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Structural Engineering and Mechanics
  Volume 22, Number 2, January30 2006 , pages 131-150

Analytical solutions of in-plane static problems for
non-uniform curved beams including axial and shear
Ekrem Tufekci and Alaeddin Arpaci

    Exact analytical solutions for in-plane static problems of planar curved beams with variable curvatures and variable cross-sections are derived by using the initial value method. The governing equations include the axial extension and shear deformation effects. The fundamental matrix required by the initial value method is obtained analytically. Then, the displacements, slopes and stress resultants are found analytically along the beam axis by using the fundamental matrix. The results are given in analytical forms. In order to show the advantages of the method, some examples are solved and the results are compared with the existing results in the literature. One of the advantages of the proposed method is that the high degree of statically indeterminacy adds no extra difficulty to the solution. For some examples, the deformed shape along the beam axis is determined and plotted and also the slope and stress resultants are given in tables.
Key Words
    curved beam; variable cross-section; axial extension; shear deformation; initial value method.
Istanbul Technical University, Faculty of Mechanical Engineering, Gumussuyu 34437, Istanbul, Turkey

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