Equivalent Static Analysis Research Articles

Effect of masonry infill wall with opening on reinforced concrete frame due to seismic loading: parametric study

This study aims to investigate the effect of masonry infill wall with opening on reinforced concrete frame due to seismic loading under the influence of storey number and panel aspect ratio. For this purpose, a total of 36 building frames including bare frame and infill frame with door and window opening were analysed by equivalent static analysis (ESA) and response spectrum analysis (RSA) using STAAD.Pro software. The seismic load was applied as lateral loading and then sway, storey-wise deflection, inter-storey drift, bending moment and shear of those frames were evaluated and compared. Results of the parametric study indicated that ESA exhibited higher results compared to RSA for a conventional design of building frames as the bare frame. The bending moment in infill frames with opening concentrated at the top of the ground floor level for RSA whereas it was at the bottom of the ground floor for bare frames. The maximum moment and shear in the infill frames with opening decreased 12%-50% and 2%-47% respectively compared to the bare frame due to the interaction of infill panels with the frame elements.

Analysis of L-Shape Building with Lift Core at Different Locations And Its Torsional Effect

In L-shape building, lift core wall is an important element for strengthening the structure of high seismic zone area. Seismic zone V is considered for most of the buildings in Nepal, which will cause maximum base shear to the structure. This study focuses the use of lift core in five and ten-storey building to resist the seismic forces, and the effect of the lift core is also taken into consideration. Based on the location of the lift core, these building are further subdivided into different models; Lift at outer corner (model 1), lift at lower edge corner (model 2), lift at upper edge corner (model 3), lift at lower and upper edge corner (model 4), lift at inner corner (model 5), and lift at inner and outer corner (model 6). Equivalent static method and response spectrum analysis was used for the analysis. The structural responses were measured in terms of modal periods, displacement, drift ratio, and torsional irregularities. Results from this study indicate that building with lift core wall at inner and outer (model 6) and lift at lower and upper edge corner (model 4) shows the minimum drift ratio, torsional irregularities, displacement and natural time period which lies within permissible limit of torsional irregularities. Hence, it can be concluded that the location of the lift core affects the torsion of an L-shape plan asymmetric building. Designing two lift core at the inner and outer corner (model 6) and lower and upper edge corner (model 4) is found to be effective in reducing the torsion.

Numerical modelling of bonded and unbonded flax fiber reinforced elastomeric isolator and their application to RC building

Earthquakes are natural disasters causing havoc to life and property since several centuries. Indian subcontinent has a history of devastating earthquakes in its recent past. One way to tackle an earthquake is to equip the building with a proper seismic resistant system. One of the most popular and effective technique for low and midrise buildings is base isolation. However, existing base isolation systems are very expensive for non-commercial buildings. Hence, this study mainly concentrates on fibre reinforced elastomeric isolators which are cost efficient without a marginal compromise in its performance. A comparison between the performance of unbonded and bonded fibre reinforced elastomeric isolators has been carried out. The unbonded fibre reinforced elastomeric isolators have better performance in terms of stresses, horizontal flexibility, and damping. A low rise reinforced concrete residential building’s response is studied with and without fibre reinforced elastomeric isolators. The results show significant reduction in storey drift, story shear, storey level acceleration in both equivalent static method and time history analysis, along with increase in the time period of building’s fundamental mode.

The effect of spectral shape on damping modification factors

The main objective of this study is to investigate the effect of spectral shape on damping modification factors η used in equivalent static and response spectrum analyses of structures with damping ratios that are different from 5% critical damping. Record-to-record variability of η is also evaluated through a statistical analysis of 5270 ground motions records from 1137 interface earthquakes recorded in Chile. The effect of spectral shape is studied using recently developed spectral shape metrics SaRatio and epsilon [Formula: see text] and evaluating their use as possible predictors for η. Similarly to previous investigations, this article also examines the effect of oscillator period, earthquake magnitude, and earthquake duration for different levels of damping ratio. Results suggest that SaRatio is an effective predictor of η, particularly for highly damped structures. However, results also indicate that for rock and firm sites, earthquake faulting mechanism and site class do not have a significant influence on η. A simple period-independent regression model for η as a function of SaRatio and damping ratio is proposed. A comparison between median η from this study and those in current Chilean seismic codes shows that code factors are unconservative.

Seismic elastic performance of L-shaped building frames through plan irregularities

The trends of irregular building construction have rapidly increased due to aesthetic and limited availability of land. Past studies have shown that the structures with configuration irregularity are damaged under strong ground motion. Structural irregularities are important factors which decrease the seismic performance of the structures. Buildings having structural irregularities result in the uneven distribution of the story drift, excessive torsion, etc. according to the irregularity type and may fail during an earthquake. One such form of irregularity is the presence of re-entrant corners and torsional irregularity that causes stress concentration due to sudden changes in stiffness and torsion amplification in buildings. In this context, the present study evaluates the effect of plan configuration irregularity when subjected to the varying angle of the input response spectrum. For this, one regular and six different L-shaped RC building frames were modeled for numerical analysis. The analysis was done through an equivalent static lateral force method and response spectrum analysis (dynamic analysis). The structural responses were measured in terms of story displacement, inter-story drift ratio, torsional irregularity ratio, torsional diaphragm rotation, normalized base shear force, and overturning moment. The results indicate that buildings with plan configuration irregularity are more sensitive to the varying angle of the input response spectrum as compared to the symmetrical building model. The significant increase in seismic response demand was observed when the finite element models were subjected to a 135-degree angle as compared to the zero-degree angle of seismic incidence. In addition, the study shows that the fundamental time period of structure based on standard code shows a lower value as compared to a finite element approach. It is concluded that to account for the irregularities present within the buildings, current code provisions are insufficient and should be amended.

Sustainable design of reinforced concrete frames with non-prismatic beams

In this paper, sustainable design of reinforced concrete frames with non-prismatic beams is studied and relationship between optimal cost and optimal carbon dioxide emission in design of this type of frames is investigated. The objective functions are minimizing the CO2 emissions and construction cost, and the design variables are defined as the geometry of the cross sections and reinforcing bars of the beams and columns, as well as the tapered length ratio for the non-prismatic beams. The performance of five metaheuristic algorithms consisting of the particle swarm optimization, colliding bodies optimization, enhanced colliding bodies optimization, vibrating particles system and enhanced vibrating particles system is compared for solution of Example 1. The most competent algorithm is identified, and the remaining examples are optimized using the identified algorithm to minimize the cost and CO2 emissions. Numerical examples include reinforced concrete frames with prismatic beams, and frames with non-prismatic beams are optimally designed under equivalent static analysis to evaluate the objectives. Study of the results shows that compared to prismatic beams, in addition to achieving acceptable height in the floor of the structure, the use of non-prismatic beams in RC frames reduces the optimal economic costs and optimal CO2 emissions.

Inertial interaction effects analysis on the estimating of dynamic amplification factor for reinforced concrete structures

This work shows the importance of the need for revision of the Algerian seismic regulations RPA 2003 in terms of the dynamic amplification factor for R/C Rigid buildings with period 0.3 < T < 0.35 in stiff site. In most national building codes, formulas for estimating the seismic base shear include many factors such as the dynamic amplification factor D presented in the Algerian and Moroccan seismic codes RPA2003 and RPS2000 respectively, the response coefficient of the building B for the Iranian code ICS1999, and the spectral acceleration amplification factor B0 for the Eurocode 8. To determine this factor, it is necessary to estimate the value of the vibration period of building based on empirical formulas that do not consider the inertial effects. Diagrams representing the variations of this factor show that the latter remains constant over a range from 0 to 0.7 s for the Algerian code corresponding to structures with 1 to 7 levels; 0 to 1 s for the Moroccan, Iranian and Eurocode 8 corresponding to structures with 1 to 10 levels. No difference was noted in the dynamic factor as a result of degradation of the soil bearing capacity in this ranges. The purpose of this paper revolves around two main themes: the effects of Soil Foundation Structures Interaction (SFSI) on the estimation of dynamic amplification factor on the equivalent static analysis, and the elaboration of a new factor DSAF* called “dynamic site amplification factor” which takes into consideration the SFSI effects, the classifications of the seismic zones and the importance of the structures with application of the Algerian seismic code RPA2003. These values are presented in their simple and easy way to the different users. The results show the importance of these safety coefficients, recommended in the seismic regulations under the effect of SFSI, when the RPA2003 placed in the non-conservative side for the structures belongs to the ranges 0 to 0.7 s.

Response Modification Factor of Steel Frames with and Without Dampers

Response modification factor (R) performs as one of the main seismic design parameters of new structures during earthquake and is considered as significant parameter of nonlinear equivalent static analysis which is a widely used method to evaluate the seismic response of a structure. A review of the literature illustrates that although various numerical studies have investigated the effect of viscous dampers on the response modification factor (R), lack of experimental study has been conducted to verify the numerical models. This study evaluates the response modification factor of steel frame with and without viscous damper. Experimental and numerical analysis have been conducted in the present research. It is found that results from finite element analysis agree well with the experimental results. Besides, the use of damper increases significantly the response modification factors of steel structures, e.g., the factor of structures with dampers are approximate 32% higher than the structures without dampers. The determined response modification factors for the different structures used in this study can be applied to conduct equivalent static analysis of buildings as an initial design stage.

An approach for adjusting the tensile force coefficient in equivalent static cable-loss analysis of the cable-stayed bridges

The sudden rupture of cable is one of the factors that can threaten the bridge safety; causing progressive collapse due to severe vibrations along with numerous changes in the internal forces of all bridge members. Therefore, analyzing the bridge behavior after the sudden cable rupture and estimating the maximum response of the bridge members is of great importance. According to Post-Tensioning Institute (PTI), the sum of the static analysis responses of two models can be used instead of dynamic analysis of cable rupture. In one of these models, the ruptured cable should be removed and twice its tensile force should be applied at the two ends of the cable. In this study, an approach proposed for investigating the tensile force coefficient (TFC) of the ruptured cable in the model of cable rupture effect. For this purpose, an optimization problem was defined to minimize the difference between the static and the maximum dynamic analysis results. The performance of the proposed approach is illustrated with a three-span cable-stayed bridge. This problem was solved for the rupture of each of the bridge cables under examination at different durations of cable rupture using ECBO meta-heuristic algorithm. Moreover, this meta-heuristic algorithm was used to adjust the tensile forces of the cables. Based on the results, a general form of equations was found between cable rupture duration and TFC, which the maximum of it, is in accordance with the PTI coefficient. According to this equation, increasing the cable rupture duration reduces this coefficient.

Analysis the effects of soil-structure interaction on the seismic behaviours of a 5-stories reinforced concrete building with basements

The paper presents analysis results of structural behaviour with and without soil-structure interaction on a five-story reinforced concrete building with basements due to seismic loads. Two numbers of basements were considered namely the building with one basement floor (M1 model) and two basement floors (M2 model). Each of the M1 and M2 model has three variations with and without the soil structure interaction namely the model with the fixed supports (MJ1 and MJ2 models), the model with solid element of the soil (MSo1 and MSo2 models), and the model with lateral soil support of spring elements (MSp1 and MSp2 models). The Soil parameters of modulus elasticity, poisons ratio, reaction modulus and spring stiffness for the MSo and MSp models were obtained from soil investigation. All six models having loads combination of gravity and earthquake loads were analysed using a finite element software package program. All loadings and design codes follow Indonesian codes. Earthquake loads were evaluated using two methods namely equivalent static loads and spectrum response analysis. The results show that the roof-floor displacements of the soil-structure interaction model (MSo and MSp) are greater 2% to 3% than to that of the non-soil-structure interaction models (MJ). The roof drift and natural fundamental period of the MSo and MSp models is greater 1% to 2% than that of the MJ model. The axial force of the columns in the MSo and MSp models is less 1% to 3% than the MJ model. The addition of basement floors to the building and modelling with soil structure interactions can minimize the roof floor displacement, the natural fundamental period of the structure, and axial force of the column by 1% to 2%.

Analisis Perilaku Struktur Gedung Bertingkat Dengan Analisis Dinamik Respon Spektrum Terhadap Beban Gempa

The effect of earthquake load on building structures can be analyzed by equivalent static and dynamic methods analysis (spectrum response and time history). Earthquake load in buildings causes to collapse in buildings. One of the region in Indonesia that have highrisk on the earthquake is Bekasi. This research was conducted at the Galaxy Park Metro Apartment, Bekasi. This study aims to conduct building modeling, analyze the stiffness, vibration period, and the basic shear force of the structure, determine the pattern of sway (mode) and gather mass. The structural performance analysis of the Metro Galaxy Park Apartments based on SNI 1726 2012, SNI 1727 2013, SNI 2847 2013, and PPURG 1987. The results of this research show that the value of the vibration period of Metro Galaxy Park Apartments is 4.281 seconds. The amount of mass participation in the X and Y directions that exceeds 90% in the 21st and 24th modes respectively. The size of the static base shear (Vstatic) obtained is 23357.8 kN. While the dynamic base shear force (Vdynamic) for the earthquake direction X and the direction of the earthquake Y are obtained at 9788,041 kN and 10777.75 kN, respectively. Design scale factor for dynamic base shear force (V dynamic) of the earthquake in X and Y earthquake direction are 2.03 and 1.843, respectively. The magnitude of the dynamic base (Vdynamic) shear force for the X earthquake direction and Y earthquake direction are 19859,93 kN dan 19863,40 kN., respectively. Modeling of Metro Galaxy Park Apartments has been successfully done and the pattern of shaking (mode) of buildings has been obtained.Keywords: dynamic analysis, earthquake, mode shape, response spectrum

Response modification factor - Review paper

Response modification factor (R) has a main function in the seismic design of new construction materials and is a seismic design parameter in equivalent static analysis. It determines the nonlinear performance of building structures during strong earthquakes. R is based on experimental test and engineering judgment, and no uniform technique exists to determine such a value for different conditions. The development in the reliability of modern earthquake-resistant buildings requires systematic assessment of building response characteristics that mainly affect the rates allocated to R, which is formulated based on three aspects, namely, strength, ductility, and redundancy factors. Response modification is affected by the height of structures. This review paper aims to summarize relevant information from different experimental and analytical studies on overstrength, ductility, and R.

Plan review two types of earthquake resistant buildings based on SNI 03-1726-2012 with computer programs

Indonesia is one of the countries that have a high earthquake intensity. Therefore, in building structure planning, there needs to be a more in-depth study of the analysis and planning of earthquake-resistant structures. The study aimed to find out the results of the building analysis reviewed in 4 Indonesian cities based on SNI 03-1726-2012 with computer programs. This research is computer-based research, with Microsoft Excel application for wall density index analysis on 1-story and 2-story buildings, and SAP2000 v.20 application on 4-story buildings for static analysis of equivalent lateral forces. In reviewing the building with analysis of wall density index, it was very influential on the magnitude of the spectral acceleration value of the earthquake. The greater of the spectral acceleration value of the earthquake in the city being reviewed, the smaller the value of the seismic capacity control of the building, which affects the level of building safety. In a building review with an equivalent static lateral force analysis, base shear and displacement values were very influential on the magnitude of the earthquake intensity if used as a comparison with other cities. In reviewing buildings with dynamic analysis of spectrum response range, base shear and displacement values were not very influential on the magnitude of the earthquake intensity if used as a comparison with other cities due to the greater burden than the earthquake load.

Providing different type of bracing in the existing building structure under seismic load

This paper presented the influence of the providing different types of the bracing system in the existing building structure. The selected object of analysis is Timbul Jaya Plaza building that located in Madiun City Indonesia. The system of building structure is Moment Resisting Frame (MRF). Seismic loading analysis use equivalent static analysis base on SNI 1726 2012. Modelling and analysis of structure use computer software ETABS version 9.00. Aim of this research to compare the use of different types of the bracing system under seismic load. Type of bracing that analyzed is X-bracing, V-bracing, and Inverted V-bracing. Model of structure without bracing used as control. Result analysis known that the providing of X-bracing will decrease maximum displacement until 36.28 % compared with existing structure without bracing and increase the stiffness of structure.

Effect of soil–pile–structure interaction on seismic behaviour of RC building frames

Pile foundations are generally used to support important industrial buildings, especially located in coastal regions where the major portion is covered by loose soil deposits. They are commonly subjected to lateral dynamic loads mainly due to earthquakes, wind, machineries, and sea waves. Thus, proper analysis and design of pile foundations should be carried out considering soil–pile–structure interaction. In general, the effects of soil–structure interaction are ignored during seismic analysis and design of super-structures. But in reality, the soil-foundation system affects the structural behaviour detrimentally. The main aim of this study was to investigate the effects of soil–pile–structure interaction on the earthquake behaviour of reinforced concrete building frames. Equivalent static analysis was carried out using direct method of approach. A geotechnical finite element program PLAXIS 3D was used for this numerical investigation. Building types ranging from low-rise to high-rise (5 storeys, 10 storeys and 15 storeys), relative densities of sandy soil ranging from loose to dense (30%, 50% and 70%) and spacing of piles ranging from close to large (2D, 4D and 6D) were the parameters considered for this study. The results of pile lateral displacement, rocking of raft foundation, storey lateral displacement and inter-storey drift were obtained for pile supported structure and compared with rigid base structural response. It is observed that soil–pile–structure interaction influences in particular the high-rise structural behaviour significantly. The storey lateral displacements and inter-storey drift values are amplified because of increase in pile lateral displacement and rocking of raft foundation due to increase in number of storeys, reduction in relative density of soil and reduction in spacing of piles. The major effect of soil–pile–structure interaction on storey displacement and inter-storey drift is observed in lower and upper storey levels more particularly in the case of high-rise structures built on loose soil deposit with closely spaced pile foundations.

Blast responses of concrete beams reinforced with GFRP bars: Experimental research and equivalent static analysis

The glass fiber reinforced polymer (GRFP) bars have advantages in corrosion resistance and high load bearing capacity. They can be used as reinforcements in concrete protective structures to replace the steel bars. In this paper, the GRFP bar reinforced concrete beams (GRCBs) were designed, casted and tested. As a reference, the steel bar reinforced concrete beams (SRCBs) having the same flexural rigidity with the GRCBs were also designed, casted and tested. Under close-in explosions, the GRCBs have smaller displacement than the SRCBs, because the GFRP bars are still in elastic state while the steel bars enter into plastic deformation. Cracks, spalling and cratering are the main damage modes of the concrete beams. Through the quasi-static four-point-bending experiments, the residual load capacity of each beam has been evaluated, which quantitatively reveals the damage degree of the exploded concrete beams. In current research the explosion produces negligible damage to the GRCBs, while the load capacity the SRCBs reduces at a level of 28% at the most. The research proves that the GRCB has greater blast-resistance.

Strengthening Methods of the Existing Reinforced Concrete School Buildings in Medina, Saudi Arabia

Nowadays, evaluation of the seismic performance of existing buildings has received great attention. This paper was carried out to study the effect of strengthening the existing reinforced concrete (RC) school buildings in Medina, Saudi Arabia through assessing the seismic performance and retrofitting where seismic analysis and design were done using equivalent static analysis method according to Saudi Building Code (SBC 301) and SAP2000 software.&#x0D; A Typical five-story RC school building designed according to the SBC301 has been investigated in a comparative study to determine the suitable strengthening methods such as RC shear walls and steel X-bracing methods. The results revealed that the current design of RC school buildings located in Medina was unsafe, inadequate, and unsatisfied to mitigate seismic loads. Moreover, adding steel X-bracing and RC shear walls represent a suitable strategy to reduce their seismic vulnerability.

Comparative Study of Static and Response Spectrum Methods for Seismic Analysis of Regular RC Buildings

Background and Objective: The main idea in this paper is to study the static and dynamic analysis methods and compare their results in order to determine the optimal conditions for application of each method. Materials and Methods: In this research, two structural models are created using the ETABS (V16.1.2) program for regular R.C buildings with typical plans, the first model with a total height of 75 m while the second model with a total height of 24 m. The buildings are analyzed using the static and dynamic methods under ASCE7-10 and IBC 2015 provisions. Results: The results show that shear forces obtained using the response spectrum analysis as a dynamic analysis in the X directions are less than those obtained using the equivalent static analysis by 35-60 and by 40-65% in the Y direction for the high-rise building, while for the low-rise building is less by 25% in X direction and 22% in Y direction. The results also show the bending moments in the X directions obtained using the response spectrum analysis are less than those obtained by using the equivalent static analysis by 45-75 and by 30-65% in the Y direction for high-rise building, while for the low-rise building is less by 22% in X direction and 20% in Y direction. Conclusion: The results of displacements in the X directions obtained using the response spectrum analysis are less than those obtained by using the equivalent static analysis by 70 and by 80% in the Y direction for the high-rise building, while for the low-rise building is less by 35% in X direction and 38% in Y direction.

Dynamic analysis of a concrete chimney considering the aerodynamic damping

Abstract Usually, the analysis of structures under wind loading is performed using an equivalent static analysis, where the influence of floating response is taken into account by the gust factor. This methodology can be used in case of rigid structures for not presenting a considerable dynamic response. More flexible structures, in particular those lightly damped, may show an important resonant response and their dynamic properties must be considered in the analysis. The aim of this paper is to present a methodology for dynamic analysis of structures under wind loading considering the geometric nonlinearity, the vibration caused by the kinetic energy of wind gusts and the aerodynamic damping due to the relative movement between this structure and the wind. The formulation proposed is applied to a 180-meter-high concrete chimney and the results were compared with those obtained through the recommendation given in the standard ABNT NBR 6123:1988 [2] for the dynamic structural analysis.

Behaviour of Thermal Power Plant Boiler Support Steel Structure under Seismic Excitations

Static and dynamic analysis of a thermal power plant boiler support steel structure is carried out to study its behaviour and responses. Non-Linear Time History Analysis (NLTHA) method is adopted to study the behaviour and response of the structure in addition with Equivalent Static Analysis (ESA) and Response Spectrum Analysis (RSA) methods using SAP2000 software application. Though NLTHA method is not used extensively in Indian boiler support structure design practices, in the present study, an attempt is made to study about the realistic behaviour and performance of boiler support steel structure using NLTHA. Three different ground motions are used for analysing the boiler support steel structure with compatible scale factors and during the analysis, behaviour of the structure under different seismic excitations are usually compared in terms of [5] load-deflection, moment-rotation, moment-curvature and stress-stain relationships. Hence it is found that NLTHA method provides more accurate and dynamic results compared to the ESA and RSA methods. Various seismic demand parameters like mode shapes, displacements, drifts, base shear forces, floor accelerations and floor response spectra curves are presented in the results to understand the behaviour and response of the boiler support steel structures during the seismic excitations.