Theoretical Shear Strength of Concrete Columns Due to Transverse Steel

The effect of discrete distribution of transverse reinforcement for shear strength of reinforced concrete beams and columns is evaluated. In order to bridge the gap between the present code formulations based on the smeared distribution of transverse steel and the reality based on the discrete distribution, correction factors are proposed for rectangular and circular hoops and spirals. The correction factor for rectangular hoops is more significant than those for circular hoops and spirals. Poorly detailed members, where $N<4$ for rectangular hoops and $N<2.5$ for circular hoops and spirals, will have a capacity reduction factor that is less than the usual undercapacity $\left(\varphi \right)$ factor of say 0.75, where $N=\text{number}$ of spaces between reinforcement hoops crossing a shear crack. In order to limit the unconservativeness to less than 10%, $N⩾10$ for rectangular hoops and $N⩾5$ for circular hoops and spirals should be used.