Search

The fundamental natural period of oscillation is a critical parameter in evaluating the design base shear of buildings. Worldwide seismic design codes typically employ height-based empirical formulas to estimate this period for various building categories, without distinguishing between regular and irregular buildings. This study proposes a formula specifically for reinforced concrete (RC) moment-resisting frame (MRF) buildings with dominant re-entrant corner type plan irregularity. A total of 190 re-entrant corner dominant building models with different shapes (C-, L-, T-, and PLUS-type), heights, and floor configurations were prepared, and eigenvalue analysis (EVA) was conducted. The fundamental natural period of oscillation for each model was evaluated and compared with the height-based formulas from seismic design codes and the period–height relationship proposed in existing literature. A nonlinear regression model, using a multi-variable power function, is proposed to estimate the fundamental natural period for these re-entrant corner dominant building models. This model considers the A/L ratio in both directions of the building, along with its height. Both unconstrained and constrained regression analyses were performed to derive a formula that best fits the fundamental natural period data. The study recommends that the unconstrained best-fit minus one standard deviation curve can conservatively define the fundamental natural period of oscillation for re-entrant corner dominant RC building models. The equation defining this curve has the potential to replace the existing seismic design code-based period-height formula.

The fundamental natural period of oscillation is a critical parameter in evaluating the design base shear of buildings. Worldwide seismic design codes typically employ height-based empirical formulas to estimate this period for various building categories, without distinguishing between regular and irregular buildings. This study proposes a formula specifically for reinforced concrete (RC) moment-resisting frame (MRF) buildings with dominant re-entrant corner type plan irregularity. A total of 190 re-entrant corner dominant building models with different shapes (C-, L-, T-, and PLUS-type), heights, and floor configurations were prepared, and eigenvalue analysis (EVA) was conducted. The fundamental natural period of oscillation for each model was evaluated and compared with the height-based formulas from seismic design codes and the period-height relationship proposed in existing literature. A nonlinear regression model, using a multi-variable power function, is proposed to estimate the fundamental natural period for these re-entrant corner dominant building models. This model considers the A/L ratio in both directions of the building, along with its height. Both unconstrained and constrained regression analyses were performed to derive a formula that best fits the fundamental natural period data. The study recommends that the unconstrained best-fit minus one standard deviation curve can conservatively define the fundamental natural period of oscillation for re-entrant corner dominant RC building models. The equation defining this curve has the potential to replace the existing seismic design code-based period-height formula. [ABSTRACT FROM AUTHOR]

The dapped end beam members have a special end with low depth at the support area, which results in a weak area against shear stresses. Classical structural analysis doesn't capture the precise steel reinforcement interaction at the dapped zone area. The main objectives of this study are to investigate the strength of the dapped end area and to analyze stresses in the steel reinforcement to evaluate the shear failure mechanism at the re-entrant corner. The experimental tests conducted on RC beam samples, in addition to the numerical simulation of these samples by a finite element program, have been compared with a mathematical model. The experimental program highlighted the strains in the steel reinforcement in the dapped region to calculate the magnitude of the stresses in the steel reinforcement. In the experimental program, six dapped beams were fabricated with a length of 3 m, a width of 150 mm, and a depth of 300 mm. The notched end has a 150-mm depth and 150-mm height. These beams were loaded by a concentrated load near support to investigate the shear strength capacity. From the results for steel reinforcement strain, it is found that hanger and horizontal steel reinforcements interact to provide dapped end shear strength. The study proposes a new approach to computing shear strength capacity at the reentrant corner by adding the contributions of the horizontal and hanger steel reinforcement using an appropriate proportion strain factor. This method revealed greater carrying capacity for the dapped end beam compared with other common structural methods. The results of the numerical analysis were done by the ABAQUS finite element program, showing the same behavior as the experimental work. This study proved the common contribution of hanger and horizontal re-entrant corner steel reinforcement and proposed a new formula to determine the updated nominal shear strength. [ABSTRACT FROM AUTHOR]

The design of structures with re-entrant angle is often the consequence of the functional, architectural or urbanistic requirement. With any form building, the engineer has full responsibility to ensure the safety of the users and the structure in the case of the earthquake. However, re-entrant angle structures have geometric dissymmetry and limited choice in the disposition of rigid structural elements. The objective of this work is to evaluate the effect of the angle formed between the two wings of an L-shaped building, softened by a transition on their dynamic behavior. Different variants were considered by taking several angle values (45°, 60°, 75°, 90°, 105°, 120° and 135°). In order to evaluate the impact of the analyzed parameter, a study of the linear and non-linear dynamic behavior of the different structures was executed by the spectral modal analysis method and the non-linear static analysis. According to the atypical geometrical configuration in the plan of the various structures, six principal seismic directions were considered Ex, Ey, Ex’, Ey’, Ex” and Ey”. The results show that seismic excitation applied on the transition zone of a building with projected parts occurs a higher deformability. In addition, along this seismic direction, the progressive pushing of a uniform lateral loading applied on the structure with a projections opening angle of 90° assures a better nonlinear behavior in terms of base shears bearing capacity, deformation ductility and damage level.

Despite the great variety of cases concerning slab-column connections found in practice, most research has concentrated so far on the punching resistance of inner columns without moment transfer. Other cases, such as edge or corner columns, have attracted less research attention despite their practical relevance. Within this context, re-entrant corner columns are a commonly used detail in practice (i.e. columns at corners of openings) where almost no experimental evidence is available and design codes typically extrapolate design recommendations from other cases. In order to advance the knowledge in this field, this paper presents an experimental and theoretical investigation on the punching resistance of slab-column connections in re-entrant corners. The research is addressed at specimens with and without shear reinforcement and introduces the results of an experimental programme on specimens reproducing realistic conditions in terms of size and loading arrangement. The experimental results are first analysed according to several design guidelines, highlighting their shortcomings. On that basis, a theoretical approach for punching design is proposed based on the Critical Shear Crack Theory. Such approach is aimed at understanding the mechanics of punching failure and to lead to consistent predictions on the resistance and deformation capacity of the slab-column connections. • The punching response of re-entrant slab-column connections was investigated. • The activation of the studs is more significant in the slabs with higher levels of eccentricity and shear force. • The rotations are significantly affected by load eccentricities. • The CSCT provides consistent estimates of the resistance, deformation capacity and also failure mode. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates numerically and experimentally the performance of reinforced concrete (RC) beam with unequal depths subjected to combined bending and shear. Such beams can geometrically be considered for unleveled reinforced concrete (RC) floor slab-beam system. However, it may generate critical disturbances in stress flow at the re-entrant corner (i.e. location of drop in beam depth). This research investigates the use of shear reinforcement and geometric properties to enhance cracking characteristics, yielding, ultimate load-carrying capacity, and exhibiting ductile failure mode. Ten reinforced concrete (RC) beams were constructed and tested experimentally considering the following key parameters: recess length, depth of smaller beam nib, and amount and layout of shear reinforcement at re-entrant corner. Finite element analysis (FEA) with material non-linearity was conducted in two RC beams that were tested experimentally to validate the computer modelling. The FEA models were then extended to conduct a parametric study to investigate the influence of geometric parameters (beam shape and width) and amount and arrangement of shear reinforcement on the structural response. Results confirmed that geometric properties and ratio of shear reinforcement at the re-entrant region significantly affect the behavior of reinforced concrete beam with unequal depths in terms of first cracking, yielding level, ultimate load carrying capacity and mode of failure.

In mixed-mode conditions, the competing contribution of the different stress intensity factors predicts fracture initiation load as well as crack propagation direction. Commonly, mixed-mode fracture resistance is based on the assumption of smooth and frictionless cracks. However, the effect of friction and roughness cannot be neglected when mixed mode loading occurs, as in the case of a crack emanating from a re-entrant corner. In this paper, the effect of friction and roughness is evaluated through a simple saw-tooth model in a three-quarter-infinite plane (corresponding to a 90 degree re-entrant corner). The crack surfaces are assumed to be globally smooth, and roughness and friction are incorporated through a constitutive law between opposite crack surfaces. The solution is found using the distributed dislocation method, and an iterative algorithm is needed due to the non-linearity of the model. The effect of friction and roughness angle is discussed for a simple case.

Half-joint beams, also referred to as dapped-end beams, have been the subject of several studies, primarily focussing on the design optimisation of new reinforced concrete beams and bridge decks. Existing half-joint structures, however, often show signs of deterioration and can exhibit improper reinforcement detailing. In order to gain a better insight into the impact of local corrosion, anchorage cracking, limited amounts of provided shear reinforcement, and improper reinforcement detailing, a test program was designed. Full-scale tests on nine half-joint beams were performed. The results of the study show that even though the impact of an individual shortcoming on the load carrying capacity of reinforced concrete half-joint beams might not be substantial, inspectors and assessors should pay attention to the possibility of combined effects. When multiple deterioration processes are noted and/or questions are raised with respect to the reinforcement detailing, the impact on the load carrying capacity of the beam might be larger than the linear combination of the individual effects. [ABSTRACT FROM AUTHOR]

Linear elasticity problems posed on cracked domains, or domains with re-entrant corners, yield singular solutions that deteriorate the optimality of convergence of finite element methods. In this work, we propose an optimally convergent finite element method for this class of problems. The method is based on approximating a much smoother function obtained by locally reparameterizing the solution around the singularities. This reparameterized solution can be approximated using standard finite element procedures yielding optimal convergence rates for any order of interpolating polynomials, without additional degrees of freedom or special shape functions. Hence, the method provides optimally convergent solutions for the same computational complexity of standard finite element methods. Furthermore, the sparsity and the conditioning of the resulting system is preserved. The method handles body forces and crack-face tractions, as well as multiple crack tips and re-entrant corners. The advantages of the method are showcased for four different problems: a straight crack with loaded faces, a circular arc crack, an L-shaped domain undergoing anti-plane deformation, and lastly a crack along a bimaterial interface. Optimality in convergence is observed for all the examples. A proof of optimal convergence is accomplished mainly by proving the regularity of the reparameterized solution. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The seismic vulnerability assessment of any important infrastructure like concrete gravity dam is an integral part for the seismic risk evaluation. Vulnerability of the concrete gravity dam depends on many factors including its geometric configuration, since the geometric shape of a concrete gravity dam assures its stability during static and dynamic loading conditions. In case of high concrete gravity dams, sometimes it becomes necessary to provide slope at its upstream face and in the consequence re-entrant corner appears in the geometry. Stress concentration in the re-entrant corner region causes initiation of crack in the dam body, which is an alarming issue among engineering community. Therefore in the present work, effects of re-entrant corner on seismic performance of concrete gravity dams are investigated using incremental dynamic analysis method on typical high concrete gravity dams. A possible solution to the problem is also proposed in the study. [ABSTRACT FROM AUTHOR]

A reinforced concrete half-joint beam has a complex geometry that includes both a locally disturbed nib region and a full depth section. While this configuration simplifies the design and construction procedures, half joint structures rely on the internal steel reinforcement to transfer force from the nib into the bulk of the beam. When assessing existing reinforced concrete half-joints, engineers can be confronted with internal reinforcement layouts that do not correspond to the as-designed drawings and/or do not comply with current design practice. Bars may be missing or the location, percentage and spacing of the steel reinforcing bars may be non-compliant. To provide a better understanding of the contribution of the internal steel reinforcing bars found in a typical half joint detail, an experimental test program on full-scale half-joint beams was undertaken. Four different scenarios were tested to identify the impact of specific reinforcing bars. A reference specimen was designed in accordance with existing practice. The reference beam, and beams with either missing diagonal reinforcement, missing horizontal reinforcement or a reduced amount of shear reinforcement were tested. All the beams exhibited nib failures with the exception of the beam where the shear reinforcement was reduced. In this case, the failure mode changed from a nib failure to a full-depth failure. The results indicated that if certain bars are missing the overall load bearing capacity of a half-joint could be approximately 40% lower than that of a properly designed detail, but that a redistribution of forces was noted. [ABSTRACT FROM AUTHOR]

Blockage of air circulation caused by the mutual sheltering effect of high-rise buildings in built-up areas in dense cities causes various health- and comfort-related problems. The combined effect of neighborhood geometry (e.g., re-entrant corners, wind incident angle, passage angle, and building separation) on wind flow at the pedestrian level is an active field of research. This study investigates the influence of the wind incident angle and passage width on the wind flow characteristics at the re-entrant corners of cross-shaped high-rise buildings. This study also examines the influence of stagnant zones and wake regions on ventilation potential and wind comfort around the case study arrangements at various wind incident directions. An investigation was performed from 16 wind directions using the standard k–ε turbulence model with revised closure coefficients. A wind tunnel experiment was conducted to validate the results, which revealed that wind circulation at re-entrant corners was substantially affected by the building orientations and separation. The wind catchment effect within the re-entrant corners and the sheltering effect of buildings at various wind incident directions and building separations are also discussed. Unstable vortices were formed in oblique wind directions; these vortices facilitate contaminant dispersion and wind comfort at re-entrant corners and near buildings. [ABSTRACT FROM AUTHOR]

Decoupling a fourth order elliptic boundary value problem into a system of second order equations may give an alternative approach to obtaining a solution for the original problem. The system approach is usually preferred for numerical methods since one may use piecewise linear finite elements to approximate a solution. In this note we compare both settings for the plate equation and prove that for planar domains with corners the system approach may fail to produce the correct solution. [ABSTRACT FROM AUTHOR]

A mathematical model of a waveguide with re-entrant corners in its variable cross section is considered. The influence of the re-entrant corner on the waveguide field mode structure is investigated. [ABSTRACT FROM AUTHOR]

Abstract: The paper deals with high order elastic singular terms at cracks and re-entrant corners (sharp V-notches), which are commonly omitted in linear elastic analyses by the argument that the strain energy and displacements in the near-tip region should be bounded. The present analysis proves that these terms are fully included in the elastic part of complete elastic–plastic stress and strain solutions. The intensities of high order singular terms are found to be linked to the linear elastic stress intensity factor and the extension of the plastic zone along the crack bisector line. The smaller the plastic radius, the smaller the intensities of high order singular terms are. A physical justification of the existence of high order singular terms is provided on the basis of the strain energy density distribution detected along the crack bisector line. Finally, the influence of the V-notch opening angle is made explicit, discussing also the relationship between the singularity orders and the solution of a Williams’ type sinusoidal eigen-equation. [Copyright &y& Elsevier]

Abstract: We consider the Upper Convected Maxwell (UCM) limit of the Phan-Thien–Tanner (PTT) equations for steady planar flow around re-entrant corners. The PTT equations give the UCM equations in the limit of vanishing model parameter κ, this dimensionless parameter being associated with the quadratic stress terms in the PTT model. We show that the critical length scale local to the corner is as κ →0, where π/α is the re-entrant corner angle with α ∈[1/2, 1) and r the radial distance. On distances far smaller than this we obtain the PTT κ =1 problem, whilst on distances greater (but still small) we obtain the UCM problem κ =0. This critical length scale is that on which intermediate behaviour of the PTT model is obtained where both linear and quadratic stress terms are present in the wall boundary layer equations. The double limit κ →0, r →0 thus yields a nine region local asymptotic structure. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the asymptotic problem of a body of infinite extent with a notch (re-entrant corner) under remotely applied plane-strain or anti-plane shear loadings. The problem is formulated within the framework of the Toupin-Mindlin theory of dipolar gradient elasticity. This generalized continuum theory is appropriate to model the response of materials with microstructure. A linear version of the theory results by considering a linear isotropic expression for the strain-energy density that depends on strain- gradient terms, in addition to the standard strain terms appearing in classical elasticity. Through this formulation, a microstructural material constant c is introduced, in addition to the standard Lamé constants ( λ, μ). The faces of the notch are considered to be traction-free and a boundary-layer approach is followed. The boundary value problem is attacked with the asymptotic Knein-Williams technique. Our analysis leads to an eigenvalue problem, which, along with the restriction of a bounded strain energy, provides the asymptotic fields. The cases of a crack and a half-space are analyzed in detail as limit cases of the general notch (infinite wedge) problem. The results show significant departure from the predictions of the standard fracture mechanics. [ABSTRACT FROM AUTHOR]

Abstract: The local asymptotic behaviour is described for planar re-entrant corner flows of a Giesekus fluid with a solvent viscosity. Similar to the PTT model, Newtonian velocity and stress fields dominate near to the corner. However, in contrast to PTT, a weaker polymer stress singularity is obtained with slightly thinner stress boundary layers of thickness , where is the Newtonian flow field eigenvalue and r the radial distance from the corner. In the benchmark case of a corner, we thus have polymer stress singularities of for Oldroyd-B, for PTT and for Giesekus. The wall boundary layer thicknesses are for Oldroyd-B, for Giesekus and for PTT. Similar to the PTT model, these results for the Giesekus model breakdown in both the limits of vanishing solvent viscosity and vanishing quadratic stress terms (i.e. the Oldroyd-B limit). [Copyright &y& Elsevier]

Abstract: The local asymptotic behaviour is given for planar re-entrant corner flows of Phan-Thien–Tanner fluids with a solvent viscosity. The solvent stress and Newtonian velocity field dominate in all regions, with the polymer stress being uniformly subdominant. At small radial distances to the corner, the velocity field vanishes as whilst the solvent stress behaviour is . The polymer stress has the less singular behaviour , where is the Newtonian flow-field eigenvalue. Stress boundary layers are needed at the walls for the polymer stress solution, which are of thickness . These results confirm the order of magnitude estimates previously obtained by Renardy , the alternative derivation given here using the method of matched asymptotic expansions. Further, we complete previous analysis by providing solutions (particularly for the polymer stresses) in the asymptotic regions that arise. These results breakdown in the limit of vanishing solvent viscosity as well as the Oldroyd-B model limit. [Copyright &y& Elsevier]

Abstract: We revisit the situation of steady planar flow of Phan–Thien–Tanner (PTT) fluids around re-entrant corners of angles where . The model is considered in the absence of a solvent viscosity, under which a class of self-similar solutions has been identified with stress singularities of and stream function behaviour (r being the radial distance from the corner). The asymptotic analysis is completed by providing a solution for the downstream boundary layer using natural stress variables. We show that the matching of the outer (core) solution into the downstream boundary layer imposes a restriction on the range of for which these self-similar solutions are applicable, i.e. they only hold for corner angles between and . [Copyright &y& Elsevier]

Abstract: We consider the planar flow of Phan-Thien–Tanner (PTT) fluids around a re-entrant corner of angle where . The model is considered in the absence of a solvent viscosity and the flow situation assumes complete flow around the corner with the absence of a lip votex. The local asymptotic solution structure is similar to that for the upper convected Maxwell (UCM) model and is shown to comprise a core flow (outer) region in which the fluid behaves elastically, together with wall boundary layers (inner regions) of similar thickness as those in the UCM model. In the core flow, the stress singularity is that for UCM, namely where r is the radial distance from the corner, although the stream function vanishes at the slower rate compared to for UCM—this latter feature being a consequence of the shear thinning property of the PTT model. The amplitudes of the velocity and stress fields are determined and are seen to be independent from this local analysis, any link between them appearing to require global flow information away from the corner. The analysis is performed here in the Cartesian stress formulation of the problem, allowing the description of a similarity solution for the core flow and upstream boundary layer. The analysis remains to be completed by a solution for the downstream boundary layer which requires the use of the natural stress basis. [Copyright &y& Elsevier]

Abstract: This paper continues the description of a two parameter family of solutions for the local asymptotic behaviour of UCM fluids at re-entrant corners. Here, the natural stress basis is used to re-derive the equations in the core flow and boundary layers, with full description of the scalings and matching being given. The parametric solution dependence is completed with numerical deteremination of the coefficient of the downstream wall shear rate. The flow structure implicitly assumes the absence of a separating streamline in the upstream region. [Copyright &y& Elsevier]

Abstract: For a given re-entrant corner geometry, we describe a two parameter family of solutions for the local asymptotic behaviour of the flow and stress fields of UCM fluids. The two parameters used are the coefficients of the upstream wall shear rate and pressure gradient. In describing this parametric solution, the relationship between the Cartesian and natural stress basis is explained, reconciling these two equivalent formulations for the problem. The asymptotic solution structure investigated here comprises an outer (core) region together with inner regions (single wall boundary layers) located at the upstream and downstream walls. It is implicitly assumed that there are no regions of recirculation at the upstream wall, i.e. we consider flow in the absence of a lip vortex. The essential feature of the analysis is a full description of the matching between the outer and inner regions in both the Cartesian and natural stress bases, as well as the derivation of numerical estimates of important solution parameters such as the coefficients of the stream function and extra-stresses in the outer (core flow) region together with the downstream wall shear rate. This work is divided into two papers, the first one describing the solution structure in the Cartesian stress basis for the core and upstream boundary layer, and the second paper using the natural stress basis which allows the downstream boundary layer solution to be linked through the core to the upstream boundary layer solution. It is the latter formulation of this problem which allows a complete solution description. [Copyright &y& Elsevier]

Abstract: Functionally graded materials (FGMs) are special composites in which the volume fractions of constituent materials vary gradually, giving continuously graded mechanical properties. The aim of this paper is the evaluation of the strength of structures composed by FGMs incorporating re-entrant corners – tending to the more common crack for vanishing corner angle. The end result is useful in engineering applications predicting the strength of the element corresponding to the unstable brittle crack propagation in such innovative materials. To show the general validity of the method, heterogeneous plates under tension and beam under bending containing re-entrant corners and by varying corner angle, depth and grading of the FGM are considered. Ad hoc performed numerical finite element simulations, by using the FRANC2D code, agree with the theoretical predictions. [Copyright &y& Elsevier]

This paper investigates numerically and experimentally the performance of reinforced concrete (RC) beam with unequal depths subjected to combined bending and shear. Such beams can geometrically be considered for unleveled reinforced concrete (RC) floor slab-beam system. However, it may generate critical disturbances in stress flow at the re-entrant corner (i.e. location of drop in beam depth). This research investigates the use of shear reinforcement and geometric properties to enhance cracking characteristics, yielding, ultimate load-carrying capacity, and exhibiting ductile failure mode. Ten reinforced concrete (RC) beams were constructed and tested experimentally considering the following key parameters: recess length, depth of smaller beam nib, and amount and layout of shear reinforcement at re-entrant corner. Finite element analysis (FEA) with material non-linearity was conducted in two RC beams that were tested experimentally to validate the computer modelling. The FEA models were then extended to conduct a parametric study to investigate the influence of geometric parameters (beam shape and width) and amount and arrangement of shear reinforcement on the structural response. Results confirmed that geometric properties and ratio of shear reinforcement at the re-entrant region significantly affect the behavior of reinforced concrete beam with unequal depths in terms of first cracking, yielding level, ultimate load carrying capacity and mode of failure. [ABSTRACT FROM AUTHOR]