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Concrete In Australia : June 2013
20 Concrete in Australia Vol 39 No 2 TECHNICAL NOTE assumption that the bottom rebar can anchor a force of T2 = 737kNoveratotallengthh0 +h1=300+482=782mm finishing directly below the first hinge rotation-centre. ere is a second half-arch which adds to a horizontal force: C2 =454kN+283kN=737kNatthe secondbending- compression yield-line. e moment strength across hinge 2 is: M2 = 737 * 0.510 = 376 kNm and the moment increment: dM21=M2--M1=376--153=223kNm. eshearV2 =V1-wb*h1=391-156*0.482=316kN. e lever-arm of the vertical shear forces is now: h21 = dM21 V1 = 223000 316 = 708 mm and, since h21=h2+h1 2 is the averaged projected length of hinges 1 and 2, the projected length of hinge 2 is now: h2 = 2*h21 -- h1 =2*708--482=934mm. Shear-reinforcement is required for a reliable smeared ideal yield-strength of rfy2 = V2 bw *h2 = 316000 350 * 934 0.967 MPa. is requires N10 stirrups (three vertical legs) at spacing: s2 = Asv*fsy*φv bw * rfy2 = 236*500*0.70 350 * 0.967 = 244 mm. 10.0 USE N10-240 (THREE VERTICAL LEGS) 10.1 Third segment Figure 6 shows the final segment with a third half-arch. Note that the mid-span bending-compression block has now been partitioned into three segments which balance the three half- arches but also provide the normal Whitney (1940) mid-span plane-section perpendicular hinge. Shear reinforcement: rfy 3 = 169 *1000 350*1084 =0.445 MPa s3 = 2*78.5*500*0.70 350 * 0.445 = 353 11.0 USE N10-350 (TWO VERTICAL LEGS) FOR LENGTH h3 11.1 The complete half-beam Figure 7 assembles the half-span from the previous part- solutions. ere are three bending hinges: one ordinary plane perpendicular Whitney (1940) bending hinge at mid-span and the other two as anchorage-limited dogleg hinges each side of the first tooth. Between these hinges, there are three half- arches one of which is complete with symmetry. ese half- arches are supported by the mid-span bending-compression yield block partitioned into three parts. e calculated values of rfy are shown for each of the three zones: h1, h2 and h3. e width of each distinct zone will need, at least, to be rounded up so as to provide a whole number of tie-set spaces in each zone. Figure 6. Third segment. Figure 7. Complete half-beam.