CT images are often affected by beam hardening artifacts due to the polyenergetic nature of the X-ray beam. Several correction methods have been proposed to be included in an FDK reconstruction scheme, which is still the prefered reconstruction algorithm in commercial X-ray CT scanners. In this work, we present a complete correction scheme for beam hardening artifact correction in an FDK-based reconstruction scenario that accounts for both cupping artifact and dark streaks. The proposed method substitutes the need of the knowledge of the spectrum by empirical measurements and two parameters. It includes two steps: a linearization step of projection data and a post-reconstruction step. Evaluation done in real studies acquired with a cone-beam micro-CT scanner showed an average cupping reduction of 80 % in homogeneous phantoms and 72% in rodent studies. The correction scheme can be incorporated easily in any cone beam micro-CT scanner.