# Research on Out-of-Plane Bending Test of PVB Laminated Glass Plate with Different Number of Layers
## 1 Introduction  
As a type of high-strength translucent composite plate, the Polyvinyl Butyral (PVB) laminated glass plate (LG) is manufactured by hot-pressing multiple borosilicate glass plates with an interlayer of PVB. Owing to its excellent transparency, high strength, and superior physical isolation properties, PVB LG has been extensively employed in buildings, vehicles, and various other structures since its inception in 1903. Initially, PVB LGwas predominantly used as a decorative feature in buildings, but with advancements in manufacturing technology and architecture, its application as a load-bearing element has become increasingly prevalent. A glass floor is a quintessential example of such use. To resist out-of-plane loads exerted by people, vehicles, and other entities, the number of glass layers in PVB LG is carefully selected, often comprising two or three layers. As a laminated component, its mechanical behavior is intricately influenced by both the PVB interlayer and the glass layers, rendering its properties exceedingly complex. Overestimating its load-bearing capacity can lead to dire consequences, whereas underestimating it can cause considerable material wastage. In light of this, accurately determining the mechanical response characteristics of laminated glass plates under out-of-plane loads is essential for their rational structural design [1]. The bending behavior of PVB laminated glass panels is complex, partly because the elastic modulus of PVB is significantly lower than that of borosilicate glass. Despite both materials being isotropic, this discrepancy in elastic modulus means that when PVB laminated glass is subjected to bending out of plane, PVB's low elastic modulus cannot adequately support the coordinated deformation of each glass layer. Consequently, a certain degree of in-plane relative sliding occurs at the interfaces between glass layers. It has been established that the flexural stiffness of laminated glass plates is lower compared to a single-layer plate of the same thickness [2]. The extent of this relative slippage is influenced by the shear stress provided by PVB, which is closely related to its elastic modulus [3]. Given that PVB is a non-linear constitutive polymer material [4], this adds to the complexity of the bending behavior of PVB laminated glass. In response to this complexity, scholars have undertaken theoretical research on the bending behavior of laminated glass under various operational conditions and mechanical hypotheses. For glass plates with unidirectional support, the plates can be simplified into an equivalent superposed beam, which reduces the number of generalized variables in the control equation and simplifies the solution process [5]. [PERSON] et al. [6] derived an analytical solution for an equivalent beam with simple support under four-point bending and compression, confirming the solution's validity. [PERSON] et al. [7] extended equivalent beam theory to three-layer glass plates, derived the control differential equation by accounting for shear deformation in the laminated layer, and used the variational method to obtain a theoretical solution. However, the layered beam theory may not capture all complexities of the plates. [PERSON] et al. [8] applied a variational approach to the partial differential equations of laminated plates, yielding an analytical solution for the non-linear bending of these plates. [PERSON] et al. [9] employed the Finite Difference Method (FDM) to discretize the bending partial differential equation for laminated glass plates, offering a convergent solution. Presenting an analytical solution directly is challenging due to the complexity involved in applying classical shell theory to laminated glass plates and the influence of numerous generalized variables, which limits its practicality. Consequently, in structural design practice, the equivalent thickness method is commonly used to compute the bending resistance of laminated glass plates.