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strength at time of loading [N/mm2] Figure 11.2. Final specific creep as a function of strength at the age of loading [7]

and pcc(t) is the hardening function.

The contribution of autogenous shrinkage decreases considerably with increasing strength of the concrete.

In lightweight aggregate concrete the conditions are quite different if the aggregate particles are saturated with water. In that case the possible supply of water from the aggregate to the drying microstructure will prevent a significant drop of the relative humidity in the paste and will thus reduce autogenous shrinkage. Therefore for LWAC the contribution of autogenous shrinkage as given by Eq. (EC-3.10/11) has to be regarded as an upper value.

### Ultimate bearing capacity of LWAC structures

With regard to the bearing capacity of structures in the ultimate limit state specially the behaviour in shear and punching is important. This holds particularly true because cracks in lightweight concretes are supposed to be smoother than cracks in normal density concrete: in normal strength concretes of moderate strength cracks are propagating around the aggregate particles, whereas in lightweight concrete the crack intersects the aggregate particles, which have generally a much lower strength than gravel aggregate particles. This might reduce the shear friction capacity of the cracks and as such reduce the total shear carrying capacity. This difference might also limit the redistribution capacity of the concrete web (rotation of compression struts to lower angles), which is particularly important since in the draft of 1.1.2000 the standard method has not been involved anymore and only the variable inclination method is given as the basis for the calculation of the shear reinforcement. Those questions will be systematically treated.

Shear capacity of reinforced concrete members without shear reinforcement

In Section 6, the shear capacity of reinforced (normal density) concrete members without shear reinforcement has been formulated as:

VlRdc = [0.12^1k(100pflck)1/3 - 0.15ocd] bwd (11.8)

fick characteristic cylinder strength of lightweight concrete k size factor = 1 + (200/d)1/3 < 2.0 pi longitudinal reinforcement ratio = Asi /bwd < 0.02 Gcd average longitudinal prestress in the cross section conversion term from NDC to LWAC, see Eq. 11.1.

The coefficient 0.12 has been replaced (0.18/yc) in order to show explicitly the safety margin. On order to seen if this formulation is also suitable for lightweight concrete, the expression has been verified with 86 test results, from Ivey/Buth [12], Walraven [13], Hansson [14], Taylor/Brewer [15], Evans/Dongre [16], Torenfeld/Drangsholt [17], Thorenfeld/Stemland [18] and Aster/Koch [29]. Fig. 11.3 shows the results. A mean value of vtest/k^1(pfcm)1/3 of x = 0.162 with a standard deviation of 0.0235 is obtained, corresponding to a coefficient of variation of 0.145. A design value can be obtained on the basis of a statistical evaluation. For such a case the classical level-2 method, as described in EC-1 Basis of Design is suitable. The way how to deal with this method has been described and illustrated by Taerwe [20].

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