Mechanics solutions for deflection and cracking in concrete

Serviceability failures in reinforced concrete elements that are the result of excessive cracking or deflection are relatively common, particularly for slender sections such as slabs. The calculation of member deflection is typically carried out by applying an elastic deflection equation with an effective flexural rigidity that is a function of the full-interaction uncracked and cracked flexural rigidities. The effective flexural rigidity achieves two purposes: it allows for variations in cracking along the member length; and approximates tension stiffening, that is slip between the reinforcement and adjacent concrete, as this is not accounted for in standard full interaction analyses. Although much research has been conducted to define effective flexural rigidity, the resulting equations are typically empirical calibrations or allow for bond without allowing for bond slip. In this paper, a new partial-interaction approach for quantifying the flexural rigidity of a cracked section based on a recently developed segmental analysis procedure is presented. It is shown that the partial-interaction cracked flexural rigidity is independent of the applied moment after the onset of cracking. Hence, for a given cross-section, the effective flexural rigidity only varies with the proportion of the member which is cracked.