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Principal static wind loads within a rigorous methodology to the envelope reconstruction problem Blaise, Nicolas Doctoral thesis (2016) Static wind loads are being used for the design of large civil structures such as high-rise buildings, large roofs and long-span bridges. Once static wind loads are known, they are used through the ... [more ▼] Static wind loads are being used for the design of large civil structures such as high-rise buildings, large roofs and long-span bridges. Once static wind loads are known, they are used through the iterative design process without repeating cumbersome dynamical analyses. In this framework, structural engineers can effectively focus on the structural sizing since static analyses are straightforward. No codified wind loads, however, exist for those large structures with unique shapes and there is no consensual view on how to formally derived them. For each new major project, the challenge consists therefore in deriving a relevant set of static wind loads. Obviously, these loads must provide the actual envelope values of structural responses of interest. This states the objective of the envelope reconstruction problem and constitutes the core of this thesis. The proposed developments to solve this problem are relevant for structures responding with a linear dynamic behavior to the buffeting action of synoptic winds in a stationary framework. The pioneering concept of Equivalent Static Wind Load is normally considered for the design. An extensive review points out two main limitations of the current formulations. They have been originally established in a Gaussian context, are associated with either a nodal or nodal-modal basis and do not have a formal definition. The proposed Conditional Expected Load method overcomes the three drawbacks by defining a Conditional Expected Static Wind Load. This novel approach presents a general rigorous formulation for linear structural behavior, irrespective of the basis used for the analysis and relevant in a non-Gaussian context. The method is particularized for a certain class of non-Gaussian processes through a bicubic translation model. This model covers a large range of non-Gaussianity in the random processes and therefore paves the way for the formal establishment of “non-Gaussian” static wind loads with a physical interpretation. Other kinds of static loads such as the covariance proper transformation loading modes and the modal inertial loads are additionally studied. Unfortunately, both sets of loads are simply relevant for two limit structural behaviors, quasi-static and resonant, respectively. Moreover, they do not adapt to the set of structural responses of interest. From both points of view, one key result from our study is the innovative concept of Principal Static Wind Load as a sound solution for the envelope reconstruction problem. The concept relies upon a robust mathematical foundation. These loads are determined by the singular value decomposition of a large set of equivalent static wind loads. This decomposition can be seen as a way to rank the most relevant load patterns for the envelope reconstruction problem. The principal static wind loads have also the added distinctive advantage to be flexible. They are, indeed, able to naturally adapt to the set of structural responses of interest. Finally, a complete methodology to solve the envelope reconstruction problem irrespective of the structure, its load-bearing system and its susceptibility to vibrations in a Gaussian or non-Gaussian context is rigorously conceptualized. The intrinsic controllability of a set of pertinent parameters provides a smart balance between over and underestimation of the actual envelope. Moreover, combinations of static wind loads are computed to speed-up the reconstruction of the envelope values. The problem of determining these combination coefficients is formulated as a constrained nonlinear optimization. Equivalent and principal static wind loads, covariance proper transformation loading modes and modal inertial loads are implemented within the proposed methodology. Three examples: a four-span bridge, a real-life large stadium roof and a low-rise building demonstrate that the envelope reconstruction accuracy is considerably improved with principal static wind loads and with combinations thereof. [less ▲] Detailed reference viewed: 88 (33 ULg)Reconstruction of the envelope of non-Gaussian structural responses with principal static wind loads Blaise, Nicolas ; ; Denoël, Vincent in Journal of Wind Engineering & Industrial Aerodynamics (2015), 149 In current practice, structural engineers commonly focus on the wind-resistant design by means of static wind loads. In case of non-Gaussianities, there is room for improvement to properly derive these ... [more ▼] In current practice, structural engineers commonly focus on the wind-resistant design by means of static wind loads. In case of non-Gaussianities, there is room for improvement to properly derive these static loads. First, this paper extends in a non-Gaussian context the concept of the load-response correlation (LRC) method establishing equivalent static wind loads (ESWLs). This is done by a proper recourse to the new concept of conditional expected static wind load and a proposed bicubic model for the joint and conditional distribution functions. Second, this paper investigates the envelope reconstruction problem targeting the efficient reconstruction of the envelope values of a set of non-Gaussian structural responses by means of principal static wind loads (PSWLs). They have been introduced in a Gaussian context and are obtained by a singular value decomposition of ESWLs. This paper addresses the extension of PSWLs to non-Gaussian structural responses, as well. The developments apply to structures with a linear behavior and subjected to an aerodynamic pressure field exhibiting mildly to strongly non-Gaussian features. In this context, the well-known load-response correlation and conditional sampling methods are used for comparisons. This study is undertaken for quasi-static analysis of structures and is illustrated on a low-rise building. [less ▲] Detailed reference viewed: 22 (4 ULg)Adjusted Equivalent Static Wind Loads for non-Gaussian linear static analysis Blaise, Nicolas ; Denoël, Vincent Conference (2015, June) In this paper, we propose a parametric bi-cubic model for the joint probability distribution of wind aerodynamic pressures and structural responses. This non-Gaussian model is a bivariate extension of the ... [more ▼] In this paper, we propose a parametric bi-cubic model for the joint probability distribution of wind aerodynamic pressures and structural responses. This non-Gaussian model is a bivariate extension of the well-known Hermite polynomial transformation. It offers a new way to determine Equivalent Static Wind Loads, with the embedded feature to –at least partly– capture the non-Gaussianity of the aerodynamic pressures and responses. In a second step, based on the observation that this model as well as the usual LRC method or the conditional sampling technique, fail in reproducing structural responses that do not overestimate the extreme values resulting from a complete structural analysis, we propose a two-step adjustment procedure that restores the non-overestimation condition and the recovery of the considered structural response. With the example of a boundary layer flow around a duo-pitched roof, it is demonstrated that the Equivalent Static Wind Loads, adjusted or not, obtained with the proposed model of non-Gaussian joint probability density function reconstruct the envelope of structural response more efficiently than with the other two techniques. [less ▲] Detailed reference viewed: 31 (9 ULg)An asymptotic expansion-based method for a spectral approach in equivalent statistical linearization Canor, Thomas ; Blaise, Nicolas ; Denoël, Vincent in Probabilistic Engineering Mechanics (2014), 38 Equivalent linearization consists in replacing a nonlinear system with an equivalent linear one whose parameters are tuned with regard to the minimization of a suitable function. In particular, the ... [more ▼] Equivalent linearization consists in replacing a nonlinear system with an equivalent linear one whose parameters are tuned with regard to the minimization of a suitable function. In particular, the Gaussian equivalent linearization expresses the properties of an equivalent linear system in terms of the mean vector and the covariance matrix of the responses, which are the unknowns of the optimization problem in a spectral approach. Even though the system has been linearized, the resulting set of equations is nonlinear. The computational effort in this method pertains to the solution of a possibly large set of nonlinear algebraic equations involving integrals and inversions of full matrices. This work proposes to develop and apply an asymptotic expansion-based method to facilitate and to improve the statistical linearization for large nonlinear structures. The proposed developments demonstrate that for slightly to moderately coupled nonlinear systems, the equivalent linearization can be applied with an appropriate modal approach and eventually seen as a convergent series initiated with the stochastic response of a main decoupled linear system. With this method, the computational effort is attractively reduced, the conditioning of the set of nonlinear algebraic equations is improved and inversion of full transfer matrices and repeated integrations are avoided. The paper gives a formal description of the method and illustrates its implementation and performances with the computation of stationary responses of nonlinear structures subject to coherent random excitation fields. [less ▲] Detailed reference viewed: 97 (28 ULg)Calculation of third order joint acceptance function for line-like structures Blaise, Nicolas ; Canor, Thomas ; Denoël, Vincent in Proceedings of the XIII Conference of the Italian Association for Wind Engineering (2014, June 24) Detailed reference viewed: 41 (12 ULg)A Fast Newton-Raphson Method in Stochastic Linearization Canor, Thomas ; Blaise, Nicolas ; Denoël, Vincent in Proceedings of the Ninth International Conference on Structural Dynamics (2014) Owing to its accessible implementation and rapidity, the equivalent linearization has become a common probabilistic approach for the analysis of large-dimension nonlinear structures, as encountered in ... [more ▼] Owing to its accessible implementation and rapidity, the equivalent linearization has become a common probabilistic approach for the analysis of large-dimension nonlinear structures, as encountered in earthquake and wind engineering. It consists in replacing the nonlinear system by an equivalent linear one, by tuning the parameters of the equivalent system, in order to minimize some discrepancy error. Consequently classical analysis tools such as the spectral analysis may be reconditioned to approximate the solution of structures with slight to moderate nonlinearities. The tuning of the equivalent parameters requires the solution of a set of nonlinear algebraic equations involving integrals. It is typically performed with the fixed-point algorithm, which is known to behave poorly in terms of convergence. We therefore advocate for the use and implementation of a Newton-Raphson approach, which behaves much better, even in its dishonest formulation. Unfortunately, this latter option requires the costly construction of a Jacobian matrix. In the approach described in this paper, this issue is answered by introducing a series expansion method that provides a fast and accurate estimation of the residual function (whose solution provides the equivalent parameters) and a fast and approximate estimation of the Jacobian matrix. An illustration demonstrate the good accuracy obtained with the proposed method. [less ▲] Detailed reference viewed: 82 (11 ULg)Equivalent static wind loads for structures with non-proportional damping Blaise, Nicolas ; Canor, Thomas ; Denoël, Vincent in Zingoni, A (Ed.) Fifth International Conference on Structural Engineering, Mechanics & Computation (2013, September) Detailed reference viewed: 47 (15 ULg)Principal static wind loads Blaise, Nicolas ; Denoël, Vincent in 6th Proceedings of European-African Conference on Wind Engineering (2013, July 07) The concept of static wind load is widely used in practice for structural wind design. In this context, this paper assesses the envelope reconstruction problem stated as follows: find the best set of ... [more ▼] The concept of static wind load is widely used in practice for structural wind design. In this context, this paper assesses the envelope reconstruction problem stated as follows: find the best set of static loadings that is optimum to reproduce by static analyses, the envelope values of structural responses resulting from a formal buffeting dynamic analysis. A solution was recently derived by means of Principal Static Wind Loads which are well-suited for this problem. The concept is illustrated with a large stadium roof and the accuracy of the envelope reconstruction is analysed. [less ▲] Detailed reference viewed: 69 (21 ULg)Uncoupled spectral analysis with non-proportional damping Canor, Thomas ; Blaise, Nicolas ; Denoël, Vincent in Proceedings of the European-African Conference on Wind Engineering (2013, July 07) The use of normal modes of vibration in the analysis of structures with non-proportional damping reduces the number of governing equations, but does not decouple them. A common practice consists in ... [more ▼] The use of normal modes of vibration in the analysis of structures with non-proportional damping reduces the number of governing equations, but does not decouple them. A common practice consists in decoupling the equations by disregarding the off-diagonal elements of the modal damping matrix. This paper proposes a method based on the asymptotic expansion of the modal transfer matrix to take into account the modal coupling in Gaussian spectral analysis. First, the mathematical background is introduced, then the relevance of the method is illustrated within the context of the analysis of a large and real structure submitted to wind loadings. [less ▲] Detailed reference viewed: 66 (8 ULg)Equivalent static wind loads for structures with non-proportional damping Blaise, Nicolas ; Canor, Thomas ; Denoël, Vincent in Proceedings of the 11th International Conference on Recent Advances in Structural dynamics (2013, July) In current practice, wind structural design is often carried out using the concept of equivalent static wind loads. The main characteristic of such loadings is to reproduce, with static analyses, the same ... [more ▼] In current practice, wind structural design is often carried out using the concept of equivalent static wind loads. The main characteristic of such loadings is to reproduce, with static analyses, the same extreme structural responses as those resulting from a formal buffeting analysis. This paper proposes a method for the computation of equivalent static wind loads for structures with slight non-proportional damping in a modal framework. Because of the smallness of the out-of diagonal terms, this method is based on recent developments related to asymptotic expansion of the modal transfer matrix of such structures. As a main benefit, the static loading is described as a perturbation of the equivalent loading that would be obtained for the uncoupled system. The main contribution of this paper is to formalize the expression of the correction terms resulting from the non-proportionality of damping. The method is presented with a detailed illustrative example. [less ▲] Detailed reference viewed: 50 (13 ULg)Principal static wind loads Blaise, Nicolas ; Denoël, Vincent in Journal of Wind Engineering & Industrial Aerodynamics (2013), 113 In current wind design practice, static wind loads are usually defined to obtain, by simple static analyses, the extreme values of any structural response that would be formally obtained with a strict ... [more ▼] In current wind design practice, static wind loads are usually defined to obtain, by simple static analyses, the extreme values of any structural response that would be formally obtained with a strict dynamic buffeting analysis. The minimum and maximum values that may reach any response define the envelope. Equivalent static wind loads (ESWLs) allow to recover extreme responses in the envelope. As a first objective, this paper formalizes a general method to determine ESWL, in a nodal basis, by extending the concept of load-response correlation, which is only valid in the background range. The general method, the displacement-response-correlation (DRC) method, covers the background and resonant contributions of the considered response. As a second objective, the paper addresses the problem of building a set of static wind loads that adequately reconstructs the envelopes of responses. The concept of principal static wind loads (PSWL) is introduced to form a reduced basis of representative loads well-suited for envelope reconstruction. Its optimality is demonstrated both analytically and with a detailed illustrative example. [less ▲] Detailed reference viewed: 105 (28 ULg)Principal Static Wind Loads on a large roof structure Blaise, Nicolas ; Hamra, Lotfi ; Denoël, Vincent in Proceedings of the 12th ANIV conference of wind engineering In Vento (2012, October 07) Usually, structural wind design is realized using static wind loads. Such loadings are expected, as a main property, to recover by static analyses, the envelope values that would be obtained by a formal ... [more ▼] Usually, structural wind design is realized using static wind loads. Such loadings are expected, as a main property, to recover by static analyses, the envelope values that would be obtained by a formal buffeting analysis. For simple structures, equivalent static wind loads might be used but they are established in order to reproduce envelope values of specific structural responses and are thus not suitable to reconstruct efficiently the entire envelope. Recently, more general methods were derived to propose global static loadings that reconstruct the entire envelope but several drawbacks remained as their robust applicability for any structure and accuracy. This paper addresses a new type of static loadings, the principal static wind loads, derived in a strict mathematical way, the singular value decomposition, to make it optimum for the envelope reconstruction problem. The method is illustrated with a large roof and the reconstruction accuracy is analysed by studying the rate of envelope reconstruction, envelope previously obtained by a rigourous stochastic analysis. The way principal loadings are derived makes them suitable for combinations in order to increase the rate of the envelope reconstruction. As a major outcome, the method provides a finite number of design load cases that matches a desired level of accuracy in the envelope reconstruction. [less ▲] Detailed reference viewed: 236 (101 ULg)Efficient uncoupled stochastic analysis with non-proportional damping Canor, Thomas ; Blaise, Nicolas ; Denoël, Vincent in Journal of Sound & Vibration (2012), 331(2012), 52835291 The use of normal modes of vibration in the analysis of structures with nonproportional damping reduces the size of the resulting set of governing equations, but does not decouple them. A common practice ... [more ▼] The use of normal modes of vibration in the analysis of structures with nonproportional damping reduces the size of the resulting set of governing equations, but does not decouple them. A common practice consists in decoupling the equations by disregarding the o -diagonal elements in the modal damping matrix. Recently, an approximation based on an asymptotic expansion of the modal transfer matrix has been proposed in a deterministic framework to partially account for o -diagonal terms, but still with a set of uncoupled equations. This paper aims at extending this method in a stochastic context. First the mathematical background is introduced and the method is illustrated with a simple example. Then its relevance is demonstrated within the context of the structural analysis of a large and realistic structure. [less ▲] Detailed reference viewed: 112 (42 ULg)Application of deterministic and stochastic analysis to calculate a stadium with pressure measurements in wind tunnel Blaise, Nicolas ; Denoël, Vincent ; De Ville De Goyet, Vincent et al in Proceedings of the 8th International Conference on Structural Dynamics EURODYN 2011 (2011, July) This paper aims at comparing different analysis methods in the design of a roof subjected to buffeting wind forces. The specificity of this study is that pressures acting on the stadium roof are measured ... [more ▼] This paper aims at comparing different analysis methods in the design of a roof subjected to buffeting wind forces. The specificity of this study is that pressures acting on the stadium roof are measured in a wind tunnel. The key idea is to fit a probabilistic model onto the measured data and to perform the stochastic analysis as a usual buffeting analysis. [less ▲] Detailed reference viewed: 99 (19 ULg)Optimal processing of wind tunnel measurements in view of stochastic structural design of large flexible structures Blaise, Nicolas ; Denoël, Vincent in Lerner, J. C.; Boldes, U. (Eds.) Wind Tunnels and Experimental Fluid Dynamics Research (2011) Detailed reference viewed: 71 (20 ULg)Etude du comportement d'une toiture de grandes dimensions soumise à un vent turbulent Blaise, Nicolas Master's dissertation (2010) The aim of this project is the development of a model allowing the calculation of the wind turbulence, using Matlab software. The problems associated wind tunnel pressure measurements (e.g. frequency ... [more ▼] The aim of this project is the development of a model allowing the calculation of the wind turbulence, using Matlab software. The problems associated wind tunnel pressure measurements (e.g. frequency noise, noise) are taken into account. In order to solve the equation of motion, several methods are applied. First, modal superposition solving decoupled equations by Newmark (NK) and by Fourier transform (FT). Secondly, a stochastic analysis (SRSS and CQC) is performed, using white noise approximation (BB). As an ultimate goal of designing the structure, the calculation of extreme values is realized using a simplified method as well as the statistic method of extreme values. Results show that Newmark method, with fixed time step, produces an elongation of the period and is therefore not recommend. The modal correlation being low, the SRSS analysis is sufficient to determine the dynamic contribution. Results provided by the FT method are closer to the results obtain with CQC-BB method, thus these methods appear to be equivalent. Regarding the calculation of extreme values, the simplified method can calculate positive and negative peak factors, whereas the statistic method of extreme values, applied considering a Gaussian process, can't. In conclusion, the stochastic methods is recommanded because she had the advantage of treating appropriately the noise frequencies for the dynamic contribution. [less ▲] Detailed reference viewed: 186 (33 ULg)Stochastic analysis of a stadium roof from deterministic wind tunnel measurements Blaise, Nicolas ; Denoël, Vincent in 13th International Conference on Wind Engineering (2010) Dynamic analyses of structures under buffeting wind loads can be performed in a deterministic (Clough and Penzien, 1997) or stochastic (Preumont, 1994) context, both with a modal approach for ... [more ▼] Dynamic analyses of structures under buffeting wind loads can be performed in a deterministic (Clough and Penzien, 1997) or stochastic (Preumont, 1994) context, both with a modal approach for computational efficiency reasons. In the first option, the forces are deterministically given, and the uncoupled modal equations of motion are solved either in the time domain with a stepby- step method, either in the frequency domain, with Fourier transformation. In the second option, the analysis relies on the determination of the Power Spectral Density (PSD) matrix of the structural response given that of the loading. The choice of one or another method usually depends on whether the loading is provided in the time or frequency domain and as a deterministic (a single time history) or stochastic manner. From a designer’s point of view, the wind loading can be defined using design codes (e.g. Eurocode, 2005) where analytical expressions of (i) the PSD of wind velocities (Davenport, Von Karman, etc) (ii) the coherence functions and (iii) the pressure coefficients are given to compute, finally, (iv) the PSD of the aerodynamic pressures. Design engineers are usually familiar with this probabilistic approach. Alternatively, the design may be conducted from aerodynamic pressures measured in a wind tunnel. This approach is more realistic than the aforementioned codified procedure since a number of phenomena as (a) the aerodynamic instabilities, (b) aerodynamic admittance (Scanlan and Jones, 1999), (c) site effects are taken into account. Pressures are thus given as unique (deterministic) time histories at each sensor. In a Finite Element context and a modal analysis, the generalized forces are computed from the measured pressures. With the firm wish to perform the analysis in a stochastic manner (for a number of good reasons mentioned next), we suggest to fit a probabilistic model to the measured data. Such a model could be fitted to the measured pressures right away, or any other subsequent quantity such as the generalized forces. The following discussion is about the most favorable quantity that has to be fitted and how to do it appropriately in view of typical measurement imperfections. [less ▲] Detailed reference viewed: 46 (12 ULg) |
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