Generalized Stiffness Matrix for Thin Walled Beams

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Abstract
Stiffness matrix for a structural member is obtained using the differential equations derived by V.Z. Vlasov. Presence of additional off-diagonal elements over the conventional tridiagonal form is observed. A number example is shown in order to compare the relative magnitudes of elements in the stiffness matrix and some of the new off-diagonal elements are found to be of considerable importance. This stiffness matrix conclusively demonstrates the inter-relationship between the three rotational degrees of freedom. This coupling is found to reduce the value of the critical axial force below all three individual buckling loads, viz: lateral buckling about major and minor axes and torsional buckling. All these effects are attributed to an internal force called as bimoment.

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