Laminated Glass Beams Research Articles

Four-point bending tests on laminated glass beams reinforced with FRP bars adhesively bonded to the glass

Four-point bending tests on laminated glass beams reinforced with FRP bars adhesively bonded to the glass

Fractional viscoelastic characterization of laminated glass beams under time-varying loading

Laminated glass is a composite made of elastic glass layers sandwiching thin viscoelastic polymeric interlayers. There are several types of polymers, traditionally modelled as linear viscoelastic materials using a Prony’s series of units in the Maxwell-Wiechert arrangement. We show that one single element with fractional viscoelastic properties (two constitutive parameters that depend on environmental temperature), is sufficient to provide an accurate description of the polymer response under arbitrary time-varying actions. This is a great advantage over the classical viscoelastic characterization, which requires at least 10–15 terms in the Prony’s series, each one characterized by a relaxation time, so that the series covers the time-scale of the applied actions. Fractional viscoelasticity is incorporated in the analytical model of a three-layer laminated beam, susceptible of a zig-zag warping of the cross section, which is analyzed under time-dependent loading. The great potential of this approach is demonstrated in representative case studies.

Flexural behaviour of post-tensioned glass beams: Experimental and analytical study of three beam typologies

The concept of post-tensioned glass beams builds on the concrete analogy of the reinforced glass beams. By additionally prestressing the reinforcement in a post-tensioned system, a compressive pre-stress is applied on the glass, enhancing the initial fracture resistance in bending. This paper presents three post-tensioned beam systems tested in four-point bending. The effects of both adhesive bonding and mechanical anchoring of tendons are explored in order to define an optimised beam system which can provide a significant level of compressive pre-stress and maximise the efficient use of material. The tests demonstrate the feasibility of post-tensioning by providing a substantial level of additional load capacity and redundancy to commonly applied laminated glass beams. Several specimens have demonstrated premature failure governed by lateral-torsional buckling or by shear. Since glass beams are generally not strengthened through transversal reinforcement, as concrete elements, further investigation of the mechanism of shear failure is particularly important. Analytical models, based on the pre-stressed concrete theory, provide expressions for determination of the initial fracture resistance, initial stiffness and ultimate flexural capacity. Compared with the experimental results, the models provide close prediction values for the initial fracture loads, while the predictions of the initial stiffness and ultimate post-fracture load capacity show less consistency. Closer prediction requires a better understanding of the effect of specific anchoring, the level of composite action and the post-fracture behaviour of laminated glass (including long-term and temperature effects).

Exploratory investigation into the post-fracture model of laminated tempered glass using combined Voronoi-FDEM approach

It is reported that the fractured glass panels can contribute to the residual load-bearing capability of laminated glass (LG) after cracking. In order to investigate the stiffness and failure characteristics of LG at the post-fracture stage, a combined Voronoi and finite-discrete element method (FDEM) approach was proposed, which includes reconstructing the post-fracture patterns and carrying out the structural simulation of the post-fracture behaviour. The fracture morphology was determined by introducing Voronoi tessellation defined with statistical parameters such as the fragment face numbers, volume and sphericity. The interaction between glass fragments was captured with the cohesive zone model. One fractured LG block under uniaxial tension, which was taken from a triple layered LG beam with ionoplast interlayers, was modelled and validated with experimentally recorded data. Through iteration analysis, the key cohesive parameters were selected. It was then followed by investigating the influence of the fragment interaction property, the bond level and fracture morphology on the post-fracture behaviour of laminated tempered glass. Results show that the combined cohesion and frictional properties can well represent the residual interaction behaviour between fragments. The frictional property has a significant effect on the post-fracture resistance, and whereas the effect on the stiffness is not that evident. Compared to other cohesive parameters, the cohesive stiffness factors have a predominant effect on both the post-fracture stiffness and resistance. The tension stiffening effect is found to be able to provide a clear increase in post-fracture resistance, which can be up to ten times the original resistance, if the glass-interlayer interface is perfectly bonded. The progressive debonding at glass-interlayer interfaces will lead to the degradation in the loading resistance of fractured LG. A higher bond level can promote the coupling effect between interlayers and mid glass layer for providing increased load resistance after the significant debonding has occurred at the outmost glass-interlayer interface. The effect of fracture morphology on post-fracture performance is not evident in most cases except that the increase in fragment size will lead to a great stiffness growth.

Phase Field Simulation of Laminated Glass Beam.

The complex failure mechanisms of glass laminates under in-plane loading conditions is modelled within the framework of phase-field strategy. Laminated glass is widely used for structural purposes due to its safe post-glass-breakage response. In fact, the combination of several glass plies bonded together with polymeric interlayers allows overcoming the brittleness of the glass and to reach a pseudo-ductile response. Moreover, the post-breakage behaviour of the laminate is strictly correlated by the mechanical properties of the constituents. Ruptures may appear as cracks within the layers or delamination of the bonding interface. The global response of a glass laminate, validated against experimental results taken from the literature, is carried out by investigating a simplified layup of two glass plies connected by cohesive interfaces through an interlayer. Delamination of the adhesive interface is described, and crack patterns within the materials are fully described. Finally, the proposed approach put the basis for future comparisons with results of experimental campaign and real-life applications.

The Lateral Torsional Buckling Behavior of Laminated Glass Beams

In this paper, the lateral torsional buckling (LTB) behavior of multi-layered long-span laminated glass (LG) beams is investigated through full-scale model test and numerical simulation. In the test program, the LG beams consisting of up to four glass plies and spanning 5000[Formula: see text]mm are constructed and tested. The load-displacement curves and development of strain in glass plies are recorded, based on which the deformation and stress state of buckled LG beams are analyzed, and the strength checking criterion is provided. The test results are also used to determine the shape and amplitude of initial imperfection through statistical analysis and to validate a numerical model based on the finite element method (FEM). Parametric analysis based on the FEM model is then conducted to investigate influential factors on the LTB resistance of LG beams, among which the influence of shape and amplitude of initial imperfection is emphasized. For the LTB design of LG beams, the applicability of existing formula to determine the critical buckling moment through effective stiffnesses is evaluated for multi-layered LG beams with the test and numerical results. Finally, the design buckling curves adopting the Ayrton–Perry formula (APF) are proposed and validated for LG beams categorized with glass type and load duration.

A cohesive zone based DE/FE coupling approach for interfacial debonding analysis of laminated glass

Laminated glass is normally a three-layer sandwiched composite structure, i.e. two glass layers and one PVB interlayer. The discrete element/finite element (DE/FE) coupling approach, which uses DEs and FEs to respectively discretize the glass and PVB layers, has proved to be an effective method for impact failure analysis of laminated glass. However, only one failure pattern, glass cracking, was considered in previous literature. This work develops a cohesive zone based DE/FE approach to account for another impact failure pattern, interfacial debonding, existing in laminated glass. In the presented approach, DE/FE cohesive pairs are constructed by recourse to a contact searching algorithm, and cohesive forces are evaluated in a pointwise manner with the aid of a mixed mode traction-separation law. In addition, the novel approach is coupled with a particle-to-segment contact algorithm to achieve a smooth transition from cohesive failure to frictionless contact sliding. The effectiveness of the DE/FE approach is validated via three benchmark tests. Finally, the impact failure process of a laminated glass beam is simulated to demonstrate the capacity of the proposed approach in debonding analysis of laminated glass.

Investigations on the flexural performance of laminated glass

Laminated Glass, regarded as the safety glass, is widely used in modern architectural applications. The structural behaviour of this type of glass is highly complex owing to the presence of the interlayer. In such a case, classical theoretical formulations are of no use and it becomes necessary to employ specially formulated equations or numerical simulations to evaluate the performance of laminated glass. Present work consists of displacement-controlled four-point bending tests on laminated glass beams to study the load-deflection behaviour and fracture pattern of the samples. Numerical simulations of the test samples are carried out in ANSYS to achieve the maximum tensile stress and deflection values corresponding to the initial failure load. Three laminated glass performance models are used to analytically evaluate the values of failure stress for laminated glass.

Enhanced Effective Thickness for laminated glass beams and plates under torsion

The torsional response of laminated rectangular panes composed by N glass plies of arbitrary thickness, coupled by N-1 polymeric interlayers, is here analyzed. Under the quasi-elastic approximation, that considers the secant stiffness of the polymer, we use the classical hypothesis that the all glass plies rotate of the same angle of twist to derive the shape function for the strain field, whose actual form is found by energy minimization. When the width of the pane is much less that its length, we find formulae that apply to the geometry of a beam, representing the counterpart for laminates of the solution à la de Saint Venant for elements with thin rectangular cross sections. This approach extends to the case of torsion the Enhanced Effective Thickness (EET) method, already proposed for bending, and generalizes other previously proposed engineering methods, which are only applicable for beams composed of a limited number of glass plies. Comparison with numerical results for different geometries confirms the accuracy of the proposed formulation. This method can be conveniently applied for the preliminary design of cold-bent laminated cells for façades, as well as to study the lateral torsional buckling of in-plane-bent beams.

Enhanced effective thickness model for buckling of LG beams with different boundary conditions

Because of their characteristic high slenderness ratios, laminated glass elements are frequently subjected to buckling phenomena. Here, simple analytical formulae for the evaluation of the effective thickness for the compressive buckling verification of laminated glass beams are proposed, based on the Enhanced Effective Thickness model, widely used for the design of laminated glass. The model applies also to multilaminates. Tables for the calculation of the relevant coefficients in the most common cases have been added for ease of reference and to facilitate the practical use. Comparison with numerical results, performed by considered paradigmatic cases, confirm the accuracy of the proposed formulae.

A SIMPLE MIXED FINITE ELEMENT MODEL FOR COMPOSITE BEAMS WITH PARTIAL INTERACTION

A simple and effective mixed finite element model is proposed for studying the behavior of beams with composite section, with particular reference to two-layer beams with partial interaction, namely, steel-concrete, timber-concrete, and two-layer laminated glass beams. The model is based on a mixed variational formulation, which as independent fields assumes the displacements of each layer and the shear stresses transmitted by the connections between the layers. The effectiveness of the model, which automatically satisfies the Newmark kinematic hypothesis for a composite beam, is evaluated by performing a set of numerical tests and comparing results with existing analytical and numerical solutions; furthermore, the convergence of the model to the well-known layered and monolithic beam behavior is shown. Numerical tests are performed in the linear elastic field, but the possible model extensions to the field of material and geometric nonlinearity are highlighted, together with a further refinement of the numerical model.

3D Adaptive Combined DE/FE Algorithm for Analyzing Impact Fracture of Laminated Glass

Laminated glass has been wildly employed in automobile windshields, modern buildings, etc. thanks to its security and durability performance. A novel 3D adaptive combined DE/FE algorithm is proposed to research its impact fracture mechanical properties if the fracture region is small relative to a specimen while the cracks are propagating at a random position. The proposed method can automatically convert the distorted finite elements into the spherical discrete elements during simulating the impact fracture of laminated glass. In this method a system is completely discretized into the finite elements at the initial moment without any discrete element existing until part of the finite elements becoming severely deformed. Subsequently each finite element, whose maximum tensile stress exceeds a user-specified conversion criterion, is converted into eight spherical discrete elements. At the same time the system is fragmented into two subdomains, the finite element (FE) and the discrete element (DE) subdomains. An extrinsic cohesive fracture model is adaptively adopted only in the DE subregion to capture the crack propagation when the normal stress between the DEs equals or exceeds the cohesive strength. The impact fracture of a glass beam is simulated by the adaptive algorithm and the discrete element method, respectively. Beside of the micro-cracks and cohesive zone, almost the same crack patterns are captured by both the numerical methods. Fortunately, the efficiency of the proposed method is much higher (10 times in this case) than that of the pure DEM. A satisfactory agreement of the simulation results certified the feasibility and effectiveness of such an adaptive algorithm. Finally, the impact fracture simulation is performed by the adaptive algorithm on a laminated glass beam which has the same size as the experimental specimens. Besides of the differences on the cracks occurrence and propagation angle, a similar agreement of the fracture patterns is observed as the experimental results. The common conclusions on the role of PVB interlayer can be obviously obtained by analyzing the simulation results, the same by analyzing the experimental ones. The proposed method is hopeful to be employed to analyze the impact fracture of an automobile windshield subjects to the head impact for the protection of pedestrians safety, the traffic accident reconstruction and the structural optimization of windshield.

Mechanical characterization of polyvinil butyral from static and modal tests on laminated glass beams

Polyvinyl butyral (PVB) is the polymeric interlayer material most used in laminated glass elements. As other used interlayers, the PVB mechanical behavior is viscoelastic. Therefore, its mechanical characterization can be carried out by static (creep and relaxation) or dynamic tests in a dynamic mechanical analyser (DMA). However, the PVB layers constrained in laminated glass elements are subject to high temperature and pressure conditions in an autoclave during the manufacturing process, which can affect to the mechanical properties of the interlayer. In this paper, the mechanical properties of PVB constrained in laminated glass beams have been determined by static and dynamic tests on laminated glass beams with different boundary conditions and at different temperatures. The estimated curves are compared with those obtained by testing free PVB specimens in a DMA.

Static and dynamic effective thickness in five-layered glass plates

In the last years, the effective thickness concept has been used to calculate deflections, stresses and modal parameters in laminated glass beams and plates, which consists of using a monolithic element with equivalent bending properties to a laminated element, i.e. the thickness of the equivalent monolithic model is time and temperature dependent because the interlayers show a viscoelastic behavior. Multi-layered laminated glass panels are those with at least three monolithic glass layers and two viscoelastic interlayers which are commonly used in floors, roofs and other applications where a high level of security is required. In this paper, a static deflection effective stiffness for a laminated glass plate consisting of three glass layers and two polymeric interlayers is derived. This static effective thickness is then extended to the frequency domain using the correspondence principle. The models are validated by static experimental tests and operational modal tests carried out on a rectangular multi-layered laminated glass plate pinned supported at the four corners.

Structural glass beams with embedded GFRP, CFRP or steel reinforcement rods: Comparative experimental, analytical and numerical investigations

The use of hybrid and composite solutions for structural applications represents a common approach for the development of safe design principles. Consolidated examples exist for concrete, steel and masonry structures. As a general rule, materials are combined so as to obtain an enhanced redundancy, strength and/or (lateral) stiffness for these systems. In this paper, structural laminated glass (LG) beams including reinforcement rods are investigated, and special attention is spent on the effect of embedded rod features, consisting of GFRP, CFRP or stainless steel reinforcement tendons. The examined embedded solution, as shown, can offer a certain benefit to the bending performance of traditional LG beams, including positive effects on stiffness, resistance and redundancy. The intrinsic properties of rods can otherwise largely affect the overall observations. To this aim, unpublished experimental tests are first briefly summarised for a set of 1 m span LG beams. Support for the preliminary discussion of the examined design concept is also derived from simple analytical calculations. Finite-Element (FE) numerical simulations are then presented, reporting on major expected behaviours due to variations in the geometrical/mechanical features of the rods, with respect to the experiments. A key role in the FE models is given by the reliable description of mechanical properties and interactions between the structural components. Comparative results are hence discussed for the post-fracture assessment of beam specimens. As shown, even a limited presence of reinforcing rods (≈100-to-400 the explored range for the ratio of glass-to-rods cross-sectional area) can provide ductility and redundancy to the LG beams. Maximum benefits (+30% residual resistance) are given by ductile steel rods, while positive effects can also be achieved with GFRP and CFRP tendon rods.

An Improved Contact Formulation for Impact Crack Simulations in a Laminated Glass Beam

Laminated glass is a simple sandwiched structure, which, however, is widely used in automotive and architectural industries. The well-known extrinsic cohesive zone model has proved to be a powerful numerical approach for the glass-ply crack simulations in laminated glass, where the classical node-to-segment contact treatment is usually employed. However, an unphysical phenomenon, named contact force jump, may arise during crack simulations, thereby resulting in numerical instabilities or incorrect simulation results. To address this issue, we develop an improved node-to-segment contact formulation to make the contact interactions in extrinsic crack simulations more stable. The main idea is to keep the number of contact constraints constant before and after cracking. The improved contact formulation is very simple and easy to implement, which, however, is effective to address the unphysical phenomenon. Three numerical examples, including the impact crack simulations of a laminated glass beam, are performed to validate the accuracy and effectiveness of the improved contact formulation.

Membrane action in reinforced glass beam systems: Experimental setup and results

Glass is increasingly used to produce structural elements for buildings. For the case of glass beams, a lot of hybrid glass concepts, in which glass is combined with another material (e.g. steel, reinforced concrete, fibre reinforced polymers) were developed and successfully tested to overcome the material’s brittle nature and hence provide post-fracture capacity. Being one of the most widely tested concepts, the reinforced laminated glass beam demonstrates satisfactory load-carrying behaviour, both for statically determinate and indeterminate support conditions, for a variety of environmental conditions (temperature, humidity, etc.) and for several reinforcement percentages and beam sizes. Contemporary building codes do not only require sufficient structural safety and robustness for individual components, but also for parts -or the entire structural system- of a building. For the reinforced glass beam concept, component safety is demonstrated by post-fracture strength and ductile ultimate collapse behaviour. System action can be achieved through plastic hinge formation and stress redistribution. Additional system safety and robustness can be provided through the activation of membrane action in case of horizontal restraints at the beam ends. When a support is (accidentally) removed, membrane action can provide an additional safety mechanism which prevents collapse of the beam system. This paper presents an experimental program to assess the potential of activating membrane action for reinforced laminated glass beams. Statically indeterminate five-point bending tests with horizontal restraints, with or without intermediate support, are performed on 4.3 m long beam specimens. In addition, the effect of reinforcement percentage is investigated.

On modal analysis of laminated glass: Usability of simplified methods and Enhanced Effective Thickness

Abstract This paper focuses on the modal analysis of laminated glass beams. In these multilayer elements, the stiff glass plates are connected by compliant interlayers with frequency and temperature-dependent behavior. The aim of our study is (i) to assess whether approximate techniques can accurately predict the behavior of laminated glass structures and (ii) to propose a simple tool for modal analysis based on the Enhanced Effective Thickness concept. For this purpose, we consider four approaches to the solution of the related nonlinear eigenvalue problem: a complex-eigenvalue solver based on the Newton method and three simplified approaches. In particular, we limit our attention to the modal strain energy method, the dynamic effective thickness method, and the Enhanced Effective Thickness method. A comparative study of free vibrating laminated glass beams is performed considering different geometries of cross-sections, boundary conditions, and material parameters for interlayers under two ambient temperatures. The viscoelastic response of polymer foils is represented by the generalized Maxwell model. We show that the simplified approaches predict natural frequencies with an acceptable accuracy for most of the examples. However, there is considerable scatter in predicted loss factors. The Enhanced Effective Thickness approach adjusted to modal analysis results in lower errors in both quantities compared to the other two simplified procedures. It reduces the extreme error in loss factors by half compared to the modal strain energy method and to one quarter compared to the original dynamic effective thickness method.

Laminated glass beams with thick embedded connections – Numerical analysis of full-scale specimens during cracking regime

Laminated and hybrid glass systems are typically realized by bonding or joining together several structural components and materials. Their structural performance and safe design is hence related to the optimal combination of several parameters, including material properties and degradation, geometrical ratios, connections type and features, etc.This research paper is focused on the numerical assessment of the load bearing performance of full-scale laminated glass (LG) beams with thick embedded connections. There, the structural interaction between multiple glass segments is offered by thick metal inserts, being embedded in the LG sections during the production stage. The overall bending response of such assemblies, given the same glass beam segments, is strictly related to the connection detailing, namely including the number, position, size, etc. of embedded connectors. In this regard, Finite Element numerical models able to properly capture their actual local and global behaviour can represent a robust support for time/cost-consuming full-scale experimental investigations. Refined FE models are hence presented for selected specimen configurations, and validated towards four-point bending experimental tests carried out on LG beams with three different types of embedded connections and available in the literature.In the typical FE model, the geometrical and mechanical properties of the reference specimens are properly taken into account, so to explore both the elastic and post-cracked performance of the LG beams object of study, under specific loading conditions. Comparative results are then critically discussed, giving evidence of major structural performances for the selected configurations, and including a concise parametric study.

A simple mixed finite element model for laminated glass beams

A simple and effective beam finite element model is here proposed for studying the behaviour of elastic laminated glass beams made of two external glass layers connected by a polymeric thin interlayer, able to transmit only shear stresses. The finite element model is based on a mixed variational formulation, which assumes as independent fields the horizontal and vertical translations and transverse section rotations of both glass layers, together with interlayer shear stresses. Several numerical tests are performed showing the effectiveness of the proposed model and its convergence to the well-known upper (monolithic) and lower (layered) limits for a laminated glass beam.