Experimental and Numerical Evaluation of Residual Displacement and Ductility in Ratcheting and Shakedown of an Aluminum Beam

Safety assessment of structures can be obtained employing limit design to overcome uncertainties concerning actual response due to inelastic constitutive behavior and more generally to non-linear structural response and loads’ random variability. The limit analysis is used for evaluating the safety of the structures, starting directly from load level without any knowledge of the load history. In the paper, the lower bound calculation is proposed where a new strain-based approach is used that allowed describing the residual stress and displacement in terms of permanent strain. The strategy uses the permanent strain as effective parameters of the procedure so that it is possible to assess the ductility requirements for the complete load program developed till collapse or shakedown. The procedure is compared to experimental results obtained on aluminum beams in shakedown

Welded section defence by LRPD devices

The present paper concerns a special application of some recently proposed structural devices, called LRPD, able to protect the welded sections of frame steel structures from undesired brittle collapse ensuring the good expected ductile behaviour. Standard I-shaped cross-sections are treated, and the proposed devices are suitably considered as moment resisting connections between beams and columns. At first the domain representing the brittle safe conditions is defined in the N,V,M space; then a sample plane frame subjected to seismic load conditions is studied and it is proved that, equipping the structure with the proposed devices suitably designed, the generalized stresses at the welded sections remain within the relevant brittle safe domain and the structure is able to dissipate a significant amount of plastic dissipation energy

Yield surface approximation for lower and upper bound yield design of 3d composite frame structures

International audienceThe present contribution advocates an up-scaling procedure for computing the limit loads of spatial structures made of composite beams. The resolution of an auxiliary yield design problem leads to the determination of a yield surface in the space of axial force and bending moments. A general method for approximating the numerically computed yield surface by a sum of several ellipsoids is developed. The so-obtained analytical expression of the criterion is then incorporated in the yield design calculations of the whole structure, using second-order cone programming techniques. An illustrative application to a complex spatial frame structure is presented

Theory and application of optimization strategies for the design of seismically excited structures

The study introduces into the theory and application of optimization strategies in earthquake engineering. The optimization algorithm substitutes the intuitive solution of practical problems done by the engineer in daily practice, providing automatic design tools and numerical means for further exploration of the design space for various extremum states. This requires a mathematical formulation of the design task, that is provided for typical seismic evaluations within this document. Utilizing the natural relation between design and optimization tasks, appropriate mechanical concepts are developed and discussed. The explanations start with an overview on the mechanical background for continua. Hereby the focus is placed on elasto-plastic structures. The given extremum formulations are treated with help of discretization methods in order to obtain optimization problems. These basics are utilized for derivation of programs for eigenvalue and stability analysis, that are applied in simplified linear analysis for the design of seismically excited structures. Another focus is set on the application in simplified nonlinear design, that uses limit state analyses on the basis of nonlinear problem formulations. Well known concepts as the response and pushover analysis are covered as well as alternative strategies on the basis of shakedown theory or cycle and deformation based evaluations. Furthermore, the study gives insight into the application of optimization problems in conjunction with nonlinear time history analyses. The solution of step-by-step procedures within optimization algorithms is shown and aspects of dynamic limit state analyses are discussed. For illustration of the great variety of optimization-based concepts in earthquake engineering, several specialized applications are presented, e.g. the generation of artificial ground motions and the determination of reduction coefficients for design spectrum reduction due to viscous and hysteretic damping. As well alternative strategies for the design of base isolated structures with controlled impact are presented. All presented applications are illustrated with help of various examples.Die vorliegende Arbeit führt in die Theorie und Anwendung von Optimiierungsverfahren im Erdbebeningenieurwesen ein. Die vorgestellten Optimierungsalgorithmen ersetzen die typische intuitive Lösung von praktischen Bemessungsaufgaben, mit Bereitstellung von automatischen Methoden und numerischen Mitteln für die Bewertung des Designraumes bezüglich extremer Zustände. Dies erfordert eine geeignete mathematische Formulierung der Bemessungsaufgaben, die für typische Anwendungsfälle bereitgestellt werden. Ausgehend von der engen Beziehung von Bemessungs- und Optimierungsaufgaben werden wesentliche theoretische Grundlagen für die Ableitung praxistauglicher Analysekonzepte entwickelt und diskutiert. Die Darstellung beginnt mit einem Überblick zum mechanischen Hintergrund. Der Schwerpunkt wird dabei auf die Analyse von elastisch-plastischen Tragwerken gelegt. Die vorgestellten Extremalformulierungen werden mit Methoden der Diskretisierung in Optimierungsprobleme umgeformt. Diese bilden die Grundlage für die Analyse von Eigenwert- und Stabilitätsproblemen im Erdbebeningenierwesen. Weiterhin werden vereinfachte lineare Bemessungsmethoden besprochen. Eine Erweiterung wird duch die Einbeziehung von nichlinearen Aspekten erzielt, die einen wesentlichen Teil der Arbeit ausmachen. Einerseits werden bekannte Konzepte auf der Basis von Antwortspektren und Pushoveranalysen einbezogen, andererseits werden auch alternative Strategien auf der Basis der Einspieltheorie oder zyklen- oder deformationsbasierten Analyse vorgestellt. Desweiteren werden Anwendungen von Optimierungsverfahren im Zusammenhang mit nichtlinearen Zeitverlaufsmethoden diskutiert. Die Lösung von Zeitverlaufsproblemen in Form von Optimierungsaufgaben wird vorgestellt und Aspekte der Grenzzustandsanalyse für dynamische Probleme behandelt. Die Vielfältigkeit von Optimierungsanwendungen im Erdbebeningenieurwesen wird anhand verschiedener Spezialanwendungen demonstriert wie z.B. die Generierung von künstlichen Erdbebenzeitverläufen und die Modifikation von Bemessungsspektren für die Analyse von nichtlinear beanspruchten Tragwerken mit viskoser und hysteretischer Dämpfung. Darüberhinaus wird eine alternative Methode für die Bemessung von basisisolierten Tragwerken unter Verwendung von kontrollierten Kollisionen vorgestellt. Alle Anwendungen werden in zahlreichen Beispielen näher erläutert

Limit analysis of conical and parabolic domes based on semi-analytical solution

The evaluation of limit loads of masonry domes has received increasing interest especially due to the importance of historical buildings where domes mainly are one of the most relevant structures. The limit design is used to obtain the safety assessment and the design guidance for restoration and transformation toward preservation and reuse of historical heritage. In the following paper, we present a formulation of the limit analysis based on the semi-analytical approach that starts on Melan's theorem. The self-equilibrated Melan's residual is obtained through the discretization of the analytical form of the equilibrium equation of the spherical dome. The procedure provides a finite-dimensional map of the eigenstress of the structure. Furthermore, the superimposition of the elastic solution to actual loads, obtained by finite element calculation, completes the admissible stress evaluation. Such amissible stress is introduced into the maximization algorithm, based on the lower bound theorem, which results in the collapse load. The same approach is used to get the safety assessment under prescribed load that allows checking the safety of prescribed load pattern and geometry