# Overview of FEM-Based Resistance Models for Local Buckling of Welded Steel Box Section Columns
## 3 Finite Element Model
### Imperfections and Residual Stresses
#### 3.4.2 Residual Stress Distribution  
There are some investigations that have defined different residual stress distribution patterns, but all of them point out that the fabrication process generates tensile stress in the corners of the box section and in the welding cord vicinity, and compressive stress along the midspan on the plates. The maximum magnitude for both tensile and compressive stress depends on welding features such as the welding size and type, voltage used, and heat  
Figure 4: Applied boundary conditions—master and slave nodes in the computation model.  
applied. The ECCS Manual [44] provides a feasible model for the residual stress pattern to be applicable for welded box sections. But it does not consider the yield strength of the material or the plate width to establish the lengths of residual stress zones; however, test results showed its importance. Other code-based residual stress models are presented in Swedish [45] and Chinese [46] design codes. Previous research results also present a wide variety of distribution; some focus on a specific yield material. [PERSON] et al. [47], and [PERSON] et al. [48] examined box sections built up with 460 and 690 MPa steel material, respectively. The unique work that presented a distribution for a wide range of yield stress values was made by [PERSON] and [PERSON] [20], which considers yield stresses from 235 to 960 MPa. These stress distribution models are shown in Figure 5.  
The residual stress distribution pattern presented in the ECCS manual [44] provides specific values for the compressive stress developed in the plates due to the welding process, taking into account the width-to-thickness plate ratio and welding type. These values are outlined in Table 2. In the case of the [PERSON] and [PERSON] RS distribution model [20], the compressive stress generated in the plates is associated with the dimensions of the plate, and it is distinguished based on plate thickness. These relationships are expressed in Equation (9). In the [PERSON] et al. model [48], the compressive residual strength is determined by a unique equation applicable to any plate geometry, considering the yield stress of the base material. This equation is presented in (10).  
Figure 5: Different residual stress models for welded square box sections: (**a**) ECCS model [44], (**b**) Swedish model [45], (**c**) Chinese model [46], (**d**) Somodi–Kövesdi model [20], and (**e**) [PERSON] et al. model [48].  
The residual stress distribution must be in equilibrium, which means the tensile force developed in the welding zone should be equal to the compressive force developed in the other parts of the cross-section. The magnitude of the tension force is directly related to the temperature reached in the welding seam, the yield stress of the material and the subsequent treatment [49]. The computational model created for this research incorporates axial residual stress. The initial residual stress pattern along the transversal direction of a plate is shown in Figure 6 as an example for a box section with a 82.5 mm width and 3.1 mm plate thickness, composed of steel having 441 MPa yield strength, which represents one of the experimental tests carried out by Clarin [1].  
\[\sigma_{\text{rc}}=\begin{cases}70-21\text{t}+\text{t}^{2}-(2900-3600(\text{t} -5))\times\left(\frac{\text{b}}{\text{t}}\right)^{-1},\text{ t}>5\text{mm}\\ \\ 70-21\text{t}+\text{t}^{2}-(2900-290(\text{t}-5))\times\left(\frac{\text{b}}{ \text{t}}\right)^{-1},\text{ t}<5\text{mm}\end{cases} \tag{9}\]  
\[\sigma_{\text{rc}}=-\text{f}_{\text{y}}\times 3.6607\times\left(\frac{\text{b}- \text{t}}{\text{t}}\right)^{-0.924} \tag{10}\]