Joints and local effects can significantly influence the global behavior of frame structures. This study is concerned with the linear elastic analysis of joints and local effects in structures composed of thin-walled rectangular cross section tubes, or box beams. Plane stress and plate bending solutions are obtained for the general boundary value problem of a thin-walled beam of closed rectangular cross section. These solutions include the stress states of nominal beam behavior, and stress states due to end effects. The end effects are the mechanisms by which local features contribute to overall structural flexibility.;The thin-walled box beam boundary value problem is analyzed by a perturbation procedure, which is based on a small parameter proportional to the square root of the ratio of wall thickness to cross section width. The solution consists of a family of end-effect eigenfunctions which decay exponentially along the beam's length. The eigenfunctions of the unperturbed problem are found to have decay distances on the order of the beam width or shorter, in accordance with Saint-Venant's principle. The perturbation procedure is carried further to obtain asymptotic solutions for relatively slowly decaying warping and distortional end effects.;The end effect solutions provide the basis for a Very Large Finite Element (VLFE) formulation for the thin-walled box beam, in which the degrees of freedom are Fourier harmonics of edge forces and displacements along the element boundary. A VLFE formulation for the thin rectangular plate, based on Levy-type solutions, is also presented. The VLFE approach leads to an order of magnitude reduction in the number of unknowns relative to conventional finite element approaches.;The effectiveness of the method is demonstrated by examples which include tension, bending, and torsion of box beams with various end conditions. A box beam T-joint is analyzed, and the contribution of tab connections to the joint's flexibility is discussed. The effect of joint flexibility on the vibration frequencies of a H-frame is calculated. In concurrence with previous experimental and analytical results, the present analysis indicates that membrane end effects, warping/distortional end effects, and tab connection flexibilities all contribute to the compliance of a box beam joint, and that joint compliances can significantly lower the global vibration frequencies of a box beam frame.
展开▼
