China
Africa
Explore chapters and articles related to this topic
Inverse problems in engineering
Published in Jamshid Ghaboussi, Soft Computing in Engineering, 2018
Structural engineers prefer to use response spectrum in evaluating the seismic response of structures and in designing structures against the destructive effects of earthquakes. A response spectrum is defined as the maximum response of an idealized damped single degree of freedom structural system subjected to the earthquake accelerogram, x¨g(t), as the ground motion. The response, x(t), of the single degree of freedom structural system is determined from the following differential equation of motion. () x¨(t)+2ξωx˙(t)+ω2x(t)=−x¨g(t)
Structural Design
Published in S.V. Kulkarni, S.A. Khaparde, Transformer Engineering, 2017
Response spectrum method: As per IEEE C57.114-1990, when the natural frequencies of a transformer are lower than about 30 Hz, the static method should not be used and one has to take into account the natural frequencies of the structure. The response spectrum method determines the dynamic response which depends on the natural frequencies of the structure. The transformer needs to be analyzed as a spring-mass model using a response spectrum curve with an appropriate damping factor. The response of the structure to an earthquake due to each mode of vibration is calculated, and the total response is determined by combining the individual modal responses (square root of sum of squares technique). A numerical method like FEM needs to be used for this purpose. The FEM analysis gives stresses, accelerations and displacement plots which help in identifying weak structures that need to be strengthened.
Seismic Code Provisions
Published in Hector Estrada, Luke S. Lee, Introduction to Earthquake Engineering, 2017
As indicated in Chapter 5, Figure 5.13, the response spectrum is affected by local soil conditions. Since SS and S1 are based on rock subsurface conditions, they must be adjusted for other types of soil conditions. ASCE-7, Chapter 20, classifies a site as Site Class A (hard rock), B (rock), C (very dense soil and soft rock), D (stiff soil), E (soft soil), or F (soil) based on soil shear wave velocity, vs; if vs is not known, ASCE-7 allows the use of standard penetration resistance or undrained shear strength values. This information is typically included as part of a geotechnical engineering report. If no soil properties are known, ASCE-7 allows the use of Site Class D as a conservative assumption.
Seismic evaluation of the bridge with a hybrid system of cable and arch: Simultaneous effect of seismic hazard probabilities and vertical excitations
Published in Mechanics Based Design of Structures and Machines, 2023
Salar Farahmand-Tabar, Majid Barghian
An actual time-history record is required to carry out the seismic analysis of a structure. However, it is not possible to have such records at every location. Also, the structural response depends on dynamic properties and the frequency content of the ground motion. So, the seismic analysis cannot be performed simply according to the Peak Ground Acceleration (PGA). To overcome these difficulties, the response spectrum can be used in seismic analysis of the structure. Using smooth design spectra has computational advantages to predict forces and displacements in structural systems. The spectra are applied to the structure according to the modal analysis of the bridge, considering the initial state of the bridge under its self-weight. According to bridge seismic design code (GB50011-2016) and considered site conditions of the bridge (soil type II), design acceleration response spectra under two probabilities are obtained. The peak accelerations of the two probabilities can be obtained through seismic risk evaluation which is the necessary procedure for the seismic design of long-span bridges. The horizontal and vertical spectra for both 3 and 10% exceeding probability (Figure 4) are utilized considering the combination rules recommended by seismic specifications of AASHTO (2012).
Damping Modification Factors Observed from the Indian Strong-motion Database
Published in Journal of Earthquake Engineering, 2021
Mitesh Surana, Yogendra Singh, Dominik H. Lang
In earthquake engineering, the majority of seismic analysis and design methods rely upon the response spectrum. Almost all national seismic design codes [e.g. ASCE 7-10 2010; CEN 2004; EN 1998 2004; IS 1893 Part 1: 2002] provide site class-dependent elastic response spectra which correspond to a viscous damping ratio of 5%. Damping modification factors (DMFs) (as illustrated in Figure 1) are further provided to convert the 5% damped elastic response spectrum to a response spectrum for any other desired damping ratio. The design response spectra corresponding to lower or greater damping ratios are often used in performance-based seismic design of structures, e.g. highly damped spectra for direct-displacement-based seismic design, estimation of target displacement when using the ‘Capacity Spectrum Method,’ seismic design of energy-dissipating devices, or isolation systems, whereas low-damping spectra are used in ‘seismic design of non-structural components’.
Dynamic Site Response Characterization Via Bayesian Inference: Analysis of the SGC Station Deposit in Bogota, Colombia
Published in Journal of Earthquake Engineering, 2019
Vicente Mercado, Elias D. Nino, Carlos A. Arteta
The response of the model is analyzed based on the estimated spectral ratio which is hereby defined as , where is the acceleration response spectrum (5%–damped) at the surface, is the acceleration response spectrum (5%–damped) at rock depth, and is the natural period of a single–degree–of–freedom (SDOF) system subjected to the associated excitation. It should be noted that is calculated using the acceleration record at rock depth; consequently, it does not correspond to the rock accelerations at the surface. In the context described here, a response spectrum summarizes the maximum response for a range of natural periods (the inverse of the natural frequency) of a SDOF system subjected to a particular excitation (e.g. earthquake acceleration). Therefore, it indirectly reflects characteristics of an acceleration wave form such as amplitude and frequency content [Kramer, 1996]. Moreover, the spectral ratio implicitly contains information on the effects of the soil deposit over the analyzed signal in terms of the amplification for each frequency range in the signal.