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See detailDevelopment and analysis of low-order models of frame structures under blast loads
Hamra, Lotfi ULg

Doctoral thesis (2016)

The main aim of this thesis is to propose an easy-to-apply tool to assess the level of damage of a structure in which one compartment is subjected to blast loading. This compartment is extracted from the ... [more ▼]

The main aim of this thesis is to propose an easy-to-apply tool to assess the level of damage of a structure in which one compartment is subjected to blast loading. This compartment is extracted from the structure accounting for the interaction with the part of the structure surrounding the loaded compartment, which is assumed to be elastic. Before studying the whole frame structure, the structural elements (i.e. the beam and its adjacent columns) are firstly studied separately taking into account the lateral restraint and mass offered by the indirectly affected part (IAP) of the structure. Secondly, the dynamic behaviour of a simple compartment made of pinned members and laterally braced is investigated. The material laws are assumed to be elastic-perfectly plastic, neglecting the effect of strain rate on the yield strength. The out-of-plane instabilities of the structural members are disregarded. • To explain the context of this study + final aim of this research Two analytical models are developed to predict the dynamic response of the frame beam subjected to blast loading, including the elastic lateral restraint and inertia offered by the IAP of the structure, the development of nonlinear membrane action (P-\delta effect) and also, the interaction between bending moment and axial force in the plastic hinges. The first model is based on a single degree of freedom (SDOF model) which is the transverse mid-span deflection of the beam while the second model is a two-degree-of-freedom (2-DOF) model which also includes the axial elongation of the beam. The accuracy of these two low-order models is assessed with finite element simulations. This validation stage shows that the proposed low-order models capture the physics of the problem in most cases of practical interest. A dimensional analysis of the problem reveals that, under the considered assumptions, four dimensionless parameters mainly influence the required ductility of the beam. Two of them are related to the behavior of the indirectly affected part (the lateral restraint and mass). Another one is related to the mechanical properties of the investigated beam (i.e. the ratio of the bending to axial resistance). The last parameter incorporates scales of the geometry and of the deformed configuration at the onset of the plastic mechanism. Concerning the columns, an analytical model is proposed to assess its dynamic response under constant axial compressive load and lateral blast loading. It accounts for large displacement (P-\delta effect), bending moment-axial force (M-N) plastic interaction as well as its interaction with the indirectly affected part (IAP) of the structure. This model is non-smooth piecewise linear and involves two degrees of freedoms (2 DOFs) in each regime of the motion of the column (related to the possibilities of development of plastic hinges). The dimensional analysis of the problem reveals that, under the considered assumptions, four dimensionless parameters mainly influence the dynamic stability of the beam-column. Two of them are related to the behavior of the indirectly affected part (the lateral restraint and mass). Another one is related to the critical load multiplier (i.e. the ratio of the axial compressive load to Euler elastic buckling resistance). The last parameter is the reduced slenderness of the beam-column. Subsequent to a parametric study, it is demonstrated that a good correlation is found between the results provided by the analytical model and a richer FEM model, despite some little discrepancies observed for some intermediate values of stiffness of the lateral restraint and lateral mass. As a possible improvement, adjustments to the analytical model are suggested. Finally, the dynamic behaviour of a simple frame under constant compressive loads and lateral blast loading is studied with a last 2-DOF analytical model. A multi-layer model of the cross-section of the beam is used to derive the bending moment-axial force (M-N) plastic interaction instead of the Lescouarc'h formula and normality rule. The coupling between the beam and the adjacent columns is ensured through appropriate boundary conditions. For the studied frame, two blast scenarios are contemplated, the first one corresponds to a quasi-static blast loading while the second one refers to a dynamic blast loading. The first case study shows that a very good agreement is achieved between the deflections predicted by the analytical and numerical models although a discrepancy is observed in the assessment of the axial force in the column due to the shape of the inertial force distribution of the beam assumed in the model. The second case study illustrates that, in both analytical and numerical models, the columns are predicted to fail by buckling due to the P-\delta effect although the axial force in the column is again inaccurately captured by the analytical model for the same reason. [less ▲]

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See detailSimplified equivalent static approach and results for deriving structural requirements - Deliverables D.11 and D.12 - Robustimpact
Demonceau, Jean-François ULg; D'Antimo, Marina ULg; Huvelle, Clara et al

Report (2016)

Deliverable 11 and 12 have been merged in the present document which can be seen as the main outcome of the activities conducted with Work Package 9 of the Robustimpact project. Section 2 presents first ... [more ▼]

Deliverable 11 and 12 have been merged in the present document which can be seen as the main outcome of the activities conducted with Work Package 9 of the Robustimpact project. Section 2 presents first the sophisticated numerical investigations conducted on a reference structure subjected to impacts of vehicles. Then, Section 3 presents in details the simplified analytical models/tools developed within the present project to predict the response of a structure (or a part of a structure) further to the impact of a vehicle. With the presented models, it is demonstrated that an accurate prediction of the structural results may be obtained and that all the parameters influencing this response are mastered. Section 4 introduces the different parametric studies which have been conducted (partly using the models/tools presented in Section 3) on 2D and 3D steel and composite structures or on composite floors. Finally, Section 5 highlights the structural requirements which can be proposed as an outcome of the performed investigations. Through this document, it is demonstrated that the different objectives of Work Package 9 have been reached in the framework of this project. [less ▲]

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See detailPressure-impulse diagram of a beam developing non-linear membrane action under blast loading
Hamra, Lotfi ULg; Demonceau, Jean-François ULg; Denoël, Vincent ULg

in International Journal of Impact Engineering (2015), 86

The p–I diagram of a frame beam subjected to blast loading is established, including the elastic lateral restraint and inertia offered by the rest of the structure, the development of nonlinear membrane ... [more ▼]

The p–I diagram of a frame beam subjected to blast loading is established, including the elastic lateral restraint and inertia offered by the rest of the structure, the development of nonlinear membrane action and also, the bending-tension (M−N) interaction that develops in the plastic hinges. The analytical procedures to compute the asymptotes in the p–I diagram as well as a parametric study on the p–I diagram are provided. A dimensional analysis of the problem reveals that, under the considered assumptions, four dimensionless parameters mainly influence the required ductility of the beam. Two of them are related to the behavior of the indirectly affected part (the lateral restraint and mass). Another one is related to the mechanical properties of the investigated beam (i.e. the ratio of the bending to axial resistance). The last parameter incorporates scales of the geometry and of the deformed configuration at the onset of the plastic mechanism. [less ▲]

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See detailAnalytical procedure to derive P-I diagram of a beam under explosion
Hamra, Lotfi ULg; Demonceau, Jean-François ULg; Denoël, Vincent ULg

in Proceeding of the IABSE Workshop - Safety, Robustness and Condition Assessments of Structures (2015, February)

The aim of this paper is to study a beam extracted from a frame and subjected to blast loading. The demand of ductility depends on six dimensionless parameters: two related to the blast loading, two ... [more ▼]

The aim of this paper is to study a beam extracted from a frame and subjected to blast loading. The demand of ductility depends on six dimensionless parameters: two related to the blast loading, two referring to the bending behaviour of the beam and two corresponding to the dynamic behaviour of the rest of the structure. We develop a full analytical procedure that provides the ductility demand as a function of these six dimensionless parameters. [less ▲]

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See detailPressure-impulse diagram of a beam under explosion - Influence of the indirectly affected part
Hamra, Lotfi ULg; Demonceau, Jean-François ULg; Denoël, Vincent ULg

in Landolfo, Raffaele; Mazzolani, Frederico (Eds.) Proceeding of the 7th European conference on steel and composite structures (Eurosteel 2014) (2014, September 10)

The paper studies the structural response of a beam subjected to a close-field local internal blast loading. In the literature, the pressure-impulse (p-I) diagram is commonly used to design elements or ... [more ▼]

The paper studies the structural response of a beam subjected to a close-field local internal blast loading. In the literature, the pressure-impulse (p-I) diagram is commonly used to design elements or structures for a given blast loading. The p-I diagram is a spectrum representing the level sets of damage or required ductility for a given structural system, nonlinear beam in this paper. This representation is much appreciated because a simple reading for the actual pressure p and impulse I of the considered load indicates the ductility demand of the structural system. Recent works of quasi-static behaviour have indicated the crucial need to account for the membrane effects taking place in the extreme loading of frame beams. This paper will thus extend the state-of-art features, establishing thus the p-I diagram for a beam including the lateral restraints offered by the rest of the structure, the development of non-linear membrane action and also, the M-N interaction that develops in the plastic hinges. [less ▲]

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See detailPrincipal Static Wind Loads on a large roof structure
Blaise, Nicolas ULg; Hamra, Lotfi ULg; Denoël, Vincent ULg

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 ▲]

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See detailSimplification du chargement aérodynamique sur une toiture de stade
Hamra, Lotfi ULg

Master's dissertation (2012)

The stochastic analysis of a structure subjected to turbulent wind gives estimation of the extreme (or peak) responses necessary for the structural design. These extreme values are established for each ... [more ▼]

The stochastic analysis of a structure subjected to turbulent wind gives estimation of the extreme (or peak) responses necessary for the structural design. These extreme values are established for each response within the structure (displacements, internal forces, reactions, etc ...). Notwithstanding, engineers from design office are used to design structures under static wind loads. The major challenge is thus to compute equivalent static loads that take into account the dynamic behavior of the structure and by simple static analyses, reconstruct the most accurately the extreme responses obtained from a stochastic dynamic analysis. Equivalent static wind loads are determined by applying various methods and the aim of this work is to extract a reduced basis, the principal static wind loads. These principal static wind loads are well suited for combinations in order to have a minimum number of design cases. Focus is made on the responses of the structure which are composed of mean, quasi-static and resonant contributions and on the number of design static wind loads to provide an accurate reconstruction of all extreme responses. [less ▲]

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