Monolithically connected piers of semi-integral viaducts often experience large pier head displacements due to shortening of the superstructure from creep and shrinkage as well as temperature changes. A realistic assessment of the constraint forces under consideration of the nonlinear and the viscous material behavior of concrete is of extraordinary importance for the success of this construction method. In this paper, long-term 4-point bending tests are presented on two 4 m long reinforced concrete (RC) beams. The specimens were loaded by imposed deformation, which was held constant over the test period of 112 days. The strain development in the concrete and the reinforcement was measured with distributed fiber optic sensors (dFOS) installed in the beams prior to concreting. Whereas the curvature, deformations and reinforcement strains in components under load actions increases with time, it was shown that the curvature in the high stressed cracked cross sections remained approximately constant under pure constraint forces. Due to the concrete relaxation, the constraint force decreased by 30%, with a simultaneous, although underproportionally, reduction in the maximum steel strains. While the viscous material behavior of concrete poses challenges to structures under load actions (e.g., resulting in larger deformations), taking the creep potential into account has a positive effect on the design of constrained components.