Analytical determination and numerical validation of the shear factor in annular sector cross sections

Abstract

In the present study, the shear factor of an annular sector cross section, including the thickness effect, has been analytically determined for the first time. The shear factors depend on the angle of the sector and on the mean radius to thickness ratio. Two approaches were used to determine circumferential and radial shear stresses. The limits of validity of the approach were established, based on the similarity of the shear factors determined from both approaches. The results obtained from the present analytical approach were compared with the results of another analytical approach developed for thin sections. To check the suitability of analytically determined shear factors, unidirectional composite cantilever beams have been analysed by the finite element method, for different cross sections and cantilever lengths. With the material properties and displacement at the cantilever tip known, shear factors were determined and compared with those obtained from the analytical approach. The script used to calculate the shear factors is included as an appendix.