Despite the large volume of work reported on the behaviour of reinforced concrete joints, only a few studies have been carried out to investigate the influence of retrofitting joints by FRP composites on the overall behaviour of an RC frame. To study the seismic performance of Moment Resisting RC frames retrofitted at joints by FRP, experimental and numerical investigations are carried out on a scaled-down frame of weak-beam, strong-column type, retrofitted by applying the FRP laminates at the web of the joints. Representing constitutive models are used to introduce the behaviour of concrete, steel and fibre-reinforced polymers in the numerical investigation. Full post-peak behaviour of the joints is captured considering strain softening of concrete. Finite element results show good agreement with the experimental findings. It is found that the maximum load carrying and displacement capacities of the joint after strengthening are increased and that the first steel yielding and development of crack occur at higher loads, further away from the joint, into the beam. The effects of different values of fracture energies on the behaviour of the reinforced concrete joint are also investigated. Nonlinear pushover analyses are also carried out to predict the seismic performance of an eight-storey and two additional low-rise frames retrofitted by steel braces and FRP. It is shown that by using FRP laminates at the web of the joints, the stiffness, the behaviour factor, R, performance level and the lateral load-carrying capacity of the damaged/plain frame are markedly increased.

Incremental dynamic analyses are conducted for a suite of low-and mid-rise reinforced-concrete special moment-resistingframe buildings. Buildings non-conforming and conforming to the strong-column weak-beam (SCWB) design criterion areconsidered. These buildings are designed for the two most severe seismic zones in India (i. e., zone IV and zone V) followingthe provisions of Indian Standards. It is observed that buildings non-conforming to the SCWB design criterion lead toan undesirable column failure collapse mechanism. Although yielding of columns cannot be avoided, even for buildingsconforming to a SCWB ratio of 1. 4, the observed collapse mechanism changes to a beam failure mechanism. This change incollapse mechanism leads to a significant increase in the building’ s global ductility capacity, and thereby in collapse capacity. The fragility analysis study of the considered buildings suggests that considering the SCWB design criterion leads to asignificant reduction in collapse probability, particularly in the case of mid-rise buildings.

In this study, the ratio of rotations created in beam and column members of reinforced concrete flexural frames, relative displacements of floors at the functional levels of uninterrupted serviceability, life safety and failure prevention have been investigated by considering different ratios for the weak beam-strong column criterion in the optimal design process within the framework of the performance-based design approach. For the purpose of performance-based optimization, the center of mass meta-exploration algorithm has been used in this study. The philosophy of the performance-based design approach and even traditional design methods allow the structure to suffer damage when exposed to strong and relatively strong earthquakes. Therefore, in order to estimate the safety of the structure against earthquakes, the use of seismic safety quantification indices and structural collapse capacity seems necessary. In this study, the relative displacements of floors and the ratio of existing to permissible rotations of beam and column members of each optimal structure have been calculated using time history analysis under earthquakes far and near the fault. Two examples of 3 and 6 stories are the frames studied in this research, which are designed by considering coefficients of 0.8, 1.2 and 1.6 to control the weak beam-strong column criterion in the performance-based optimization process. According to the obtained results, it is observed that increasing the weak beam-strong column ratio to control the aforementioned criterion in the optimization process leads to a decrease in the rotation ratio created in the beams and columns of the structure.

Most reputable international design codes have included provisions for achieving ductile behavior and avoiding brittle and hazardous behavior in reinforced concrete frames. These provisions aim to achieve the concept of the weak beam-strong column, where plastic hinges during an earthquake occur first in the beams. Analysis of frequent and repetitive failures in strong earthquakes in recent decades of reinforced concrete structures shows that the strong beam-weak column failure mode typically leads to severe damage in these structures. The frequent occurrence of this failure mode can be attributed to two main factors. Firstly, stiffer beams are often used against more flexible columns due to the absence of seismic provisions that limit the relation between beam height and column width, which results in column severe damage to the columns and, finally, collapse of them. Secondly, the effect of the cast-in-situ slab in increasing the negative flexural strength of the beam is often underestimated or ignored, leading to the flexural strength of the columns being less than that of the beams. A series of computational models were created and analyzed in a parametric study to assess the impact of the ratio of beam height to column width on the seismic performance of MRFs. Before that, the FEA performance was validated by comparing its results with experimental data. The findings emphasize the urgent need for a new seismic provision that limits the beam height to column width ratio to a maximum of 1.25. Also, it is indicated that the values of effective slab width obtained from the provisions of ACI and EC8 are insufficient to ensure the implementation of the weak beam-strong column design methodology. Findings demonstrate that the value of effective slab width is minimally impacted by the beam height when the ratio of longitudinal beam height to column width ( h_lb⁄C ) is less than 1.5.

In this paper, a discontinuity in beams whose intensity is adjusted by the spring stiffness factor is modeled using a torsional spring. Adapting two analyses in strong and weak forms for discontinuous beams, the improved governing differential equations and the modified stiffness matrix are derived respectively. In the strong form, two different solution methods have been presented to make an analogy between the formulation of the Euler-Bernoulli and Timoshenko theories that indicates the influence of the shear deformation in discontinuous beams. The flexural stiffness of discontinuous beams is corrected by using theDirac’s delta function. In the weak form, the reduced stiffness matrix is derived from the strain energy equation established by the continuity, kinematics and constitutive equations. The linearity assumption of the geometry and material is considered to construct the kinematics and constitutive equations respectively. The continuity conditions mathematically connect two divided parts of the Euler-Bernoulli beam for which an improved Hermitian shape function is employed to interpolate displacement field. An application shows the comparison and validation of the results of the strong and weak forms, and also the static behavior of discontinuous beams.

In this paper, a discontinuity in beams whose intensity is adjusted by the spring stiffness factor is modeled using a torsional spring. Adapting two analyses in strong and weak forms for discontinuous beams, the improved governing differential equations and the modified stiffness matrix are derived respectively. In the strong form, two different solution methods have been presented to make an analogy between the formulation of the Euler-Bernoulli and Timoshenko theories that indicates the influence of the shear deformation in discontinuous beams. The flexural stiffness of discontinuous beams is corrected by using the Dirac’s delta function. In the weak form, the reduced stiffness matrix is derived from the strain energy equation established by the continuity, kinematics and constitutive equations. The linearity assumption of the geometry and material is considered to construct the kinematics and constitutive equations respectively. The continuity conditions mathematically connect two divided parts of the Euler-Bernoulli beam for which an improved Hermitian shape function is employed to interpolate displacement field. An application shows the comparison and validation of the results of the strong and weak forms, and also the static behavior of discontinuous beams.

Sectional distinctiveness is a requirement for trademark protection. However, all legal systems in determining the distinction of a part of the way to support distinguishing marks, and also the effect of the minimum descriptiveness of the mark, in a way that does not harm the distinctiveness of the trademark, They have not adopted a common approach, so that by delving into the judicial procedure and doctrine of different countries, It is possible to separate the symptoms into weak and strong according to their degree of differentiation, and accordingly different legal protection of trademarks, depending on which of the above categories it is mentioned. The decision of the Federal Court of Switzerland in 2000 and the Benelux Court of Justice, which was later repeatedly upheld by the courts, Doctrine and Administration of Internal Market Harmonization of the European Union is included, It has not had any effect on the jurisprudence of Iran's courts, even if indirectly, And the trace of this separation is evident in the recent decisions of the appeals courts in the field of trademarks.

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain the following non-commutative analog of a result of Kaplansky. A bounded operator T on a Banach space X whose point spectrum sp(T) contains a nonzero complex number, is weakly regular.