Creep in composite continuous beams I: theoretical treatment

In this first part of the paper, the viscoelastic analysis of composite steel-concrete continuous beams with flexible shear connectors is performed. The method proposed evaluated the stress redistribution between the concrete slab and the steel beam, and the evolution of the redundant restrain reactions, which occur with time as a result of creep and shrinkage of the concrete part. The effects produced both by geometric and static actions are considered. The mathematical formulation of the problem involves the equations of equilibrium, internal and external compatibility conditions and constitutive relationships. i.e. an elastic law for the steel part and an integral-type creep law for the concrete part. Thus, the problem for a continuous beam with r redundant reactions is governed by a coupled system of r + 5 equations, of which two are integral-differential-type equations. Successively, this system is resolved by numerical step-by-step techniques. Therefore, performing two standard discretizations, in time and along the beam axis a numeric algorithm is proposed.