• Coupled systems mechanics
• /
• v.12 no.6
• /
• pp.519-530
• /
• 2023

This paper presents a mathematical model suitable for the calculation of laminated glass, i.e. glass plates combined with an interlayer material. The model is based on a beam differential equation for each glass plate and a separate differential equation for the slip in the interlayer. In addition to slip, the model takes into account prestressing force in the interlayer. It is possible to combine the two contributions arbitrarily, which is important because the glass sheet fabrication process changes the stiffness of the interlayer in ways that are not easily predictable and could introduce prestressing of varying magnitude. The model is suitable for reformulation into an inverse procedure for calculation of the relevant parameters. Model consisting of a system of differential-algebraic equations, proved too stiff for cases with the thin interlayer. This novel approach covers the full range of possible stiffnesses of layered glass sheets, i.e., from zero to infinite stiffness of the interlayer. The comparison of numerical and experimental results contributes to the validation of the model.

• Steel and Composite Structures
• /
• v.31 no.6
• /
• pp.591-600
• /
• 2019

Based on the energy-variational principle, a coupling vibration analysis model of high-speed railway simply supported beam bridge-track structure system (HSRBTS) was established by considering the effect of shear deformation. The vibration differential equation and natural boundary conditions of HSRBTS were derived by considering the interlayer slip effect. Then, an analytic calculation method for the natural vibration frequency of this system was obtained. By taking two simply supported beam bridges of high-speed railway of 24 m and 32 m in span as examples, ANSYS and MIDAS finite-element numerical calculation methods were compared with the analytic method established in this paper. The calculation results show that two of them agree well with each other, validating the analytic method reported in this paper. The analytic method established in this study was used to evaluate the natural vibration characteristics of HSRBTS under different interlayer stiffness and length of rails at different subgrade sections. The results show that the vertical interlayer compressive stiffness had a great influence on the high-order natural vibration frequency of HSRBTS, and the effect of longitudinal interlayer slip stiffness on the natural vibration frequency of HSRBTS could be ignored. Under different vertical interlayer stiffness conditions, the subgrade section of HSRBTS has a critical rail length, and the critical length of rail at subgrade section decreases with the increase in vertical interlayer compressive stiffness.

• Structural Engineering and Mechanics
• /
• v.51 no.1
• /
• pp.163-180
• /
• 2014

In the displacement based finite element analysis of composite beams that consist of two Euler-Bernoulli beams juxtaposed with a deformable shear connection, the coupling of the displacement fields may cause oscillations in the interlayer slip field and reduction in optimal convergence rate, known as slip-locking. In this study, the B-bar procedure is proposed to alleviate the locking effects. It is also shown that by changing the primary dependent variables in the mathematical model, to be able to interpolate the interlayer slip field directly, oscillations in the slip field can be completely eliminated. Examples are presented to illustrate the performance and the numerical characteristics of the proposed methods.

• Structural Engineering and Mechanics
• /
• v.22 no.3
• /
• pp.263-278
• /
• 2006

Starting with the geometrically non-linear formulation and the subsequent linearization, this paper presents a consistent formulation of the exact mechanical analysis of geometrically and materially linear three-layer continuous planar beams. Each layer of the beam is described by the geometrically linear beam theory. Constitutive laws of layer materials and relationships between interlayer slips and shear stresses at the interface are assumed to be linear elastic. The formulation is first applied in the analysis of a three-layer simply supported beam. The results are compared to those of Goodman and Popov (1968) and to those obtained from the formulation of the European code for timber structures, Eurocode 5 (1993). Comparisons show that the present and the Goodman and Popov (1968) results agree completely, while the Eurocode 5 (1993) results differ to a certain degree. Next, the analytical solution is used in formulating a general procedure for the analysis of layered continuous beams. The applications show the qualitative and quantitative effects of the layer and the interlayer slip stiffnesses on internal forces, stresses and deflections of composite continuous beams.

• Structural Engineering and Mechanics
• /
• v.34 no.6
• /
• pp.667-683
• /
• 2010

A mathematical model and its analytic solution for the analysis of stress-strain state of a linear elastic two-layer beam is presented. The model considers both slip and uplift at the interface. The solution is employed in assessing the effects of transverse and shear contact stiffnesses and the thickness of the interface layer on behaviour of nailed, two-layer timber beams. The analysis shows that the transverse contact stiffness and the thickness of the interface layer have only a minor influence on the stress-strain state in the beam and can safely be neglected in a serviceability limit state design.

• Steel and Composite Structures
• /
• v.4 no.6
• /
• pp.489-507
• /
• 2004

The flexibility of the connection between steel and concrete largely influences the global behaviour of the composite beam. Therefore the way the connection is modelled is the key issue in its structural analysis. Here we present a new strain-based finite element formulation in which we consider non-linear material and contact models. The computational efficiency and accuracy of the formulation is proved with the comparison of our numerical results with the experimental results of Abdel Aziz (1986) obtained in a full-scale laboratory test. The shear connectors are assumed to follow a non-linear load-slip relationship proposed by Ollgaard et al. (1971). We introduce the notion of the generalized slip, which offers a better physical interpretation of the behaviour of the contact and gives an additional material slip parameter. An excellent agreement of experimental and numerical results is obtained, using only a few finite elements. This demonstrates that the present numerical approach is appropriate for the evaluation of behaviour of planar composite beams and perfect for practical calculations.

• Structural Engineering and Mechanics
• /
• v.90 no.5
• /
• pp.447-458
• /
• 2024

This study investigated the influence of scale ratio and vertical load on the seismic performance of Puzuo joints in traditional Chinese timber structures. Three low-cyclic reversed loading tests were conducted on three scaled specimens of Bujian Puzuo in Yingxian Wooden Pagoda. This study focused on the deformation patterns and analyzed seismic performance under varying scale ratios and vertical loads. The results indicated that the slip and rotational deformations of Bujian Puzuo were the primary deformations. The scale of the specimen did not affect the layer where the maximum interlayer slip occurred, but it did decrease the proportion of slip deformation. Conversely, the reducing vertical load caused the layer with the maximum slippage and the position of the damaged Dou components to shift upward, and the proportion of slip deformation increased. When the vertical load was decreased by 3.7 times, the maximum horizontal bearing capacity under positive and negative loadings, initial stiffness, and energy dissipation of the specimen decreased by approximately 60%, 58.79%, 69.62%, and 57.93%, respectively. The horizontal bearing capacity under positive loading and energy dissipation of the specimen increased by 35.63% and 131.54%, when the specimen scale was doubled and the vertical load was increased by 15 times.

• Structural Engineering and Mechanics
• /
• v.17 no.2
• /
• pp.153-166
• /
• 2004

An elasticity solution for sandwich plates assembled with non-rigid bonding and subjected to edgewise loads is presented. The solution satisfies the equilibrium equations of the face and core elements, the compatibility equations of stresses and strains at the interfaces, and the boundary conditions. To investigate the effects of bonding stiffnesses on the responses of sandwich plates, numerical evaluations are conducted. The results obtained have shown that the bonding stiffness, up to a certain level, has a strong effect on the plate mechanical response. Beyond this level, the usual assumption of perfect bonding used in classical theories is quite acceptable. An answer to what constitutes perfect bonding is found in terms of the ratio of the core stiffness to the bonding stiffness.

• Steel and Composite Structures
• /
• v.27 no.1
• /
• pp.1-12
• /
• 2018

This paper presents a semi-analytical solution of simply supported horizontally composite curved I-beam by trigonometric series. The flexibility of the interlayer connectors between layers both in the tangential direction and in the radial direction is taken into account in the proposed formulation. The governing differential equations and the boundary conditions are established by applying the variational approach, which are solved by applying the Fourier series expansion method. The accuracy and efficiency of the proposed formulation are validated by comparing its results with both experimental results reported in the literature and FEM results.

• Steel and Composite Structures
• /
• v.24 no.1
• /
• pp.23-35
• /
• 2017

Current form of Corrugated-strip connectors are not popular due to the fact that the two ends of this form need to be welded to steel face plates. To overcome this difficulty, a new system is proposed in this work. In this system, bi-directional corrugated-strip connectors are used in pairs, and only one of their ends is welded to the steel face plates on each side. The other end is embedded in the concrete core. To assemble the system, common welding devices are required, and welding process can be performed in the construction sites. By performing the Push-out test under static loading, the authors experimentally assess the effects of geometric parameters on ductility, failure modes and the ultimate shear strength of the aforesaid connectors. For this purpose, sixteen experimental samples are prepared and investigated. For fifteen of these samples, one end of the shear connectors is welded to steel face plates, and the other end is embedded in the concrete. Another experimental sample is prepared in which both ends are welded to the steel face plates. According to the achieved results, several relations are proposed for predicting the ultimate shear strength and load vs. interlayer slip (load-slip) behavior of corrugated-strip connectors. Moreover, these formulas are compared with those of the well-known codes and standards. Accordingly, it is concluded that the authors' relations are more reliable.