The main objective of this thesis was to make a step forward in the application of the component method to the design of tubular joints. Following the existing research conducted by CIDECT, the study tried to solve the most challenging issues of the component method in relation to RHS T joints under three loading cases, namely axial loading, in-plane bending and out-of-plane bend-ing. The verification of the component method with EN 1993-1-8:2005 demonstrated that the method employs the inverted Eurocode equations and therefore provides the same resistance of joints. However, the main concerns of the method relate to the design of initial stiffness.
To employ extensive numerical studies in the analyses, the thesis developed a FE model for RHS T joints. The model was constructed with two quadratic solid finite elements in the thickness direction. Some recommendations are proposed in regards to the required length of the members and the possibilities for the modeling of butt and fillet welds. In addition, the thesis presented three methods to investigate pure axial loading of the joint, preventing the in-plane bending of the chord. The FE model was employed further in the thesis to develop the design equations for the initial stiffness of joints, investigate the influence of initial imperfections and fillet welds, as well as the surrogate modeling.
The main attention of the thesis was paid to the initial stiffness of RHS T joints. The validation with the experimental results showed that the theoretical solution provided by CIDECT consid-erably underestimates the in-plane rotational stiffness of joints. A more accurate equation was proposed for the component “chord face in bending”. The equation demonstrated good correlation with the experimental data. In terms of initial axial stiffness, the CIDECT report showed
consid-3 Conclusions
erable overestimation of the experimental values. New equations were developed for the compo-nents “chord face in bending” and “chord side walls in compression”. In addition, the thesis nu-merically investigated the influence of chord axial stresses on the initial rotational and axial stiff-ness of RHS T joints. The compressive stresses were found to reduce considerably the stiffstiff-ness of joints, with the opposite trend for tensile stresses. The influence was found particularly strong for the joints with small braces (β = 0.25) and wall thickness (2γ = 35). To consider this effect in the design, the thesis developed and verified corresponding chord stress functions.
Another part of the thesis investigated the beneficial effect of fillet welds on the structural behav-ior of tubular joints. The FE analyses of RHS Y joints demonstrated that the joints with full-strength fillet welds had considerably higher initial stiffness than the identical joints with butt welds. The influence was particularly strong for the joints with highβ, reaching more than 2.0 times for S355 and more than 3.0 times for S700. The observed phenomenon was also supported by a series of experimental results on RHS T joints, which demonstrated the difference of 60%
between the resistance and stiffness of the joints with large fillet welds and the butt-welded joints.
The current building standards do not take this effect into account, providing the same resistance regardless the type and the size of welds. To avoid conservative results, the thesis proposed a simple equation to consider the influence of fillet welds on the initial in-plane stiffness of RHS Y joints. Although the equation is based on a limited number of joints, additional studies can be conducted to develop a more general solution, incorporating resistance and other loading cases.
Attention was also paid to the issue of the reduction factors for HSS tubular joints. A study ana-lyzed the experimental results of HSS RHS T joints under in-plane bending with varying geome-try, steel grades and three types of welds. The comparison between the experimental results and the existing Eurocode equation for moment resistance demonstrated the need for the reduction factors only for butt-welded joints. The joints with large fillet welds showed sufficiently safe resistance without any reduction. Applying the factors for these joints would have led to exces-sively conservative results. The necessity of the reduction for the joints with small fillet welds depended on the steel grade: the factors were needed only for the joints with steel grades above S500. In all cases, the required reduction coefficients were greater than those specified by Euro-code, leading to smaller reduction of resistance. The thesis proposes certain values of the reduc-tion coefficients (factors) for moment-loaded joints, depending on the steel properties and the relative throat thickness of the weld. The proposed coefficients well correlate with the observa-tions of other researchers for axially loaded RHS joints. It should be noted that the recommended values of the reduction factors do not consider the substantial beneficial influence of fillet welds.
If this effect is accepted in the standards, the recommended values of the HSS reduction factors have to be further specified.
The same experimental data was used to evaluate the ductility of HSS RHS joints. The results showed that all considered joints demonstrated sufficient rotation capacity, clearly exceeding the
specified 3%b0 deformation limit for tubular joints. This finding allows to conclude that RHS T joints can be safely designed with undersized welds (welds smaller than full-strength fillet welds), provided that the resistance of welds is checked. This finding is supported for axially loaded joints by the recent European research (Feldmann et al. 2016).
In addition, the thesis considered the influence of initial imperfections on the behavior of RHS T joints, such as welding residual stresses and initial geometric imperfections. Welding residual stresses were investigated numerically, with the simulation of the welding process and the subse-quent static loading of the joint under in-plane bending moment and axial loading. The results showed that the welding sequence did not influence the structural behavior of the analyzed joints;
therefore, the idealized simplified sequence was proposed to reduce computational efforts. In the considered range of joints, welding residual stresses were found to increase the resistance of joints.
The conducted parametric studies demonstrated that the improving effect was particularly pro-nounced for the joints with small wall thickness (large 2γ ratio), reaching 19% for in-plane bend-ing and 17% for axial loadbend-ing. The observed influence on initial stiffness was insignificant. The obtained results allow to conclude that welding residual stresses can be safely ignored in the the-oretical and numerical design of RHS T joints, with no unbeneficial consequences.
The influence of initial geometrical imperfections was investigated numerically, considering RHS T joints under in-plane bending and axial loading. The analyses employed the common approach for the modeling of geometrical imperfections on thin-walled structures, applying scaled buckling modes to the joint with perfect geometry. The buckling modes were scaled according to the al-lowable tolerances specified in Eurocode. In case of axial loading, the most conservative results were observed when imperfections were modelled by the buckling mode that repeats the defor-mation pattern under the corresponding loading. In case of in-plane bending moment, none of the buckling modes was found suitable for modeling imperfections; therefore, they were simulated using the modes from axial loading. The conducted parametric studies demonstrated the reducing effect of imperfections on the resistances and initial stiffness of the tested joints, both those gov-erned by chord face failure (β≤ 0.85), and those governed by chord side walls failure (β > 0.85).
However, the effect was inconsiderable, reaching 5% for resistance and 7% for initial stiffness.
In practice, such small reductions do not have to be considered in the design.
Finally, the thesis developed a surrogate model for initial rotational stiffness of RHS Y joints.
The model was constructed employing the Kriging method and using the sample points calculated numerically. The model considered the joints in the whole range of the practical interest, follow-ing the limitations of Eurocode. The model allowed to receive an immediate and relatively accu-rate outcome without considerable computational efforts. Such a method demonstaccu-rated that sur-rogate modeling can represent a very effective tool for the engineering tasks with extensive com-putations and for which no analytical solution exists.