A cracked frame element based on the force formulation method and compliance concept is proposed. The formulation is developed according to the Euler-Bernoulli theory. There is an open stable edge crack in the element, which its effects on the local flexibility is computed by utilizing linear elastic fracture mechanics principles. This additional flexibility is added to the non-cracked element flexibility matrix which is derived by force-formulation method in a basic coordinate system without rigid body motions. The suggested element is applicable for non-prismatic frames and the effects of the internal forces interactions are also included. A consistent mass matrix is also derived for the element. The proposed element is applicable for static and dynamic analysis of cracked and non-cracked frame structures. In addition, due to its capability in calculating free vibration responses accurately, the presented element can be used for inverse crack detection techniques.

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