SEISMIC RETROFIT OF GUSSET PLATE CONNECTIONS THROUGH FINITE ELEMENT ANALYSIS MASTER PROJECT

Steel concentrically braced frame (CBFs) are widely used as a laterally-resisting system in the case of seismic actions as they are generally easier and faster to erect, and in most cases, they cost less than moment-resisting frame system. However, special care must be made in the design of gusset plate connections as over the years, a great deal of steel structure has emphasized their importance through different types of failure. In this master project, the failure of a gusset plate connection from a steel concentrically braced frame is analyzed with finite element modelling. This CBFs was part of two-story parking garage structure where most of the braces oriented in the east-west direction had fractured at their gusset plate connections after the 2011 Tohoku Earthquake in Japan. With finite element analysis, the cause of the buckling of the gusset plate failure mechanism was explained. As a matter of fact, the concentration of stresses and inelastic deformation during cyclic loading, particularly when the brace was in compression, led to fracture in the gusset plate. The fracture initiation process was then predicted with the Cyclic Void Growth Model. Therefore, four retrofit schemes are proposed to rectify the poor behavior of the gusset plate. They are evaluated based on a static pushover analysis and the results have shown several issues that might arise depending on the modifications. It has been shown, that one of the retrofit scheme where the gusset plates are design using elliptical clearance theory provided the best results. The simulation showed that the brace could buckle in compression without having premature failure in the gusset plate as the brace end rotation capacity was high enough. This study shows the importance of a well thought connection design in a concentrically braced frame system and how can different retrofit concepts alter or improve their behavior. It is relevant to note that not every concept and ideas will provide the desired impact and consequences.

Application des réseaux de Bragg à la détermination des déformations distribuées dans les matériaux composites

The behaviour of brittle matrix fibre reinforced-composites is dependent of the properties of its constituents (fibre, matrix and fibre-matrix interface) and is affected by the mechanical and environmental loads. The fracture of a unidirectional composite material is the result of various micro-mechanisms (matrix and/or fiber fractures, crack fibre interactions, interface failure, delamination, …) that generally occur simultaneously. Among these, one distinguishes the failure by fibre-matrix debonding and the frictional sliding along the composite interfaces. The initiation and debonding growth are influenced by the specimens' geometry, the loading conditions, the nature of the constituent materials, the residual stress and the fibre-matrix interface. Several works have been carried out that deal with theoretical and experimental aspects of micro-mechanisms of fracture. However, a complete understanding is still lacking due to the difficulties to characterise quantitatively the individual contribution of these different micro-mechanisms. In the recent past, optical Fibre Bragg Grating (FBG) have been used as embedded strain sensors. They are particularly adapted to polymer composites where they can provide accurate internal strain measurements at selected locations. Until today, short FBGs have been often used in uniform loading conditions. In such cases, the grating parameters do not vary along the grating length and when uniform variations in strain and/or temperature occur, the FBG spectral response exhibits a simple shift of the Bragg peak without modification of the spectrum shape. This wavelength shift has been used extensively as a global indicator of internal strain in classical sensing applications. This approach however is not realistic when the FBG is found near damage, i.e. crack, delamination, residual strain field, etc. To achieve non-uniform strain measurements using long gauge FBG sensors, a new Optical Low-Coherence Reflectometry (OLCR-based) technique has been developed and tested in order to study crack-fiber interaction and the interface between the glass fibre and epoxy matrix material during composite damage process. When a long FBGs is subjected to non-homogeneous distributed strains, the grating parameters are position-dependent. Due to the extensive grating length, the optical sensor undergoes substantial non-uniform variation along the fibre direction. Inhomogeneity of the grating is a result of the application of a non-uniform strain or temperature field in the interface region and/or the FBG writing process (manufacture). The coupled-mode formalism provides a mathematical tool to describe the interaction of light propagation. This analysis leads to the introduction of a unique complex coupling coefficient to be determined from the FBG complex impulse response. A novel optical low coherence reflectometry acquisition system, designed at EPFL, allows precise measurement of the FBG complex impulse response with high precision and low noise (generally below -120dB). The working principle of the apparatus is well documented elsewhere (93). The OLCR-based method enabled us to obtain the local Bragg wavelength along the grating located in the core of the optical fibre. In this study, epoxy is used as the main material. An established standard protocol is followed with a couple of D.E.R. 330/732 Dow Epoxy Resins (70%/30% mass weight) and a D.E.H. 26 curing agent (+13%). Once the polymerization process is well advanced (24h@28°C), the specimen is removed from its mould and placed in an oven for the post curing phase (10h@70°C). The specimen is left to cool inside the oven until ambient temperature was reached. Three main experiments are conducted with a centrally located long FBG (14 to 25mm length): one on a Double Edge Notch Specimen (DENS) in order to investigate and validate the newly-developed OLCR method and two pull-out tests on two different single fibre cylindrical specimens (with or without fibre protective acrylate coating). The last experiments are conducted in order to describe the interface behavior. Thus, the optical fibre plays the role of fibre-reinforcement and strain sensor. Various Finite Element Models are developed in order to understand better the phenomena and analyse the experimental results. All materials are considered to be linear elastic and with isotropic properties. To model the matrix shrinkage effect the problem is considered analogous to a thermo-elastic one. A shrinkage function, evaluated experimentally, from the FBG response is introduced in the general strain-stress relations. Displacement boundary conditions are applied to the fibre end and the epoxy to simulate the loading conditions. The first set of simulations is dedicated to the stress analysis of the DENS and the comparison of the OLCR data with those of the simulations. The other set allows to identify the properties of the fiber/matrix for weak (glass-acrylate) or strong interfaces (acrylate-epoxy or glass-epoxy) respectively. In particular for the weak interface, interaction between the glass fibre and the coating is described using the regularized Coulomb friction model. That defined the critical shear stress as a fraction of the contact pressure. Higher than this limit, the contact surfaces start sliding relative to one another. Except of the friction coefficient μ, an elastic slip parameter γlim is also introduced into the model to take into account the interface stiffness in the elastic regime (i.e. the sticking stiffness). For the strong interface, interaction between the glass fibre and the epoxy resin is described using the energy release rate G parameter. The observed interface crack grow is used as an input to simulate evolution during debonding propagation. The J-integral equivalent is numerically calculated around the crack tip for different crack lengths during the test. A G(z) distribution along the glass-epoxy interface is identified as possible criterion for adhesion rupture. A single Coulomb identification model μ is proposed to describe the behavior of the interface once it fails. The main results of the simulations are given bellow: The redistribution of the axial stress is obtained for two interfaces and at different force levels. The strain data show that residual stress effects due to epoxy matrix shrinkage and positive strains reveal the presence of the interfacial crack propagation when the fibre is in tension. Numerical models are compared with experimental results of the fibre pull-out tests. The overall experimental results are reproduced for the proposed parameter values although discrepancies exist when the load is released. Two parameter models explain the data very well. At the glass-acrylate weak interface: two interface parameters μ and γlim are identified. At the glass-epoxy strong interface: a constant friction coefficient μ and a distributed energy release rate G(z) are estimated. In this study, a mixed experimental-numerical approach is developed to investigate the strain response of long-gauge FBG and the interface of glass-epoxy and glass-acrylate epoxy. This work demonstrated the potential of the FBG sensor associated with OLCR technique to understand micromechanics damage in fracture.

EPFL2009

Fracture and Fatigue of Adhesively-Bonded Fiber-Reinforced Polymer Structural Joints

Ye Zhang

Being good structural replacement for other conventional material, the pultruded glass fiber reinforced polymer (GFRP) profiles are being increasingly used in civil engineering structures. The connection between components is considered the most suspect area for failure initiation. The adhesive bonding is preferred for FRP composite structures, rather than the mechanical fastening, due to the brittle failure nature of composite materials. During past decades, many efforts have been made by researchers to better understand the mechanism of adhesive bonding, to analyze the stress distributions and to improve the strength of composite structural joints. However there is still no commonly accepted design code/standard existing for adhesively-bonded joints in civil engineering infrastructures since several important knowledge gaps are to be filled. Besides the joint strength at failure, the characterization and modeling of the progressive failure process, in particular involving the so-called crack initiation and propagation phases, is also an important concern. By employing the strain energy release rate (SERR) as the fracture parameter, the linear-elastic fracture mechanics (LEFM) approach is considered an efficient method to model the fracture behavior of structural joints. However, due to the uncontrollable crack initiation and the complex geometric configurations, the crack measurement techniques and the calculation method for the SERR are to be validated. In fracture mechanics, the fracture of a material or component can be described by a single mode or the combinations of the following three basic modes: opening mode (Mode I), shearing mode (Mode II), and tearing mode (Mode III). During the fracture of a structural joint, crack initiation and propagation are driven by combined through-thickness tensile (peeling), and shear stresses, thus resulting in a mixed mode fracture. In order to use the fracture results of structural joints to form the mixed fracture criterion for a specific composite material, a feasible analytical or numerical method are to be developed to determine the Mode I and II components of the SERR during fracture. Although many efforts have been made to better understand the short-term behavior of structural joint under quasi-static loading, the long-term performance under fatigue loading and different environmental conditions is a more demanding task when adhesively-bonded joints are applied in a real structure. Most of structural failures occur due to mechanisms that are driven by fatigue loading and for composite structures, the fatigue produced by the repeated application of live load is more critical due to its lighter self-weight, in other words the lower dead load. Besides the fatigue loading, a structure in practice may also experience the combined environmental effects of two basic factors: temperature and humidity. These environmental conditions may directly affect properties of structural joints, including the failure mechanism, the stiffness and strength, the crack initiation and propagation and etc.. Thus, the missing knowledge and confidences in the long-term behavior under cyclic loading and the durability under different environmental conditions are the main obstacles to the further development of FRP composites in civil engineering infrastructures. In this research, the mechanical and fracture behavior of adhesively-bonded double-lap and stepped-lap joints (DLJs and SLJs) composed of pultruded GFRP laminates and an epoxy adhesive were experimentally and numerically investigated under both quasi-static and fatigue loadings. The crack measurement techniques and the calculation methods for the SERR were validated for DLJs and SLJs. The LEFM approach was successfully applied to characterize and model the progressive failure process of structural joints. The Mode I and II components of the SERR of DLJs and SLJs were determined using the Virtual Crack Closure Technique in finite element analysis. Combining with the results of pure Mode I and II experiments, a mixed mode fracture criterion for pultruded GFRP composite was formed. Under fatigue loading, the fatigue behavior of structural joints was successfully modeled by using the stiffness-based and fracture mechanics approaches, besides the F-N curves. Based on the stiffness degradation, a linear and a sigmoid non-linear model were established and the fatigue live corresponding to the failure and allowable stiffness degradation can be predicted. Concerning fracture mechanics approach, the Fatigue Crack Growth (FCG) curves were formed for DLJs and SLJs and the corresponding fracture parameters were obtained. Similarly to stiffness-based approach, fatigue lives corresponding to the failure and allowable crack length can be predicted. The environmental effects on both short- and long-term performances of structural joints were experimentally evaluated and numerically modeled based on experimental results. The temperature-dependent joint stiffness can be predicted using the finite element analysis based on the thermomechanical properties of constituent materials. A relationship between the equivalent quasi-static joint strength under different environmental conditions and the cyclic stresses and the fatigue life was established.

EPFL2010

Influence of Residual Stresses on Fatigue Response of Welded Tubular K-Joints

Claire Acevedo

Seeking light and transparent bridge designs, engineers and architects have found an efficient and artistic way to fulfill their requirements: steel tubular bridges. In these modern tubular truss bridges, welded K-joints have been shown to be critically susceptible to fatigue failure induced by repeated traffic loads. Despite the research devoted to the study of fatigue during the last 35 years, especially in the offshore oil industry, estimating their fatigue resistance of tubular truss bridges is difficult and solutions are approximate. This is due to the complexity of the parameters influencing bridge fatigue strength, including: 1) complex loadings, 2) applied stress concentrations in joints, 3) welding imperfections, 4) welding residual stresses, and 5) size effects. Some design rules and studies are available to estimate these effects; however, residual stresses in tubular K-joints remain unknown as well as their influence on fatigue crack propagation. Residual stresses are well known to have detrimental influence on fatigue crack propagation in other metallic structures, and further study is a necessary for improving the understanding of K-joint fatigue behaviour. To address this problem, the main objective of this research is to assess, experimentally and numerically, welding residual stresses and their influence on the fatigue response of K-joints. In this thesis, experimental measurements of the residual stress fields were investigated through neutron-diffraction, hole-drilling and X-ray methods. Results have shown that, principal residual stresses are oriented transversely, i.e. perpendicularly to the weld direction, both at and near the surface. Residual stresses can reach the S355 steel yield strength at the weld toe. This orientation is particularly detrimental for fatigue because it is also the orientation of the principal applied stresses, and as a consequence high residual and applied stresses superimpose. Moreover, it is proved that a restraining effect occurs in the gap region in-between the braces remaining the critical residual stresses high in the gap region. Two large scale tubular truss beams were subjected to high-cycle fatigue in order to assess the effect of residual stresses on fatigue response of welded tubular K-joints. These tests revealed that tensile residual stresses do not affect the fatigue crack growth in details loaded in tension (hot-spot 1), whereas they play a significant role in details loaded in compression (hot-spot 1c). Tensile residual stresses enable crack opening, making the fatigue cycle partly or entirely effective to crack propagation. Based on these tests and previous tests from the ICOM test database, it is recommended to design all (tension or compression) K-joints using a strength curve Srhs Srhs – Nf category 100 (for T = 16 mm). A thermo-mechanical finite element model was also developed to numerically reproduce the residual stress creation (using ABAQUS and MORFEO codes). Once the numerical results were validated by comparison with experimental results, the finite element model was used to model other K-joint geometries. A geometrical parametric study was performed to identify the most influential parameters affecting the residual stress distribution (technological size effect). It is found that a raise of the wall chord thickness T (proportional scaling) or of the wall thickness τ = t/T (non-proportional scaling) strongly increases the magnitude of tensile transverse residual stresses. Based on this parametric study, residual stress distributions with depth for transverse, longitudinal and radial directions are proposed. Finally, an extended finite element method (X-FEM) model was used to propagate a fatigue crack under residual and applied stresses. An analytical model based on the effective stress intensity factor range ΔKeff (fracture mechanics) and combined with the proposed distribution for residual stresses was also established to predict fatigue crack propagation in joints loaded in tension and in compression.

EPFL2011