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Concrete In Australia : June 2013
Concrete in Australia Vol 39 No 2 17 TECHNICAL NOTE Shear in simply-supported reinforced concrete beams Colin Gurley -- Teacher of Civil Engineering, TAFE NSW Sydney Institute, Ultimo 1.0 INTRODUCTION is note describes the writer s method for the design of vertical shear reinforcement in simply-supported beams. e method can be used for the design of simply-supported ends of beams that are elsewhere continuous over several spans. A further note on supports at which the beam is continuous will appear later. is author came to teach at TAFE NSW s Sydney Institute, Ultimo after some decades practising as a structural designer. As a teacher of civil engineering, this author believes structural concrete design can be directly related to the simple conditions of static equilibrium and that it should be. Simple-supports are common in small buildings supported on load-bearing unreinforced brickwork. is occurs in Australia and in other countries, rightly or wrongly, with not much concern about earthquake risk. e assumption of a simple- support at or near the centre of a brick pier will err on the safe side so far as the concrete beam is concerned, and also one hopes, so far as the pier is concerned. See AS3700. 2.0 EXAMPLE: SIMPLY SUPPORTED BEAM AND RELIABILITY FACTORS (φ) Figure 1 shows a 602 mm deep by 350 mm wide beam with a clear-span of 5000 mm as an example. e supporting brick pier is 350 mm square. Cylinder strength: fc = 25 MPa. All 5N24 bottom rebars are assumed stopped at 50 mm end- cover, including an allowance for tolerance in cutting to exact length. N24 is the largest bar that will meet the requirement of AS3600:2009 c22.214.171.124 for 12*db minimum straight anchorage past the face of the 350 mm pier. e mid-span plastic hinge moment capacity Mu and the distributed load capacity wu are "ideal" values corresponding to φ =1. If collapse is indeed solely in bending, then the appropriate reliability factor will be φ M = 0.80 and the reliable values, φMu > M* and φM wu > w* (w* = factored design load) will both be 80% of ideal values. Collapse can be solely in bending. Indeed, the writer suggests that the shear reinforcement be calculated so as to force failure solely in bending regardless of any excess reliable bending strength φ MMu > M* required by the factored loads w*. is is usual practice in New Zealand and California, where it is part of a system intended to produce buildings that are much more robust under abnormal events at, one hopes, a small extra cost. is will be covered in a later note. Shear failures are much more brittle than solely-bending failures. 3.0 ANCHORAGE LENGTH e anchorage length for full yield-strength is here assumed to be 50*db = 1200 mm for N24 rebars. is value is safer than that now in AS3600:2009, but the author does not want to change the calculations, originally done in early-2009, because that would require redraw of the figures. AS3600:2009 c126.96.36.199 is explicit that the force developed along a length shorter than full anchorage be considered proportional to the actual length available from the point concerned. e actual length of rebar over the pier is h0 = 300 mm, or one-quarter of a full anchorage length, so the force available in the rebars at the span face of the pier is 25% of the full yield strength:T1=25%*5*452*500MPa=283kN. 4.0 TYPICAL COMBINED-COLLAPSE MECHANISM Figure 2 shows a typical "dogleg" mechanism with symmetric "dogleg" hinges, similar to that in the 1978 Danish literature by Nielsen et al (1978). is mechanism is obviously appropriate if some proportion of the main bottom rebars is stopped at dimension x. It is Figure 1. 602 mm deep by 350 mm wide beam clear-span of 5000 mm.