This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

Basalt-based fiber-reinforced materials and structural applications in civil engineering

An innovative numerical modeling strategy for the structural analysis of historical monumental buildings

Seismic fragility of Italian RC precast industrial structures

Since the late 1970s, nonlinear static analysis have had an increasing use in the seismic assessment of existing unreinforced masonry (URM) buildings. Different modelling strategies can be used to evaluate the global seismic response of these buildings, such as the Continuous Constitutive Laws Model (CCLM) and the Equivalent Frame Model (EFM). Despite the CCLM modelling approach seems to be the most suitable at this aim, it needs many input data, which are often quite difficult to be known, and requires a high computational effort. For this reason, the EFM, which is based on strongly simplified hypotheses, is preferred in professional practice, where a small computational burden and a time- and cost-saving structural analysis by using few mechanical parameters is needed. In this paper, a review of its uses and limits is proposed, in order to identify the most critical issues and define its proper use in professional practice when applied to existing URM buildings. As a result, it is highlighted that the EFM can be reasonably used as a first conservative approach for the seismic assessment of existing URM buildings with box behaviour and quite regular opening patterns. Thus, up to now, from this review its use is encouraged in seismic analysis of existing URM buildings after providing them a reduction of their floors and roofs deformability, an adequate wall-to-floor and wall-to-roof connections and a regularization of the opening patterns.

Uses and limits of the Equivalent Frame Model on existing unreinforced masonry buildings for assessing their seismic risk: A review

Grouted sleeve connections used in precast reinforced concrete construction – Experimental investigation of a column-to-column joint

Summary
The paper analyses the seismic fragility of precast reinforced concrete buildings using observational damage data gathered after the 2012 Emilia earthquakes that struck Northern Italy. The damage level in 1890 buildings was collected, classified and examined. Damage matrices were then evaluated, and finally, empirical fragility curves were fitted using Bayesian regression. Building damage was classified using a six-level scale derived from EMS-98. The completeness of the database and the spatial distribution of the buildings investigated were analysed using cadastral data as a reference. The intensity of the ground motion was quantified by the maximum horizontal peak ground acceleration, which was obtained from ShakeMaps. Copyright © 2017 John Wiley & Sons, Ltd.

Empirical seismic fragility for the precast RC industrial buildings damaged by the 2012 Emilia (Italy) earthquakes

Seismic risk assessment of a 50 m high masonry chimney using advanced analysis techniques

The 2012 Emilia (Italy) earthquakes struck a highly industrialized area including several thousands of industrial prefabricated buildings. Due to the lack of specific design and detailing for earthquake resistance, precast reinforced concrete (RC) buildings suffered from severe damages and even
partial or total collapses in many cases. The present study reports a data inventory of damages from field survey on prefabricated buildings. The damage database concerns more than 1400 buildings (about 30% of the total precast building stock in the struck region). Making use of the available shakemaps of the two mainshocks, damage distributions were related with distance from the nearest epicentre and corresponding Pseudo-Spectral Acceleration for a period of 1 second (PSA at 1 s) or Peak Ground Acceleration (PGA). It was found that about 90% of the severely damaged to collapsed buildings included into the database stay within 16 km from the epicentre and experienced a PSA larger than 0.12 g. Moreover, 90% of slightly to moderately damaged buildings are located at less than 25 km from the epicentre and were affected by a PSA larger than 0.06 g. Nevertheless, the undamaged buildings examined are almost uniformly distributed over the struck region and 10% of them suffered a PSA not lower than 0.19g. The damage distributions in terms of the maximum experienced PGA show a sudden increase for PGA

Observational failure analysis of precast buildings after the 2012 Emilia earthquakes

A new closed-form equation for the local instability of pultruded fiber-reinforced plastic beams in bending is derived by substituting suitable buckling approximating functions for compression flange and web into the total potential energy functional. Being obtained from a full-section approach, the equation does not require independent calculations for web and compression flange, which are typical of discrete plate analysis. Moreover, the contribution of the elastic restraint stiffness commonly used to reproduce the web–flange junction behavior naturally arises in the proposed formulation because of the assumed buckling shape. From comparisons with available experiments on 10 beams and FE solutions for 55 beams, the proposed equation appears to be accurate and reliable.

Fabio Minghini

Papers

Grouted sleeve connections used in precast reinforced concrete construction – Experimental investigation of a column-to-column joint

Empirical seismic fragility for the precast RC industrial buildings damaged by the 2012 Emilia (Italy) earthquakes

Seismic risk assessment of a 50 m high masonry chimney using advanced analysis techniques

Observational failure analysis of precast buildings after the 2012 Emilia earthquakes

A closed-form equation for the local buckling moment of pultruded FRP I-beams in major-axis bending