Optimal Design of New Steel Connections

The Limited Resistance Rigid Perfectly Plastic Hinge (LRPH) are special steel connections mainly usable to join beam elements of plane or spatial steel frames. The fundamental characteristics of these devices are the mutual independence of their own resistance and stiffness features as well as the respect of assigned constraints related to the elastic and limit behaviour of the joined elements. Within the frame structural scheme, the device plays the role of a rigid perfectly plastic hinge, constituted by a suitably sized sandwich section. The efficient use of the LRPH in the relevant frame depends on the appropriate design of the device geometry. In the present paper, a new approach devote…

Probabilistic Evaluation of the Adaptation Time for Structures under Seismic Loads

Abstract In this paper, a probabilistic approach for the evaluation of the adaptation time for elastic perfectly plastic frames is proposed. The considered load history acting on the structure is defined as a suitable combination of quasi-statical loads and seismic actions. The proposed approach utilizes the Monte Carlo method in order to generate a suitable large number of seismic acceleration histories and for each one the related load combination is defined. Furthermore, for each load combination the related adaptation time is determined, if any, as the optimal one for which the structure is able to shakedown under the unamplified applied actions. A known generalized Ceradini's theorem i…

Optimal design of steel frames accounting for buckling

A formulation of a special design problem devoted to elastic perfectly plastic steel frame structures subjected to different combinations of static and dynamic loads is presented. In particular, a minimum volume design problem formulation is presented and the structure is designed to be able to elastically behave for the assigned fixed loads, to elastically shakedown in presence of serviceability load conditions and to prevent the instantaneous collapse for suitably chosen combinations of fixed and ultimate seismic loadings as well as of fixed and wind actions. The actions that the structure must suffer are evaluated by making reference to the actual Italian seismic code. The dynamic respon…

Multicriterion design of frames with constraints on buckling

The present paper is devoted to the optimal design of frame structures subjected to static and dynamic loading assuming the material behaviour as elastic perfectly plastic. The relevant optimal design problem is formulated as a minimum volume search problem. The minimum volume structure is determined under suitable constraints on the design variables as well as accounting for different resistance limits: the elastic shakedown limit and the instantaneous collapse limit, considering for each limit condition suitably chosen amplified load combinations. The effects of the dynamic actions are studied on the grounds of the dynamic features of the structure taking into account the structural perio…

Seismic shakedown design of frames based on a probabilistic approach

The present study concerns the optimal design of elastic perfectly plastic structures subjected to a combination of fixed and seismic loads. In particular, plane frames are considered and suitable measures of the beam element cross sections are chosen as design variables. The optimal design is required to behave in a purely elastic manner when subjected just to the fixed load and to have the capability to eventually shakedown when simultaneously subjected to fixed and seismic loads. Due to the natural uncertainness related to the definition of the seismic load history, a new probabilistic approach is proposed, consisting into two subsequent search steps. At first a suitably chosen large num…

Dynamic Shakedown Sensitivity Analysis by Means of a Probabilistic Approach

The shakedown limit load multiplier problem for elastic plastic structures subjected to a combination of fixed and seismic loads is treated. In particular, reference is firstly made to the unrestricted dynamic shakedown theory. The relevant seismic load history is modeled as a repeated one and, with reference to classically damped structures, appropriate modal analyses are utilized. With the aim of evaluating the reliability of the results arising from the application of the cited theory, a recent probabilistic approach is also utilized. This approach adopts the Monte Carlo method in order to define the necessary seismic acceleration histories and finally compute the related shakedown limit…

On the Post-Elastic Behavior of LRPH Connections

The paper concerns the study of the post-elastic behavior of a recently proposed innovative device, named Limited Resistance Rigid Perfectly Plastic Hinge (LRPH). In particular, LRPH is a steel device of finite length realizing a moment connection between beam elements of a steel frame; it is designed in order to possess two main and independent requirements: its bending moment resistance must be suitably lower than the one of the connected beam element and its overall bending stiffness must be equal to that of the connected beam element characterized by the same length. In order to make the proposed device reliable, LRPH must be capable of realizing a full plastic hinge for the assigned be…

Comparison between unrestricted dynamic shakedown design and a new probabilistic approach for structures under seismic loadings

The paper concerns a study related to the comparison between two different approaches utilized for the formulation of an optimal shakedown design problem for elastic plastic frame structures subjected to a combination of fixed and seismic loading. The first formulation utilizes the unrestricted dynamic shakedown theory, while the second one is based on a new probabilistic approach. The comparison is effected in terms of mathematical formulations, in terms of adopted loading models and in terms of numerical results. The performed applications are related to plane steel frames.

Evaluation of the bending behaviour of laminated glass beams via electronic speckle pattern interferometry

The paper is devoted to the experimental analysis of the kinematical and mechanical behaviour of laminated glass beam structures. In particular, the utilized laminated glass specimens are composed of two glass layers bonded by a polymer layer constituted by Ethylene-vinyl acetate whose thickness has been nominally considered as constant for all the specimens. The experimental behaviour of the analyzed specimens is deduced by applying Electronic Speckle- Pattern Interferometry technique; actually, among optical methods this technique (handled by phase-stepping technique) is very effective to obtain a full-field displacement map and to numerically achieve the longitudinal strain. In particula…

On the optimal design of base isolation devices

The paper deals with the optimal design of a base isolation system for a given structure subjected to seismic loads. In particular, an appropriate minimum displacement seismic protection device optimal design formulation is proposed for an assigned elastic perfectly plastic steel frame constrained to behave in conditions of elastic shakedown. The chosen base isolation device is constituted by elastomeric isolators. Suitable combinations of fixed and seismic loads are considered. According to the unrestricted shakedown theory, the seismic input is given as any load history appertaining to a suitably defined seismic load admissibility domain. The relevant dynamic structural response is obtain…

Discrete variable design of frames subjected to seismic actions accounting for element slenderness

An optimal design problem formulation of elastic plastic frames under different combinations of fixed and seismic loads is presented. The optimal structure must behave elastically for the fixed loads, shakedown for serviceability conditions and prevent instantaneous collapse for fixed and high seismic loads. P-Delta effects and element buckling are considered. An appropriate modal technique is utilized. The design variables can have components in a continuous field or, alternatively, in chosen discrete sets or, yet, both kind of variables can be present. The design problem is formulated on the ground of a statical approach. The applications are related to steel frames.

An efficient framework for the elasto-plastic reliability assessment of uncertain wind excited systems

Abstract In this paper a method to efficiently evaluate the reliability of elastic-perfectly plastic structures is proposed. The method is based on combining dynamic shakedown theory with Subset Simulation. In particular, focus is on describing the shakedown behavior of uncertain elasto-plastic systems driven by stochastic wind loads. The ability of the structure to shakedown is assumed as a limit state separating plastic collapse from a safe, if not elastic, state of the structure. The limit state is therefore evaluated in terms of a probabilistic load multiplier estimated through solving a series of linear programming problems posed in terms of the responses of the underlying linear elast…

Minimum volume design of structures with constraints on ductility and stability

Abstract A minimum volume design problem of elastic perfectly plastic frame structures subjected to different combinations of fixed and seismic loads is presented, in which the design variables are considered as appertaining alternatively to a continuous assigned range as well as to appropriate discrete sets. The structure is designed so as to behave elastically for the applied fixed loads, to shakedown in presence of serviceability seismic conditions and to prevent the instantaneous collapse for suitably chosen combinations of fixed and high seismic loadings. In order to avoid further undesired collapse modes, the P-Delta effects are considered and the structure is also constrained to prev…

Minimum displacement design of base isolation devices

Speckle Interferometry Analysis of Full-bending Behavior of GFRP Pultruded Material

Abstract The use of Glass Fiber Reinforced Polymer materials (GFRP) has increased in the last years even among civil structural engineering due to their high specific strength, lightweight and excellent corrosion resistance. With application of the pultrusion method, the manufacture of large-scale profiles with various cross-section forms became potentially possible with relatively low costs. Usually two different technological approaches are available to realize the element: in the first one a mat-roving-mat sequence is adopted, in the second one only roving is present. Continuous filament mat (CFM, fibers distributed randomly in all directions) is often used to build up laminate thickness…

Reliability-based design optimization of trusses under dynamic shakedown constraints

A reliability-based design optimization problem under dynamic shakedown constraints for elastic perfectly plastic truss structures subjected to stochastic wind actions is presented. The simultaneous presence of quasi-static (cyclic) thermal loads is also considered. As usual in the shakedown theory, the quasi-statical loads will be defined as variable within a deterministic domain, while the dynamic problem will be treated considering an extended Ceradini-Gavarini approach. Some sources of uncertainties are introduced in the structural system and in the load definition. The reliability-optimization problem is formulated as the minimization of the volume of the structure subjected to determi…

Reliable measures of plastic deformations for elastic plastic structures in shakedown conditions

A new formulation for evaluating reliable measures of the plastic deformations occurring in the transient phase of a structure in shakedown conditions is proposed. The structure is thought as constituted by elastic perfectly plastic material and subjected to a combination of fixed and cyclic loads. The proposed formulation consists in the search for the optimal plastic strain field that minimize a suitable objective function defining a strain energy measure related to the plastic strains at the shakedown limit. The typical self-stress field can be obtained as the elastic structural response to an assigned plastic strain field respecting appropriate ductility limits for the material. Without…

Optimization of structures with unrestricted dynamic shakedown constraints

The unrestricted dynamic shakedown theory is here utilized with the aim to formulate different optimal design problems for structures mainly subjected to seismic loads. In particular, reference is made to plane frame structures constituted by elastic perfectly plastic material subjected to load combinations characterized by the presence of simultaneous fixed and seismic actions. The design problems, formulated on the ground of a statical approach, are devoted to structures with and without seismic protection devices, with special emphasis to seismic isolators. For the proposed design problem formulations different constraints are utilized; actually, for structures without protection devices…

Discrete variables structural design of frames safe against buckling

On the structural optimization in presence of base isolating devices

The minimum volume design of plane frames constituted by elastic perfectly plastic material and subjected to appropriate combinations of fixed, cyclic and dynamic loads is studied. The influence on the design, in terms of cost (volume) and behavioural features, of seismic protecting devices is particularly focused. The considered protecting device is a lead rubber bearing base isolation system. Two optimal design problem formulations are proposed for the structure with or without the protecting device, both based on the so-called statical approach. The minimum volume frame is reached accounting for three different resistance limits: the purely elastic limit, the (elastic) shakedown limit an…

Analysis and design of elastic plastic structures subjected to dynamic loads

In the last decades, the concept of “optimization” has reached considerable value in many different fields of scientific research and, in particular, it has assumed great importance in the field of structural mechanics. The present study describes and shows the scientific path followed in the three years of doctoral studies. The state of the art concerning the optimization of elastic plastic structures subjected to quasi-static loads was already well established at the beginning of the Ph.D. course. Actually, it was already faced the study of structures subjected to quasi-static cyclic loads able to ensure different structural behaviors in relation to different intensity levels of the appli…

Structural Design of Frames Able to Prevent Element Buckling

Two formulations of a special multicriterion optimal design problem devoted to elastic perfectly plastic steel frame structures subjected to different combinations of static and dynamic loads are presented. In particular, two minimum volume design problem formulations are proposed: in the first one the structure is designed so as to be able to elastically behave for the assigned fixed loads, to elastically shakedown for serviceability seismic load conditions and to prevent the instantaneous collapse for suitably chosen combinations of fixed and ultimate seismic loadings; in the second one the structure must also satisfy further appropriate constraints related to element buckling. The action…

LRPH device optimization for axial and shear stresses

The paper concerns an in-depth study of a special connection for steel structures and the formulation of the related optimal design problem. The connection is called Limited Resistance Rigid Perfectly Plastic Hinge (LRPH) and it represents an innovative device devoted to join steel beam elements of frame structures. The device consists in a sequence of steel cross sections constituted by two parallel flanges with suitably different thickness connected by as many webs with constant and equal thickness. The fundamental innovation of the device is the possibility of designing special connections with elastic stiffness and limit strength independent of each other. Such a special characteristic …

Evaluation of the shakedown limit load multiplier for stochastic seismic actions

A new approach for the evaluation of the shakedown limit load multiplier for structures subjected to a combination of quasi-statically variable loads and seismic actions is presented. The common case of frame structures constituted by elastic perfectly plastic material is considered. The acting load history during the lifetime of the structure will be defined as a suitable combination of never ending quasi-statical loads, variable within an appropriate given domain, and stochastic seismic actions occurring for limited time interval. The proposed approach utilizes the Monte Carlo method in order to generate a suitable large number of seismic acceleration histories and the corresponding shake…

Dynamic shakedown design of structures under repeated seismic loads

The paper is devoted to the formulation of an optimal design (minimum volume) problem of elastic perfectly plastic structures subjected to suitable combinations of static (fixed) and dynamic (seismic) loads. The structure is constrained to simultaneously respect two different safety criteria; actually, it must exhibit an elastic shakedown behaviour for the combination of loads characterizing the serviceability conditions and it must prevent the instantaneous collapse for the highest expected load condition (combination of loads characterized by the presence of fixed loads and maximum expected intensity of seismic action). The shakedown limit behaviour for the optimal structure will be impos…

Experimental and numerical analysis of flexural behaviour of GFRP pultruded material

Performance-Based Engineering of Wind-Excited Structures: A General Methodology

The current prescriptive design philosophy that relies simply on meeting requirements stipulated in standards is shifting towards a performance-based design (PBD) approach for achieving designs that rationally meet society’s need for a truly safe built environment. Extensive research has facilitated the successful adoption of PBD in earthquake engineering, but the same cannot be said for wind engineering. Therefore, the need exists to initiate a similar effort by defining a framework that fully embraces the concepts of PBD during the design of building systems to resist severe wind events. This paper illustrates the development of such a PBD framework. In particular, a method is proposed sp…

Optimal design of elastic plastic frames accounting for seismic protection devices

The optimal design of elastic perfectly plastic steel frames with or without suitable protection devices and subjected to static as well as seismic loadings is studied. Two minimum volume problem formulations are proposed, on the grounds of the so-called statical approach, accounting for three different resistance limits: the purely elastic limit, the (elastic) shakedown limit and the instantaneous collapse limit. The adopted load combinations are characterized by the presence of fixed loads, of quasi-static perfect cyclic loads and dynamic (seismic) loads. The linear elastic effects of the dynamic actions are studied by utilizing a modal technique. The proposed treatment is referred to the…