Computed deflection of continuous reinforced concrete flexural members

Abstract

Bending deflection is important to the design of some concrete members. While deflection is rarely a safety issue when it governs, deflection limits are always a code requirement. For beams and slabs, deflection checks are not required if a member meets the recommended depth-to-span ratio. In design of thinner steel reinforced concrete slabs and most FRP reinforced members, though, deflection requirements often govern. Because commonly used deflection calculations, as per ACI 318-05 and CSA A23.3-04, are often inaccurate in important ways, this work studies improved calculations. This report extends Bischoff’s method for computing an effective moment of inertia for simply supported members to an effective moment of inertia for continuous members. This comparison is done for immediate deflections with a uniformly-distributed load, a center-point load, and equal loads at third-points. Bischoff’s work with simply supported members is reviewed. Branson’s equation and the S806 method are also reviewed and used for comparison. The results indicate that Bischoff’s equations for simply-supported members also work well for continuous members. These proposed equations work very well for centered point loads and uniformly distributed loads (within proposed limits). For a member with equal point loads at third-points, a minor calculation modification is suggested which improves its usable range and accuracy. For members with unequal end- moments, accuracy requires use of the maximum positive bending moment (not the moment at midspan). For situations where the end-moment magnitude greatly exceeds the positive moment, a numerical integration approach is recommended.