Exact Matching Condition at a Joint of Thin-Walled Box Beams Under Out-of-Plane Bending and Torsion

Abstract

To take into account the flexibility resulting from sectional deformations of a thin-walled box beam, higher-order beam theories considering warping and distortional degrees of freedom (DOF) in addition to the Timoshenko kinematic degrees have been developed. The objective of this study is to derive the exact matching condition consistent with a 5-DOF higher-order beam theory at a joint of thin-walled box beams under out-of-plane bending and torsion. Here we use bending deflection, bending/shear rotation, torsional rotation, warping, and distortion as the kinematic variables. Because the theory involves warping and distortion that do not produce any force/moment resultant, the joint matching condition cannot be obtained just by using the typical three equilibrium conditions. This difficulty poses considerable challenges because all elements of the 5 x 5 transformation matrix relating the field variables of one beam to those in another beam should be determined. The main contributions of the investigation are to propose additional necessary conditions to determine the matrix and to derive it exactly. The validity of the derived joint matching transformation matrix is demonstrated by showing good agreement between the shell finite element results and those obtained by the present box beam analysis in various angle box beams.

Implementation of Thin-Walled Approximation to Evaluate Properties of Complex Steel Sections Using C++

“…Without the introduction of any artificial stiffness, coupling performance at a joint amongst beam cross-section deformations can be derived in their investigation. To counterpart arbitrarilyoriented thin-walled box beam rudiments for out-of-plane bending complications, Choi et al [50] derived a joint transformation matrix. Joints associated with three box beams, were scrutinized in [51][52][53] for out-of-plane bending difficulties, and the outcomes were presented to be ominously adjacent to those acquired by pure shell elements such as T-joints.…”

“…Joints associated with three box beams, were scrutinized in [51][52][53] for out-of-plane bending difficulties, and the outcomes were presented to be ominously adjacent to those acquired by pure shell elements such as T-joints. The joint corresponding circumstances for higher order thin-walled beams in [48][49][50][51][52][53] are only effective for rectangular cross sections. Contemporary beam theories such as the generalized beam theory [19][20][21][22] and the Carrera unified formulation [23][24][25] are also consider by the Higher-order cross-section modes.…”

Warping Transmission in 3-D Beam Element Including Secondary Torsional Moment Deformation Effect

“…iv. General warping and bimoment continuity (see for example [8,9,13]). In this case the warping DOFs of the elements' nodes at a joint of intersecting space members are linked together with general relations.…”

Warping Transmission in 3-D Beam Element Including Secondary Torsional Moment Deformation Effect

“…The actual transmission conditions depend on the geometry of the joint of intersecting members [6]. However, in many geometric configurations encountered in engineering practice [6][7][8][9] the aforementioned treatments are not realistic. Shell or 3-D finite element idealizations permit very accurate modelling of every possible geometric design, however their use is costly and complex as compared to beam element models.…”