Recommendations for Assessment of Reinforced Concrete Slabs: Enhanced structural analysis with the finite element method

Reinforced concrete structures show a pronounced non-linear response, with cracking of concrete for service loads and reinforcement yielding and concrete crushing at ultimate load. With non-linear finite element (FE) analysis, the structural response can be captured, and such analyses have shown great potential to reveal higher load carrying capacity compared to simplified and linear analysis methods. A multi-level structural assessment strategy, developed in previous research, provides a framework for more advanced, successively improved analysis of reinforced concrete slabs.This report provides recommendations for practicing structural engineers on structural assessment using FE analysis. The focus is on enhanced assessment with non-linear FE analysis, and the scope is reinforced concrete slabs with limited membrane effects. The intention is to facilitate the use of non-linear analysis in engineering practice by providing detailed recommendations on how such analyses can be made to provide increased understanding of the structural behaviour and reliable estimations of the load-carrying capacity of concrete slabs. However, the framework presented is general, and the approach can in many aspects also be used for other types of reinforced concrete structures. The recommendations given here are based on previous research performed by the authors, information from literature and engineering judgement based on practical experience. They are intended to give conservative estimates of the load-carrying capacity, fulfilling the required safety level. The report includes a thorough description of the assessment strategy. The global safety format recommended for non-linear analysis is presented and its application for different assessment levels is described. Furthermore, recommendations on how to take deterioration into account are given. Non-linear FE analysis of concrete structures is presented together with general advices for its application. Furthermore, general recommendations are presented for simplified and linear analysis, corresponding to today’s practice. For assessment with non-linear FE analysis, detailed recommendations for use in engineering practice are presented. Advices are given on idealization of the structure, choice of material models, determination of material parameters, modelling and analysis. Furthermore, the evaluation of structural response, determination of load carrying capacity and response under service conditions are described. For non-linear analysis with shell elements, resistance models on higher Level-of-Approximation according to Model Code 2010 are used. Finally, examples are showing the application of the strategy on two slabs tested in laboratory and one bridge deck slab

Two-way slabs: Experimental investigation of load redistributions in steel fibre reinforced concrete

In the design of two-way reinforced concrete slabs, e.g. using the strip or yield line design method, the possibility of redistributing the load between different loading directions is used. The main aim of the present study was to investigate how fibres affect the structural behaviour such as the possibility for redistribution, crack patterns and load-carrying capacity. The investigation was conducted by means of experiments on two-way octagonal slabs, simply supported on four edges, centrically loaded with a point load. The slabs spanned 2.2 m in both directions and the reinforcement amount was twice as large in one direction as in the other, in order to provoke uneven load distribution. Three slabs of each reinforcement configuration were produced and tested: conventionally reinforced slabs, steel fibre reinforced slabs and a combination of both reinforcement types. The reaction force on each supported edge was measured on five rollers per edge. A moderate fibre content (35 kg/m3) of double hook-end steel fibres was used. The steel fibres affected the structural behaviour significantly by providing post-cracking ductility and by increasing the ultimate load-carrying capacity by approximately 20%. Most significant, the steel fibres influenced the load redistribution in such a way that more load could be transferred to supports in the weaker direction after cracking. Further, more evenly distributed support reactions were obtained in the slabs containing both reinforcement types compared to the case when only conventional reinforcement was used. The slabs reinforced by steel fibres alone did not experience any bending hardening; however, a considerable post-cracking ductility was observed. Furthermore, the work presented in this paper will provide results suitable for use in benchmarking numerical and analytical modelling methods for steel fibre reinforced concrete, as the experimental programme also included extensive testing of material properties

Development of modelling strategies for two-way RC slabs

Analyses of tested two-way reinforced concrete (RC) slabs were carried out with varying modelling choices to develop better modelling strategies. The aim was to study how accurately the response of a slab subjected to bending could be predicted with nonlinear finite element (FE) analysis using three-dimensional (3D) continuum elements, and how the modelling choices might influence the analysis results. The load-carrying capacity, load-deflection response, crack pattern and reaction-force distribution of the two-way slab studied were compared to experimental data available. The influence of several modelling parameters was investigated, including geometric nonlinearity, element properties, concrete model, reinforcement model and boundary condition. The results show the possibility of accurately reflecting the experimental results concerning load-carrying capacity, load-deflection response and crack pattern giving proper modelling choices. Moreover, the reaction force distribution was found to be highly influenced by the stiffness of the supports

Internal force distribution in RC slabs subjected to punching shear

Reinforced concrete (RC) two-way slabs without shear reinforcement are commonly used in many structural systems. This paper investigated the structural behaviour of RC slabs subjected to concentrated loads leading to punching shear failure using shell and continuum nonlinear finite element analysis (NLFEA). Shear force distributions are studied for four types of slabs with different geometry of support, geometry of slab and layout of reinforcement. All factors investigated have been proven to influence the shear force distributions along the control perimeter around the support. Significant shear force redistributions due to cracking and reinforcement yielding have been observed using NLFEA. Reduced control perimeters to be used for simplified approaches accounting for calculated shear force distributions are calculated using both NLFE approaches

Structural Analysis of Existing RC Bridge Deck Slabs Structural Analysis of Existing RC Bridge Deck Slabs

Due to ageing of the bridge stock, continuously increasing load requirements, the need for assessing existing bridges is becoming increasingly important. Reinforced concrete (RC) bridge deck slabs are among the most critical parts to the load carrying capacity of bridges. Previous research indicated that the assessment method used in current practice largely underestimate the load-carrying capacity.The objective of the study reported in this licentiate thesis is to develop and calibrate improved methods for assessment of load-carrying capacity and response of existing bridge deck slabs. This study proposes an enhanced assessment through improved structural analysis and resistance evaluation in order to achieve higher detectable load-carrying capacity. To achieve this objective, the scientific approaches including literature study, laboratory tests, analytical analyses and finite element analyses were adopted. Two major studies and a series with supporting tests were conducted as following:A large test series, in which three specimens containing traditional steel bar reinforcement in ordinary concrete, were carried out to study the load carrying capacity and structural behavior of two-way slab.A proposed multi-level assessment method was validated through two case studies: a two-way slab and a cantilever slab. The multi-level assessment method includes simplified analysis, 3D linear FE analysis, 3D nonlinear analysis with shell elements, 3D nonlinear FE analysis with continuum elements include fully bonded reinforcement as well as 3D nonlinear FE analysis with continuum elements including bond-slip for the reinforcement.To develop the modeling strategies for two-way RC slabs with continuum elements, parameter studies has been carried out to investigate the influence of different modeling choices. Parameters including finite element properties, modeling of concrete, modeling of reinforcement and stiffness of supports were varied in different comparative models to investigate the influence. The study shows that existing methods currently used in assessment are not able to accurately reflect the response of RC bridge deck slabs, and underestimate their capacity. With enhanced assessment methods, such as the nonlinear finite element method, it is possible to better reflect the structural behavior, and more accurately determine the load carrying capacity. Two case studies have proven that the multi-level assessment method is able to reflect the structural behavior at different levels of approximation, which is beneficial in evaluating existing RC slabs. The parameter studies indicate that modeling choices such as geometric nonlinearity, crack bandwidth and Poisson’s ratio have significant impact on determination of the load-carrying capacity. Finite element properties, reinforcement model and stiffness of supports influence crack pattern and load distribution respectively

Multi-level assessment of a full-scale tested bridge deck slab

For reinforced concrete (RC) slabs without shear reinforcement, shear and punching can be the governing failure mode at the ultimate limit state if subjected to large concentrated loads. Shear and punching of RC slabs without shear reinforcement has been a challenging problem in assessment based on current standards. To examine a previously developed enhanced analysis approach, this study was conducted by applying a Multi-level Assessment Strategy to a 55-year old RC bridge deck slab subjected to concentrated loads near the main girder in a field failure test. The differences between analysis methods at different levels of assessment was discussed regarding one-way shear and punching shear behavior of the slab. The influences of parameters such as boundary conditions, location of concentrated loads and shear force distribution were investigated

Structural Analysis Methods for the Assessment of Reinforced Concrete Slabs

Reinforced concrete (RC) slabs are among the most critical parts of the load-carrying capacity of such structures as bridges and parking decks. Previous research indicated that the assessment methods used in current practices largely underestimated the load-carrying capacity. The objective of the study reported in this thesis is to develop and calibrate improved methods for the assessment of load-carrying capacity and the response of RC slabs.A Multi-level Assessment Strategy has been proposed. The strategy is based on the principle of successively improved evaluation in structural assessment. The strategy includes simplified analysis, linear finite element (FE) analysis and non-linear shell FE analysis, as well as non-linear continuum FE analysis with and without consideration of the interaction between reinforcement and surrounding concrete.According to the Multi-level Assessment Strategy, enhanced FE analyses have shown to possess great possibilities for achieving a better understanding of the structural response and revealing the\ua0higher load-carrying capacity of existing structures. However, non-linear 3D continuum FE analysis, at the highest level of the proposed strategy, is demanding and an analysis involves many modelling choices that are decisive for results. For the purpose of mapping the influence of different modelling choices on the structural behaviour of the FE model of RC slabs, sensitivity analyses have been conducted for RC slabs subjected to bending and especially to shear and punching failure. The selected modelling choices, within five major categories are: geometric non-linearity, element properties, modelling of concrete and reinforcement, as well as modelling of supports. The results show the possibility of accurately reflecting the experimental results concerning load-carrying capacity, load-deflection response, crack pattern and load distribution, given that proper modelling choices are used. Thereafter, the selected modelling choices were applied in FE analyses to investigate the load distribution and several influencing factors, including cracking, flexural reinforcement and the geometry of slabs and supports. The effect of flexural reinforcement and the size of specimens on structural response were also studied.To examine the previously developed enhanced analysis approach, the Multi-level Assessment Strategy was applied to several laboratory tests and to a 55-year-old field-tested existing RC bridge deck slab, and results were compared to the experiments. The difference between assessment methods at different levels of detail was discussed. The results show that in general, advanced models are more capable of demonstrating load-carrying capacity that better reflects reality. The high-level continuum FE analysis and shell FE analysis coupled with a mechanical model, such as the Critical Shear Crack Theory (CSCT) are capable of predicting the shear and punching behaviour of RC slabs with reasonable accuracy. In addition, the influence of parameters such as boundary conditions, the location of concentrated loads and shear force distribution were found to affect the shear capacity of the field-tested bridge deck slab

Shear assessment of a reinforced concrete bridge deck slab according to level-of-approximation approach

Reinforced concrete (RC) slabs without shear reinforcement are commonly used for existing bridge structures. For such structures, shear and punching can be the governing failure modes at the ultimate limit state if subjected to large concentrated loads. The aim of this study is to examine a structured approach for the analyses of the RC bridge deck slabs, which make up a considerable proportion of the currently used bridge decks. The method used for analyses is the levels‐of‐approximation introduced in fib Model Code for Concrete Structures 2010. The different levels include simplified calculation method, linear finite element analysis as well as non‐linear finite element analysis. The differences between analysis methods at different levels of analyses were discussed regarding one‐way shear and punching shear behavior of the slab

Multi-level assessment of a full-scale tested bridge deck slab

For reinforced concrete (RC) slabs without shear reinforcement, shear and punching can be the governing failure mode at the ultimate limit state if subjected to large concentrated loads. Shear and punching of RC slabs without shear reinforcement has been a challenging problem in assessment based on current standards. To examine a previously developed enhanced analysis approach, this study was conducted by applying a Multi-level Assessment Strategy to a 55-year old RC bridge deck slab subjected to concentrated loads near the main girder in a field failure test. The differences between analysis methods at different levels of assessment was discussed regarding one-way shear and punching shear behavior of the slab. The influences of parameters such as boundary conditions, location of concentrated loads and shear force distribution were investigated

Stock market and its future development's'in Latvia

Bakalaura darbā „Vērtspapīru tirgus un tā attīstības tendences Latvijā” ir izpētīti vērtspapīru tirgus funkcionēšanas teorētiskie aspekti, Latvijas vērtspapīru tirgus veidošanās un funkcionēšana, ir veikta Latvijas vērtspapīru tirgus attīstību ietekmējošo faktoru analīze, izvērtētas attīstības tendences, kā arī izstrādāti priekšlikumi vērtspapīru tirgus turpmākai attīstībai. Darba izstrādē pielietotas ekonomiskās un ekonometriskās analīzes, datu grupēšanas, grafiskās attēlošanas un salīdzināšanas metodes. Bakalaura darba apjoms ir 81 lappuse, ir ievietotas 12 tabulas, 8 attēli, 4 pielikumi. Darba izstrādē ir izmantoti 16 literatūras avoti un 15 interneta resursi.Stock market and its future development in Latvia is bachelor’s research which is focused on theoretical studies of stock market, its development and operation in Latvia. The major factors and trends, which affects the development of stock market in Latvia are explored and analysed, suggestions for its further development are drawn up in this paper. Economic and econometric analysis, data grouping, graphs and comparison of facts are the main methods used in the study. The paper contains 82 pages, 12 tables, 8 graphs, 4 attachments. There are 16 literar resources an 15 Internet resources used in the research