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Concrete In Australia : December 2013
Concrete in Australia Vol 39 No 4 49 The following letters are in response to a technical note published in the last issue: Shear in simply-supported reinforced concrete beams, by Colin Gurley, Concrete in Australia Volume 39, Issue 2, June 2013 (pp 17-23). Further explanation for clarity The author is to be commended for his efforts over many years (decades) to encourage structural designers to think more carefully about building robustness into their structures by careful detailing and capacity design. This technical note, presumably the first of a series, deals with the shear design of a simply-supported beam carrying a uniformly distributed load, using an “exact” yield-line solution developed by the author. The method is straightforward and logical, and lends itself to programming in Excel. It might have been helpful to have an explanatory second paragraph in section 2.0 to indicate where the beam came from. This could be along the lines of: “The beam carries an ultimate design load w* of 125 kN/m, producing a mid-span bending moment M* of 439 kN.m . This moment is carried by 5/N24 bottom bars. To ensure that bending failure occurs in preference to shear failure, shear stirrups will be designed to carry a load wu equal to 156 kN/m – the load that produces a central moment equal to Mu.” In section 3.0, the anchorage length has been chosen as 1200 mm rather than the basic development length of 1111 mm in accordance with AS3600-2009. When 1111 mm is used, the spacing of stirrups increases to 114 mm for the first segment rather than 102 mm calculated in section 7.0 . The writer believes that a strength reduction factor of 0.8, rather than 0.7 for shear, would be more appropriate in this setting, which is more akin to steel in tension of a strut-and-tie analysis (AS3600 Table 2.2 .4). This, along with 1111 mm as the development length, would open up the stirrup spacing to 131 mm over a length of 540 mm – a more palatable figure. The calculated stirrup spacing in the second segment becomes 368 mm over a length of 1195 mm (3/N10 legs) and in the third segment is 399 mm (2/N10 legs). Incidentally, AS3600-2009 cl 13.1 .2.4 is a better reference to proportionality because it relates to bars in tension – the relevant situation for this beam. Use of a truss analogy with the end struts inclined at an angle to match the tension capacity of the 300 mm anchorage of the bottom bars produces similar stirrup spacing in the end regions: 136 mm with phi equal to 0.8 compared with 131 mm above. The author hints at only a small extra cost to achieve more robustness under abnormal events. Using the author’s method, but with a development length of 1111 mm, phi equal to 0.8 and load w* of 125 kN/m, a stirrup spacing of 227 mm is required in the end region compared with 131mm. For example, with practical spacing of 220 mm and 130 mm over a length of about 660 mm, this converts to six stirrups rather than four, i.e. two additional stirrups at each end – not a high price to pay for a large additional benefit. Use of a more disciplined and consistent terminology would assist the reader. All of the following appear: First hinge, First hanger segment, First fragment & first hinge, Hinge 1, First segment, First dogleg hinge; Second hanger segment = first tooth, Second hinge and first tooth, Hinge 2; Third segment; and Dogleg yield hinge. W H Boyce, FIEAust In over their heads I have passed around your paper to fellow staff and we agree, for the apprentice drafters enrolling in the structural or civil engineering courses we believe that this content is going to be too technical for the students who attend. This sort of information is more suitable for university students who would have a better understanding of and appreciate the complexity of designing a beam. It is the main reason why this should not be included in the course and why engineering firms have apprentices attend TAFE and not university. The last thing we all want is for our apprentices to struggle through the courses. Also, if I’m not mistaken, they have something similar in the syllabus that is more suited to apprentices and technical students. Anthony Bayadi, NSW CAD Manager, Aurecon For loads at the top of the beam May I thank Colin Gurley for drawing my attention to his treatment of shear in reinforced concrete (RC) beams. In the following discussion I have reverted to consideration of loads applied at the top of the beam, the most common if not the most critical situation. I have also used an alternative notation where S = the yield capacity of vertical shear reo per metre. That is, if shear reo is provided such that Asv/s=Vutanθ/dfy S=Asvfy/s=Vutanθ/d where θ is the inclination of the compression struts, and is measured from the intersect point of the forces above the reaction in Colin’s Figure 4 to the centre of the compression block; not along the dotted line. This touches on the node detailing at this point in the strut-tie model, which will also define the point at which the anchorage must have taken place (assumed in Colin’s example to be the face of the support). I have also ignored strength reduction (φ) factors since the intention is to demonstrate behaviour, not provide design rules. Colin’s paper looks at the support condition initially, and allows θ to be determined by the anchorage force developed at the bearing face. This, in his example, has increased θ compared with the value that would apply were a higher anchorage force chosen, and provided for (e.g . by anchor plates as per cl. DISCUSSION PAPER 49-56 - Discussion.indd 49 49-56 - Discussion.indd 49 25/11/13 4:15 PM 25/11/13 4:15 PM