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*Appl. Sci.*
**2019**,
*9*(20),
4220;
https://doi.org/10.3390/app9204220

Article

An Investigation on Base Metal Block Shear Strength of Ferritic Stainless Steel Welded Connection

Department of Architectural Engineering, Hanbat National University, 125, DongSeoDae-ro, Yuseong-Gu, Daejeon 34158, Korea

^{*}

Author to whom correspondence should be addressed.

Received: 17 September 2019 / Accepted: 7 October 2019 / Published: 10 October 2019

## Abstract

**:**

This study develops a finite element analysis model to predict the ultimate strength of the base metal block shear fracture based on previous experimental results and compares the experimental results with the analysis results to verify the effectiveness of the analysis model. This study also analyzed additional variables of the welding direction and weld length on the applied load to investigate the structural behaviors and fracture conditions. In addition, predicted strength according to the analysis results were compared with those by the current design equations, and the equations proposed by previous researchers. As a result, the design formula by the current design equations, such as Korea Building Code (KBC)/American Institute of Steel Construction (AISC) and European Code (EC3), and the equations proposed by Oosterhof and Driver underestimated the base metal block shear strength of ferritic stainless steel by up to 42%. Equations suggested by Topkaya and Lee et al. for carbon steel and austenitic stainless steel welded connections provided more accurate strength predictions, while they did not reflect the difference of material properties. Therefore, this study proposed a modified strength equation for ferritic stainless steel welded connection with base metal block shear fracture considering the stress triaxiality effect of the welded connection and the material properties of ferritic stainless steel.

Keywords:

finite element analysis; tensile stress factor: shear stress factor; stress triaxiality; design equation## 1. Introduction

As a structural material of buildings or infrastructure, stainless steel has important characteristics such as corrosion resistance, durability, fire resistance, and aesthetics compared to carbon steel. Therefore, the use of stainless steel as nonstructural members of interior and exterior materials, as well as structural members of buildings at home and abroad, has been increasing recently. Structural design specifications for cold-formed stainless steel were established in the United States (American Society of Civil Engineers, ASCE) [1], Europe (Eurocode 3, EC 3 part 1–4) [2], Japan (Stainless Steel Building Association of Japan, SSBA) [3], and Australia/New Zealand (AS/NZS 4673) [4]. However, in Korea, stainless steel has not been designated as a structural steel material in the Korean Building Code (KBC) up to now [5]. Moreover, the structural design standards for stainless steel structural members are not yet available. In Korea, recently, many researchers have performed studies on structural behaviors, such as fracture mode and ultimate strength of bolted and welded connections of thin-walled (cold-formed) stainless steel plates through experimental and analytical methods [6,7,8,9].

Since ferritic stainless steel among various types of stainless steels does not contain smaller amounts of alloying elements such as molybdenum, nickel, titanium, and niobium, the material cost is lower than austenitic and duplex stainless steels, and its demand for use as interior and exterior materials and structural materials of general buildings, which are not harshly corrosive environments such as coastal areas and chemical plants, is increasing [10]. Additionally, it usually possesses better deep drawability and resistance to stress corrosion cracking. However, ferritic stainless steel has lower ductility than austenitic stainless steel and contains a large amount of carbon (C), which causes embrittlement (brittle fracture) of the heat affected zone (HAZ) and poor weldability than austenitic stainless steel. Ferritic stainless steels are hardened by cold working and not hardened (strengthened) by quenching, and develop minimum hardness and maximum ductility, impact toughness, and corrosion resistance in the annealed and quenched condition [11].

With the development of welding technology for ferritic stainless steel, recently, all of the ferritic types are considered weldable with the majority of the welding processes except for the free machining grade (AISI

**430F**, which contains high sulphur content). ASCE specifies that Type 430 stainless steel shall not be used for welded connections due to deterioration of corrosion resistance and toughness. Thus far, there have been few studies on the structural behaviors of ferritic stainless steel welded connections.As a series of the block shear strength estimation for stainless steel welded connection, experimental and analytical studies have been performed on the structural behavior of the base metal and weld metal fracture of welded connections made of austenitic stainless steel STS304 (ASTM 304 type) [12] and STS304L (ASTM 304L type) [13]. The predicted block shear strength according to the current design equations of KBC, AISC, and EC3. Moreover, the proposed equations of previous studies on carbon steel welded connections by Topkaya [14] and Oosterhof and Driver [15] were compared with the experimental and analytical results. However, these research projects did not include the consideration of welded connections with ferritic stainless steel, which has different material properties such as yield stress, tensile strength, yield ratio, elongation, etc. [16]. Teh and Deierlein have studied block shear behavior of bolted connections and proposed the block shear equation considering a limiting shear tearout stress of 0.6 Fu on each effective shear area and shear failure plane to be midway between the gross and the net shear planes [17].

Studies on buckling behaviors and web crippling design of ferritic stainless steel structural members have been carried out by Bock et al. [18], Zhao et al. [19] and Yousefi et al. [20]. Kim [21] performed an experimental study on the ferritic stainless steel (STS430) welded connection with base metal block shear fracture and evaluated the ultimate strength depending on the length of the weld line according to loading direction. It was found that the current design equations for carbon steel welded connections did not consider the shear lag effect, stress triaxiality effect, and stress distribution factor in the critical fracture section for ferritic stainless steel welded connection.

This study examines the stress and strain distribution of welded connections based on the previous experimental results of ferritic stainless steel (STS430) fillet-welded connections with base metal block shear fracture and develops a finite element analysis model to predict the ultimate strength of welded connection with the base metal block shear fracture. Additional analysis on the weld length on the welding direction without further testing to compare and review the fracture mode and strength according to the variables was also performed. In addition, this study considered the applicability of the design formula by comparing the ultimate block shear strength of the analysis results with the predicted strength according to the current design equations and the equations proposed by Topkaya [14], Oosterhof and Driver [15], and Lee et al. [13]. The current design equations such as KBC/AISC and EC3 and the equations proposed by Oosterhof and Driver were conservative to predict the base metal block shear strength of ferritic stainless steel. Although proposed equations by Topkaya and Lee et al. for carbon steel and austenitic stainless steel provided more accurate ultimate strengths, it is required that tensile stress and shear stress factors in the block shear path to reflect the characteristics of ferritic stainless steel material properties. Finally, a modified block shear strength equation considering the effects of the stress triaxiality on ultimate strength, stress distribution at the critical block shear section of ultimate state and weld length of the ferritic stainless steel welded connection was proposed.

## 2. Overview of Previous Experimental Studies

A total of seven specimens of ferritic stainless steel (STS430) welded connections with base metal fracture were tested by Kim [21] and this chapter summarizes the test results. Table 1 includes the names of the specimens and the test results according to the combination of the weld length (L) in the loading direction and the weld length (T) perpendicular to the loading direction. The test specimens were composed of three parts (test part, coupling part, and clamping part). Test and clamping parts were chosen with 3.0 mm thick plane plates and coupling part was machined with 6.0 mm thick plane plate. Two plates of test part and clamping part were joined to Arc weld with 3.0 mm weld size (${S}_{a}$) on both sides of coupling part (refer to the Figure 4a of the reference [21]). In order to evaluate the difference of structural behaviors according to the weld length and welding direction of the STS 430 welded connection, the specimens were produced by combining the weld lengths in the loading direction and perpendicular to the applied load as the main variables. Post weld heat treatment (PWHT) for Arc welded specimens after arc welding was not performed additionally and they were air cooled. Electrode for Arc welding of ferritic stainless steel (STS430) plates was chosen as E430-16 (minimum specified strength of Fxx = 480 MPa) with the diameter of 3.2 mm specified in KS D 7014 (corresponds to E430-16 in AWS A5.4).

Three tensile coupons were tested to determine material properties of nominal 3.0 mm thick ferritic stainless steel (STS430) plate in accordance with KS B 0802 (Method of tensile test for metallic materials, corresponds to ISO 6892). The average plate thickness (te) is 2.93 mm, elastic modulus (E) was 179.50 GPa, the yield stress (${\sigma}_{y}$) was 259.93 MPa, the tensile strength (${\sigma}_{u}$) was 412.87 MPa, the yield ratio (${\sigma}_{y}/{\sigma}_{u}$) was 62.93%, the ultimate strain at tensile stress was 0.36 mm/mm, and the elongation (EL) at failure was 42.28% [21]. Material test for the heat affected zone (HAZ) of welded connection with 3.0 mm thick ferritic stainless steel plate was not conducted in the previous study. Based on the previous test results, the fracture modes and the load-displacement curves of the representative specimens at the end of the experiment are shown in Figure 1 and Figure 2, respectively. As shown in Figure 1, the block shear fracture, which is a combination of a tensile fracture in the perpendicular direction to the load and a shear fracture in the loading direction, occurred in the base metal near the toe of the weld metal, rather than in the weld metal. As shown in the load-displacement curves of Figure 2, it was found that stress was concentrated on the welding end point of shear plane and shear yielding or shear crack started at the point. As a result, temporary strength drop on the curves of the specimens were observed due to the shear yielding or shear fracture of both ends (welding end point) in the loading direction. However, the shear yielding or shear fracture did not contribute to the determination of ultimate strength. Finally, tensile fractures in the direction perpendicular to the load occurred as the enforced displacement increased, and determined the ultimate strength. In the existing experimental study of ferritic stainless steel (STS430), welded connections with base metal block shear fracture [21] and block shear strengths were investigated according to weld lengths and welding methods and were compared with those calculated by current design equations.

## 3. Finite Element Analysis and Parametric Study

#### 3.1. Analysis Model

This study develops a finite element analysis model using ABAQUS 2016, a nonlinear analysis program and compares the analysis results with the experimental results referring to existing numerical analysis procedures [12,13]. In addition, the influence of the weld length on the base metal block shear fracture of the welded connection is evaluated by parametric analysis.

#### 3.1.1. Welded Connection Modeling

The finite element analysis model for the ferritic stainless steel (STS430) fillet-welded connection is displayed in Figure 3. Four parts (test part, coupling part, rigid part, and weld metal) of welded connections were modeled with continuum solid element type (C3D8R). However, base metal and heat affected zone (HAZ) in the test part were not divided into different regions and were assumed to have same material properties [12,13]. Coupling part (6.0 mm thick plate) in the center and weld metal were modeled to be deformed. In the fixed parts (rigid part and clamping part) on the right side of Figure 3, the weld length of both sides in the loading direction was set to 80 mm to induce a block shear fracture of the base metal in the test part. The mesh area of the plate was divided into two different parts based on the line of 30 mm away from the toe of the weld metal in the direction perpendicular to applied force in the test part, and the mesh size around the weld metal where the fracture was predicted was divided into by 0.1 mm for the surface and three equal parts for the thickness direction referring to previous studies for weld connection conducted by Lee et al. [12,13]. Another part far from the fillet-welded connection was less refined and the maximum element aspect ratio for test part and rigid part was limited to 5:1 in order to minimize analysis time.

#### 3.1.2. Material Model and Boundary Conditions

Since material properties of SFT30-2 coupon from the material test results of the three tensile coupons by Kim [21] were the closest to the average values, the nominal stress-strain data of SFT30-2 coupon were used to input the material model with true stress-strain data for the finite element analysis. Elastic modulus and Poisson’s ratio (ν = 0.3) of the SFT30-2 coupon are applied in the elastic region, and for the plastic behavior after the elastic region, the true plastic strain is entered, in which the elastic strain is deducted from the total strain.

Under symmetrical boundary conditions on the x-y plane in the welded connection of Figure 3, one intermediate coupling part and half the test part and clamping part in the thickness direction were modeled. In order to obtain load-enforced displacement relationship data on the welded connection, the entire left side of Figure 3 was connected to the reference point (RP1) as a rigid body. Displacement control method was used to gain load and enforced displacement curves of STS430 welded connection model. The interaction between coupling part and weld metal and the interaction between both 3.0 mm plates (test part and rigid part) and weld metal are modeled to be rigid link in the rigid body option of constraint. That is, the intermediate coupling part and the weld metal are constrained to the reference point (RP2) by the rigid body. The contact conditions at the non-welded areas between both plates and the intermediate connecting material are assumed to be free of friction, i.e., frictionless formulation of tangential behavior in contact property option was adopted.

#### 3.2. Comparison of Experimental Results and Parametric Study

#### 3.2.1. Ultimate Strength and Fracture Mode

Based on the material test results and experimental results of the existing welded connections in Chapter 2, numerical analysis was performed with finite element (FE) analysis methods presented in Section 3.1, and Table 2 summarizes the FE analysis and experimental results for the fracture mode and ultimate strength. This study focused on the comparison of ultimate strength and fracture mode between test results and analysis results except from initial stiffness and deformation to verify the effectiveness of finite element analysis procedures. Figure 4 shows the load-displacement curves of three typical specimens obtained from the test and analysis results. Since the coupling part (6.0 mm thick plate) in the center and weld metal in the analysis model were assumed to be deformed, initial stiffness and deformation were not considered in the comparison. In addition, Mises stress distribution at the ultimate strength point obtained from the analysis results of FT20L20, FT30L30, and FT40L40 specimens are shown in Figure 5 to compare with the fracture modes of the experimental results in Figure 1. From the analysis results, the block shear fracture mode (a combination of tensile fracture and shear fracture) was observed in the base metal near the toe of the weld metal as in the experimental results, and namely, Mises stress distribution was concentrated first on the critical tensile area perpendicular to the direction of loading and both corner parts of the weldment, as displayed in Figure 5. Mean ultimate strength ratio (Pua/Pue) of analysis result against test result was 0.98 in Table 2, and it can be noted that ultimate strength and block shear fracture mode predicted by finite element analysis model presented in this paper provided a good correspondence to the test results.

#### 3.3.2. Parametric Analysis on the Weld Length

In order to examine the structural behavior according to the additional variables of ferritic stainless steel (STS430) fillet-welded connections where the base metal is fractured, this study also performed a parametric analysis instead of an experimental method. An additional finite element analysis model is introduced with a weld length (T = 20–40 mm) in the direction perpendicular to the load and a weld length (L = 20–85) in the loading direction as variables.

Welded connection with same plate thickness of 3.0 mm and same weld size of 5.0 mm were modeled to compare the ultimate strength (Pua) of the analysis results against the welded connection of the same weld dimension. Figure 6 and Table 3 show the load-displacement curves, ultimate strength and fracture mode obtained from the parametric analysis results. The block shear fracture (BS) of the base metal occurred when the ratio (l/e) of the total weld length (l) in the loading direction to the end distance (e) ranged from 0.45 to 1.49, and a gross tensile fracture (GT) occurred when the ratio (l/e) of the total weld length in the loading direction to the end distance (e) exceeded 1.49.

The strength of the block shear fracture of STS430 welded connection increased as the weld length (L) in the loading direction got larger, and since the weld length in the loading direction is independent of the tensile fracture strength, the strength of the tensile fracture in the connection did not show a significant difference in strength even though the weld length increased.

#### 3.2.3. Stress and Strain Investigation in Critical Path

In order to investigate the distribution of the stress and strain of the base metal surface in the direction perpendicular to the tensile fracture line and shear fracture line with the increase of enforced displacement in FT20L20, which is one of the block shear fracture models in Table 3, Path 1 and Path 2 were set, respectively, from the weld toe (location ⓪) of the weld metal as shown in Figure 7a. The distribution of direct stress (S22) and plastic strain (PE22) in the loading direction (2(y)-axis direction) in Path 1, and the distribution of shear stress (S12) and shear plastic strain (PE12) in Path 2 were examined. As shown in Figure 7b,c, the maximum value of stress and strain was investigated near the point about 2 mm away from the weld toe.

#### 3.2.4. Comparison of Stress Distribution by Fracture Mode

From the investigation results of the location of maximum stress and strain in Section Section 3.2.3, The distributions of direct stress (S22, ${\sigma}_{22}$) and shear stress (S12, ${\sigma}_{12}$) by designating Path 3 and Path 4 were also examined in the tensile and shear areas 2mm away from the weld toe as shown in Figure 8a. The test specimens were selected as FT20L20 with block shear fracture (BS) and FT30L77 with tensile fracture (GT) in Table 3.

In terms of FT20L20 with block shear fracture (BS) in Figure 8b,c, the stress concentration was observed across the entire path in the tensile and shear areas. In terms of FT30L77 with gross tensile fracture (GT), a similar stress concentration to FT20L20 was observed in the tensile area, although the shear stress distribution was lower than that of FT20L20 in the shear area.

## 4. Strength Comparison with Design Prediction and Recommendation

#### 4.1. Comparison of Design Strength and Analysis Strength

Table 4 summarizes the current block shear fracture design equations [2,5,22] and the block shear fracture shear strength equations proposed by other researchers [13,14,15]. In Table 4, Ant is the net area subjected to tension, Agt is the gross area subjected to tension, ${A}_{gv}$ is the gross area subjected to shear, Anv is the net area subjected to shear, ${\sigma}_{y}$ is the yield stress, and ${\sigma}_{u}$ is the ultimate tensile strength of STS430 material.

Table 5 compares the predicted ultimate strength (Put) according to these equations with the analytical ultimate strength (Pua). The critical section areas of the tensile and shear fractures in the design block shear equation are shown in Figure 9. Equations (1)–(3) in Table 4 are derived from the results of the research on the block shear fracture of the bolted connections, and since the stress triaxiality effect, which is a characteristic of the welded connection on block shear strength, is not considered sufficiently, AISC2016/KBC2016 and EC3 underestimated the block shear strength by an average of 38% and 42%, respectively, when compared with analysis strength. The equation proposed by Oosterhof and Driver [15] underestimated the block shear strength by an average of 22%. Although the Equations (4) and (6) proposed by Topkaya [14] and Lee et al. [13] estimated the strength of the ferritic stainless steel base metal fracture welded connection most closely with strength ratios (${P}_{ut}/{P}_{ua}$) between 0.94–1.07 and 0.95–1.05, it is necessary to examine the block shear fracture mechanism considering the characteristics of ferritic stainless steel, which has different material properties from carbon steel and austenitic stainless steel (304 Type), as well as the stress triaxiality effect.

#### 4.2. Stress Analysis for Extended Variables

The block shear strength equations in Table 4 are the values presented as a result of research on carbon steel bolted and welded connections, in which the first term on the right is the tensile fracture strength and the second term is the shear fracture strength or shear yield strength. The stress factor for tensile fracture strength is defined as 1.0 in Equations (1)–(3), and 1.25 in Equations (4) and (5), and the stress factor for shear fracture or shear yield strength is 0.6 or $1/\sqrt{3}$. In order to examine the tensile and shear stress factors at the ferritic stainless steel base metal fracture welded connections, the following stress factors were calculated from the finite element analysis results by investigating the stress distributions extracted from Path 3 and Path 4 of Figure 8a and the concept of triaxial stress of ductile fractured steel according to the von Mises yield criterion.

#### 4.2.1. Tensile Stress Factor

Table 6 summarizes the ratio of maximum stress to the triaxial stress, material tensile strength (σ

_{u}), and the two average stresses (σ_{11}/σ_{tu}and σ_{22}/σ_{tu}), in which the tensile stress distribution in the tensile fracture section of the critical section of the welded connection according to Path 3, are non-dimensionalized by the true stress (σ_{tu}). The triaxial stress value was calculated as the ratio (ST = σ_{22/}σ_{Mises}) of maximum stress (σ_{22}) to the von Mises yield stress (σ_{Mises}). Figure 10 shows the relationship between the triaxial stress and the ratio of maximum stress to the triaxial stress and material tensile strength. As a result of the stress triaxiality effect, the tensile stress increased by 1.55 times the material tensile strength in the tensile section, and from the relation between the triaxial stress and the increased tensile stress, the tensile stress increased by 1.36 times the ferritic stainless steel tensile strength in the total tensile section of the block shear fracture.#### 4.2.2. Shear Stress Factor

Figure 11 shows the stress ratio (σ

_{12}/(σ_{tu}+ σ_{ty})/2), in which the mean ((σ_{tu}+ σ_{ty})/2) of the maximum and yield shear stresses from the stress distribution according to Path 4 in the shear section of the critical section of the welded connection, is non-dimensionalized by the shear stress (σ_{12}) in analysis, and the mean value is 0.59. When the shear stress factor is expressed in the form of $1/\sqrt{3}$ by the Mises yield criterion, it can be expressed in the form of 1.0(σ_{u}+ σ_{y}$)/2\sqrt{3}$.#### 4.2.3. Strength Equation Proposal

In Table 5, block shear fracture strength equation (Equation (4)) by Topkaya provided the closest estimates, and the values were overestimated as the weld length (L) increased in the direction perpendicular to the load. Based on the results obtained from the finite element analysis, the tensile stress factor of 1.25 was modified to 1.36, in reference to Topkaya’s equation (4), as a tensile stress 1.36 times the tensile strength (σu) of ferritic stainless steel material in the tensile section of the block shear fracture was generated by the stress triaxiality effect of the welded connection from Table 6 and Figure 10b. It can be noted that suggested tensile stress, 1.36, is similar to that (=1.35) of austenitic stainless steel welded connection by Lee et al. [13], and the block shear fracture critical section in this study is identical to that of Equations (4) and (6) by Topkaya [14] and Lee et al. [13]. Furthermore, the shear stress factor (Sf) was modified to the average shear stress (${\sigma}_{u}+{\sigma}_{y})/2\sqrt{3}$) of the material in the shear section based on the rightmost mean value (=0.97) of Table 7. Consequently, the following block shear fracture strength equation for the base metal block shear fracture ferritic stainless steel (STS 430) welded connection was proposed:

$${P}_{utp}=1.36{A}_{gt}{\sigma}_{u}+\frac{{\sigma}_{u}+{\sigma}_{y}}{2\sqrt{3}}{A}_{gv}$$

In order to verify the validity of the proposed block shear fracture strength equation (Equation (7)) with modified tensile stress factor considering the stress triaxiality effect and stress distribution of the critical shear section at the ferritic stainless steel welded connection, Table 8 summarizes the predicted strength (${P}_{utp}$) by Equation (7), test ultimate strength (${P}_{ue}$) and the analytical ultimate strength (${P}_{ua}$). The average strength ratios (${P}_{utp}/{P}_{ue}$, ${P}_{utp}/{P}_{ua}$) to the predicted strength (${P}_{utp}$) by proposed equation for the test strength (${P}_{utp}$) and analytical strength (${P}_{ua}$) was 0.96 and 0.94, respectively, and the proposed equation provided improved (more conservative) evaluations than Equations (4) and (6) by Topkaya and Lee el al., which are the block shear fracture equations for the carbon steel welded connection and austenitic stainless steel welded connection, respectively.

## 5. Conclusions

A finite element analysis model based on the previous experimental study results of ferritic stainless steel (STS430) fillet-welded connections with base metal block shear fracture was developed. In addition, the stress distribution in the critical section of the welded connection through additional parametric analysis by using the weld lengths in the direction of the load and perpendicular to the load was examined, and the predicted strengths by the analysis results, current design equations, and equations proposed by other researchers were compared. The design equations of KBC2016, AISC2016, and EC3 underestimated the block shear strength of the welded connections because they do not fully consider the stress triaxiality effect on the ultimate strength of welded connection. Moreover, Topkaya’s equation, based on the results of research of carbon steel welded connections, showed the closest evaluation of the block shear fracture strength. Since the material properties of ferritic stainless steel are different from those of carbon steel; therefore, the tensile stress factor was modified from 1.25 to 1.36 by examining the critical section and stress distribution at the point of ultimate strength in the welded connection from the analysis results and the shear stress factor was also modified by the average value of the tensile strength and yield stress of the STS430 material. As a result, it is found that the prediction accuracy of the ferritic stainless steel (STS430) welded connection with base metal block shear fracture strength by the proposed equation was improved.

## Author Contributions

T.K. and B.H.; methodology, T.K.; software, S.Y. and W.A.; validation, W.A.; formal analysis, S.Y. and W.A.; investigation, T.K. and S.Y.; resources, T.K. and B.H.; data curation, T.K.; writing—original draft preparation, S.Y. and W.A.; writing—review and editing, T.K.; visualization, W.A.; supervision, T.K.; project administration, T.K.; funding acquisition, T.K.

## Funding

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (KRF-2015R1D1A3A01016603) and the Human Resources Development of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Trade, Industry & Energy (No. 20184030201900).

## Conflicts of Interest

The authors declare no conflict of interest.

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**Figure 1.**Fracture shapes of specimens at test end: (

**a**) FT20L20, (

**b**) FT20L40, (

**c**) FT30L40, (

**d**) FT30L40, (

**e**) FT40L30, (

**f**) FT40L40.

**Figure 2.**Load-displacement curves of specimens: (

**a**) FT20 series and (

**b**) FT30 series and FT40 series.

**Figure 4.**Comparison of load-displacement curves obtained from test and analysis results: (

**a**) FT20L20, (

**b**) FT30L30, (

**c**) FT40L40.

**Figure 5.**Fracture shape and stress distribution in the ultimate strength of analysis results: (

**a**) FT20L20 (Displacement = 4.07 mm, Pua = 80.77 kN), (

**b**) FT30L30 (Displacement = 8.25 mm, Pua = 113.80 kN), (

**c**) FT40L40 (Displacement = 17.32 mm, Pua = 134.56 kN).

**Figure 6.**Load-displacement curves of parametric analysis results: (

**a**) FT20 series (T = 20 mm), (

**b**) FT30 series (T = 30 mm), (

**c**) FT40 series (T = 40 mm).

**Figure 7.**Stress and strain distribution along Paths 1 and 2 for FT20L20: (

**a**) Definition and symbol of Paths 1 and 2 for FT20L20, (

**b**) direct stress (S22, ${\sigma}_{22}$) and shear stress (S12, ${\sigma}_{12}$) in Path 1 and Path 2, (

**c**) plastic direct strain (PE22) and plastic shear strain (PE12) in Path 1 and Path 2.

**Figure 8.**Stress distribution for FT20L20 and FT30L77 in Paths 3 and 4: (

**a**) Definition and symbol of the Paths 3 and 4 for FT20L20, (

**b**) Tensile direct stress (S22) distribution for FT20L20 and FT30L77 in Path 3, (

**c**) Shear stress distribution for FT20L20 and FT30L77 in Path 4.

**Figure 10.**Triaxiality (T) and normalized maximum longitudinal stress (σ

_{22/}σ

_{u}) from the toe of the weld line on the tension plane (Path 3): (

**a**) Triaxiality (T), (

**b**) Relationship between triaxiality (T) and normalized maximum longitudinal stress ratio (σ

_{22/}σ

_{u}).

Specimen | Weld Length in the Transverse Direction (T) (mm) | Weld Length in the Longitudinal Direction (L) (mm) | Measured Plate Thickness (Test Part) ${\mathit{t}}_{\mathit{e}}\left(\mathbf{mm}\right)$ | $\mathbf{Ultimate}\mathbf{Strength}{\mathit{P}}_{\mathit{u}\mathit{e}}\left(\mathbf{kN}\right)$ | $\mathbf{Ultimate}\mathbf{Displacement}{\mathit{\delta}}_{\mathit{u}}\left(\mathbf{mm}\right)$ | Fracture Mode (FM) at Test End |
---|---|---|---|---|---|---|

FT20L20 | 20 | 20 | 2.87 | 84.77 | 4.65 | Block Shear Fracture (BS) |

FT20L30 | 30 | 2.85 | 99.86 | 5.84 | ||

FT20L40 | 40 | 2.88 | 116.33 | 9.71 | ||

FT30L30 | 30 | 30 | 2.96 | 113.19 | 5.95 | |

FT30L40 | 40 | 2.64 | 124.07 | 9.05 | ||

FT40L30 | 40 | 30 | 2.90 | 117.80 | 6.85 | |

FT40L40 | 40 | 2.86 | 131.03 | 12.08 |

Specimen | Test Results | Analysis Results | $\mathbf{Strength}\mathbf{Ratio}{\mathit{P}}_{\mathit{u}\mathit{a}}/{\mathit{P}}_{\mathit{u}\mathit{e}}$ | ||
---|---|---|---|---|---|

$\mathbf{Ultimate}\mathbf{Strength}{\mathit{P}}_{\mathit{u}\mathit{e}}\left(\mathbf{kN}\right)$ | Fracture Mode | $\mathbf{Ultimate}\mathbf{Strength}{\mathit{P}}_{\mathit{u}\mathit{a}}\left(\mathbf{kN}\right)$ | Fracture Mode | ||

FT20L20 | 84.77 | BS (Block shear fracture) | 80.77 | BS (Block shear fracture) | 0.95 |

FT20L30 | 99.86 | 94.50 | 0.95 | ||

FT20L40 | 116.33 | 107.04 | 0.92 | ||

FT30L30 | 113.19 | 113.80 | 1.00 | ||

FT30L40 | 124.07 | 116.54 | 0.94 | ||

FT40L30 | 117.80 | 122.36 | 1.04 | ||

FT40L40 | 131.03 | 134.56 | 1.02 | ||

Average | 0.98 |

Specimen | Ratio of the Total Weld Length to the End Distance, l/e | $\mathbf{Ultimate}\mathbf{Strength}{\mathit{P}}_{\mathit{u}\mathit{a}}\left(\mathbf{kN}\right)$ | $\mathbf{Strength}\mathbf{Ratio}{\mathit{P}}_{\mathit{u}\mathit{a}}$$/{\mathit{P}}_{\mathit{u}\mathit{a}-\mathit{L}\mathit{m}\mathit{i}\mathit{n}}$ | Fracture Mode (FM) |
---|---|---|---|---|

FT20L20 | 0.45 | 87.09 | 1.00 | BS |

FT20L30 | 0.64 | 101.65 | 1.17 | BS |

FT20L40 | 0.82 | 114.87 | 1.32 | BS |

FT20L50 | 1.00 | 126.84 | 1.46 | BS |

FT20L60 | 1.18 | 137.67 | 1.58 | BS |

FT20L70 | 1.36 | 147.48 | 1.69 | BS |

FT20L77 | 1.49 | 153.59 | 1.76 | BS |

FT20L80 | 1.55 | 156.71 | 1.80 | GT |

FT20L83 | 1.60 | 158.68 | 1.82 | GT |

FT20L85 | 1.64 | 160.46 | 1.84 | GT |

FT30L20 | 0.50 | 102.86 | 1.00 | BS |

FT30L30 | 0.70 | 117.24 | 1.14 | BS |

FT30L40 | 0.90 | 130.57 | 1.27 | BS |

FT30L45 | 1.00 | 135.84 | 1.32 | BS |

FT30L60 | 1.30 | 151.15 | 1.47 | BS |

FT30L65 | 1.40 | 156.08 | 1.52 | BS |

FT30L68 | 1.48 | 158.94 | 1.55 | BS |

FT30L72 | 1.54 | 162.33 | 1.58 | GT |

FT30L75 | 1.60 | 165.03 | 1.60 | GT |

FT30L77 | 1.64 | 166.01 | 1.61 | GT |

FT30L79 | 1.68 | 166.29 | 1.62 | GT |

FT40L20 | 0.56 | 116.74 | 1.00 | BS |

FT40L30 | 0.78 | 130.87 | 1.12 | BS |

FT40L40 | 1.00 | 143.46 | 1.23 | BS |

FT40L50 | 1.22 | 153.25 | 1.31 | BS |

FT40L60 | 1.44 | 162.17 | 1.39 | BS |

FT40L62 | 1.49 | 164.12 | 1.41 | BS |

FT40L65 | 1.56 | 167.66 | 1.44 | GT |

FT40L67 | 1.60 | 169.09 | 1.45 | GT |

FT40L69 | 1.64 | 170.30 | 1.46 | GT |

FT40L72 | 1.71 | 171.03 | 1.47 | GT |

Carbon Steel Welded Connection | KBC2016/AISC2016 | ${P}_{n}={\sigma}_{u}{A}_{nt}+0.6{\sigma}_{y}{A}_{gv}$ | (1) | The minimum value out of the two strengths |

${P}_{n}={\sigma}_{u}{A}_{nt}+0.6{\sigma}_{u}{A}_{nv}$ | (2) | |||

EC3 | ${P}_{n}={\sigma}_{u}{A}_{nt}+\frac{{\sigma}_{y}}{\sqrt{3}}{A}_{nv}$ | (3) | ||

Topkaya | ${P}_{n}=1.25{\sigma}_{u}{A}_{gt}+\frac{{\sigma}_{u}}{\sqrt{3}}{A}_{gv}$ | (4) | Proposed equations by considering the stress triaxiality effect in welded connections. | |

Oosterhof and Driver | ${P}_{n}=1.25{\sigma}_{u}{A}_{nt}+\frac{{\sigma}_{y}+{\sigma}_{u}}{2\sqrt{3}}{A}_{gv}$ | (5) | ||

Austenitic Stainless Steel Welded Connection | Lee et al. | ${P}_{n}=1.35{\sigma}_{u}{A}_{gt}+1.15\frac{{\sigma}_{y}+{\sigma}_{u}}{2\sqrt{3}}{A}_{gv}$ | (6) |

Specimen | $\mathbf{Analysis}\mathbf{Ultimate}\mathbf{Strength}{\mathit{P}}_{\mathit{u}\mathit{a}}\left(\mathbf{kN}\right)$ | $\mathbf{Strength}\mathbf{Ratio}({\mathit{P}}_{\mathit{u}\mathit{a}}$$/{\mathit{P}}_{\mathit{u}\mathit{t}})$ | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

KBC2016 (AISC2016) Equations (1) and (2) | EC3 Equation (3) | Topkaya Equation (4) | Oosterhof and Driver Equation (5) | Lee et al. Equation (6) | |||||||

${\mathit{P}}_{\mathit{u}\mathit{t}}\left(\mathbf{kN}\right)$ | ${\mathit{P}}_{\mathit{u}\mathit{a}}$$/{\mathit{P}}_{\mathit{u}\mathit{t}}$ | ${\mathit{P}}_{\mathit{u}\mathit{t}}\left(\mathbf{kN}\right)$ | ${\mathit{P}}_{\mathit{u}\mathit{a}}$$/{\mathit{P}}_{\mathit{u}\mathit{t}}$ | ${\mathit{P}}_{\mathit{u}\mathit{t}}\left(\mathbf{kN}\right)$ | ${\mathit{P}}_{\mathit{u}\mathit{a}}$$/{\mathit{P}}_{\mathit{u}\mathit{t}}$ | ${\mathit{P}}_{\mathit{u}\mathit{t}}\left(\mathbf{kN}\right)$ | ${\mathit{P}}_{\mathit{u}\mathit{a}}$$/{\mathit{P}}_{\mathit{u}\mathit{t}}$ | ${\mathit{P}}_{\mathit{u}\mathit{t}}\left(\mathbf{kN}\right)$ | ${\mathit{P}}_{\mathit{u}\mathit{a}}$$/{\mathit{P}}_{\mathit{u}\mathit{t}}$ | ||

FT20L20 | 87.09 | 48.00 | 0.55 | 42.66 | 0.49 | 82.19 | 0.94 | 60.02 | 0.69 | 83.57 | 0.96 |

FT20L30 | 101.65 | 57.30 | 0.56 | 51.60 | 0.51 | 96.49 | 0.95 | 71.64 | 0.70 | 96.93 | 0.95 |

FT20L40 | 114.87 | 66.59 | 0.58 | 60.54 | 0.53 | 110.79 | 0.96 | 83.26 | 0.72 | 110.30 | 0.96 |

FT20L50 | 126.84 | 75.89 | 0.60 | 69.48 | 0.55 | 125.09 | 0.99 | 94.88 | 0.75 | 123.66 | 0.97 |

FT20L60 | 137.67 | 85.18 | 0.62 | 78.43 | 0.57 | 139.39 | 1.01 | 106.50 | 0.77 | 137.03 | 1.00 |

FT20L70 | 147.48 | 94.47 | 0.64 | 87.37 | 0.59 | 153.69 | 1.04 | 118.12 | 0.80 | 150.39 | 1.02 |

FT20L77 | 153.59 | 100.98 | 0.66 | 93.63 | 0.61 | 163.70 | 1.07 | 126.26 | 0.82 | 159.75 | 1.04 |

FT30L20 | 102.86 | 60.39 | 0.59 | 55.04 | 0.54 | 97.67 | 0.95 | 75.50 | 0.73 | 100.29 | 0.97 |

FT30L30 | 117.24 | 69.68 | 0.59 | 63.98 | 0.55 | 111.97 | 0.96 | 87.12 | 0.74 | 113.65 | 0.97 |

FT30L40 | 130.57 | 78.98 | 0.60 | 72.93 | 0.56 | 126.27 | 0.97 | 98.74 | 0.76 | 127.02 | 0.97 |

FT30L45 | 135.84 | 83.62 | 0.62 | 77.40 | 0.57 | 133.42 | 0.98 | 104.55 | 0.77 | 133.70 | 0.98 |

FT30L60 | 151.15 | 97.56 | 0.65 | 90.81 | 0.60 | 154.87 | 1.02 | 121.98 | 0.81 | 153.75 | 1.02 |

FT30L65 | 156.08 | 102.21 | 0.65 | 95.28 | 0.61 | 162.02 | 1.04 | 127.79 | 0.82 | 160.43 | 1.03 |

FT30L68 | 158.94 | 105.00 | 0.66 | 97.97 | 0.62 | 166.31 | 1.05 | 131.28 | 0.83 | 164.44 | 1.03 |

FT40L20 | 116.74 | 72.77 | 0.62 | 67.42 | 0.58 | 113.15 | 0.97 | 90.98 | 0.78 | 117.01 | 1.03 |

FT40L30 | 130.87 | 82.07 | 0.63 | 76.37 | 0.58 | 127.45 | 0.97 | 102.60 | 0.78 | 130.37 | 1.00 |

FT40L40 | 143.46 | 91.36 | 0.64 | 85.31 | 0.59 | 141.75 | 0.99 | 114.22 | 0.80 | 143.74 | 1.00 |

FT40L50 | 153.25 | 100.65 | 0.66 | 94.25 | 0.62 | 156.05 | 1.02 | 125.84 | 0.82 | 157.10 | 1.03 |

FT40L60 | 162.17 | 109.95 | 0.68 | 103.20 | 0.64 | 170.35 | 1.05 | 137.46 | 0.85 | 170.47 | 1.05 |

FT40L62 | 164.12 | 111.81 | 0.68 | 104.99 | 0.64 | 173.21 | 1.06 | 139.79 | 0.85 | 173.14 | 1.05 |

Mean | - | 0.62 | - | 0.58 | - | 1.00 | - | 0.78 | - | 1.00 |

Specimen | Direct True Stress (σ_{1}_{1,} σ_{2}_{2})-True Ultimate Stress (σ_{tu}) Ratio | Stress Triaxiality (ST) | Direct True Stress-Nominal Stress Ratio | |
---|---|---|---|---|

Transverse Direct Stress (1-axis)/(σ_{12}/σ_{tu}) | Longitudinal Direct Stress (2-axis) (σ_{2}_{2}/ σ_{tu}) | ST = σ_{2}_{2}/σ_{Mises} | σ_{2}_{2}/F_{u} | |

FT20L20 | 0.51 | 1.08 | 1.17 | 1.59 |

FT20L30 | 0.47 | 1.08 | 1.17 | 1.59 |

FT20L40 | 0.42 | 1.06 | 1.17 | 1.59 |

FT20L50 | 0.45 | 1.09 | 1.16 | 1.58 |

FT20L60 | 0.44 | 1.09 | 1.15 | 1.57 |

FT20L70 | 0.42 | 1.08 | 1.14 | 1.55 |

FT20L77 | 0.44 | 1.08 | 1.16 | 1.58 |

FT30L20 | 0.50 | 1.07 | 1.15 | 1.57 |

FT30L30 | 0.48 | 1.08 | 1.09 | 1.48 |

FT30L40 | 0.48 | 1.09 | 1.15 | 1.56 |

FT30L45 | 0.44 | 1.07 | 1.13 | 1.54 |

FT30L60 | 0.44 | 1.08 | 1.16 | 1.58 |

FT30L65 | 0.45 | 1.08 | 1.15 | 1.57 |

FT30L68 | 0.45 | 1.08 | 1.13 | 1.54 |

FT40L20 | 0.48 | 1.05 | 1.16 | 1.57 |

FT40L30 | 0.48 | 1.07 | 1.11 | 1.51 |

FT40L40 | 0.47 | 1.08 | 1.11 | 1.52 |

FT40L50 | 0.46 | 1.08 | 1.11 | 1.52 |

FT40L60 | 0.49 | 1.09 | 1.11 | 1.51 |

FT40L62 | 0.47 | 1.08 | 1.12 | 1.52 |

Mean | 0.46 | 1.08 | 1.14 | 1.55 |

**Table 7.**Proposed stress factors for specimens with block shear fracture by parametric analysis results.

Specimen | Shear Stress Factor | ||
---|---|---|---|

${\mathit{\sigma}}_{12}/{\mathit{\sigma}}_{\mathit{t}\mathit{u}}\mathbf{for}\mathbf{Ultimate}\mathbf{True}\mathbf{Strength}\mathbf{of}\mathbf{Material}$ | ${\mathit{\sigma}}_{12}/\left(\frac{{\mathit{\sigma}}_{\mathit{t}\mathit{u}}+{\mathit{\sigma}}_{\mathit{t}\mathit{y}}}{2}\right)\mathbf{for}\mathbf{Ultimate}\mathbf{and}\mathbf{Yield}\mathbf{True}\mathbf{Strength}\mathbf{of}\mathbf{Material}$ | ${\mathit{S}}_{\mathit{f}}={\mathit{\sigma}}_{12}/\left(\frac{{\mathit{\sigma}}_{\mathit{t}\mathit{u}}+{\mathit{\sigma}}_{\mathit{t}\mathit{y}}}{2\sqrt{3}}\right)\mathbf{for}\mathbf{Von}\mathbf{Mises}\mathbf{Yield}\mathbf{Criterion}$ | |

FT20L20 | 0.43 | 0.59 | 1.02 |

FT20L30 | 0.43 | 0.60 | 1.03 |

FT20L40 | 0.42 | 0.58 | 1.00 |

FT20L50 | 0.41 | 0.56 | 0.98 |

FT20L60 | 0.39 | 0.53 | 0.92 |

FT20L70 | 0.37 | 0.51 | 0.89 |

FT20L77 | 0.36 | 0.50 | 0.87 |

FT30L20 | 0.45 | 0.62 | 1.07 |

FT30L30 | 0.44 | 0.61 | 1.06 |

FT30L40 | 0.43 | 0.59 | 1.03 |

FT30L45 | 0.42 | 0.57 | 0.99 |

FT30L60 | 0.38 | 0.53 | 0.91 |

FT30L65 | 0.37 | 0.51 | 0.89 |

FT30L68 | 0.37 | 0.51 | 0.87 |

FT40L20 | 0.45 | 0.62 | 1.08 |

FT40L30 | 0.45 | 0.62 | 1.07 |

FT40L40 | 0.43 | 0.58 | 1.01 |

FT40L50 | 0.40 | 0.54 | 0.94 |

FT40L60 | 0.37 | 0.51 | 0.88 |

FT40L62 | 0.36 | 0.50 | 0.87 |

Mean | 0.41 | 0.56 | 0.97 |

Specimen | Ultimate Strength (kN) | Strength Ratio | |||
---|---|---|---|---|---|

$\mathbf{Test}{\mathit{P}}_{\mathit{u}\mathit{e}}$ | $\mathbf{Analysis}{\mathit{P}}_{\mathit{u}\mathit{a}}$ | $\mathbf{Proposed}\mathbf{Equation}\left(7\right){\mathit{P}}_{\mathit{u}\mathit{t}\mathit{p}}$ | ${\mathit{P}}_{\mathit{u}\mathit{t}\mathit{p}}/{\mathit{P}}_{\mathit{u}\mathit{e}}$ | ${\mathit{P}}_{\mathit{u}\mathit{t}\mathit{p}}/{\mathit{P}}_{\mathit{u}\mathit{a}}$ | |

FT20L20 | 84.77 | 87.09 | 79.58 | 0.94 | 0.91 |

FT20L30 | 99.86 | 101.65 | 91.20 | 0.91 | 0.90 |

FT20L40 | 116.33 | 114.87 | 102.83 | 0.88 | 0.90 |

FT20L50 | - | 126.84 | 114.45 | - | 0.90 |

FT20L60 | - | 137.67 | 126.07 | - | 0.92 |

FT20L70 | - | 147.48 | 137.69 | - | 0.93 |

FT20L77 | - | 153.59 | 145.83 | - | 0.95 |

FT30L20 | - | 102.86 | 96.42 | - | 0.94 |

FT30L30 | 113.19 | 117.24 | 108.05 | 0.95 | 0.92 |

FT30L40 | 124.07 | 130.57 | 119.67 | 0.96 | 0.92 |

FT30L45 | - | 135.84 | 125.48 | - | 0.92 |

FT30L60 | - | 151.15 | 142.91 | - | 0.95 |

FT30L65 | - | 156.08 | 148.72 | - | 0.95 |

FT30L68 | - | 158.94 | 152.21 | - | 0.96 |

FT40L20 | - | 116.74 | 112.65 | - | 0.96 |

FT40L30 | 117.80 | 130.87 | 124.27 | 1.05 | 0.95 |

FT40L40 | 131.03 | 143.46 | 135.89 | 1.04 | 0.95 |

FT40L50 | - | 153.25 | 147.51 | - | 0.96 |

FT40L60 | - | 162.17 | 159.14 | - | 0.98 |

FT40L62 | - | 164.12 | 161.46 | - | 0.98 |

Mean | 0.96 | 0.94 |

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