structural systems and study the parameters like Displacement, Storey drift, Time period, Axial force, Base Shear, Bending Moment, etc with the help of structural analysis software ETABs.

Application of SV curves in performance based design of structures

The conventional Incremental Dynamic Analysis (IDA) used to evaluate the seismic response of structures, involves a series of nonlinear dynamic analyses, which requires extensive computational time and effort. This technical note utilizes a computationally efficient method to estimate IDA curves using Strength Variation (SV) curves. The accuracy of the proposed method is verified through comparisons with results of finite element analysis for 20 story SAC Los Angeles model subjected to different earthquake records, considering the P-Delta effects. Results demonstrated a reasonable agreement between the IDA curves established using the proposed method with those obtained from the conventional approach. Consequently, a new methodology for Performance Based Design (PBD) of structures is introduced utilizing SV curves. It is shown that the proposed method for establishing the IDA curves could enhance the PBD process for structures.

P-delta effect analysis of continuous distribution system based on generalized differential quadrature method

Based on the generalized differential quadrature method, an analysis method of p-delta effect for continuous distribution system is proposed. Firstly, the structural system with continuous distribution of mass and stiffness is taken as the research object. Based on the principle of virtual work, the axial and transverse vibration equations considering the effect are given. Secondly, the partial differential equations are discretized by using the generalized differential quadrature method, and the dynamic ordinary differential equations are obtained to analyze the p-delta effect of the continuous distribution system. Finally, an example based on 5MW wind turbine parameters is analyzed, and the results show that the GDQM has high calculation accuracy, which can be obtained by dividing only a few nodes; This method can not only consider the second-order effect of gravity, but also consider the time-varying p-delta effect caused by vertical earthquake, and can reveal the influence of vertical earthquake on the lateral dynamic characteristics of structures in real time; No matter the gravity second-order effect or the time-varying p-delta effect, this method does not need iteration and has high computational efficiency.

A simplified computational model for seismic performance evaluation of steel plate shear wall-frame structural systems

The steel plate shear wall (SPSW)-frame structure is a high-performance lateral force-resisting system, which has been widely utilized in high-rise buildings, especially in seismic-prone regions. The complexity of SPSW modeling and the interaction between SPSWs and frame, make it very time-consuming and low-efficiency for the performance-based seismic performance evaluation of SPSW-frame systems. This paper developed a simplified computational analytical model of SPSW-frame system based on the lateral deformation characteristics of the system. The simplified flexure-shear (F-S) model was composed of the flexure springs and shear springs, to respectively simulate the behaviors of SPSW and frame. Also, the P-delta column was incorporated into the simplified model to account for the P-delta effect. The material parameters of the flexure spring and shear spring were calibrated by the response spectrum method. By employing the PEER full probability theory, the seismic performance evaluation of two 7- and 15-story SPSW-frame structures were carried out using the simplified F-S model and refined finite element method (FEM). The analytical results demonstrated that the simplified flexure-shear model can achieve nearly the same performance parameters, compared with the refined FEM. Furthermore, the repair cost and repair time of the SPSW-frame structures mainly came from the non-structural components.

Significance of P-Delta Effects in High Rise RC Structure in Various Seismic Zones

Indian codes deal with Linear static (Equivalent static method) and linear dynamic (Response Spectrum method) methods of analysis. Guidelines are also given for Non-Linear dynamic analysis (Time history analysis) for the lateral load analysis. IS codes are silent about the guidelines for geometric non-linearity in the structure. In the case of low or medium rise structures, the geometric non-linearity will not have a significant effect, but for high rise structures, geometric non-linearity becomes a major issue. In this paper a G+50 storey RC structure with vertical irregularity is considered in such a way that P-delta effect is significant and the structure is analyzed by Linear Dynamic analysis as per IS codes and P-delta effects are included and analyzed as per ASCE code. The results such as displacement, storey drift, storey shear are compared and the significance of P Delta effects in high rise structure is studied.

Field measurement and validation of structural dynamic parameters of skyscrapers under super typhoon excitation

This paper analyzes the field measurement data of wind-excited vibration responses of two skyscrapers (393 and 432 m in height) during Super Typhoon Mangkhut (1822), and utilizes such measurement data to validate the design parameters adopted in both buildings. In this paper, the structural accelerations of the two monitored skyscrapers measured during Mangkhut are presented. Based on the measured acceleration data, building modal parameters, including natural frequencies and damping ratio, are identified and they generally agree with the predicted values by the finite element modelling (FEM) or are within the expectation of their assumed values at the design stage. Furthermore, the amplitude dependencies of the parameters are estimated by the random decrement technique, and the results show that the fundamental frequencies slightly decrease with the vibration amplitude, which may be attributed to the P-Delta effect according to the similar trend revealed by the FEM results, whereas no evident varying trend of damping ratios is demonstrated. The study also identifies the beating effect existing in the monitored building response signals, investigates its impact on modal parameter identification and discusses the correlation between the beating effect and the structural modal characteristics. Finally, the root-mean-square structural accelerations of one of the two buildings are re-calculated based on the wind tunnel test data and the measured building modal parameters, and their comparison with the in situ measurements demonstrates a reasonable agreement.

Analysis of the Second Order Effect of the SSI on the Building during a Seismic Load

The type and the properties of the soil can potentially intensify the internal forces on buildings during seismic loads. To predict the effects of the soil parameters on the soil–structure interaction of buildings, it is necessary to consider the soil–structure interaction (SSI) in the modeling process. Therefore, this document aims to evaluate the seismic effect on the maximal displacement and inter-story drift, and evaluate the behavior of buildings under the second-order effect known in the literature as the P-delta effect. For this purpose, three cases of buildings with 5, 10 and 15 stories were modelled using a FLAC 2D finite-difference element calculation software with infinite soil conditions, including five types of base with four types of soil (one cohesive soil and three non-cohesive soils) considering the soil–structure interaction and a fixed base (without soil–structure interaction). According to the results for the above-mentioned boundary, as the height of the building increases and due to the weak properties of the soil, we notice that the maximal displacements and inter-story drift increase considerably. To that purpose, we recommend considering the second-order effect in seismic design, especially for non-cohesive soil.

Probabilistic pushover analysis of reinforced concrete frame structures using dropout neural network

When taking into consideration nonlinear phenomena such as material plasticity, plastic hinge, and P-Delta effect, the pushover analysis can provide more realistic structures’ nonlinear responses. However, this method is not widely used in practice as it is more complex and requires more expertise than elastic approaches. On the other hand, the data-driven method emerges as an increasingly appealing alternative since it requires only input parameters, then directly yields results in conditions that enough training data are provided, as well as an appropriate machine learning model is devised. Thus, this study develops a probabilistic data-driven approach using the Multiple Layer Perceptron network coupled with the Dropout mechanism to perform the pushover analysis of reinforced concrete (RC) frame structures, predicting base shear, lateral displacement, as well as their relationship between the two formers. Moreover, corresponding confidence intervals of predicted values are also available owing to the probabilistic nature of the method, thus helping engineers design conservative solutions.
 Keywords:
 pushover analysis; reinforced concrete; structure; probabilistic analysis; machine learning; dropout mechanism; OpenSees.

Derivation of yield force coefficient for RC frames considering energy balance and P-delta effects

Currently, prominent energy balance concept can efficiently be used to calculate the yield base shear force of structures. Energy balance equation is an additional constraint for the balance of seismic input energy by the energy absorption of the structure. This equation can be defined as the sum of elastic and plastic energies of structural systems using elastic and plastic load-deformation characteristics and the total energy dissipation capacity can finally be equated to the seismic energy demand. The objective of this paper is to present a procedure for the determination of energy-based yield force coefficient of reinforced concrete (RC) frame structures considering P-delta effects. The total of elastic and plastic energies are computed by means of elastic spectral velocity and energy modification factor, which is originally derived for structural systems with geometric nonlinearity. Total inelastic energy of single-degree-of-freedom (SDOF) system is transformed into the total inelastic energy of the multi-degree-of-freedom (MDOF) system using the conversion based on structural dynamics. Plastic energy of MDOF system is formulated after total seismic energy demand is obtained. It is accordingly equated to the total work done by inelastic MDOF structure with P-delta effects and consequently, a dimensionless yield force coefficient is derived. Nonlinear static analyses are performed for selected multi-story RC frames and yield force coefficients are compared with the results of the energy-based formulation. The results show that the proposed formulation taking P-delta effects into account can be effectively used to estimate the yield force coefficient of RC frame structures.

Influence of the P-Delta Effect on the Design of Steel Moment Resisting Frame in Seismic Areas

Steel moment resisting frames (MRFs) compliant with EN1998-1 are generally overdesigned in order to satisfy the requirements for lateral deformability and P-Delta effects. On the contrary, the North American codes (e.g. ASCE7) give different rules for P-Delta effects. The current draft version of the amended EN1998-1-1 introduces a different methodology to account for the structural lateral displacements. In this paper static non-linear analyses were carried out to evaluate the effectiveness of the new EC8 provisions with respect to the former version of EC8 and the current ASCE7. The results show that the structures designed according to the latest draft version of the EN1998-1-1 and those compliant with the North American code exhibit similar behavior.

Seismic response of multi-storey reinforced concrete buildings with soft floor

ABSTRACT The high-rise building in which ground storey consists of open space is known as building with soft floor. Such floor plays an important role in seismic performance of the building. This is due to the abrupt changes in lateral stiffness and strength caused by such storey. In this study, the seismic performance of RC buildings with soft storey using finite element method is investigated. The parameters considered in this research include the height of soft storey, irregularity in building plan dimensions, and the location of soft storey along the building height. An attempt is made in this research to find the optimum location of the soft storey through the building height to minimize its effect. In addition, the impact of applying simple strengthening techniques is investigated to promote structural safety without significant changes in the architectural and functional requirements of the building. The results include the effect of the investigated parameters on stiffness, displacement and storey drifts by using equivalent static load method and modal response spectrum method (MRS). P-Delta effect and cracked stiffness ratio are included in analysis. The results show that the factors such as increasing height of soft storey or increasing length-to-width ratio in the building have a significant effect on the stiffness and resistance. The results also demonstrate the effectiveness of the presence of shear walls for increasing stiffness and reducing displacements. Besides, providing a bracing system for retrofitting the building with soft storey has a positive effect on the behavior of these buildings.

Nelinearno ponašanje zgrada podvrgnutih monotono rastućem bočnom opterećenju

Rad obuhvaća parametarsku studiju i primjenu nelinearne metode N2 za ocjenu potresnog ponašanja četverokatne i osmerokatne armiranobetonske okvirne konstrukcije. U istraživanju su korištene tri raspodjele horizontalnog opterećivanja konstrukcije potresnim silama: trokutasta (linearna), jednolika i modalna. Također, istražen je utjecaj P-Delta učinka na ponašanje promatranih konstrukcija..

Analisis Pengaruh P-Delta Effect Terhadap Perbedaan Ketinggian Struktur Gedung Tahan Gempa (Studi Kasus : Non-Highrise Building)

The need for earthquake resistant buildings in Indonesia is something that needs to be considered. Considering that Indonesia is an earthquake prone area. A building structure must be designed to be able to withstand lateral loads such as earthquakes within the limits set by the code/standards. For conservative reasons analysis of the P-Delta Effect needs to be considered because the building development ratio will always increase every time. according to SNI 1726-2019 the P-Delta effect is only required for the design of tall buildings. In this case, the P-Delta effect will be calculated in the modeling of non-high-rise buildings and get the results that P-Delta Effect increased story forces: moment of the building under 10%.

A Comparison of Simplified Modelling Approaches for Performance Assessment of Piles Subjected to Lateral Spreading of Liquefied Ground

The lateral spreading of the ground due to liquefaction during earthquakes may considerably damage the embedded piles, which is an important issue in the seismic design of pile foundations. In this paper, nonlinear pseudostatic analyses were performed for the responses of piles subjected to actions of laterally spreading ground, which were modelled as flow displacement and flow pressure, respectively. The former is a displacement-based approach, in which the free-field ground displacement profile is assigned to the pile-soil interaction system; while the latter is a force-based approach, which regards the actions of laterally spreading ground as flow pressure and directly applies it to the pile. The concept of the Winkler foundation was utilized to account for the interaction between pile and soil. The soil springs with elastic-plastic p-y curves were used to describe the relationship of soil reaction versus lateral displacement around the pile. The distributed plastic hinges were deployed to simulate the possible flexural failure of the pile. One of the pile failure cases caused by liquefaction-induced lateral spreading in the 1995 Kobe Earthquake was adopted for case study. The analyzed pile response to flow displacement and flow pressure was compared with the field observations, and the validity and capability of both approaches were accordingly discussed. The influence of axial load on laterally loaded piles, namely, the P-delta effect was also examined. These results help to reasonably assess the performance of piles subjected to lateral spreading of liquefied ground.

Assessment of P-Delta Effect on High Rise Building with Outriggers and Belt Truss

The behaviour of structures, when subjected to critical loads is a complex phenomenon and is basically dependent on the type of forces/loads acting on the structure, magnitude of force, direction etc. Generally, the analysis of buildings is done by using linear elastic methods, which is first order structural analysis. The first order analysis is performed by assuming small deflection behaviour where the resulting forces, moments and displacements take no account of the additional effect due to deformation of the structure under vertical loads prior to imposing lateral loads. In the traditional first order analysis of structures, the effects of change in the structure actions due to structure deformations are neglected. However, when a structure deforms, the applied loads may cause additional actions in the structure that are called second order or p-delta effects. P-delta effect is secondary effect on structure. It is also known as ‘Geometric nonlinearity effect’. As number of storey’s increases, P-delta effect becomes more important. In this study the P-delta effect on skyscraper is studied. Linear static analysis (without P-delta effect) and nonlinear static analysis (with P-delta effect) on high rise buildings having outrigger with belt truss is carried out. For the analysis G+55 composite skyscraper is modelled. Earthquake load is applied on model of structure as per IS-1893(2002) for zone II in ETABS software. Load combinations for analysis are set as per IS-456(2000). Bending moment of column, story displacement with and without P-delta effect is calculated and compared for both models.

Seismic Behavior of Flat Slab Buildings of Varied Heights Considering P-Delta Effect

Seismic Behavior of Flat Slab Buildings of Varied Heights Considering P-Delta Effect

Difficulties in Earthquake Design due to Standards Limits on an Extensive Offshore Bridge, Sheikh Jaber Al-Ahmad Al-Sabah Causeway in Kuwait

The project design of the Subiyah link of the Sheikh Jaber Al-Ahmad Al-Sabah Causeway in Kuwait was implemented after lengthy discussions and research due to limits in the standards. With 36 km of viaducts in this link, all design decisions had a significant impact on quantities and hence on costs. The project is based on 2.5 and 3.0 m monopiles, but the requirements of the design standards are not fully adapted for such diameters. Moreover, some additional project requirements, which are not addressed in most of the codes, made the design more complex. All of these parameters led to difficulties in earthquake design regarding the R factor value, capacity design, seismic detailing, P-delta effect, asynchronous motion and seismic design of bearings. The aim of this article is to present all the difficulties in the design of atypical structures, the related discussions and research, and the numerous comparisons that have been made with Eurocode 8-2 to find a consistent design.

General Dynamic Collapse Criterion for Elastic–Plastic Structures Under Double Impulse as Substitute of Near-Fault Ground Motion

A dynamic collapse criterion for elastic-plastic structures under near-fault ground motions is derived analytically by approximately transforming near-fault ground motions into double impulse and using an energy balance law. A negative post-yield stiffness is introduced to treat the P-delta effect in the single-degree-of-freedom (SDOF) model. The principal part of fling-step near-fault ground motions is modeled by a one-cycle sine wave and then a double impulse. The double impulse enables the efficient use of the energy approach in the derivation of compact expressions of complicated elastic-plastic responses of structures with the negative post-yield stiffness. In contrast to the previous work (Kojima and Takewaki 2016b) for the resonant critical case, a general collapse criterion is provided for the velocity amplitude and the frequency of the double impulse. It is significant that no iteration is needed in the derivation of the dynamic collapse criterion except the solution of transcendental equations. It is shown that discussions on several patterns of dynamic collapse behaviors introduced in the previous critical case are useful for deriving a boundary between the collapse and the non-collapse in the plane of the input velocity and the input frequency. The most important point to be remarked is that the critical state (Kojima and Takewaki 2016b) corresponding to the nonlinear resonance does not necessarily provide the minimum input velocity level with respect to arbitrary impulse timing. The validity of the proposed dynamic collapse criterion is examined by the numerical response analysis for structures under double impulses with collapse or non-collapse parameters.

Performance of P-Delta Analysis of Flat Slab and R C Framed Buildings

Two-way slab directly rests on column known as flat plates, in flat slab building formwork is simple as compare to normal slab (that means slab rest on beam column frame building) and reinforcement layout are also simple and storey height decreases. In flat slab building check second order effect (second order effect known as p-delta effect). P-delta analysis means laterally displacing structures (for high rise building) with gravity loads will deflect. In P-delta analysis when lateral force act on member then it will deflect at delta distance and create secondary moments. For stability design of a building P-delta analysis is required. In the present work seismic analysis (consider zone V & soft soil) of a multi storey flat slab building with and without P-delta effects is analysed by using ETAB software. The seismic zone factor of 0.36 is considered. From the analysis check displacement and drift of flat slab building at different storey (G+9, G+19, and G+ 29) of flat slab building.

A comprehensive FE model for slender HSC columns under biaxial eccentric loads

A finite element (FE) model for analyzing slender reinforced high-strength concrete (HSC) columns under biaxial eccentric loading is formulated in terms of the Euler-Bernoulli theory. The cross section of columns is divided into discrete concrete and reinforcing steel fibers so as to account for varied material properties over the section. The interaction between axial and bending fields is introduced in the FE formulation so as to take the large-displacement or P-delta effects into consideration. The proposed model aims to be simple, user-friendly, and capable of simulating the full-range inelastic behavior of reinforced HSC slender columns. The nonlinear model is calibrated against the experimental data for slender column specimens available in the technical literature. By using the proposed model, a numerical study is carried out on pin-ended slender HSC square columns under axial compression and biaxial bending, with investigation variables including the load eccentricity and eccentricity angle. The calibrated model is expected to provide a valuable tool for more efficiently designing HSC columns.