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Figure 6.15. Calculation of contribution Vp from prestressing to the shear resistance according to Hedman and Losberg (1978) However, this method works well for the evaluation of laboratory tests but is less suitable for real

Figure 6.15. Calculation of contribution Vp from prestressing to the shear resistance according to Hedman and Losberg (1978) However, this method works well for the evaluation of laboratory tests but is less suitable for real members mostly subjected to uniformly distributed loading. A solution is to replace M0/a by M0/(Mx/Vx), where Mx and Vx are the bending moment and the shear force in the section considered. However, this would complicate the shear design because then Vp would be different in any cross-section.

Another disadvantage is that Vp would go to infinity in a moment inflexion point, where Mx = 0. It can simply be derived that for a rectangular cross-section with a width b, a height h and an eccentricity of the prestressing force ep, the contribution Vp to the shear resistance is

Assuming d = 0,85h this would result in;

In most tests on shear critical beams the ratio ep/h is about 0,35. With a/d varying between 2,5 and 4,0, like in most shear tests, this would mean that Vp would vary between 0,15tfcpb d and 0,25tfcpb d. Evaluating test results it is therefore not amazing that the coefficient 0,15 turns out to be a safe lower bound in shear critical regions.

Nielsen (1990) compared the shear equation in ENV 1992-1-1 which gives about the same results as Eq. 6.2a in prEN 1992-1-1:2001 for moderate concrete strengths, with 287 test results and found that it was at the safe side.

The effect of longitudinal compression should, of course, not be mixed up with the effect of the cable curvature, which exerts a favourable transverse load on the member. This effect, known as the load balancing effect, is introduced as a load (load balancing principle).

For axial tension in prEN 1992-1-1 the same formula is used, with a different sign for 0,15tfcp, so that an axial tensile force gives rise to a slight reduction of the shear capacity. It should be noted that in continuous beams there is tension in both top and bottom and excessive curtailment at sections of contra flexure may lead to diagonal cracking and shear failure in such a region. This was the main cause of failure in an actual structure [Hognestadt and Elstner, 1957]. If a structural member is well designed for axial tension the shear capacity of the members is hardly reduced. This was for instance shown by Regan [Regan, 1971 and 1999] who carried out a systematic investigation into the effect of an axial tensile force on the shear capacity of both members unreinforced and reinforced for shear. Tests have been carried out according to the principle shown in Fig. 6.16. Beams with a rectangular cross-section were provided with nibs, enabling the transmission of an axial tensile force in the middle part. The axial tensile force varied between 0 and 130 kN. The force could be applied in two ways: before subjecting the member to transverse loading, or in proportion to the transverse loading. In both cases the shear capacity was hardly influenced, although the member sometimes showed wide open cracks across the total cross section in the moment inflexion region.

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