# ANALYSIS ON THE CONTRIBUTION OF CROSS BEAM TO A TORSIONAL BUCKLING OF THIN, RECTANGULAR BEAM SECTION

### Abstract

In the analysis, a cross beam is idealized as a spiral spring having an equal rotational stiffness to the cross beam. Based on the torsional buckling exact solution, assuming a simply supported beam with a stiffened web subjected to a constant moment, the numerical solution of a torsional buckling is acquired. Moreover,

the beam is assumed to have a constant segmental moment distribution. Based on basic equilibrium condition of the differential equation of each segment, constants of integration of the exact solution of the segmental rotations can be herein obtained. The number of constants of integration is twice the number of

segments. On the basis of geometric boundary conditions at the beam’s supports and at the joint nodes between segments, as well as natural boundary conditions of the segment joints equipped with spiral spring springs, the homogeneous equations as a function of constants of integration will be obtained. The

determinant of the coefficient matrix of such homogeneous equation as a function of constants of integration is then evaluated. The determinant having a zero value identifies the critical torsional buckling moment. By decreasing the segmental length, the critical moment will convergence to the torsional buckling moment. It is proven that the analysis based on the segmental approach having a constant moment will closely match the exact solution. For a spiral spring having ratio of rotational stiffness to the beam’s torsional stiffness equals to 1, the torsional buckling moment will closely approach that of the beam when it is supported at the location of the spiral spring. Moreover, for n equally distributed spiral springs, the torsional buckling moment will be (n+1) times the torsional buckling moment of an identical beam without spring. It is therefore concluded that the presence of Cross Beam can significantly increase the

torsional buckling moment of a beam.

**EACEF - International Conference of Civil Engineering**, [S.l.], v. 1, p. 015, aug. 2011. Available at: <http://proceeding.eacef.com/ojs/index.php/EACEF/article/view/368>. Date accessed: 19 may 2024.