Consistency aspects of out-of plane bending, torsion and shear in a quadratic curved beam element

Curved beams in civil engineering applications call for out-of- plane bending and torsion under the action of out-of-plane transverse shear loads. The design of a quadratic displacement type curved beam element capable of representing shear deformation as in the Timoshenko beam theory will call for special attention to be-paid to the manner in which the shear strain is to be represented. Field-inconsistent representations of the out- of- plane transverse shear strain will result in a loss Gf efficiency and introduce spuriou oscillations in the bending moment, torsional moment and shear force. The optimal field-consistent assumed strain interpolation for the shear is derived here and it is demonstrated that it has very high accuracy and is free from spurious force and moment oscillations