Element stiffness matrix and modified coefficients for circular tube with tapered ends

By axially connecting a constant-section circular tube to two tapered circular tubes, a so-called circular tube with tapered ends structural member is obtained. To get the element stiffness matrix of a tube with tapered ends, a transfer matrix method is introduced in this paper. Transfer matrices for the constant-section tube and tapered tubes are derived firstly, and then the element stiffness matrix for a tube with tapered ends is obtained on the basis of the relationship of the transfer matrices. Two typical examples are given to verify the element stiffness matrix. And the stiffness matrix for a tube with tapered ends can be treated as a modification of the stiffness matrix for a constant-section tube. Stiffness modified coefficients are introduced to represent the modification, and a table of stiffness modified coefficients for tubes of frequently used dimensions is given at the end of the paper.