# Yield Behaviour of Welded I-Shaped Steel Cross-Sections
## 1 Introduction  
In many cases of practical interest, in the design of steel frame structures, it is very useful to adopt factory-welded I-shaped beams instead of the standard rolled ones. One of these cases is that of seismic retrofitting of existing masonry structures. In such a case, to obtain the required seismic behaviour, it is necessary to modify the stiffness of the masonry panels. For this goal, steel hooping is considered the most adequate, and the adoption of suitably designed and factory-welded steel elements allows us to obtain optimal structures with reduced size and, consequently, with little effect on usability. Another task is that of new openings in masonry panels, which requires the steel hooping to restore both strength and stiffness of those panels where the opening is created. In such cases, usually, the required stiffness is often very high and, consequently, the chance of adopting steel frames realized with suitably designed and factory-welded I-shaped beam elements with assigned geometric characteristics is a fundamental strategy which also allows for a reduction in the opening dimensions. On the other hand, the above referenced chance of adopting welded structural elements is also often advantageous in new frame design. As is well known in such structures, the connections between beams and columns are very critical, since their design plays a crucial role in the safety and ductility of the overall structure. This topic is relevant when elastoplastic analysis is performed both statically [1; 2; 3; 4] or dynamically [5; 6; 7; 8; 9], as well as in design problems for frame and truss structures [10; 11; 12], both taking into account buckling and slenderness [13; 14; 15; 16] and in the case of seismic and dynamic actions [17; 18; 19; 20]. In practical applications, an important strategy is to plan interventions able to reduce the strength of the element in suitably selected portions of the element close to the connections between beams and columns. In this way, the onset of plastic strain also allows for the protection of the welded connections between beams and columns. The most common approach belonging to this strategy is the so-called dogbone, while a recently proposed approach is referred to as the Limited Resistance Plastic Device (LRPD). Another approach is based on dissipative approaches leading, e.g., to devices for seismic-resistant steel frames developed by the FUSEIS EC project (RFSR-CT-2008-00032) or other devices [21; 22; 23; 24]. The main idea of the dogbone [25; 26; 27; 28; 29] is that of suitably reducing the base of the I-shaped beam in a portion close to the column to obtain a reduction in the limit bending moment. Such a reduction in the case of high loads causes the required yielding and decreases in the actions on the welded connections between beams and columns. The seismic performances of structures equipped with dogbones is the topic of many papers available in the literature (see, e.g., [30; 31; 32]), and developments of the main idea (i.e., reducing the web) have been also proposed (see, e.g., [33; 34; 35; 36]). In recent years, a number of innovative systems based on energy dissipation and damping have been invented as a result of national and European research projects, such as dissipative connections assigned to braced steel frames (developed in \"Two INnovations for Earthquake Resistant Design\", INERD project) [24] and dissipative links (see, e.g., [37; 38]). These innovative systems consist of small and dismountable dissipative parts where seismic damage is concentrated; hence, they have increased repairaibility while displaying comparable stiffness and ductility to the conventional ones. The structural behaviour of structures equipped with these devices is assessed in many papers available in the literature (see, e.g., [39]).