The Effect Of Diaphragm Density On Distortion Of Thin-Walled Bar With Rectangular Cross Section

In this paper, the distortion of thin-walled bar with rectangle cross section is examined individually and the effect of diaphragm density on distortion is analyzed.Firstly, with uniaxial symmetrical rectangle cross section, the warping displacement function and tangential displacement function under anti-symmetrical load are supposed. Then taking shear deformation into account and with potential principle, the governing differential equation for distortion angle subjected to uniformly distributed distortion load is established. The differential equation is solved and the format of initial parameters is deduced. With a case, the theory proposed in this paper is compared with the traditional distortion theory which doesn't take shear deformation into account and ANSYS finite element software to verify the accuracy of the proposed method. It is drawn that taking shear deformation into account results in a fairly higher accuracy.Based on the initial parameters format of the distortion theory in this paper, the element stiffness matrix and the corresponding equivalent nodal force vector subjected to uniformly distributed load is developed.At last, with the stiffness method, the effect of diaphragm density on restraining the distortion of thin-walled bar is analyzed. With different load cases of uniformly load and concentrated load and different boundary conditions of two fixed ends and two simply supported ends and cantilever, the distortion and torsion of the same rectangle thin-walled girder is examined. By changing the amount of the diaphragm, the distortion effect under different density of diaphragm is investigated. The diagram of distortion effect to diaphragm density is drawn and the distortion effect is compared with the effect of rigid torsion. It is concluded that a certain amount of diaphragm will reduce the distortion effect greatly, but on the other hand, even with a fairly great density of diaphragm, such as the ratio of diaphragm span to the greatest dimension of the cross section is as small as 1.25, the distortion effect can't be neglected compared with the effect of rigid torsion. As a result, it is suggested that distortion should be taken into account to calculate the thin-walled bar with restrained torsion.