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During service period, due to the overload or other non-load factors, diagonal cracks of the pre-stressed concrete beam are seriously affecting the safety of the bridge structure. The purpose of this paper is to quickly realize the shear bearing capacity and shear stiffness through maximum width of the diagonal cracks and make correct judgments.

Through the shear failure test of four test beams, collecting data of diagonal cracks and shear stiffness loss value. According to the deformation curve of the shear stiffness, and combined with the calculation formula of the maximum width of diagonal cracks, the formula for calculating the effective shear stiffness based on the maximum width of diagonal cracks is deduced, then the results are verified by test data. Data regression method is used to establish the effective shear stiffness loss ratio calculation formula, the maximum width of diagonal cracks used as a variable factor, and the accuracy of this formula is verified by comparing the shear failure test results of pre-stressed hollow plates.

With the increase in width of the diagonal crack, the loss rate of shear stiffness of the concrete beams is initially fast and then becomes slow. The calculation formulae for shear stiffness based on the maximum width of the diagonal cracks were deduced, and the feasibility and accuracy of the formulae were verified by analysis and calculation of shear test data.

A method for quickly determine the shear stiffness loss of structures by using maximum width of the diagonal cracks is established, and using this method, engineers can quickly determine effective shear stiffness loss ratio, without complex calculations. So this method not only ensures the safety of human life, but also saves money.

A new model for handling non‐orthogonal cracks within the smeared crack concept is described. It is based on a decomposition of the total strain increment into a concrete and into a crack strain increment. This decomposition also permits a proper combination of crack formation with other non‐linear phenomena such as plasticity and creep and with thermal effects and shrinkage. Relations are elaborated with some other crack models that are currently used for the analysis of concrete structures. The model is applied to some problems involving shear failures of reinforced concrete structures such as a moderately deep beam and an axisymmetric slab. The latter example is also of interest in that it confirms statements that ‘reduced integration’ is not reliable for problems involving crack formation and in that it supports the assertion that identifying numerical divergence with structural failure may be highly misleading.

This paper aims to study the effect of external glass fibre reinforced polymer (GFRP) plates on the flexural and shear behaviour of structurally deficient reinforced concrete (RC) beams, a total of ten 180mm×250mm×2,500mm beams, including over‐designed, unplated under‐designed and plated under‐designed, were tested under four‐point bending condition. Experimental results indicate that the use of GFRP plates enhances the strength and deformation capacity of RC beams by altering their failure modes. Application of side plates on shear‐deficient RC beams appears to be more effective than using bottom plates on flexure‐deficient RC beams. However, without any improvement of concrete compressive capacity, additional shear capacities provided to the beams under the action of side plates increase the likelihood of beam failure by concrete crushing. Simultaneous use of bottom and side plates on flexural‐ and shear‐deficient RC beams may result in reduced deflection.

This paper aims to develop a non-linear finite element model predicting the response of externally strengthened beams under a three-point flexure test.

The ANSYS software is used for modeling. SOILD65, LINK180, SHELL181 and SOLID185 elements are used, respectively, to model concrete, steel reinforcement, polymer and steel plate support. A parametric study was carried out. The effects of compressive strength, Young’s modulus, layers number and carbon fiber-reinforced polymer thickness on beam behavior are analyzed. A comparative study between the non-linear finite element and analytical models, including the ACI 440.2 R-08 model, and experimental data is also carried out.

A comparative study of the non-linear finite element results with analytical models, including the ACI 440.2 R-08 model and experimental data for different parameters, shows that the strengthened beams possessed better resistance to cracks. In general, the finite element model’s results are in good agreement with the experimental test data.

This model will predict the strengthened beams behavior and can describe the beams physical conditions, yielding the results that can be interpreted in the structural study context without using a laboratory testing.

On the basis of the results, a good match is found between the model results and experimental data at all stages of loading the tested samples. Crack models obtained in the non-linear finite element model in the beams are also presented. The submitted finite element model can be used to predict the behavior of the reinforced concrete beam. Also, the comparative study between an analytical model proposed by of current code of ACI 440.2 R-08 and finite element analysis is investigated.

This paper aims to propose the five-phase sphere equivalent model of recycled concrete, which can be used to deduce the theoretical formulas for the Poisson’s ratio and effective elastic modulus.

At a mesoscopic level, the equivalent model converts the interfacial layer, which consists of the new interfacial transition zone (ITZ), the old mortar and the old (ITZ), into a uniform equivalent medium. This paper deduces a strength expression for the interfacial transition zone at the microscopic level using the equivalent model and elastic theory. In addition, a new finite element method called the base force element method was used in this research.

Through numerical simulation, it was found that the mechanical property results from the five-phase sphere equivalent model were in good agreement with those of the random aggregate model. Furthermore, the proposed model agree on quite well with the available experimental data.

The equivalent model can eliminate the influence of the interfacial layer on the macroscopic mechanical properties, thereby improving the calculation accuracy and computational efficiency. The proposed model can also provide a suitable model for multi-scale calculations.

Reinforced concrete (R.C.) beams are part of the structure so their design depends on the structural code and its requirements. In this paper, two simply supported R.C. beams were designed in terms of flexural and shear strength design requirements and investigated in terms of deflections and crack widths, when subjected to two asymmetric concentrated loadings, where one load is double the other one. Both beams had dimensions of 3,500 mm length, 200 mm width, and 300 mm height. The first beam (beam B1) was designed according to the combination of the structural requirements of American and Saudi building codes (ACI318-and-SBC304), while the second beam (beam B2) was designed according to the structural requirements of Eurocode (EC2). The paper aims to discuss these issues.

The design of ultimate capacity (section capacity) to design both flexure and shear capacity according to the design provisions in EC2 code deals with the Ultimate Limit State Design Approach, while it deals with the Ultimate Strength Design Approach according to the design provisions in both ACI318 and SBC304 codes. In the serviceability (mid-span deflection and flexural crack width) check, the three codes deal with the Serviceability Limit State Design Approach.

The laboratory behaviour of both test beams was as expected in flexure and failed in shear, but there was more shear cracks in the left shear span for both beams. This refers to the left applied loading and the spacing of shear links, where the failure occurred at the higher loading points. Perhaps, if the number of links was increased in the left side of the beam during the manufacture and reinforcing of the beam, the failure loading will be delayed and the diagonal cracks will be decreased.

From this study, it was concluded that: the ACI318 and SBC304 design approaches are safer than the EC2 design approach. The EC2 design approach is more economic than the ACI318 and SBC304 design approaches. The structural behaviour of both test beams was as expected in flexure but both beams failed in shear. The shear failure was in the left side of both test beams which was referred to a high loading point. Diagonal cracks followed the applied loading until both beams reached to the failure.

This study aims to investigate the factors responsible for substrate cracking reliability problem in through-glass vias (TGVs), which are critical components for glass-based 2.5 D integration.

Numerical models were used to examine the driving force for substrate cracking in glass interposers due to stress coupling during heating. An analytical solution was used to demonstrate how the energy release rate (ERR) for the glass substrate cracking is affected by the via design and the mismatch in thermal strain. Then, the numerical models were implemented to investigate the design factors effects, such as the pitch distance, via diameter, via pattern, via design, effect from a stress buffer layer and the interposer materials selection on the susceptibility to substrate cracking.

ERR for substrate cracking was found to be directly proportional to the via diameter and the thermal mismatch strain. When a via pattern is implemented for high-density integration, a coupling in the stress fields was identified. This coupling effect was found to depend on the pitch distance, the position of the vias, and the via arrangement, suggesting a via pattern-dependent reliability behavior for glass interposers. Changing the design of the via to an annular shape or a substrate-cored via was found to be a promising approach to reduce the susceptibility to substrate cracking compared to a fully filled solid via. Also, the use of a stress buffer layer, an encouraging design prospect presented for the first time for TGVs in this study, was found to significantly reduce cracking. Finally, alternative via and substrate materials showed lower tendency for substrate cracking, indicating that the reliability of glass interposers can be further enhanced with the implementation of such new materials.

This study signifies the first attempt to comprehensively evaluate the susceptibility to crack formation in glass interposers during heating. Therefore, this study provides new perspectives on how to achieve a significant potential reliability improvement for TGVs.

A nonlinear finite element (FE) beam-column model for the analysis of reinforced concrete (RC) frames with due account of shear is presented in this paper. The model is an expansion of the traditional flexural fibre beam formulations to cases where multiaxial behaviour exists, being an alternative to plane and solid FE models for the nonlinear analysis of entire frame structures. The paper aims to discuss these issues.

Shear is taken into account at different levels of the numerical model: at the material level RC is simulated through a smeared cracked approach with rotating cracks; at the fibre level, an iterative procedure guarantees equilibrium between concrete and transversal reinforcement, allowing to compute the biaxial stress-strain state of each fibre; at the section level, a uniform shear stress pattern is assumed in order to estimate the internal shear stress-strain distribution; and at the element level, the Timoshenko beam theory takes into account an average rotation due to shear.

The proposed model is validated through experimental tests available in the literature, as well as through an experimental campaign carried out by the authors. The results on the response of RC elements critical to shear include displacements, strains and crack patterns and show the capabilities of the model to efficiently deal with shear effects in beam elements.

A formulation for the nonlinear shear-bending interaction based on the fixed stress approach is implemented in a fibre beam model. Shear effects are accurately accounted during all the nonlinear path of the structure in a computationally efficient manner.

The stiffness and damage evolution in a quasi‐static tensile loaded non‐crimp fabric reinforced epoxy was measured. To determine the effective stiffness of the damaged material numerically a finite element analysis was performed. The finite element analysis bases solely on the measured ±45° and 90°‐ crack densities and on ply properties calculated by the Rule of Mixtures. The measured and calculated effective tensile stiffness were compared and a fair agreement could be found.

Before beginning a detailed technical discussion on cracks it is necessary to put the subject into perspective and ask what ‘cracking’ means to a house owner or prospective house purchaser.