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Concrete In Australia : December 2013
Concrete in Australia Vol 39 No 4 55 X say, 350 deep that are not reinforced for shear. The author does not agree with AS3600 c8.2.5(a) which permits beams up to 750 deep without shear reinforcement if the nominal shear stress: is small, say < 0.35 MPa. The implication of the second limitation is that the author is in pursuit of a usable general yield-line method for in-plane (plane-stress) problems. The basic theory for this has already been covered by Nielsen 2010 in his excellent 900-page book now in its 3rd edition. What remains is to achieve a library of solved problems similar to that provided some decades ago by Johansen for yield-line theory for slabs loaded perpendicular to their own plane. This definitely includes all of that material that would otherwise be addressed by AS3600 s7 STRUT-AND-TIE MODELLING and s12 DESIGN OF NON-FLEXURAL MEMBERS, END ZONES AND BEARING SURFACES. A significant difference is that the S&T method seems to require special computer software whereas this author’s yield-line solutions can be done with a calculator and pencil on the back of an envelope (alternatively, in Microsoft Excel). But there are more subtle points to be made. The author has spent most of his career as a structural designer in consulting offices, including 10 years in New Zealand running a branch office. He has never been a full-time academic engineer (except Auckland 1979) and he has never had access to a structural research laboratory. Instead, he is left to think about how things work and how they fail. Perhaps this has been some sort of advantage? The author is familiar with the New Zealand/Californian system for capacity design as it was up to the mid-1980s. The aim is to create buildings that are more ductile and robust, and localize the extent of collapse, for example, in earthquakes but also in any abnormal event. The Chicago-based ASCE expert committee for the 1995 Oklahoma City bombing found that the extent of damage could have been reduced by 80%, perhaps similarly reducing the 100% death-toll of 167 – all this at an extra cost of about 1% to 2% of the total building cost. This is indeed the point of capacity design (Gurley, 2012). One of the features of capacity design is the notion that beams can be reinforced in shear sufficiently, and at reasonable cost, to prevent yielding of the shear reinforcement and enforce yield only of the main bending rebar under all relevant mechanisms. This does seem to be true and it would suit the present purpose in that one could then, for new buildings at least, avoid the complications of diagonal struts that fail in compression across yield-lines. The compressive strength of such yield-lines is different to (less than, often much less than) the strength of bending compression yield-lines and may be related to the principal tensile strain that will be larger than the principal compressive strain (Gurley, 2011a; b). And what about hyperbolic yield-lines as described by Peter Mueller of Lehigh, Peter Marti of Zurich and Braestrup since the late 1970s? Such yield lines would tend to be prevented by capacity design. This will make a designer’s life significantly easier. The author has been thinking solely of the design of new buildings to be ductile and robust as he understands that objective. There are, of course, honest differences between different structural designers and different firms. The author does make an effort to explain this to his students, to clarify ideas that may seem contentious and to suggest that they need to listen carefully to the instructions of their employer. Writing a code of practice like AS3600 is a more difficult process. Code-writing has to consider, for example, the alteration of existing buildings and the professional judgment of design engineers each of whom will have their own approach. It would be useful to review and calibrate the proposed approach against accumulated experimental data. The author is not equipped to do that but he would co-operate with anyone who is. Clearly, anchorage of the main bending rebar and the amount of shear reinforcement are not separable issues. If one could replace the bending rebar with the same area of larger rebars, then the anchorage length would increase and so too would the required area (mm2/m) of shear reinforcement under the proposed approach. Maybe a local bond is also/alternatively involved. Local bond was deleted from most codes of practice about the mid-1970s. Perhaps the same could be said of local horizontal shear stresses as well. All of these are related to the transfer of the horizontal component of arch thrust to the main bending rebar. References Gurley, C.R ., 2011a. Upper bounds, lower bounds and “exact” yield-line design: structural concrete in plane stress. Magazine of Concrete Research doi: 10.1680/macr.9 .00198 Paper 900198. ICE London. Gurley, C.R ., 2011b. Analysis of core coupling-beams in tall buildings. Magazine of Concrete Research doi: 10.1680/ macr.9 .00199 Paper 900199 ICE London. Gurley, C.R . 2012 . Structural Design of Robust Buildings for Extreme Events. Australian Earthquake Engineering Society 2012 Conference, Dec 7-9, Tweed Heads. www.aees.org. au/ Nielsen M.P. and Hoang, Linh, 2010. Limit Analysis and Concrete Plasticity. CRC Press, 2010, 928 pages. What next ... After the next paper on continuous beams? Figure 1 shows the panel zone failure (US terminology) of a beam-column joint in a building subject to major horizontal loads: wind, earthquake or any sort of explosion. NZS3101 and ACI318 may require quite heavy horizontal ties in the joint area. Engineers familiar with earthquake damage will note some similarity. But these horizontal ties will be at about 45° to the yield-lines and perhaps, rather less effective. Figure 2 shows a suggestion for ‘X ’ and ‘T ’ (trimmer) rebars diagonally through the joint area. Nobody seems to have tested this, presumably because nobody thought of the mechanism of Figure 1 before. There is an anchorage problem with the X-bars. At the CIA NSW Seminar at North Sydney 23 October 2013, Rod McKay- Sim of Hillside Engineering, Sydney suggested headed shear 49-56 - Discussion.indd 55 49-56 - Discussion.indd 55 25/11/13 4:15 PM 25/11/13 4:15 PM