Shrinkage and Creep Influence on Deflections and Moments of Reinforced Concrete Beams
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The long term deflection behavior within the working load range of reinforced concrete beams is analyzed. The effects of creep and shrinkage are included by resolving the total compressive strain into its constituent parts. It is shown that, due to shrinkage, the planes of zero stress and zero strain no longer coincide in the beam, and that their locations depend on the concrete stress and thus on the moment. The nonlinear relations between moments and stresses are then derived. Fortunately, it turns out that the relation between moment and the sum of the strains remains almost linear and can often be expressed by AM + B = zc where A and B are essentially constant for large ranges of M. The above expression can be integrated with various boundary conditions to obtain deflections of simple beams, and fixed-end moments and deflections of statically indeterminate beams. Due to the second constant, B, in the equation, a part of the deflection is shown to be inde-pendent of the load.