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Concrete In Australia : June 2014
Concrete in Australia Vol 40 No 2 33 As discussed in Ref. 5, the top flange of the idealised cross section (ie the cross section shown in Figure 3) may be disregarded when a linear diagonal crack is assumed in the crack sliding analysis. This simplified procedure has been shown to give good agreement between tested and calculated shear capacity (Hoang, 1997). In reality, the diagonal crack which suffers sliding failure does not propagate all the way through to the compression flange. The failure is more complicated and involves crack sliding in the web and a kind of membrane action in the compression flange. The area and the distance from the top face to the centre of gravity of the effective cross section may be calculated as follows: , uf uw cefntbhb At (10) ()() () 2 11 22 fu u w u fuw u bth t bht btbht e − + − = + − (11) where n is the total number of voids in the hollow core cross section. 4.0 ROTATION FAILURE Figure 6: Rotation failure with pull out of strands. As pointed out in Ref. 5, the capacity calculated by the Crack Sliding Model must be supplemented with an analysis of a rotational mechanism, where diagonal cracking immediately leads to pull out of the strands. Indications of this type of failure can be seen in photos of reported test specimens, see eg Ref. 16. In this context, the most dangerous crack will be a diagonal crack that emerges from the edge of the support plate. Once this crack is developed, pull out of strands may be assumed to take place due to poor anchorage of the strands. The reason is an unfortunate combination of the bond slip length, l slip at the end of the element and the relatively small support width s, (in practice in the order of 65–85 mm). The mechanism is shown in Figure 6, where the final failure simply is a rotation of part I relative to part II. By setting up the work equation for the mechanism, the following expression for the load carrying capacity is obtained: 2 1 ,() 1 2 sr uR tef c ex d F hhh Vx fA xs hh (12) Similar to the calculation of the cracking load above, it is also assumed here that the normal stress distribution along the crack is constant and equals ftef . To distinguish from the crack sliding analysis described above, the projection of the diagonal crack is here denoted as x* and the index is now changed to “u,R”. Further, F sr is here the prestressing force at the point where the crack crosses the strands. As an approximation, F sr may be estimated as follows, independent of the value of x*: Fsr 0, s+(h−d)<lslip Fse s+(h−d)−l slip lt , s+(h−d)≥lslip ⎧ ⎨ ⎪⎪⎪ ⎩ ⎪⎪⎪ (13) Formula (12) displays a minimum at x* given by: 2 * 11 1 42 sr tef c F xs ds hhf A eh (14) When formula (12) leads to a load carrying capacity lower than that determined from a crack sliding analysis, the rotation failure will be governing. This failure is especially critical for highly prestressed slabs and/or for slabs with small shear span to depth ratio. The rotation failure, which essentially is an anchorage failure, has of course been treated in a very simplified manner here. In reality, there are also other effects, eg the effect of the support pressure on the anchorage capacity of the strands. It should be noticed that the rotation failure, as observed in tests (see Ref. 16), actually involves a straight diagonal crack running all the way to the top face. Therefore, when calculating the load carrying capacity from Eq. (12), the full area, A c of the idealised cross section may be used. Naturally, in this equation, e should then be understood as the distance from the top face to the centre of gravity of the full idealised cross section. Comparison with test results 257 test results selected from eight series have been used to evaluate the calculation procedure presented in this paper. Table 1 shows an overview of the selected tests and Table 2 gives the range of geometrical and mechanical parameters for each of the eight series. The 257 test results are, to the best knowledge of the authors, the largest collection of data that has been used to evaluate a calculation model for hollow core slabs. 159 test results (from the series: TUE, CBR, TUD and DSB) were already considered in the original treatment of the subject, Hoang (1997). The remaining tests are more recent and have also been analysed by Bertagnoli and Mancini (2009). Detailed information regarding the test series may be found in the background document to this paper (see Jørgensen, 2014). Note, however, the following: 30-36 - Hoang.indd 33 30-36 - Hoang.indd 33 22/05/14 11:53 AM 22/05/14 11:53 AM