Arches are usually calculated using the Finite Element Method (FEM). However, they can be calculated using graphic statics as well. In the graphic statics method, the complementary energy is used to calculate the flow of forces in the structure. The correct solution can only be found through trial-and-error: by changing the horizontal reaction forces, the equilibrium changes, providing a different distribution of load-carrying through normal forces and bending moments. The distribution which results in the lowest amount of complementary energy is the correct way the forces flow. This method is only applied in an iterative way. If the total amount of energy is described in a mathematical way and the derivative of that equation is set equal to zero, the correct solution can be calculated directly. However, the extensiveness of this mathematical description prevents this method from being applied in a direct way. This paper proposes a new method in which the complementary energy due to normal forces is neglected and only the complementary energy due to bending moments is minimized. This simplification allows for a derivation of the equation for the complementary energy which changes the calculation method from an iterative to a direct one. The derivation is shown for a simple three-bar system, showing how such a direct method can be developed. The new method is compared to indirect calculations and FEM calculations, showing only small deviations. The proposed method can be extended to more complex arch structures and can function as a starting point for finding a graphic method for calculating shell structures. @en