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Figure 11.4. Principal strain directions 0in relation to the longitudinal member axis, as a function of the shear force for gravel concrete (left) and lightweight concrete (Aardelite, right), for high (H), medium (M) and low (L) shear reinforcement ratio's [21]

On the basis of those observations, for the design of members with shear reinforcement in lightweight concrete, the same principle as for normal density concrete was maintained in the new version for EC-2, including a lower limit for the strut inclination of 21.8° (cot 0 = 2.5).

In ENV 1992-1-4, the part on lightweight aggregate concrete, the efficiency factor v, defining the crushing capacity of the concrete struts, was formulated as v = 0.6 - flck/235 > 0.425 (11.14)

The efficiency factor v is only slightly smaller than the corresponding expression for NDC in the new EC-2 version. Comparison with tests shows that the combination of the equations 11.12.a-c and 11.14 does not give an appropriate lower bound. An analysis showed that this can not be solved by restricting the strut rotation to a higher value of 0min. reducing the allowable inclined compressive stress. Implicitly this means that a reduction of the efficiency factor v is necessary. A better formulations is therefore vlwac = 0.85 vndc (11.15a)

or vlwac = 0.85 0.6 (1 - fck/250) > 0.425 (11.15b)

Fig. 11.5 shows the comparison of the combination of Eq. 11.12a-c and 11.15 with test results from Walraven [21], Hamadi [22] and Thorenfeld [23].

Figure 11.5. Verification of the design equation 11.12/15 for lighweight concrete members with shear reinforcement by test results

Figure 11.5. Verification of the design equation 11.12/15 for lighweight concrete members with shear reinforcement by test results

In normal density concrete the punching shear capacity is calculated with the nominal design punching shear stress vRd,c = 0.12ii1k (100 pl fck)1/3 - 0.08 Gcd (11.17)

which is multiplied with a basic control section at a distance of 2d from the loaded area. Since Eq. 11.17 is the same as the equation used for shear, it may be wondered whether also here, like in the case of Eq. 11.9, a factor 0.10 should be applied in stead of the factor 0.12 basically valid for NDC. Fig. 11.6 shows a comparison between Eq. 11.17 (only reinforced concrete, so Gcd = 0) and test results by Tomaszewicz [24], Regan [25]. Hognestad [26], Corley [27] and Ivey [28]. Although the number of available tests was limited, a statistical derivation according to the level 2 method leads to the conclusion that the coefficient 0.12 is correct, so that Eq. 11.16 can be maintained (for the 22 tests a mean value of ^Rd = vtest/vcalc =0.181 is obtained, with a standard deviation of 0.0183, which means a coefficient of variation of 0.10. The level-2 method yields then a design value, including the model uncertainty, of xd = 0.181 - 0.8-3.8- 0.0183 = 0.125).

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