In this work, a finite element-based approach is presented to study the effective width variation in non-pre-stressed steel-concrete beams under the serviceability stage, including time dependent effects such as concrete creep, shrinkage and cracking. For this purpose, the viscoelasticity theory in conjunction with a nonlinear cracking monitoring algorithm is used to trace the nonlinear viscoelastic response of the structure along time. The present numerical model is fully three-dimensional and permits the inclusion of partial interaction at the slab-beam interface. A comprehensive study is carried out on the long-term response of a composite girder bridge previously studied by other researches. Then, previous results are revised and extended herein. Potential shortcomings of some standard codes related to the effective width evaluation are also investigated. It is demonstrated that the slab effective width varies sharply along the beam axis in the short-term, while it approaches to the actual slab width in the long-term. For the studied example, the common assumption of using only the middle layer of the reinforced concrete (RC) slab for the effective width calculation is revised with a through-thickness integration procedure. The influence of some creep and shrinkage models as well as the ultimate tensile concrete strain on the effective width response is also assessed. Finally, a simple formula is proposed to evaluate the short-term slab effective width for the studied example.