Abstract
The typically-used element torsional stiffness GJ/L (where G is the shear modulus, J the St. Venant torsion constant, and L the element length) may severely underestimate the torsional stiffness of thin-walled nanostructural members, due to neglecting element warping deformations. In order to investigate the exact element torsional stiffness considering warping deformations, this paper presents a matrix stiffness method for the torsion and warping analysis of beam-columns. The equilibrium analysis of an axial-loaded torsion member is conducted, and the torsion-warping problem is solved based on a general solution of the established governing differential equation for the angle of twist. A dimensionless factor is defined to consider the effect of axial force and St. Venant torsion. The exact element stiffness matrix governing the relationship between the element-end torsion/warping deformations (angle and rate of twist) and the corresponding stress resultants (torque and bimoment) is derived based on a matrix formulation. Based on the matrix stiffness method, the exact element torsional stiffness considering the interaction of torsion and warping is derived for three typical element-end warping conditions. Then, the exact element second-order stiffness matrix of three-dimensional beam-columns is further assembled. Some classical torsion-warping problems are analyzed to demonstrate the established matrix stiffness method.
Subject
General Materials Science,General Chemical Engineering
Reference28 articles.
1. Developing the mechanical models for nanomaterials;Compos. Part A,2007
2. Graphene-related nanomaterials: Tuning properties by functionalization;Nanoscale,2013
3. Giannopoulos, G.I., and Georgantzinos, S.K. (2021). A tunable metamaterial joint for mechanical shock applications inspired by carbon nanotubes. Appl. Sci., 11.
4. Trahair, N.S., Bradford, M.A., Nethercot, D.A., and Gardner, L. (2008). The Behaviour and Design of Steel Structures to EC3, Taylor & Francis. [4th ed.].
5. Chen, J. (2011). Stability of Steel Structures Theory and Design, Science Press. [5th ed.]. (In Chinese).
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