Brincker, Henriksen, Christensen and Heshe conducted very extensive experimental work. Tensile failure of concrete in the initial stage and compressive failure of concrete in the final stage have been modeled using fracture mechanics concepts. In this way, experimental dimensional effects are properly simulated and accounted for.
Oz bolt and Bruckner use a finite element code based on an on local micro plane model to numerically analyze reinforced concrete beams of various sizes. They even consider the dynamic region after cracking, where the minimum rebar ratio increases with increasing size after the beam reaches a critical size. This inference is not consistent with previous deductions and further theoretical and experimental studies are needed.
Description
The ESIS-Technical Committee 9 on Concrete was established in 1990 and has met seven times. A proposal entitled “Scale Effects and Transient Failure Phenomena in Bending of Reinforced Concrete Beams “was submitted to European and non-European institutes and received several positive responses.
The central topic discussed by the committee concerned the minimum rebar content of concrete members. Minimum reinforcement is defined as the “peak load at the first concrete crack “equal to the “ultimate load after steel yield”. In this way, if the member is not over-reinforced, not only brittle behavior is avoided, but also localized failure. In other words, there is a range of reinforcement percentages, depending on the size scale, to which the static and kinematic theorems of plastic limit analysis can be applied.
Carpinteri, Ferro, Bosco and El-Katieb have proposed the LEFM model. According to this model, the reinforcement reaction is applied directly to the crack surface and a compliance condition corresponding to local reinforcement is imposed on the crack opening displacement. The theoretical model is found to provide a satisfactory estimate of the minimum reinforcement fraction that, depending on the scale, can prevent brittle failure of the bending elements.
The books in your web site really were useful, hope to put latest udpate books, thanks in advance.
WBR
Engineer Murtaza Hashimi
Afghanistan Kabul