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Concrete In Australia : June 2012
4 Concrete in Australia Vol 38 No 2 Overseas publication by Ken Day It may be of interest to some readers that a Chinese language translation of the 3rd edition of my book Concrete Mix Design, Quality Control and Specification (T&F) has just been released by the China Building Materials Industry Press. e request for permission to publish came "out of the blue" and was a surprise, and of course a pleasure, to me. It may be of particular interest to anyone hoping to offer services in China to build on the modest start, 20+ years ago, of using my Conad mix design and QC program there. At age 81, I will not personally be trying to follow this up and anyone wishing to do so is welcome, but should bear in mind that the full Conad system is now owned by Command Alkon and retitled "CommandQC", so that only the limited free program "Ken sQC" on my website (www.kenday.id.au) (and in the Chinese translation) is available free of charge. Incidentally, since I have no knowledge of Chinese, if any reader of this is fluent in Chinese, I would be interested to provide one copy of the Chinese version free of charge in order to have his/her opinion as whether it is an accurate and useful translation. e book runs to 309 pages. Why plastic methods for structural concrete design? by Professor LG Hagsten -- Engineering College of Aarhus, Denmark & Professor LC Hoang -- University of Southern Denmark, Denmark e paper "Why plastic methods for structural concrete design?" in Concrete in Australia Vol 37 No 3 by Colin Gurley contains some interesting reflections on the use of plastic methods for the design of concrete structures. As former consulting engineers and now lecturers in structural concrete courses with emphasis on plastic theory, we would like to add a few comments to the paper. When advocating for the use of plasticity methods it is relevant to mention that the results of a plastic analysis can also provide useful information regarding the service behaviour, and not only as the author wrote: "Plastic methods seek only to calculate collapse strength ... ey are unable to provide any estimate of service load deflections ...". In continuous beams for example, at the service load level (where the structure usually is cracked) a substantial part of the moment redistribution has already taken place due to different flexural stiffness in regions with hogging moments and in regions with sagging moments (remember that for cracked sections, the flexural stiffness depends mainly on the amount of reinforcement bars stressed in tension). is means that the extent of moment redistribution from the cracked, elastic state to the ultimate state is not so large as one would think when comparing the plastic moment diagram with the elastic diagram for an uncracked structure. So, rather than using the "standard text book elastic moment diagrams" it might be more accurate to estimate crack widths and deflections on the basis of a moment diagram obtained simply by down-scaling the plastic moment diagram by the factor qs/qu, where qs and qu represent the service load and the ultimate load, respectively. is simple approach is quite common among experienced Danish engineers and its validity has been confirmed in a recent experimental study where 14 two-span continuous beams were tested to collapse (Hagsten, 2011). In these beams, the moment capacity at the intermediate support varied from 0.41 to 2.14 times the moment capacity at mid span. By measuring the reactions, the moment diagram at each loading stage could be determined. It turned out that at 60% of the measured collapse load (rough estimate of the service load level), most of the moment redistribution has already taken place. For beam BB06 with a moment capacity ratio of 0.41, the ratio between the hogging and sagging moment at 60% of the collapse load was measured to 0.55. For beam BB05 with moment capacity ratio of 2.14, the corresponding measurement was 1.78. For comparison, we note that an elastic calculation based on uncracked sections will give a ratio of 1.2 between the maximum hogging and the maximum sagging moment. So, if this elastic solution is used to estimate crack widths, one will overestimate the crack widths at the intermediate support for beam BB06 and also overestimate the crack widths at mid span for beam BB05. Such calculated crack widths would most probably keep designers not well- acquainted with plastic methods from adopting a plastic design! For plane stress problems, the type of stress field assumed in plastic analyses (for example, the diagonal compression field in beam shear) combined with energy principles can be used to estimate service behaviour. For example, this has been demonstrated by Christiansen (2000). Reference: Christiansen, MB, Serviceability limit state analysis of reinforced concrete structures, Department of Structural Engineering, Technical University of Denmark, PhD thesis, Report No. R-69, 2000. FIB Symposium: Concrete 21st Century Superhero. London. 2009. Hagsten, LG, Experimental Investigation of Moment Redistribution in Continuous Reinforced Concrete Beams, 2011.