Abstract
This study establishes the improved element stiffness and mass matrices of the thin-walled box girder, using a cubic Hermite polynomial shape function and based on an improved displacement function for shear-lag warping meeting the axial equilibrium condition of shear-lag warping stress and the consistency requirements of the displacement function. The improved thin-walled box girder element comprehensively considers multiple influencing factors, such as the thin-walled box girder shear-lag effect, shear deformation, and rotational inertia. The element shape function has first-order continuity at the element interface and satisfies the calculation precision with relatively few degrees of freedom. A finite beam element method program that can be used to calculate the natural vibration frequencies of thin-walled box girders was compiled based on the improved thin-walled box girder element. This program was used to calculate the natural vibration frequencies of many thin-walled box girder samples with differ...
Highlights
Because shear strain exists in the top, cantilever, and bottom slabs of thin-walled box girders (TWBGs), the longitudinal strain of the portion of these slabs far from the web is less than that of the portion near the web
The natural vibration characteristics of TWBGs suffer from the coupled effects of shear lag and shear deformation
Based on the TWBG element stiffness matrix Ke, element mass matrix Me, and element nodal displacement vector qe = fqTu, qTu, qTwgT proposed by this study, the total stiffness matrix K, total mass matrix M, and the total freedom vector q of the TWBG can be obtained using principle of ‘‘set in the right position.’’ The boundary conditions commonly used by TWBGs can be expressed as follows:[15,16]
Summary
Because shear strain exists in the top, cantilever, and bottom slabs of thin-walled box girders (TWBGs), the longitudinal strain of the portion of these slabs far from the web is less than that of the portion near the web. The TWBGs in his paper had a single-cell cross-section without side cantilever slabs, and a quadratic parabola was adopted as the displacement function for shear-lag warping. In most of these papers, the warping displacement functions for shear lag of the TWBG with cantilever slabs have some deficiencies because the corresponding warping stresses cannot satisfy the axial equilibrium condition. Zhang and colleagues[2,3,7] established an improved displacement function for shear-lag warping in a box girder with cantilever slabs through the axial equilibrium condition for shear-lag warping stress These models failed to consider shear deformation. Based on the previously mentioned boundary conditions, the displacement function for shear-lag warping of the top slab, cantilever slab, bottom slab, and web can be approximated by four quadratic parabolic equations as giðx, yÞ = ciðyÞU ðxÞ ci ð yÞ. Substituting equation (16) into equation (23) leads to the TWBG element mass matrix[25]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
