Stiffness Matrix for Structures With Bars of Variable Section or Rigidity

Abstract

The matrix calculation by the Rigidity Matrix Method of structures composed of straight bars is normally carried out considering the bars of constant section and inertia and this hypothesis is considered sufficiently safe in all cases.

However, in practice, many structural systems are made up of bars of variable section or inertia, such as haunched bars, cracked reinforced concrete bars, steel bars with semi-rigid joints or mixed concrete and steel bars.

In this study, the Stiffness Matrix of a straight bar of variable section or inertia is proposed, whose rigidity coefficients are a function of the laws of variation of the area of its section, its Torsion Module and the Moments of Inertia referred to the axes normal to its guideline.

This approach does not increase the number of nodes in the structure or the number of unknowns in the matrix equation and allows, by establishing sufficiently approximate criteria for the calculation of its rigidity coefficients, to determine a more realistic behavior of its structural elements.