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Concrete In Australia : December 2013
52 Concrete in Australia Vol 39 No 4 DISCUSSION PAPER Author’s response to discussion Colin Gurley, teacher of civil engineering at TAFE NSW Sydney Institute in Ultimo, responds to discussion on his technical note: Shear in simply-supported reinforced concrete beams, Concrete in Australia, Vol 39, Issue 2, June 2013. The author here responds to detailed discussion from Bill Boyce of Queensland and from Anthony Bayadi, NSW CAD manager, Aurecon Sydney. There were also personal communications from Danish friends: Mikael Braestrup of Ramboll and Bjarne Christian Jensen, E/Prof at the University of Southern Denmark, Odense. There was a personal communication from a distinguished New Zealand engineer. There was a CIA NSW seminar on “Shear in Concrete” on 23 October 2013, at which this author was one of three speakers. Finally, there was lengthy discussion from David Herbert of Sydney and Bathurst in which he sets out some detailed calculations using the S&T (strut and tie) method. This note will try to draw together these sources and issues arising from the discussion, personal communications and the seminar. There seems no doubt that the approach proposed is valid and proper. It has been published by ICE London in their magazine Concrete Research. The present purpose is to boil it down to a simple procedure for teaching. Braestrup said: “I have no problems with your analysis – that seems OK.” Jensen said: “I have read your limitations and speculations (see below) and I do not have any comments except that the method you are using is a lower-bound solution. The distribution of forces is inspired by a possible failure mechanism. You ensure equilibrium of the forces and the capacity to resist the forces – purely a lower-bound solution. The method has been used in Danish codes since 1984 – I was in the code committee introducing the method in the codes.” As one remembers, Jensen is, or was, also the Danish representative on the Eurocode 2 committee. The New Zealand comment seems to seek better calibration with experimental results and this author would support and co-operate with that although he is not in a position to do it himself. To enter into a detailed conversation with David Herbert’s discussion would lead us too far astray. The S&T method is a plastic solely lower-bound approach originating in Stuttgart and Zurich. It would be proper to make a detailed comparison of the outcomes (just how much shear reinforcement?) from the S&T method and from this author’s method, although the results from the S&T method are subject to more arbitrary guesses that S&T analysts have to make in order to proceed. This author’s method does not require arbitrary guesses as to the location of truss nodes and the size and location of members that join them. Some notes on the history of structural plasticity are below. Response to discussion from Bill Boyce Boyce has had a distinguished career both as an academic engineer and also as principal structural engineer, Queensland and Papua New Guinea (PNG), for Cameron – MacNamara/ Kinhill/KBR Engineers. Yes, the author does have in mind that this is the first of a series. He thanks Bill for the comments on his second paragraph. The author’s problem, at the moment, is to find a 2D (not 3D) drawing package simple enough for one too old to be CAD literate. He is exporting TIFFs and running on an Apple computer. Suggestions are welcome! Boyce and Braestrup of Ramboll both raise different aspects of an issue that the author mentioned but did overlook some of the consequences. The practice of capacity design has been around in New Zealand and Californian structural practice for more than 40 years and, of course, PNG has used New Zealand codes because of the higher earthquake risk. Nevertheless, capacity design is relevant to the design of buildings anywhere that are robust and ductile, and perform well under any form of abnormal event by limiting the extent of failure and collapse. This includes, for example, as they would have done at the Oklahoma City bombing in 1995 or the recent gravity load collapse in Bangladesh. One of the first principles of capacity design is that shear failure should be prevented (because it is frequently brittle). The term capacity design means that the shear reinforcement should be sufficient to carry the capacity loads corresponding to bending failure. The implication is that φ wu > w* where wu is determined from a normal collapse mechanism with a normal/ conventional Whitney plane-section hinge at mid-span and slightly modified dogleg hinges at continuous ends. Then wu takes over the role of w* in design for shear. This is the issue that Boyce describes in his third paragraph, with which I agree, but there are other implications. There is usually a margin for safety against yield of the shear reinforcement by assuming that the main rebar, at yield, is about 30% over-strength (includes strain-hardening). New Zealand and maybe Californian/ACI codes have maximum limits on the yield-strength of the main rebar. Braestrup points out that the method of the paper implies that shear strength depends only slightly on concrete cylinder strength, in that that cylinder strength affects only the depth of the bending compression stress-block. Braestrup is correct. The method proposed definitely neglects the tensile strength of concrete, but we do know that the tensile strength of concrete is sometimes proportional to the square root of the compressive strength (except zero at cracks) perhaps reducing as the content of shear-reinforcement is increased. AS3600 has assumed that bending strength and shear strength were quite separate and unrelated. This is not true. But this author has been thinking only of the design of new buildings and of an approach that would tend to make new buildings more robust. AS3600 also has to address existing buildings, which may sometimes have quite low contents of shear reinforcement and cases of zero shear reinforcement, such 49-56 - Discussion.indd 52 49-56 - Discussion.indd 52 25/11/13 4:15 PM 25/11/13 4:15 PM