Structural Mechanics

The prediction of the ultimate shear strength of reinforced concrete (RC) beams is very important especially when this value is used in the practical design. An unconservative value of the shear capacity may lead to an unexpected and at early stage brittle failure of the structural RC beam so, a great deal of research efforts have been put recently on the proper explanation, modeling and simulation of the shear crack phenomena [1], [5]. Although the current design codes for shear in RC beams rely almost entirely on the test results, a number of simplified methods are given in [1], based on theory of plasticity and the relevant effectiveness factors.

A special purpose 3D concrete finite element is employed in this research to model the complex nonlinear behaviour of reinforced concrete beams with no shear reinforcement. The theory is based on the 5 parameter plasticity failure surface due to Willam-Warnke and takes into account the tensile cracking in three orthogonal directions plus crushing status of certain Gaussian integration point. A comparison is made with experimental and numerical results taken from the literature. The load deflection curve analysis indicates a big sensitivity of the solution to small changes of the material parameters which shows that a further research for their adjustment is needed. Although in a smeared manner the shear cracking is available, the preliminary conclusions suggest that the typical big sliding accompanying the development of the critical shear crack is not fully handled by the present model.

A special two nodes singular boundary element for plane stress/strain analysis is developed for a general corner case. The main purpose of this element is to handle the singularity at the tip of a general corner or crack as a particular case, which means to tackle the infinite stress which appears at this point even for small values of the external load. Using this element, put at the corner/crack tip and combining it with the conventional type boundary elements, it is proved by a numerical test solution that the results for displacements and stresses are very good. As a result this solution may be used to calculate the stress intensity factors in linear fracture mechanics. Some comparison is made with finite element solution in order to prove that the developed element is working well and can be successfully applied in two dimensional analysis of structures containing internal corners and cracks.

The methods of linear elastic fracture mechanics (LEFM) are well developed when one deals with ideally brittle materials such as ceramics and glass - see references [1], [2]. The existing powerful numerical techniques such as FEM (Finite Element Method) and BEM (Boundary Element Method) enable researchers to perform the best linear static analysis in order to calculate the stress intensity factors (SIF) – the basic fracture mechanics parameters of LEFM. It was shown in paper [3], how using a specially developed singular boundary element such an analysis can be performed on a structure containing general corners.

It was shown by the authors [3], [4], how the powerful numerical techniques such as Finite Element Method (FEM) and Boundary Element Method (BEM) could be applied to solve some problems of the Linear Elastic Fracture Mechanics (LEFM). The structural material considered was presumed ideally brittle, such as ceramic or glass. A small inelastic process zone in front of the crack tip was also included in the solution, using the idea of the first and second Irwin’s corrections.

A fracture mechanics analysis of the shear strength of non-shear reinforced concrete
beams is carried out.
The starting point of the shear crack is determined by means of the crack sliding
theory. The crack path is determined by using the principal stress conditions of linear
fracture mechanics. Crack growth is calculated by a theoretical crack growth formula.
The formula is based on a non-linear two parameter fracture mechanics model and
gives a possibility to investigate the full crack development.
The numerical simulations are carried out using APDL (ANSYS Parameter Design
Language) programming language of the finite element package ANSYS.
The calculations seem to indicate that the final shear failure in the beams treated is not
a fracture mechanics problem. If this is a general trend is not yet clear. More
calculations have to be carried out.

Cracks are present to some degree in all plain and reinforced concrete structures. They exist either as basic defects in materials or they may be induced in the construction during the time of the service. Cracks often act as stress concentrators, so in many cases they are the main reason for catastrophic crack propagation and structural failure under increasing load. Such failures being of a very great concern have led to the evolution and development of the theory of fracture mechanics.

A theoretical crack growth formula for the development of cracks in non-shear reinforced beams is presented and compared with experiments. The formula is based on a non linear two parameter fracture mechanics model and gives a possibility to investigate the full crack development.
The shear crack path in longitudinally reinforced beams is determined using the principal stress criterion of linear elastic fracture mechanics. An investigation and analysis of the crack path, according to different reinforcement percentages, is made. The numerical simulations are carried out using APDL (ANSYS Parameter Design Language) programming language of the finite element package ANSYS. The calculations seem to indicate that the shear failure in the beam treated is not a fracture mechanics problem. If this is a general trend is not yet clear. More calculations have to be carried out.

The objective·• of the present paper is to introduce a finite element model performing a nonlinear numerical analysis on concrete structures with different sizes. The cohesive crack method of Hillerborg is employed, which can be also found in literature under the name fictitious crack method. For mode 1 cracking, the present model is capable of predicting the behavior of the whole range of structural sizes, including the extreme cases of the limit analysis and linear elastic fracture analysis. The numerical simulation for large concrete structures shows a good coincidence with LEFM model. The inclusion of small nonlinear zone in front of the crack tip, based on Irwin's correction procedure, is also discussed and comparisons are made. A special form of the brittleness number is used in order to reveal the strong size effect of the structures with different sizes or/and
different fracture mechanics parameters.

There are many general purpose software systems developed on the basis of the finite element methods, such as ANSYS, ABAQUS, COSMOS etc. The only general purpose software system, based on the boundary element method is BEASY and it has UK origin. It is well known that the boundary element method offers some important advantages over other numerical techniques, but the difficulties associated with the numerical treatment of the integral equations have led to this lack of huge development of the relevant software.
The development of new software package using the theory of the boundary element method is explained in this paper. The algorithmic language used is Visual Basic 6 and the concept is made on the basis of the classical approach by creating the three basic program structures: preprocessor, processor and postprocessor. The program may perform static analyses of plane structures and some methods of the fracture mechanics theory are also developed. That program may be considered as a first variant and new developments will be soon available.

There are many general purpose software systems developed on the basis of the finite element methods, such as ANSYS, ABAQUS, COSMOS etc. The only general purpose software system, based on the boundary element method is BEASY and it has UK origin. It is well known that the boundary element method offers some important advantages over other numerical techniques, but the difficulties associated with the numerical treatment of the integral equations have led to this lack of huge development of the relevant software.
The development of new software package using the theory of the boundary element method is explained in this paper. The algorithmic language used is Visual Basic 6 and the concept is made on the basis of the classical approach by creating the three basic program structures: pre-processor, processor and pos-tprocessor. The program may perform static analyses of plane structures and some methods of the fracture mechanics theory are also developed. That program may be considered as a first variant and new developments will be soon available.

From experiments, it is a well-known fact that the shear crack path depends on the size of the beam and on the shear span ratio. The critical shear crack can be an almost straight line, a curved line, or in some cases beams collapse without forming a shear crack.
In present paper is determined the shear crack path in RC beams using the principal stress criterion of LEFM. The numerical simulations are carried out using APDL (ANSYS Parameter Design Language) programming language of ANSYS. An investigation and analysis of crack path for different reinforcement percentages, is presented. Comparisons with experimental results, final analysis and conclusions are made.

The prediction of the ultimate shear strength of reinforced concrete (RC) beams is very important especially when this value is used in the practical design. An unconservative value of the shear capacity may lead to an unexpected and early stage brittle failure of the structural RC beam, therefore a great deal of research efforts have been put recently on the proper explanation, modeling and simulation of the shear crack phenomena [1],[5].

It is well known fact that the bearing capacity of reinforced concrete beams depends on their cross section sizes, longitudinal reinforce ratio and the possibilities to develop shear cracks. The present article investigates the size effect concerning reinforced concrete shear beams. A shear strength comparison among such beams was made, according to design codes that are up to date and according some models that pay attention to size effect. Comparisons with real experimental data are given and some conclusions and deductions are made.

It is well known fact that the bearing capacity of reinforced concrete beams depends on their cross section sizes, longitudinal reinforce ratio and the possibilities to develop shear cracks. The present article investigates the size effect concerning reinforced concrete shear beams. A shear strength comparison among such beams was made, according to design codes that are up to date and according some models that pay attention to size effect. Comparisons with real experimental data are given and some conclusions and deductions are made.

A Visual Basic for Application’s program for calculating crack growth in concrete and reinforced concrete beams is presented in this paper. This program is useful for obtaining quick results for initial analysis and parametric study. In the present program Nielsen’s crack growth formula is incorporated which is a new and original effective crack model. Some results are presented and comparisons with experiments are performed.

В настоящата статия са представени два подхода, от гледна точка на механика на разрушението, за определяне на пътя на развитие на пукнатина в бетонови и стоманобетонови греди. За числената реализация на процеса са използвани два различни числени метода: метод на крайните елементи (МКЕ) и метод на граничните елементи (МГЕ). За приложението на МКЕ е използван програмния пакет ANSYS, в който са разработени отделни макроси. За приложението на МГЕ е използвана програмата BEPLANE, в която е разработен модул за осъществяване на процедурата. Направени са сравнения на резултатите между различните подходи и методи. Извършена е съпоставка на числените резултатите с експерименталните данни за бетонови и стоманобетонови греди.

С навлизането на ново поколение мощна изчислителна техника се забелязва развитие на нови изчислителни алгоритми и числени методи, насочени към решаване на задачи с голям брой неизвестни. Това касае най-вече метода на крайните елементи а също така и метода на граничните елементи (МГЕ). Типичен пример е задачата за статическо изследване на конструктивни елементи, направени от композитни материа-ли. Обикновено този тип материали са нехомогенни и се състоят от най-малко две фази: матрица и усилвания във вид на еластични включвания – най-често това са някакъв вид нишки. Коректното изследване на такъв материал изисква определянето на т.нар. ефективни еластични материални характеристики, за получаването на които се отделя специална подобласт от елемента, обикновено това е квадрат с малки размери, наречен представителен обем (ПО). Този обем се изследва с подхода на микромеханиката, като за решението се прилага някой от числените методи. При моделирането се вземат предвид всички реални компоненти на композитния материал, като ще допълним, че нехомогенността на материала може да се получи и при наличие на отвори или система от пукнатини, свободни от напрежения.

В настоящата статия е направена ретроспекция на механика на разрушението като клон на строителната механика. Направен е кратък исторически преглед и са пояснени основните параметри и модели. Придставена е основната концепция на линейната механика на разрушението, след което са описани на кратко някои нелинейни модели за квазикрехки материали като бетон. В залючение се набяга на важността за инженера на този бързоразвиващ се клон от механиката и се дават препоръки за включването на елементи от нея в Еврокод.