Optimal design of glass plates loaded transversally Paolo Foraboschi ⇑ Università IUAV di Venezia, Dipartimento di Architettura Costruzione Conservazione, Convento delle Terese, Dorsoduro, 2206, 30123 Venice, Italy article info Article history: Received 16 March 2014 Accepted 17 May 2014 Available online 27 May 2014 Keywords: Glass design Laminated Glass Minimum thicknesses Optimal design Polymeric interlayers Sacrificial ply abstract This paper focuses on glass used in buildings and presents a criterion for fail-safe optimal design of glass plates. First, the paper shows that the glass plate is fail-safe only if the load-bearing system is composed of two glass layers bonded to one another with an elastomeric interlayer (Laminated Glass), and if the live loads act upon a sacrificial glass ply (tri-layer system). Then, activity was directed at analyzing the simply-supported fail-safe glass plate loaded out-of-plane, and carrying out research targeted at reducing the incidence of weight and cost (optimal design). The results, obtained using an analytical exact model, show that the limit states are always dictated by the maximum deflection and not by the load-carrying capacity. Thus, optimal design requires finding the thickness of the glass layers and the stiffness of the interlayer that provide the plate with exactly the minimum allowable stiffness, while the stress verifications are fulfilled automatically. Finally, for every span and load that is found in building applications of glass, the paper provides the thicknesses and the materials of the glass layers and interlayers that adjust capacity to match demand. These results may also replace structural analysis and assessment of Laminated Glass plates. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction To optimize the performance and cost of a structure, the task of a structural designer is to determine the material(s) and geometry of component(s) under some functional requirements and con- straints [1–15]. To select the optimal structure among possible similar structures is called ‘‘optimal design’’. This paper is devoted to the optimal design of plates made of glass, loaded predominantly out-of-plane, and used as primary or secondary structures, or as non-bearing elements. Primary struc- tures include floors and roofs [16–21]; secondary structures include overhead glazing supported by primary structures and ele- ments of staircases [16,20]; non-bearing elements include façades and partitions [22,23]. Not only do glass elements have to withstand the design loads, but also they have to fulfill fail-safe design [16,21,22,24–28]. Fail safe design of glass is based on a fundamental evaluation – namely, the ratio between the load-carrying capacity and ultimate load demand, and the ratio between the span and maximum deflection do not provide an exhaustive description of safety. That these ratios are adequate is a necessary but not a sufficient condition. In order to achieve an exhaustive description of safety, three other conditions have to be considered in designing and assessing glass elements. When these conditions are satisfied, glass is called fail-safe. 2. Fail-safe transparent plates Glass ensures safety, security, and safeguarding only with a fail- safe design. Moreover, glass ensures transparency only if its thick- ness is not excessive. 2.1. Fail-safe conditions Glass is fail-safe if it satisfies the following three conditions. 2.1.1. First fail-safe condition: Redundancy The presence of flaws is unavoidable in glass. From the struc- tural point of view, the flaws that are worthy of attention are the cracks, since glass breaks when the combination of a load and a crack causes the stress intensity factor to reach the critical stress intensity factor [24,25,29–33]. Cracks can be divided into two types – namely, cracks that occur during manufacturing due to production processes, and cracks that occur during the service life due to concentrated loads, http://dx.doi.org/10.1016/j.matdes.2014.05.030 0261-3069/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Tel.: +39 041 2571289. E-mail address: paofor@iuav.it Materials and Design 62 (2014) 443–458 Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/matdes