Minimum Reinforcement in High‐Strength Concrete

A dimensional analysis criterion is proposed to compute the minimum amount of reinforcement for high‐strength concrete members in flexure. Such an amount is assumed to be provided by the condition of simultaneous first cracking aand steel yielding. The fracture mechanics model utilized defines a brittleness number $N_P\text{,}$ which is revealed to be a measure of the experimental brittleness or ductility of the test. $N_P$ is a function of steel‐yield strength $f_y\text{,}$ concrete fracture toughness $K_{\mathrm{IC}}\text{,}$ steel percentage $A_S/A\text{,}$ and beam depth. The brittleness of the structural member increases by increasing the size and/or decreasing the steel content. On the other hand, a physically similar behavior is revealed in the cases where the brittleness number $N_P$ is the same. The experimental investigation carried out by the writers shows that the failure mechanism changes completely when the beam depth is varied, the steel percentage being the same. Only when the steel percentage is inversely proportional to the square root of the beam depth is the mechanical behavior reproduced.