Simulating reinforced concrete members. Part 2: displacement-based analyses

A companion paper described the partial-interaction localised properties that require the development of pseudo properties. If the quantification through experimental testing of these pseudo properties could be removed by the use of mechanics-based models, which is the subject of this paper, then this would: (a) substantially reduce the cost of developing new reinforced concrete products by reducing the amount of testing; (b) increase the accuracy of designing existing and novel reinforced concrete members and structures, bearing in mind that experimentally derived pseudo properties are only applicable within the range of the testing from which they were derived; and (c) reduce the cost and increase the accuracy of developing reinforced concrete design rules. This paper deals with the development of pseudo properties and behaviours directly through mechanics, as opposed to experimental testing, and their incorporation into member global simulations. It also addresses the need for a fundamental shift to displacement-based analyses as opposed to strain-based analyses.Deric J. Oehlers, Phillip Visintin, Jian-Fei Chen and Tim J. Ibel

Worldwide trends in body-mass index, underweight, overweight, and obesity from 1975 to 2016: a pooled analysis of 2416 population-based measurement studies in 128·9 million children, adolescents, and adults.

BACKGROUND: Underweight, overweight, and obesity in childhood and adolescence are associated with adverse health consequences throughout the life-course. Our aim was to estimate worldwide trends in mean body-mass index (BMI) and a comprehensive set of BMI categories that cover underweight to obesity in children and adolescents, and to compare trends with those of adults. METHODS: We pooled 2416 population-based studies with measurements of height and weight on 128·9 million participants aged 5 years and older, including 31·5 million aged 5-19 years. We used a Bayesian hierarchical model to estimate trends from 1975 to 2016 in 200 countries for mean BMI and for prevalence of BMI in the following categories for children and adolescents aged 5-19 years: more than 2 SD below the median of the WHO growth reference for children and adolescents (referred to as moderate and severe underweight hereafter), 2 SD to more than 1 SD below the median (mild underweight), 1 SD below the median to 1 SD above the median (healthy weight), more than 1 SD to 2 SD above the median (overweight but not obese), and more than 2 SD above the median (obesity). FINDINGS: Regional change in age-standardised mean BMI in girls from 1975 to 2016 ranged from virtually no change (-0·01 kg/m2 per decade; 95% credible interval -0·42 to 0·39, posterior probability [PP] of the observed decrease being a true decrease=0·5098) in eastern Europe to an increase of 1·00 kg/m2 per decade (0·69-1·35, PP>0·9999) in central Latin America and an increase of 0·95 kg/m2 per decade (0·64-1·25, PP>0·9999) in Polynesia and Micronesia. The range for boys was from a non-significant increase of 0·09 kg/m2 per decade (-0·33 to 0·49, PP=0·6926) in eastern Europe to an increase of 0·77 kg/m2 per decade (0·50-1·06, PP>0·9999) in Polynesia and Micronesia. Trends in mean BMI have recently flattened in northwestern Europe and the high-income English-speaking and Asia-Pacific regions for both sexes, southwestern Europe for boys, and central and Andean Latin America for girls. By contrast, the rise in BMI has accelerated in east and south Asia for both sexes, and southeast Asia for boys. Global age-standardised prevalence of obesity increased from 0·7% (0·4-1·2) in 1975 to 5·6% (4·8-6·5) in 2016 in girls, and from 0·9% (0·5-1·3) in 1975 to 7·8% (6·7-9·1) in 2016 in boys; the prevalence of moderate and severe underweight decreased from 9·2% (6·0-12·9) in 1975 to 8·4% (6·8-10·1) in 2016 in girls and from 14·8% (10·4-19·5) in 1975 to 12·4% (10·3-14·5) in 2016 in boys. Prevalence of moderate and severe underweight was highest in India, at 22·7% (16·7-29·6) among girls and 30·7% (23·5-38·0) among boys. Prevalence of obesity was more than 30% in girls in Nauru, the Cook Islands, and Palau; and boys in the Cook Islands, Nauru, Palau, Niue, and American Samoa in 2016. Prevalence of obesity was about 20% or more in several countries in Polynesia and Micronesia, the Middle East and north Africa, the Caribbean, and the USA. In 2016, 75 (44-117) million girls and 117 (70-178) million boys worldwide were moderately or severely underweight. In the same year, 50 (24-89) million girls and 74 (39-125) million boys worldwide were obese. INTERPRETATION: The rising trends in children's and adolescents' BMI have plateaued in many high-income countries, albeit at high levels, but have accelerated in parts of Asia, with trends no longer correlated with those of adults. FUNDING: Wellcome Trust, AstraZeneca Young Health Programme

Computing Redistribution Moments of Concrete Members in the Plastic Stage Using Linear Analysis: Short Review

Reinforced concrete members can utilize their load carrying capacity by the redistribution of moments. When sufficient rotation takes place in a reinforced concrete member a plastic hinge forms and the rotational capacity of this hinge determines the amount of redistribution that can occur in the member. Reinforced concrete exhibits different behaviours (elastic, elastoplastic and plastic) at different instances of load and this informs the different approaches in the analysis of reinforced concrete members. Of the different methods of anal- ysis, linear elastic analysis with moment redistribution is the most used method in practice. Various studies on moment redistribution in reinforced concrete beams, hinge formation, linear analysis and code provisions have been reviewed, discussed and key findings have been presented in this study. A continuous beam was also analysed using linear elastic analysis and a moment redistribution of 20% from support to the beam spans was considered. The beam was also analysed considering the various loading combinations that gave the maximum effects at different beam segments

A mechanics solution for hinges in RC beams with multiple cracks

The formation of hinges in reinforced concrete beams is important as hinges influence the ability of the beam and, subsequently, the frame to absorb energy and resist extreme loads such as hurricane or seismic loads. A common approach for quantifying the rotational capacity of beams at the ultimate limit is to use a strain based moment-curvature analysis combined with an empirical hinge length to determine the rotation capacity of the member. Being empirically based, this approach is very restrictive as it can only be applied within the bounds of the tests from which they were derived. In this paper, a mechanics displacement based hinge approach is described that can simulate the formation of cracks, the discrete rotation at each individual crack and the formation of wedges. Being mechanics based, this hinge model can be applied to any type of reinforced concrete, such as those with brittle reinforcement and also to all strengths of concrete. This mechanics based model is shown to have good agreement with test results and can be used at all stages of loading from serviceability to failure. Furthermore, it can also used to develop closed form solutions that do not require the moment-curvature assumption of full interaction but specifically allow for partial interaction that is slip between the reinforcement and the concrete. © 2011 Elsevier Ltd

Simulating reinforced concrete members. Part 1: partial interaction properties

Reinforced concrete members are extremely complex under loading because of localised deformations in the concrete (cracks, sliding planes) and between the reinforcement and concrete (slip). An ideal model for simulating behaviour of reinforced concrete members should incorporate both global behaviour and the localised behaviours that are seen and measured in practice; these localised behaviours directly affect the global behaviour. Most commonly used models do not directly simulate these localised behaviours that can be seen or measured in real members; instead, they overcome these limitations by using empirically or semi-empirically derived strain-based pseudo properties such as the use of effective flexural rigidities for deflection; plastic hinge lengths for strength and ductility; and energy-based approaches for both concrete softening in compression and concrete softening after tensile cracking to allow for tension stiffening. Most reinforced concrete member experimental testing is associated with deriving these pseudo properties for use in design and analysis, and this component of development is thus costly. The aim of the present research is to reduce this cost substantially. In this paper, localised material behaviours and the mechanisms they induce are described. Their incorporation into reinforced concrete member behaviour without the need for empirically derived pseudo properties is described in a companion paperDeric J. Oehlers, Phillip Visintin, Jian-Fei Chen and Tim J. Ibel

Closed-form expressions for predicting moment redistribution in reinforced concrete beams with application to conventional concrete and ultrahigh performance fiber reinforced concrete

Publication Date : 2020-03-27The redistribution of moment within a statically indeterminate reinforced concrete beam at the ultimate limit state occurs through variations in the flexural rigidities and through the formation of hinges. The phenomena of moment redistribution (MR) is used to increase the efficiency of reinforced concrete design by allowing moments to be transferred away from critical cross sections thereby resulting in lower design moments. To allow for this effect in design, two main approaches are adopted. The first is to perform an elastic analysis and then to adjust the resulting distribution of moment using a codified MR factor. The second is to apply a plastic analysis allowing for the formation of hinges, and to calculate the rotational requirements at the hinges from first principles. This paper uses fundamental plastic analyses to derive closed‐form expressions for the hinge rotational requirements for full MR (that required to achieve the theoretical maximum applied load within the beam based on the moment capacity of sections within the beam). These closed‐form solutions are then used to quantify the maximum load on a beam when the rotational capacities at a hinge are less than the rotational requirements for full MR (partial MR). Closed‐form solutions are then used to derive MR factors which do not require semimechanical calibration.Alexander B. Sturm, Phillip Visintin, Deric J. Oehler