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200 400 600 800 1000 1200 Vu [kN]

200 400 600 800 1000 1200 Vu [kN]

100 200 300 400 500 600 V [kN]

Figure 6.29. a Strut rotation as measured in beams with normal strength concrete (Walraven, 1995) b.Strut rotation as measured in beams made of high strength concrete (Walraven, 1999)

Fig. 6.30 shows a verification of the combination of Eq. 6.19 and Eq. 6.20 with the limit cot 0 = 2.5 with test results from Sörensen (1974), Regan and Rezai-Jorabi (1987), Placas and Regan (1971), Leonhardt and Walther (1961), Kahn and Regan (1971), Moayer and Regan (1971), Hamadi and Regan (1980), Muhidin and Regan (1977), Levi and Marro (1993) and Walraven (1999).

_ Vj / b^z fd f^kifrirrfiit T .ind I sfitflürv; 3 - 0 &

Fig. 6.30 shows a verification of the combination of Eq. 6.19 and Eq. 6.20 with the limit cot 0 = 2.5 with test results from Sörensen (1974), Regan and Rezai-Jorabi (1987), Placas and Regan (1971), Leonhardt and Walther (1961), Kahn and Regan (1971), Moayer and Regan (1971), Hamadi and Regan (1980), Muhidin and Regan (1977), Levi and Marro (1993) and Walraven (1999).

_ Vj / b^z fd f^kifrirrfiit T .ind I sfitflürv; 3 - 0 &

ü Kor«ïfl«v T herum* D Reijan. Rezai. T/t A FI'V r. RegLifi_ T 1 Uï»HI(Jt. WJUlLl a Klidn. K'u.ir

* Moavef liegan Hnan-iit I Sogan i MJiklii*. Rt.'yûn Z LM, MJMG

ü Kor«ïfl«v T herum* D Reijan. Rezai. T/t A FI'V r. RegLifi_ T 1 Uï»HI(Jt. WJUlLl a Klidn. K'u.ir

* Moavef liegan Hnan-iit I Sogan i MJiklii*. Rt.'yûn Z LM, MJMG

f>ivfy I fti

Figure 6.30. Non prestressed beams with vertical stirrups - relationship between shear strength and stirrup reinforcement

6.2.3.2. Prestressed members with shear reinforcement

If the same rules are applied to prestressed members with shear reinforcement, like in ENV 1992-1-1 and MC'90, it can be seen that there is apparently an increase of both safety and scatter, Fig. 6.30. The test used for this figure are from Hanson and Hulsbos (1964), Bennett and Debaiky (1974), Moayer and Regan (1974), Levi and Marro (1993), Lyngberg (1976), Aparicio and Calavera (2000), Görtz and Hegger (1999), Leonhardt, Koch and Rostasy (1974). Many of the test results are collected

Figure 6.31. Experimental results of shear tests on prestressed beams with shear reinforcement, in comparison with the calculated results according to the variable strut inclination method (no special web crushing criterion for prestressed concrete)

Figure 6.31. Experimental results of shear tests on prestressed beams with shear reinforcement, in comparison with the calculated results according to the variable strut inclination method (no special web crushing criterion for prestressed concrete)

In ENV-1992-1-1 the effect of prestressing on the upper limit of the shear capacity VRd,i is partially neutral and partially negative. In 4.3.2.2 (4). The following statement is found: "In the absence of more rigorous analysis, at no section in any element should the design shear force exceed VRd,2. Where the member is subjected to an applied axial compression, VRd2 should be in accordance with the following equation:

VRd,red = 1.67 VRd,2 (1 - CTcp.eff/fcd) < VRd,2 (6.26)

Fig. 6.32 shows the dependence of the upper limit for the shear capacity on the level of prestressing.

VRdred VRd,2

Fiugure 6.32. Reduction of maximum shear capacity by axial compressive stress according to ENV 1992-1-1, Clause 4.3.2.2 (4)

In his "Commentaries on Shear and Torsion", Nielsen (1990) states that prestressing has a positive influence on the shear capacity of beams with shear reinforcement. He proposed to multiply v (which was then equal to v = 0.7 - W200 > 0.5) with a factor ac = 1 + 2.0 Ocp,eff / fc with Ocp,eff / fc < 0,5 (6.27)

A comparison with 93 tests results shows, however, that the expression is not sufficiently conservative, to serve as a safe lower bound over the whole region of test results, Fig. 6.33. It should furthermore be noted that all test results, used in the comparison, have ratio's of Ocp/fc lower than 0,4 and that the multiplication factor is obviously applicable only for this region. Another proposal for taking the influence of prestressing into account in the v-value was given by Foure (2000):

- for small compression, with 0 < Ocp < 0,4fcd ac = (1 - 0,67 Ocp/fctm) (6.28)

Vtheorv [kN]

Figure 6.33. Comparison of results of shear tests with variable inclination truss analogy with effectivity factor v= (0,7 -

Vtheorv [kN]

Figure 6.33. Comparison of results of shear tests with variable inclination truss analogy with effectivity factor v= (0,7 -

However, for the region of low compressive stresses this expression gives about the same results as Eq. 6.27

A more moderate expression, taking into account the influence of prestressing, is ac = (1 + Ocp/fc) for 0 < Ocp/fc < 0.25 fc ac = 1.25 for 0.25fc < Ocp < 0.5fc ac = 2.5 (1 - Ocp/fc) for 0.5fc < Ocp < 1.0fc

In Fig. 6.35 the same data as used in Fig. 6.31 are evaluated using Eq. 6.29. It appears that the safety margin and the scatter are reduced (the details of the calculation are found in Appendix 1). The new proposal is compared with the other ones in Fig. 6.34.

VRd;p

Figure 6.34. Comparison of new proposal (Eq. 6.29) with original formulation in ENV- 1992-1-1 (without influence of prestressing) and proposals by Nielsen (1990) and Foure (2000) for fck

0< acp/fc<0.25 ac = 125 for 0.25«jcp/fc<0.50

ac = 2.5 (1- CTcp/fc) for 0.5<CTcp/fc<1 00 prestressed I and T beams

Hanson, HulsLios Bennett Balasaorya Bennett Debaiky f/oayer, Rag an Levi, Marra LyngLierg

Aporicio, Colauera Görtz, Hegger Leonhardt Koch; Rostasy

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