Elastic Design Response Spectrum Research Articles

Development of elastic design response spectra with emphasis on far-source earthquakes for low to moderate seismic region

The development of design response spectra is crucial for earthquake design of structures. However, there are disagreements from the engineering community on the suitability of design values proposed by the existing design code which underestimates the long-period responses for flexible soils, typical of far-source earthquakes. This study uses soil response analysis to investigate the effect of near and far sources’ earthquakes on the response spectral acceleration of Malaysia in three seismically different regions, namely Peninsular Malaysia, Sabah and Sarawak. 1923 borehole data have been collected and analysed under 5 near and 4 far sources earthquakes, subjected to the intensity from the probabilistic seismic hazard analysis. The results show that for Peninsular Malaysia, the far-source earthquake will govern the response at a period of more than 1 s, indicating its importance for structures with long periods such as tall buildings. It is also found that the corner period TC is slightly higher than the code recommended and is dependent on the soil property, while TD is significantly higher for far-source earthquakes due to the larger magnitudes. The finding of this research shows that the Eurocode 8 supplemented by the Malaysian National Annex (MS-EN1998-1, 2017) can be used to design structures in Malaysia, with some adjustments to the longer period motion for Peninsular Malaysia. Finally, it is recommended to perform an enhanced analysis for important structures of long periods to ensure their loadings are not underestimated.

Modified Partial Capacity Design (M-PCD): achieving partial sidesway mechanism by using two steps design approach

Partial Capacity Design (PCD) has been developed by using magnification factor to keep some columns undamaged during major earthquake. By doing so, the structures will experience the partial side sway mechanism which is also stable, instead of the beam sidesway mechanism. However, in some cases, structures designed by PCD method failed to show the partial side sway mechanism since unexpected damages were still occurred at some columns. In this research, modification of PCD method is proposed by using two structural models in the design process. The first model is used to design beams and columns which are allowed to experience plastic damages, while the second model is used to design columns which are intended to remain elastic when the structure is subjected to a target earthquake. Two nominal earthquakes corresponding to Elastic Design Response Spectrum (EDRS) level with seismic modification factors (R) of 8.0 and 1.6 are used in the first and second structural models, respectively. It should be noted that the second model is identical to the first model except that the stiffnesses are reduced for elements to simulate potential plastic damages. This proposed method is applied to symmetrical 6 and 10 storey buildings with seismic load according SNI 1726:2012 and with soil classification of SE in Surabaya city. A Non-linear Static Procedure (NSP) or pushover analysis and Non-linear Dynamic Procedure (NDP) or time history analysis are employed to evaluate the performance of the structure. The evaluation is conducted at three earthquake levels which are nominal earthquake that is used in second model, earthquake corresponding to EDRS level, and maximum considered earthquake (MCER) specified by the code (50% higher than EDRS level). The building performances satisfy the drift criteria in accordance with FEMA 273. However, the partial side sway mechanism was not achieved at NDP analysis at maximum seismic load, MCER.

Alternative approach in Partial Capacity Design (PCD) by using predicted post-elastic story shear distribution

The Capacity Design Method is an approach widely used to design earthquake resistant structures. It allows the structures to dissipate earthquake energy by forming plastic hinges through beam side sway mechanism. In the design process, the columns need to be designed stronger than the beams connected to them. Several previous studies have been conducted to propose alternative method allowing partial side sway mechanism namely the Partial Capacity Design (PCD) Method. In this method, selected columns are designed to remain elastic and the plastic hinges are allowed to occur only at the columns base. These columns are designed to resist increased forces. Despite of some successful attempts, PCD method still needs to be developed because sometimes the intended mechanism was not observed. This study proposes a new approach to improve the Partial Capacity Design (PCD) method. Symmetrical 6 and 10 story buildings with 7 bays are analyzed using seismic load for city of Surabaya. Structure behavior under non-linear static analysis is well predicted by this approach. However, under non-linear dynamic analysis, a few unexpected plastic hinges of elastic columns were observed at upper stories. But it should be noted that the earthquake used for performance analysis (maximum considered earthquake) is 50% larger than the one used for design (earthquake level corresponding to elastic design response spectrum).

The effect of rotational component of earthquake excitation on the response of steel structures

AbstractThis work is on the influence of the rotational component of earthquake excitations to the response of steel structures. In most studies, seismic input is being modeled only using the translational component of the ground acceleration, while the rotational one is ignored. This was due to the observation that the rotational component had minimal effect on low‐rise buildings. Hence, the accelerometers used would not measure it, leading to a lack of records. Nowadays, technology provides such instruments and relative records are made available. Indicative of that is that elastic design response spectra for rotational components are introduced to the design codes. In this paper, the results on structural response and internal forces due to the rotational component of a seismic excitation on the steel structures are examined. Dynamic time history analysis and response spectrum analysis of different steel structures are performed (a) considering the rotational component of the excitation and (b) without it. From the numerical results it is shown that the impact of rotational component in structural response and internal forces of the steel structures is significant and should not be ignored during structural design.

Influence of Earthquake Rotational Components on the Seismic Safety of Steel Structures

In this work a seismic analysis of structure associated with the complete description of ground motion components is performed. All earthquake excitation components corresponding to the six degrees of freedom, translational and rotational ones need to be taken into account for a realistic simulation of structural performance. The impact of the rotational components of an earthquake to the overall response of a steel structure is examined. Typically, in response to the history analyses, the seismic input is descripted by its translational component only, while the rotational components are ignored. This is because the rotational component requires special devices to be recorded in adequate detail. This is one of the reasons why this component is often ignored. With the currently available technology, such an instrument can be constructed and provide detailed records that can be used for the response history analysis of structures. The applicable design codes using a simplified response spectrum analysis accounting for rotational components is proposed and elastic design response spectra are introduced. Another reason why the rotational component was not taken into account in structural analysis is that it does not have significant effect on low-rise buildings. In this work, the analysis results in terms of response and internal forces when accounting for the rotational component is demonstrated. A case study on the response history analysis of symmetrical and non-symmetrical steel structures subjected to earthquake excitation with and without the rotational component of the excitation was performed. Numerical results show that the influence of the rotational component on the structural behaviour is important and should be taken into account in the design process.

Influence of Rotational Component of Earthquake Excitation to the Response of Steel Slender Frame

This work is about the influence of rotational component of earthquake excitation to the response of high steel slender frames. In most of studies seismic input is being represented by translational only component of ground accelerations while the rotational one is ignored. This was due to the luck of records which measure the rotational component. Nowadays, technology provides such an instruments and relative records can be found. Elastic design response spectra for rotational components are introduced in regulations. Furthermore, the rotational component was not taken into account since its influence in low structures is not significant. In this paper the results in response and in internal forces of rotational component to the slender steel frame is examined. Time history analysis of a ten-story steel frame with and without rotational excitation component is performed. From the numerical results it is shown that the impact of rotational component in response and the internal forces of the frame is significant and should not be ignored to the design of structures.

High-resolution grid of H/V spectral ratios and spatial variability on microtremors at Port of Spain, Trinidad

We performed dense single mobile microtremor measurements at 1181 sites throughout the city of Port of Spain, Trinidad. The results yielded fundamental periods of the soil of 1.2–1.7 s in the coastal areas, 0.3–1.2 s in the downtown area, and 0.0–0.3 s in the surrounding areas of the city. We employed the variogram plot to retrieve the spatial variability of fundamental periods. The results suggest that the variability of the period yields about 0.010 s2 at short distances of 100 m and it can be modeled as a Gaussian distribution which is directionally dependent. Finally, we propose an elastic design response spectra for different zones in the city in accordance with the observed periods of vibration and compatible with the International Building Code (IBC) provisions.

Deterministic seismic hazard assessment close to a gas field in northern Oman

The Northern Oman region has one of the most important on-land gas reservoirs in Oman, which has been exploited since 1979. Earthquakes with small magnitude and shallow depth that have been induced by gas exploitation were proved to cause light damage to structures on gas and gas fields in the region. Therefore, a long-term (unfortunately intermittent) monitoring program for the seismicity of this area was started in 1999 in order to contribute to the seismic risk reduction. The main aim of the current study is to conduct a deterministic seismic hazard assessment in order to provide the maximum ground-motion spectra at 12 selected sites inside the area of interest and to recommend the elastic design response spectra of any intended structures at each of the selected sites. The 5 % critical damping spectra were calculated at the median and 84th percentile levels. The site effect considered in all the used ground-motion prediction equations was evaluated based upon the value of the average shear-wave velocity in the upper most 30 m (V S30) at each of the selected 12 sites. Shear-wave velocity (V s) was evaluated using the multichannel analysis of surface waves. The 12 sites were investigated with survey lines of 40 m length. 1-D and interpolated 2-D shear-wave velocity profiles have been generated up to a depth range of 25–40 m. The median PGA ranges from 54 cm/s2 at site no. 4 to 72 cm/s2 at site no. 9, which resulted from an earthquake with magnitude 3.6 at 4.45 and 2.92 km distance respectively from the interested sites. High frequency ground motions are found to be controlled by nearby seismic zones, whereas the low frequency ones are controlled by the distant western Makran large magnitude earthquakes. Finally, the hazard results were used to calculate the elastic design response spectra at each site of interest.

Rapid assessment of seismic demand in existing building structures

AbstractSeismic assessment of building structures can be a very involved process. This paper presents a simplified and rational manual procedure for rapid predictions of maximum inter‐storey drift demand in tall buildings, which does not require frame analysis nor finite element analysis to be carried out and can be expedited by the use of a spreadsheet program. The methodology comprises a series of stages, beginning with the development of an elastic design response spectrum (or a uniform hazard spectrum) for specifying the level of seismic hazard, followed by the inclusion of a site‐specific factor that represents the effects of soil amplification. The maximum seismic inter‐storey drift demand of the building is then predicted from the displacement response spectrum for a given height and the estimated lateral natural periods of the building. The proposed manual procedure can be further developed to cater for limited ductility demand behaviour in the building. The predicted drift demand is an important indicator of potential seismic damage (risk), and may be utilized for the rapid assessment of damage and loss (cost) for considered earthquake scenarios. Copyright © 2008 John Wiley & Sons, Ltd.

Variability of seismic demands according to different sets of earthquake ground motions

AbstractIt is a challenging task to predict seismic demands for earthquake resistant design, particularly for tall buildings. In current seismic design provisions, seismic demands are expressed as a design base shear of which the key components are linear elastic design response spectra, force reduction factor (‘R factor’), and building weight. For tall buildings, response spectrum analysis or response history analysis is recommended in current design provisions. In recent years, new methods for predicting seismic demands have been developed, such as the capacity spectrum method (CSM) and displacement coefficient method. This study investigates the effect of different earthquake ground motion (EQGM) sets on seismic demands. Key components of the base shear and performance points in the CSM are considered as the seismic demands to be tested. For this purpose three EQGM sets are collected independently at rock sites. This study found that seismic demands can vary significantly according to different EQGM sets even though those sets were obtained at sites with similar soil conditions. This study also attempts to provide a criterion for reducing the variability in seismic demands according to different EQGM sets. Copyright © 2007 John Wiley & Sons, Ltd.

Relationships between Median Values and between Aleatory Variabilities for Different Definitions of the Horizontal Component of Motion

Ground-motion prediction equations (GMPE) for horizontal peaks of acceleration and velocity, and for horizontal response spectral ordinates, have employed a variety of definitions for the horizontal component of motion based on different treatments of the two horizontal traces from each accelerogram. New definitions have also recently been introduced and some of these will be used in future GMPEs. When equations using different horizontal-component definitions are combined in a logic-tree framework for seismic-hazard analysis, adjustments need to be made to both the median values of the predicted ground-motion parameter and to the associated aleatory variability to achieve compatibility among the equations. Because there is additional aleatory variability in the empirical ratios between the median values for different components, this uncertainty also needs to be propagated into the transformed logarithmic standard deviation of the adjusted equations. This study provides ratios of both medians and standard deviations for all existing component definitions with respect to the geometric mean of the two horizontal components, which is currently the most widely used in prediction equations. The standard deviations on the ratios of the medians are also reported. This article also discusses the issue of the ratios of different horizontal component definitions in relation to the specification of seismic input for dynamic structural analyses, highlighting the importance of consistency between the component definition used to derive the elastic design-response spectrum and the way that biaxial dynamic loading input is prepared.

Multi-objective optimization of skeletal structures under static and seismic loading conditions

Almost every real world problem involves simultaneous optimization of several incommensurable and often competing objectives which constitutes a multi-objective optimization problem. In multi-objective optimization problems the optimal solution is not unique as in single-objective optimization problems. This paper is concerned with large-scale structural optimization of skeletal structures such as space frames and trusses, under static and/or seismic loading conditions with multiple objectives. Combinatorial optimization methods and in particular algorithms based on evolution strategies are implemented for the solution of this type of problems. In treating seismic loading conditions a number of accelerograms are produced from the elastic design response spectrum of the region. These accelerograms constitute the multiple loading conditions under which the structures are optimally designed. This approach for treating seismic loading is compared with an approximate design approach, based on simplifications adopted by the seismic codes, in the framework of multi-objective optimization.

Large scale structural optimization: Computational methods and optimization algorithms

The objective of this paper is to investigate the efficiency of various optimization methods based on mathematical programming and evolutionary algorithms for solving structural optimization problems under static and seismic loading conditions. Particular emphasis is given on modified versions of the basic evolutionary algorithms aiming at improving the performance of the optimization procedure. Modified versions of both genetic algorithms and evolution strategies combined with mathematical programming methods to form hybrid methodologies are also tested and compared and proved particularly promising. Furthermore, the structural analysis phase is replaced by a neural network prediction for the computation of the necessary data required by the evolutionary algorithms. Advanced domain decomposition techniques particularly tailored for parallel solution of large-scale sensitivity analysis problems are also implemented. The efficiency of a rigorous approach for treating seismic loading is investigated and compared with a simplified dynamic analysis adopted by seismic codes in the framework of finding the optimum design of structures with minimum weight. In this context a number of accelerograms are produced from the elastic design response spectrum of the region. These accelerograms constitute the multiple loading conditions under which the structures are optimally designed. The numerical tests presented demonstrate the computational advantages of the discussed methods, which become more pronounced in large-scale optimization problems.

Nonlinear seismic response of stiffening SDOF systems

Stiffening behavior can result from interaction between a structure (base system) and its surrounding environment as in the bridge soil-structure interaction. In this paper the base single-degree-of-freedom (B-SDOF) systems are designed for several ductility factors and then the effects of different interacting environments (defined in terms of stiffness, strength and gap size) on its dynamic response are investigated. For this, nonlinear time history analyses are performed using an earthquake record scaled to an elastic design response spectrum at each period. Several damage criteria, namely, displacement ductility, dissipated hysteretic energy, and low-cycle fatigue concepts are considered. On average the displacement ductility is lower for stiffening systems, consistent with push-over analysis based on seismic codes. However, it is shown that considering other seismic damage criteria than displacement ductility, it is quite likely that a stiffening single-degree-of-freedom (S-SDOF) system (i.e., a base system with an interacting environment) will sustain more damage than an elastic-plastic B-SDOF system (i.e., a base system alone). Design implications and the needs for future research are also discussed.

OPTIMUM DESIGN OF SPACE FRAMES UNDER SEISMIC LOADING

The objective of this paper is to perform structural optimization under seismic loading. Combinatorial optimization methods and in particular algorithms based on Evolution Strategies are implemented for the solution of large-scale structural optimization problems under seismic loading. In this work the efficiency of a rigorous approach in treating dynamic loading is investigated and compared with a simplified dynamic analysis in the framework of finding the optimum design of structures with minimum weight. In this context a number of accelerograms are produced from the elastic design response spectrum of the region. These accelerograms constitute the multiple loading conditions under which the structures are optimally designed. This approach is compared with an approximate design approach based on simplifications adopted by the seismic codes. The results obtained for a characteristic test problem indicate a substantial improvement in the final design when the proposed optimization procedure is implemented.

Method of selecting design earthquake ground motions for tall buildings

In most current seismic design procedures, an earthquake hazard of the design earthquake load is usually defined as a 10% probability of exceedance in 50 years. However, tall buildings and emergency hazard facilities need to be safe against more severe ground shakings than code-defined design earthquake hazards. Earthquake hazard can be expressed by a 5% damped Linear Elastic Design Response Spectrum (LEDRS) obtained from statistical research using spectral responses of selected EarthQuake Ground Motion (EQGM). In tall buildings that have severe irregularity in plan and elevation or have long natural periods, the use of EQGM records as input loads is recommended instead of using LEDRS. The objectives of this study are to determine the LEDRS considering return periods and to calibrate the EQGM records for making their response spectra fit the determined LEDRS. The parameters of calibration for selecting the EQGMs are investigated. In this study 22, 14 and 8 EQGMs are selected for S1, S2, S3 soil sites, respectively. Selected EQGM records from this study can be used for time-history analysis as an input earthquake load, especially for low and moderate seismic zone. Copyright © 2000 John Wiley & Sons, Ltd.

Seismic vulnerability evaluation of a 32-story reinforced concrete building

Seismic evaluation of a 32-story reinforced concrete framed tube building is performed by checking damageability, safety, and toughness limit states. The evaluation is based on Standard 2800 (Iranian seismic code) which recommends equivalent lateral static force, modal superposition, or time history dynamic analysis methods to be applied. A three dimensional linearly elastic model checked by ambient vibration test results is used for the evaluation. Accelerograms of three earthquakes as well as linearly elastic design response spectra are used for dynamic analysis. Damageability is checked by considering story drift ratios. Safety is evaluated by comparing demands and capacities at the story and element force levels. Finally, toughness is studied in terms of curvature ductility of members. The paper explains the methodology selected and various aspects in detail.

An Evaluation of Inelastic Seismic Design Spectra

After reviewing general methods available for determining seismic design forces for structures which can tolerate limited amounts of inelastic deformations, the reliability of two representative procedures is evaluated. In the methods evaluated, inelastic design response spectra are obtained by modifying a linear elastic design response spectrum in terms of a specified ductility factor as suggested by Newmark and Hall and the Applied Technology council. The effect of different accelerograms, as well as of different system damping and hysteretic characteristics, on the inelastic response of single degree-of-freedom systems designed using these methods is thoroughly investigated, considering maximum displacement ductilities, maximum and permanent drifts, number of yield events, and hysteretic energy dissipation. Application of these design methods to multistory buildings is also briefly considered. Results obtained for ideal inelastic systems indicate that these methods do not reliably limit displacement ductilities to specified values.

The development of a velocity risk map of Taiwan for seismic resistant design of buildings

Abstract A seismic risk analysis procedure previously developed for ground acceleration calculations of Taiwan is extended for ground velocity determination. The procedure is particularly suitable for Taiwan and other areas, where only limited information on seismicity is available. A velocity attenuation formula is established and used for risk calculation. This attenuation is consistent with an acceleration attenuation law of Taiwan. The resulting velocity risk map can be used in conjunction with an acceleration risk map produced before to serve as a basis for elastic design response spectrum construction. A risk level is chosen for building design. This level corresponds to a probability of ten percent for the design earthquake motion parameters being exceeded in a time span of fifty years. A form of elastic design spectrum and an equivalent lateral force coefficient are suggested as an application of the risk maps developed.

Aseismic design implications of near‐fault san fernando earthquake records

AbstractNear‐fault records of the 1971 San Fernando earthquake contain severe, long duration acceleration pulses which result in unusually large ground velocity increments. A review of these records along with the results of available theoretical studies of near‐fault ground motions indicates that such acceleration pulses may be characteristic of near‐fault sites in general.The results of an analytical study of a building severely damaged during the San Fernando earthquake indicate that such severe, long duration acceleration pulses were the cause of the main features of the observed structural damage. The implications of such pulses on current aseismic design methods, particularly those used to establish design earthquakes, are examined for buildings located near potential earthquake faults. Analytical studies of the non‐linear dynamic response of single and multiple degree‐of‐freedom systems to several near‐fault records, as well as to a more standard accelerogram, indicate that at near‐fault sites: (a) very large displacement ductilities may result for current levels of code design forces; (b) smoothed elastic design response spectra should reflect the larger ground velocities that may occur; and (c) peak inelastic response cannot reliably be inferred from elastic response predictions.