Creep behavior of Cross-Laminated-Timber (CLT) beams with a finite-thickness layer of flexible adhesives is investigated. Creep tests were carried out for all component materials as well as for the composite structure itself. Three-point bending creep tests were performed for spruce planks and for CLT beams, and uniaxial compression creep tests were performed for two flexible polyurethane adhesives: Sika^® PS and Sika^® PMM. All materials are characterized with the use of the three-element Generalized Maxwell Model. The results of creep tests for component materials were used in elaboration of the Finite Element (FE) model. The problem of linear theory of viscoelasticity was solved numerically with the use of the Abaqus software. Obtained results of Finite Element Analysis (FEA) are compared with experimental results.

This study addresses the challenges of modeling flexible connections in composite structures employing a polymeric adhesive layer. These types of connections provide a more uniform stress distribution compared to conventional rigid connectors. However, they lack standardized design rules and still require much research to sufficiently comprehend their properties. The novelty of this research lies in proposing an analytical solution to address these issues. Its aim is to investigate the influence of the stiffness of the polymer adhesive on the girder’s deflection and on the maximum stresses in both the adhesive and concrete. The analyzed composite structure consists of a reinforced concrete (RC) slab and an RC beam connected with a layer of flexible polyurethane (FPU) adhesive. Analytical and numerical approaches for the description of the mechanical response of a composite bridge girder are presented. Another objective is to validate the analytical design formulas using 3D nonlinear numerical analysis, both in the case of uncracked and cracked concrete. Seven types of FPUs are tested in the uniaxial tension test, each examined at five strain rates. The obtained data is used to predict the mechanical response of the considered girder using finite element analysis (FEA) as well as with a simplified one-dimensional composite beam theory. Fair agreement is found between the FEA results and theoretical predictions. A comparison of the results obtained for these two models is performed, and the similarities and discrepancies are highlighted and discussed.

The problem of optimal design of a steel plated girder according to the Eurocode 3 is considered. Code regulations admit the Finite Element Analysis (FEA) in designing plated structures with variable cross-sections. A technique of determining an approximate solution to the optimization problem is presented. It is determined a solution of a control theory optimization task, in which Eurocode requirements regarding the Ultimate Limit State (bearing capacity, local and global stability) as well as Serviceability Limit State (flexural rigidity) are used as appropriate inequality constraints. Static analysis is performed within the framework of linear elasticity and Bernoulli-Euler beam theory making an account for second-order effects due to prescribed imperfections. Obtained solutions, after regularization, may be used for direct verification with the use of FEA or as the first guess for iterative topology optimization algorithms. Code requirements governing the determination of optimal shape are visualized in the constraint activity diagram, which is a proposed tool for analysis of optimization process.

In this study, we investigated the vibration of adhesively bonded composite cantilevers consisting of two beech wood lamella and a bondline of flexible polyurethane. The beams had a constant total height, while the thickness of the adhesive layer varied. We analyzed both the driven and free vibration of a single cantilever beam and a cantilever with an additional mass attached to its end. The eigenfrequencies were determined using Fourier analysis of a sweep load response, the response to an impact load excited using an impact hammer, and the response observed via the manual displacement of the beam’s tip. The system’s damping was estimated according to the recorded logarithmic decrement. Theoretical estimates of the fundamental natural frequency were obtained using the γ-method and employing a linear elastic theory of composite beams. A numerical modal analysis was carried out using the finite element method. Upon comparing the results of our experiments with the numerical estimates and theoretical predictions, a fair agreement was found.

This study investigated the optimal shape of glue-laminated timber beams using an analytical model of a slender beam, taking into account the anisotropy of its strength properties as well as boundary conditions at the oblique bottom face of the beam. A control theory problem was formulated in order to optimize the shape of the modeled beam. Two optimization tasks were considered: minimizing material usage ($V_{min}$) for a fixed load-carrying capacity (LCC) of the beam and maximizing load-bearing capacity ($Q_{max}$) for a given volume of the beam. The optimal solution was found using Pontryagin’s maximum principle (PMP). Optimal shapes were determined using Dircol v. 2.1 software and then adjusted according to a 3D finite element analysis (FEA) performed in Abaqus. The final shapes obtained through this procedure were used in the CNC-based production of three types of nine beams: three reference rectangular beams, three $V_{min}$ beams, and three $Q_{max}$ beams. All specimens were subjected to a four-point bending test. The experimental results were contrasted with theoretical assumptions. Optimization reduced material usage by ca. 12.9% while preserving approximately the same LCC. The maximization of LCC was found to be rather unsuccessful due to the significant dependence of the beams’ response on the highly variable mechanical properties of GLT.

Practical aspects of modelling of flexible adhesives with the energy conjugate measures of stress and strain of the Darijani–Naghdabadi (D-N) family are discussed. A possibility of description of materials exhibiting non-linear physical characteristics with the use of non-linear geometric relationships and linear elastic constitutive law is considered. Nominal stress vs. stretch relations are specified in cases of simple tension and simple shear with the use of the Kirchhoff–de Saint-Venant elastic potential and D-N energy conjugate stress and strain measures. Obtained theoretical estimates were compared with experimental results of simple tension and simple shear tests performed on Sika PM polyurethane (Cracow, Sika Poland). The deformation rate was fixed in order to minimize the influence of viscosity. Values of parameters $\alpha ,\beta$ in the definition of the D-N strain tensor were optimized in order to provide good agreement between model predictions and experimental results. Observed discrepancies indicate that the proposed approach is not appropriate for constitutive modelling of the PM polymer. The presented approach is proposed to be used as a simple design model providing practical formulas describing the behavior of materials of non-linear characteristics in chosen mechanical states. Admissible values of exponents $\alpha ,\beta$ are discussed regarding its bijectivity in a limited range of variation of principal stretches.