(1) (2) where D is overall depthof the cross section; is the shrinkage strain; is the creep coefficient at timet as a result of the load first applied at the age and is the instantaneous curvatureas a result of sustained load. The term ? is a creep modification factor andaccounts for the effects of cracking and the restraining action of thereinforcement on creep and is a function of the extent of cracking on the crosssection and the area and position of the bonded reinforcement in the tensileand compressive zones. For an uncracked (UC) singly RC cross section, ? rangesbetween 1.
1 and 1.8, depending on the amount of reinforcement, while forcracked singly reinforced cross sections, ? range between 4.0 and 8.
0. The term is the shrinkage modification factor and depends on the extent ofcracking, the level of tension stiffening, and the area and position of bondedreinforcement in the tensile and compressive zones. It should be emphasizedthat because creep and shrinkage occur simultaneously, it is in fact impossibleto calculate the creep and shrinkage-induced deflection separately. Author reasonablyassumed that the shrinkage-induced deflection of a slab is independent of theload level (although it is affected to some extent by the level of cracking)and that the creep-induced deflection is roughly proportional to the level ofloading. These assumptions justify the application of and to calculate creep andshrinkage-induced deflections separately. As a basic assumption to derive theempirical equations, Gilbert assumed that the drying process takes place onboth surfaces of the slab and that the shrinkage profile through the thicknessof slab is uniform. Thus, the D.
Hoseini proposed a modelbased on some modification to the provisions of ACI 209.2R-08 (ACI 2008) fordeflection calculation in composite slabs. That model is used in this paper andis briefly described here. According to ACI 209.2R-08 the shrinkage strain atany time t, and the creep coefficient, may be estimated using equations (3) and(4) respectively as follows. (3) (4) where is the ultimate (or final) shrinkage strainunder standard conditions (at time infinity), is the final creep coefficient at timeinfinity, is the time from the end of initial curing (indays), and is thetime since the application of load.
The suggested values for the constantswithin these equations under standard conditions are f = 35 (for 7 days ofmoist curing), =780×10-6, d=10 and =0.035. The effect of the percentage ofrelative humidity (RH) on concrete shrinkage and creep is taken into accountusing correction factors and respectively, where = 1.
40 – 0.0102 RH and = 1.27- 0.0067 RH The effect of member size on concrete shrinkage andcreep are considered by using correction coefficients and defined as follows: (5) (6) where ‘V’ is the specimen volume (mm3) and S is the specimen surface area (mm2).
The long-term behavior ofcomposite concrete slabs under sustained service loads were discussed. Inparticular, the time-dependent effects of creep and shrinkage were outlined byusing a simplified calculating procedure suitable for routine use in structuraldesign. The graphs were developed. Good agreement was obtained between thecalculated and measured deflections.