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Concrete In Australia : June 2013
Concrete in Australia Vol 39 No 2 23 Denmark and, perhaps, the UK. Eurocode 2 and AS3600 are both clear that plastic design is permitted and, by implication that does include the use of "upper-bound" mechanisms. But those codes then go on to provide much more detail about "lower-bound" methods specifically the strut-and-tie (S&T) method. Perhaps there is an assumption that "upper-bound" mechanism methods are just too difficult. at may be true if the mechanism for the problem at hand is not known but, once it has been published, then the approach is very simple. e calculations of this note use simple static equilibrium to calculate shear reinforcement with a calculator and pencil. Of course, that can also be done in Microsoft Excel. Lower- bound methods require special computer software incorporating arbitrary restrictions such as the restriction that angles between struts and ties be not be less than 30°. It may be that the AS3600 Committee will consider that upper-bound collapse methods need to be recalibrated against experimental results perhaps leading to a change in the numeric value of the φ -factor for shear. is author would support that but his own priorities will be to widen the pool of solved problems so as to provide a library. Two examples from earlier issues of Concrete in Australia exemplify the width of plane-stress mechanisms problems solved or on the way: • Scott Rathie, then of Arup Brisbane, December 2008 described the detailed S&T computer analysis of a simple corbel. Figure A1 is a pencil-and-calculator lower-bound analysis of that same corbel. It is not at all arbitrary. e pencil-and-calculator upper-bound analyses that lead to this solution were published in MCR London 2011. One does need upper bound mechanism solutions to lead to successful lower-bound solutions which are then "exact". • A beam/column joint failing in the "panel-zone" (ACI terminology) under a major horizontal load: wind or earthquake was published in Concrete in Australia September 2012 Vol 38 Issue 3 Discussion. Note that this mechanism identifies a problem with Eurocode 2, Figure 9.1. e Eurocode figure seems to be thinking solely of gravity loads, but not wind or earthquake, where all/most of the end- moment needs to be transmitted to the column. e S&T civil engineering community seems to have turned its back on all of the rich information that can be provided by upper-bound collapse mechanism analyses. Why is that? Figure A1. A pencil-and-calculator lower-bound analysis of a corbel.