Análise e determinação do momento de inércia à torção de seções não-circulares

Abstract

The object of study is the formulation of the Torsional Moment of Inertia of non-circular cross sections bars, since the circular section is the most commonly studied section in Civil Engineering undergraduate courses. The Torsional Moment of Inertia is the main geometric property of structures subjected to torsional moment and is one of the main factors that contribute to the resistance of an axis, depending on its shape, when it is deformed by the action of a torque. The work was developed in the context of the Theory of Elasticity seeking to explain the construction and, when possible, the solution of the differential equations that govern the problems of uniform torsion. The Torsional Moment of Inertia of open thin walled and cellular sections was determined using the membrane analogy. The developed expressions were applied in some examples of thin walled sections. A comparison was made between some of the results obtained by the analytical expressions and others obtained through the use of Flexo II® and SAP2000® software. The results obtained analytically were satisfactory. Keywords: uniform torsion; moment of inertia; elasticity theory; differentials equations