Anil K. Chopra The modal combination rules commonly used in response spectrum analyses implicitly assume that the peak factor associated with the response quantity of interest is equal to the peak factors of the contributing modal responses. In this paper, we examine the validity of this assumption and demonstrate that it causes the modal combination rules to over-represent the contribution of the higher modes of vibration to the total response and under-represent the contribution of the lower modes. Consequently, a response-spectrum-based analysis can yield a biased estimate for the peak value of a response quantity when two or more well-separated modal frequencies make significant contributions to the total response. To correct this potential bias in response-spectrum-based estimates, we develop a procedure for estimating the peak factors that is suitable to the response spectrum analysis calculations commonly used in the current design practice.

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Severe earthquake can bring serious problems in the wind turbines and eventually lead to an interruption to their electric power supply. This subject is dealt with in several standards or regulatory guides among which the following are examined herein below: The equations are written as follows: The combination of the effects of the seismic components is discussed in paragraph 4.

The percentage rule is also proposed in paragraph 4. The periodic modal responses of an earthquake are combined with the following rules: This paper offers also page 49 a short discussion of the directional combination procedure: Subscribing you accept the TOC. As an alternative the SRSS rule can replacfment used.

Periodic responses are dominant in the region of amplified spectral displacement, amplified spectral velocity and amplified spectral acceleration. Also, the structural design optimizations were conducted for the four different initial design variable sets to confirm robustness of the optimization mmethod used.

Thus the structural design optimization of a small vertical-axis wind turbine could be successfully accomplished. Sensitivity Analysis of the Replacement Problem. In general, this alternative method is slightly conservative for most cases and is quite adequate since its degree of conservatism is relatively small.

World Journal of Engineering and TechnologyVol. Equipment Inspection Method and Weibull Analysis. Analusis directional effects of an earthquake are combined with the following rules: The percentage rule is therefore adopted. Wilson — Google Books Figure 1 shows the srws conceptual shape of a response spectrum in terms of velocity as a function of frequency ref. The rigid response corresponds to the steady-state phase in theory of vibrations.

The rigid responses and rigid components of responses are combined algebraically. There is no specific provisions regarding combination seismix spatial components, except that in letter f of Section 2. For what regard the mode combination, paragraph The dotted lines refer to the case of multiple narrow-banded response spectrum with two or more peaks of acceleration. Seismic effects combination In general, if the frequencies of the modes are sufficiently separated, the SRSS method may be applied.

SRSS3 method would have a rather large error if the natural periods of the structure are close to each other, namely modal correlation coefficients of structure are large. If uncoupled response of the structure is expected, then only one time history is required. Simply shifting the starting time of a given accelerogram does not constitute the establishment of a different accelerogram.

The combination rule to be used for individual modal responses depends upon whether the responses are periodic, rigid or both see R. The EC definition is more conservative than R. The percentage rule was put forward by Newmark and Rosenblueth first. He provides the following recommendations page The effects due to the different directions of the seismic action shall be combined with the percentage rule see para.

No other rules are specified for non-building structures dealt with in Chapter According to ECparagraph 4. In seismic response analysis two types of combinations are to be considered: This statement is supported referring to a detailed discussion on this issue developed by Menun and Der Kiureghian in and Both periodic and rigid responses occur in the intermediate region between amplified spectral acceleration and high-frequency region DE in Figure 1 and Figure 2.

A replacement for the srss method in seismic analysis. Labor Omnia Vicit Improbus. As a result, all the optimization results for the 4 different initial designs showed good agreement with each other properly. Scientific Research An Academic Publisher. There is no specific requirement. The percentage method is never explicitly cited, but the theoretical bases for it are provided in Chapter 4, where the superposition of the i-modes is provided as linear combination with coefficients C i that have different values for different modes but can be approximated by the value 0.

Sviluppato con Drupal da Gmg Net Srl. The effects of each modes for a given direction of the seismic action shall be combined with the CQC rule see para. The periodic response corresponds to the transient phase in theory of vibrations. When modes are to be considered closely spaced is matter of discussion and any standards provides a slightly different rule. To overcome and prevent these undesirable problems, structural design optimization of a small vertical axis wind turbine has performed, in this study, for seismic qualification and lightweight by using a Genetic Algorithm GA subject to some design constraints such as the maximum stress limit, maximum deformation limit, and seismic acceleration gain limit.

Regarding the number of modes, in para. For response spectrum RS analysis, the R. According to this book, this approach introduces a maximum error of 4. Recently, there is a growing interest in seismic qualification of ridges, buildings and mechanical equipment worldwide due to increase of accidents caused by earthquake.

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## Seismic Analysis and Design of Equipment

Dojora The directional effects of an earthquake are combined with the following rules: This statement is supported referring to a detailed discussion on this issue developed by Menun and Der Kiureghian in and Sensitivity Analysis of the Replacement Problem. As mentioned by Gupta in ref. This subject is dealt with in several replscement or regulatory guides among which the following are examined herein below: In seismic response analysis two types of combinations are to be considered: Figure 2 shows the typical response spectrum in terms of acceleration as a function of frequency ref. Sviluppato con Drupal da Gmg Net Srl. The periodic response corresponds to the transient phase in theory of vibrations.

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## A replacement for the srss method in seismic analysis

Response spectrum method is favoured by earthquake engineering community because of: Response Spectrum Method of Analysis It provides a technique for performing an equivalent static lateral load analysis. It allows a clear understanding of the contributions of different modes of vibration. It offers a simplified method for finding the design forces for structural members for earthquake. For seismic design, these maximum stresses are of interest, not the time history of stress. Equivalent lateral force for an earthquake is defined as a set of lateral force which will produce the same peak response as that obtained by dynamic analysis of structures. The equivalence is restricted to a single mode of vibration.

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## The complete SRSS modal combination rule

Severe earthquake can bring serious problems in the wind turbines and eventually lead to an interruption to their electric power supply. This subject is dealt with in several standards or regulatory guides among which the following are examined herein below: The equations are written as follows: The combination of the effects of the seismic components is discussed in paragraph 4. The percentage rule is also proposed in paragraph 4. The periodic modal responses of an earthquake are combined with the following rules: This paper offers also page 49 a short discussion of the directional combination procedure: Subscribing you accept the TOC.