Elaboration of maps for climatic actions in Italy

The present chapter discusses the procedures used to elaborate the maps for climatic actions in Italy, namely the maps for snow load, thermal action and wind actions. Those maps are present in the Italian National Annexes of Parts 1-3, 1-4 and 1-5 of Eurocode 1: Actions on structures. For each climatic action, several worked examples are presented aiming at illustrating the practical application of the climatic actions maps in different Italian sites

Tie Rod-Equivalent Non-Linear Constitutive Law for Uniformly Loaded Cables

Cables are typically used in engineering applications as tensile members. Relevant examples are the main cables of suspension bridges, the stays of cable-stayed bridges, the load-bearing and stabilizing cables of tensile structures, the anchor cables of floating mooring structures, the guy-ropes for ship masts, towers, and wind turbines, the copper cables of electrical power lines. Since cables are characterized by non-linear behavior, analysis of cable structures often requires advanced techniques, like non-linear FEM, able to consider geometric non-linearity. Nevertheless, a traditional simplified approach consists in replacing the cable with an equivalent tie rod, characterized by a suitable nonlinear constitutive law. Currently used equivalent constitutive laws have been derived by Dischinger, Ernst and Irvine. Since the equivalence is restricted to taut cables, characterized by small sag to chord ratios, these traditional formulae are not appropriate for uniformly loaded sagging cables: the main cables of suspension bridges are a particularly emblematic case. Despite some recent attempts to find more refined solutions, the problem is still open, since closed form solutions of general validity are not available. In the paper, general analytical formulae of the non-linear constitutive law of the equivalent tie rod are proposed, distinguishing two relevant cases, according as the length of the cable can vary or not. The expressions, derived by applying the general form of the theorem of virtual work, can be applied independently on the material, on the sag to chord ratio, on the load intensity and on the stress level, so allowing the replacement of the whole cable with a single equivalent tie rod. The expressions are critically discussed referring to a wide parametric study also in comparison with the existing formulae, stressing the influence of the most relevant parameters

OPERATIONAL METHODS FOR THE ASSESSMENT AND MANAGEMENT OF AGING INFRASTRUCTURE

The aims and scope of the Handbook is to provide designers with a general methodology for the assessment of existing structures, which is illustrated step by step, referring to the selected case studies. The case studies have been chosen not only in order to cover as much as possible the actual variety of infrastructures and materials, but also different building periods, from the sixteenth century to the most recent past. In this way, it is possible to consider structures designed according to different approaches; in fact, while recent structures have been designed according to Codes, Standards, Guidelines or theoretical models, the most ancient ones have been designed according to empirical rules or architectural canons, therefore the understanding of original design ideas often requires that survey and in-situ measurements and investigations are supplement with historical studies. In the presentation of case studies, beside the reference to the general procedures provided by modern Codes and ISO 13822 in particular, the above mentioned necessity of understanding original design ideas and the significance of the engineering judgement in the diagnosis of the structural decays are emphasized, aiming to communicate to the reader a correct way to approach existing structures. The references mentioned in each chapter provide additional background materials, further guidance and information, allowing to widen the significance and the field of application of the assessment methods illustrated for each case study

Reduction of Housner’s coefficient of restitution for masonry walls under one-sided rocking

This paper presents the results of static and seismic vulnerability analyses performed on a single-span masonry bridge located in Northern Italy. The structure, dated back to the 17th century, is a bridge with single-span of about 16 meters and height of 8 meters, built with rubble and irregular masonry. A preliminary static analysis was performed on the bridge through traditional graphic approaches such as the Méry’s rule and the Durand-Claye’s method. Afterwards, a kinematic non-linear analysis was executed once the collapse mechanism under horizontal earthquake-type actions was identified. Finally, a static finite element analysis with brick elements was performed to state the seismic vulnerability of the bridge, by changing its mechanical properties to evaluate their influence on the structural response. Collapse load factors have been also computed considering non-uniform gravitational loads and horizontal settlements at the bridge foundations

Numerical Simulation of the Behavior of Cracked Reinforced Concrete Members

Refined non-linear static or dynamic analyses of reinforced concrete structures require the knowledge of the actual force-displacement or bending moment-rotation curves of each structural member, which depend on the crack widths and on the crack pattern, and after all on the slip between concrete and reinforcing steel. For this reason the definition of improved local models taking into account all these local aspects is a fundamental prerequisite for advanced assessment of r.c. structures. A numerical procedure which allows to predict the relative displacement between steel reinforcement and the surrounding concrete in a reinforced concrete element, once assigned the stress in the naked steel bar and the bond-slip law is discussed. The method provides as final outcomes the sequence of crack openings and the individual crack widths, regardless of the particular bond-slip correlation adopted. The proposed procedure is implemented referring to two relevant experimental case studies, demonstrating that it is able to predict satisfactorily actual strain fields and slips along the investigated reinforced concrete elements

Fatigue behavior of stiffener to cross beam joints in orthotropic steel decks

In the paper the possibility to evaluate the fatigue strength of stiffener to cross beam joints in orthotropic steel decks is discussed. The proposed methodology, based on Paris-Erdogan law, allows to derive a sound estimate of the stress intensity factor K combining the indirect approach, based on the Rice J-integral, with the direct one, based on the extrapolation of experimental or numerical data. The practical implementation of the proposed methodology allowed to predict correctly the actual fatigue life of a previously tested real scale specimen, so validating its potentialities

Rehabilitation and seismic upgrading of the masonry arch bridge over the Magra river in Villafranca

The paper deals with the rehabilitation of an historical masonry bridge crossing the Magra river and connecting the small towns of Mulazzo and Villafranca in the northern part of Tuscany (I).The masonry arch bridge, characterized by eight arches spanning 19 m around each and by around 12 m height intermediate masonry piers on shallow foundations, was built in 1874. Since the original carriageway width was not sufficient to allow two lanes, in 1961 it was widened by means of two lateral prestressed concrete beams, supported by the piers, so hiding the arches and modifying severely the original aspect of the bridge itself. In 2011, during the Magra flooding, two arches on the Mulazzo side collapsed due to scour of the extreme pier. The reconstruction the collapsed arches and rehabilitation and the strengthening of the bridge, which has been completed last year, is discussed and the execution of the interventions, which has performed without erection of temporary support in the riverbed, is also illustrated. Particular attention is devoted to the original solutions which have been adopted for the full seismic upgrading of the bridge according to the Italian Building Code currently in force, recovering the original architectural aspect of the bridge and widening the carriageway as well

Probabilistic methodology for the assessment of the impact of climate change on structural safety

Structural design is often governed by climatic actions, such as snow, wind, thermal and atmospheric icing loads, that will occur during the design service life. Since in structural standards climatic actions are usually derived from historical data series assuming stationary climate, alterations induced by climate change should be specifically evaluated, also to assess their influence on structural reliability. In the paper, a probabilistic methodology for the assessment of climate change impact on long-term structural reliability is presented, based on the analysis of observed data series and climate projections, provided by high resolution climate models. Factor of change uncertainty maps for climate extremes are derived starting from the analysis of weather series generated by an ad hoc weather generator, which considers homogenous populations of data suitably derived from climate model output. The long-term structural reliability is then assessed for reference structures at a given site considering the non-stationary nature of climatic actions by means of the pdfs of changes in extreme value parameters. Specifically, variations of the failure probability with time due to climate change are evaluated by moving time windows of forty years considering changes in mean load intensity and standard deviation of yearly maxima of the investigated climatic action. The results show the capability of the method to assess the impact of climate change on structural safety, highlighting the necessity of adaptation measure to maintain the required target reliability of the structure during its life

Reliability of roof structures subjected to snow loads

A proper evaluation of snow loads on roofs is crucial for structural design especially to guarantee an adequate reliability level of lightweight roof structures. The definition of roof snow load in structural codes is based on both the evaluation of ground snow loads and conversion factors from ground to roof load, which are function of the roof’s geometry, its exposure to wind and its thermal properties. However, reference values of roof snow loads are based only on an extreme value analysis carried out to derive characteristic values of ground snow load, while conversion factors are considered as deterministic quantities due to the lack of the data. In this paper, first a methodology to evaluate the reference value of roof snow load is presented based on the definition of probability density functions for ground snow loads and conversion factors accounting for roof’s geometry and its exposure to wind. The results lead to the definition of a design conversion factor which depend on the coefficient of variation of ground snow loads and are compared with the constant values provided by the Eurocode models, in EN1991-1-3:2003. Then, structural reliability is assessed for reference steel and timber structures located in different sites. Considering different proportions between variable and permanent loads, the reliability of flat roofs designed according to Eurocode provisions, provided by the current version and the new draft, is finally compared with the required target reliability levels

Extreme ground snow loads in Europe from 1951 to 2100

Lightweight roofs are extremely sensitive to extreme snow loads, as confirmed by recently occurring failures all over Europe. Obviously, the problem is further emphasized in warmer climatic areas, where low design values are generally foreseen for snow loads. Like other climatic actions, representative values of snow loads provided in structural codes are usually derived by means of suitable elaborations of extreme statistics, assuming climate stationarity over time. As climate change impacts are becoming more and more evident over time, that hypothesis is becoming controversial, so that suitable adaptation strategies aiming to define climate resilient design loads need to be implemented. In the paper, past and future trends of ground snow load in Europe are assessed for the period 1950–2100, starting from high-resolution climate simulations, recently issued by the CORDEX program. Maps of representative values of snow loads adopted for structural design, associated with an annual probability of exceedance p = 2%, are elaborated for Europe. Referring to the historical period, the obtained maps are critically compared with the current European maps based on observations. Factors of change maps, referred to subsequent time windows are presented considering RCP4.5 and RCP8.5 emission trajectories, corresponding to medium and maximum greenhouse gas concentration scenarios. Factors of change are thus evaluated considering suitably selected weather stations in Switzerland and Germany, for which high quality point measurements, sufficiently extended over time are available. Focusing on the investigated weather stations, the study demonstrates that climate models can appropriately reproduce historical trends and that a decrease of characteristic values of the snow loads is expected over time. However, it must be remarked that, if on one hand the mean value of the annual maxima tends to reduce, on the other hand, its standard deviation tends to increase, locally leading to an increase of the extreme values, which should be duly considered in the evaluation of structural reliability over time