In this paper, vulnerability curves of key building types in the Philippines are developed and presented. Vulnerability curves, expressed as damage ratio versus Modified Mercalli Intensity (MMI) scale, for each building type are derived using computational, empirical, and/or heuristic methods. In the computational method, nonlinear static pushover of each building model was carried out and the capacity spectrum method was used to compute the fragility curves and then the vulnerability curves are derived from assumed damage ratios. Empirical vulnerability curves are derived using available data on damage to buildings compiled from field surveys and reports after past earthquakes. Heuristic vulnerability curves are derived by processing opinion of structural engineers in the Philippines on the possible damage to buildings when subjected to different earthquake intensities. For most building types made from reinforced concrete and steel, computational curves are recommended while for building types made of wood, masonry, and/or light materials, empirical or heuristic curves are recommended. The set of vulnerability curves proposed represents a coherent set of damage functions across structural types, construction material, number of floors, and age of construction.
During strong earthquakes, reinforced concrete (RC) structures experience cyclic lateral loads that result to degradation in load-carrying capacity, and failure of columns in shear and/or flexure. This study presents a simple hysteretic hinge model that may be used in displacement-based analysis of RC columns, classified as flexure critical, shear critical, and shear-flexure critical, subjected to cyclic loads. The proposed hinge model made up of zero-length nonlinear springs can simulate the hysteretic behavior of reinforced concrete material in axial, shear, and flexure. The nonlinear parameters of the springs were derived from geometric and material properties of the column and estimated using Response-2000 software. Pushover analysis and response to cyclic loading were performed using the Open System for Earthquake Engineering Simulation (OpenSees) program and validated by comparing the force-displacement response of select forty-three RC columns available in the PEER Structural Performance Database. Results show that for the six rectangular columns, the numerical experiments using the proposed hinge model and the actual force-displacement curves gave R- squared values greater than 0.80 signifying good agreement of results. Therefore, it was concluded that the model can reasonably replicate nonlinear behavior of shear-, shear-flexure, and flexure-critical columns subjected to cyclic loading and, therefore, may be used to assess performance of actual RC columns.
Vibration-based damage detection from frequency changes requires the calculation of natural frequencies from assumed damage scenarios and conduct a comparison to the actual frequency of the structure. Analytical solutions in obtaining the natural frequency of homogeneous beams are currently limited to beams with uniform cross-sectional area. Changes in cross-sectional area might occur due to damage within the length of the beam. Finite element modeling and analysis is required in these instances, but may not be efficient in terms of computational effort. For the assumed damaged scenarios, there are unlimited number of possible damage combinations for which the natural frequency will be obtained. There is a need for an analytical alternative as a substitute to the finite element method to calculate these frequencies. This study presents an analytical method to estimate the natural frequencies of locally damaged homogeneous beams based on statistical data obtained from finite element modeling and analysis. The method proposes a multiplier function in terms of the extent of area reduction, length, and location of damage in order to estimate the damaged frequency. The function was derived using curve-fitting techniques of data obtained from finite element modeling and analysis of typical beams with assumed damage cases. Examples show that the method is a good alternative to finite element analysis in estimating the natural frequencies of locally damaged homogeneous beams. The method can be used for vibration-based structural health monitoring to predict the damage state of beams given the change in frequency without the computational burden of finite element modeling and analysis.
Keywords: natural frequency, finite element method, least squares fitting, beam, area reduction, corrosion, vibration based damage detection
Peer-review under responsibility of the organizing committee of EURODYN 2017.
During the past decades, the complexity of conventional methods to perform seismic performance assessment of buildings led to the development of more effective approaches. The rigid body spring-discrete element method (RBS-DEM) is one of these approaches and has recently been applied to the study of the behavior of reinforced concrete (RC) buildings subjected to strong earthquakes. In this paper, the governing equations of RBS-DEM planar elements subjected to lateral loads and horizontal ground motion are presented and used to replicate the hysteretic behavior of experimental RC columns. The RBS-DEM models of columns are made up of rigid components connected by systems of springs that simulate axial, shear, and bending behavior of an RC section. The parameters of springs were obtained using Response-2000 software and the hysteretic response of the models of select columns from the Pacific Earthquake Engineering Research (PEER) Structural Performance Database were computed numerically. Numerical examples show that one-component models were able to simulate the initial stiffness reasonably, while the displacement capacity of actual columns undergoing large displacements were underestimated.
For the past decade, several efforts were made by different government and private institutions to develop vulnerability curves of key building types in the Philippines using empirical, heuristic, and/or computational methods. This paper presents the recent development of seismic vulnerability curves of buildings based on experts’ opinion. A building typological system in terms of structural type and materials used in construction was proposed and a paper survey was conducted where experts input for different levels of earthquake intensity the damage ratio of each building type. Analyses revealed that there is a very low correlation between number of years of experience and the confidence level of the respondents. Results also show that the heuristic vulnerability curves of low- and mid-rise buildings are similar for both concrete and steel types. Moreover, seismic vulnerability of buildings, according to specialists, is dictated by the material used in construction rather than the number of floors of a building.
The study proposes a method utilizing 3D nonlinear dynamic analysis of buildings with the objective of achieving predictable seismic performance and building strengthening that translates to the owner’s requirement. The frame model assumes that the nonlinear behaviour of the structure is concentrated in plastic hinges, modelled as spring system located at element ends. The nonlinear parameters of the spring systems are derived from the actual member section. The model is verified via agreement of elastic and nonlinear behavior with that obtained using conventional software. The dynamic simulation allows the analysis of progressive collapse sequence providing ease in the assessment of performance and identification of critical members. The ground acceleration data used is selected to be compatible with the project site’s seismic design spectrum. Strengthening critical members is accomplished by recalculation of spring parameters based on the capacity increase and the material used. This paper analyzes a newly designed and an existing residential building using the proposed method and shows that it is capable of simulating the seismic performance and the potential collapse mechanism. The results show that increasing member dimension and applying CFRP are applicable to prevent collapse.
In pursuit of testing earthquake-resilient building models, ground motion records are necessary input in the analysis. Although using actual seismic records has many advantages, there is a lack of strong ground motion records in the Philippines. To compensate these shortcomings, available records in Japan and Taiwan were used to verify the seismological model that was applied in the simulation of the time-history records. A local earthquake record was used to determine the region-specific source parameters of this model to match the local site conditions of the country. Stochastic simulations were performed to generate acceleration time-history records for scenario earthquakes in West Marikina Valley Fault with different magnitudes and distances depending on the current seismic stations in Metro Manila. The peak acceleration produced by a M7.0 earthquake corresponds to the maximum PGA estimate of 0.5g in Metro Manila while the extreme scenario of M7.2 and M7.5 produced 0.57g and 0.63g, respectively.
Keywords: accelerogram, artificial, specific barrier model, local
This paper presents a method that can analyze earthquake response of typical non-structural components in a hospital. Wheel-movable, free-standing and desk-mounted equipment typically found in emergency rooms, intensive care units and operating rooms were modeled and restraints were designed to minimize or eliminate rolling, sliding and overturning. The method utilizing rigid bodies subjected to inertial forces due to earthquake was introduced and validated using simple analytical computations and numerical experiments. Examples show that non-slip mats are effective in restraining equipment that are unlikely to overturn while the 1⁄4”-diameter bungee cord with optimal orientation or pre-tensioning significantly reduces the acceleration response of the equipment. Heavy equipment, like the 175-kg medical cabinet, may be restrained using bolts or 4-mm accessory cord. This study recommends that soft materials be attached to the equipment at points of possible collision with the wall in order to prevent further damage and large displacement of the equipment.
An analytical building model including the nonlinear e®ects caused by gravity is presented in this paper. Governing equations are derived for both single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) models with large displacements taken into account, and solutions are obtained by direct integration and modal analysis. The response of typical structures subjected to harmonic ground excitation was expressed in exact and approximate forms, compared with the response of an equivalent shear building. Numerical examples show that while gravity generally decreases the natural frequency of elastic SDOF systems with small displacement approximations, actual natural frequency increases with ground motion. The di®erence in the natural frequency and response of MDOF systems to the equivalent shear building is not only due to gravity, but also caused by the geometry of the structure. Exact solution shows that the frequency varies with ground motion amplitude.
Keywords: Flexure building; gravity e®ect; nonlinearity; analytical building; building model.
A new method for wave propagation modeling is introduced in this paper. By using the constraint optimization (Lagrange multiplier) method, the sum of weighted squared Fourier amplitudes is minimized when subjected to a constraint. The sum of the maximum amplitudes obtained from all output models is normalized to unity and is taken as a constraint. In this method, all the actual time histories are considered as outputs and dealt with equally. Independently of the combinations of time histories (or the first time history selected) during the analysis, the method captures the relationship of actual time histories by showing clear peaks. This paper describes the formulation of the models and illustrates the advantage of this method over the normalized input-output minimization (NIOM) method. The Mod-NIOM is then used to analyze the time histories of the Hyogoken-nanbu earthquake recorded at the Port Island vertical array site in Kobe, which suffered from liquefaction caused by the strong motions during the main shock. This method showed good correlations between the observed time histories at the site even though the surface time history was greatly modified by the liquefaction.
In Japan, the past few decades revealed the vulnerability of wood-framed residential buildings to strong earth- quakes. The Kobe earthquake in 1995 caused tremendous loss of lives resulting from the collapse and damage of such structures that significantly affected economic condition. This disaster motivated many researchers to study the mecha- nisms of collapse of engineering structures in order to prevent further loss of lives in the future. In this paper, an innova- tive methodology in simulating the dynamic response of wood-framed buildings, for purposes of seismic performance assessment and retrofitting, is presented. The proposed method, which can simulate inelastic behavior of structures, is ca- pable of showing realistic progressive collapse mechanisms and accurate seismic response of structures. The sequence of analyses and results in the form of computer animations are used to help building owners gain a better understanding of the seismic performance of their buildings before and after the structural reinforcement. Applications to real wood-framed residential buildings were used to show the effectiveness of the methodology in seismic performance assessment as well as retrofit plan development.