Partial-interaction short term serviceability deflection of RC beams

A widely accepted approach for quantifying the serviceability short term deflection of RC beams is to use some combination of the flexural rigidities of the uncracked (EIfi-uncr) and cracked (EIfi-cr) sections that are obtained from a full-interaction analysis of transformed sections; a full-interaction analysis implies that there is no slip between the reinforcement and concrete. The combination of EIfi-uncr and EIfi-cr, that is the effective flexural rigidity (EIeff) to be used for calculating the deflection, has to be determined purely from testing. In this paper partial-interaction theory, which allows for slip between the reinforcement and concrete and consequently the bond-slip characteristics, is used to determine the partial-interaction flexural rigidity of a cracked section (EIpi-cr). It is shown that: by replacing the cracked section EIfi-cr with EIpi-cr obviates the need to determine EIeff directly from testing; the replacement of EIfi-cr by EIpi-cr allows closed form solutions to be derived for EIeff and also allows for the distinction between the formation of primary and secondary cracks. The partial interaction approach also provides a way of determining, through mechanics, the minimum crack spacing and hence can be used to study the random component of cracking and its influence on member deflection. The partial-interaction flexural rigidity should be a convenient tool for not only refining existing deflection procedures but also for quantifying the deflection of RC beams with new types of reinforcement and new types of bond, in particular those associated with FRP reinforced members.