# LATERAL TORSIONAL BUCKLING OF DOUBLE SYMMETRICAL I BEAM WITH VERTICAL STIFFENERS

### Abstract

Lateral Torsional Buckling (LTB) Formula of an I beam having a constant moment is derived using an exact mathematical approach, taking into assumption that the web is not deformed. Generally on the beam design, the vertical stiffener is only designed to increase the shear strength of the web. The effects of vertical stiffeners to the LTB moment of the beam is not taken into account in the design. In this paper, we will study the effect of the vertical stifenners to the LTB of the beam, assuming that the web is remain straight and the materials of beam is still elastic when the beam buckles. The same elementary differential equation of section rotation is used for both areas between two vertical stiffener adjacent and between the vertical stiffener and the support. The homogenous equations of the constant of integration is defined using the natural boundary conditions on the vertical stiffeners and on the support. The natural boundary condition at the vertical stiffener is nothing but the moment balance between the left flange moment, the right flange moment and the torque of the vertical stiffener. The coefficient matrix of the homogenuous equation is a function of the critical moment. By trial and error, we can then define the critical moment in which the determinant of the coefficient matrix is equal to zero. The analysis is carried out using Fortran language, validated using the existing empirical formula. The analysis shows that the vertical stiffeners increase the critical moment by up to 13%.

**EACEF - International Conference of Civil Engineering**, [S.l.], v. 1, n. 1, p. 070, aug. 2013. Available at: <http://proceeding.eacef.com/ojs/index.php/EACEF/article/view/72>. Date accessed: 13 may 2021.