Experimental and Numerical Investigation on Stress Concentration Factors of Offshore Steel Tubular Column-to-Steel Beam (STCSB) Connections

Abstract

Steel tubular column-to-steel beam (STCSB) connections are critical parts in offshore structures, where complex component connections and the stress concentration are of significant concern. This study conducted stress concentration tests on welded STCSB connections and subsequently developed a finite element (FE) model for the connections, with the experimental results validating the accuracy of the model. The discussion focused on the influence of parameters such as the width-to-diameter ratio of the beam to the column, the diameter-to-thickness ratio of the column, the diameter-to-thickness ratio of the column to the beam, and the height-to-thickness ratio of the beam web on the fatigue performance. The study proposed optimization methods including the addition of stiffeners and outer flange plates. The findings indicate that optimized connection configurations can effectively mitigate stress concentration in the connected areas, thereby enhancing the structural stability and fatigue life. The width-to-diameter ratio of the beam to the column and the diameter-to-thickness ratio of the column significantly affect the fatigue performance of welded STCSB connections, with an increased width-to-diameter ratio of the beam to the column or a reduced diameter-to-thickness ratio of the column leading to a substantial decrease in the maximum stress concentration factors (SCFs). The addition of stiffeners and adjustment of the outer flange plate can improve stress concentration effects in the connection area.

1. Introduction

In response to the imperatives of achieving carbon neutrality and peaking, alongside the strategic deployment of offshore wind energy, this study underscores the necessity of substantial technological and economic advancements. Such evolutions are pivotal to the realization of comprehensive global decarbonization efforts [1]. The Chinese government has taken steps to undergo a transition from traditional fossil fuels to low-carbon clean energy, where offshore wind energy holds immense potential. As a result, it will be promising for China to promote the development of renewable energy and ensure the low-carbon development of the sustainable economy [1,2]. Offshore wind energy boasts distinct advantages, such as high wind speed, low wind shear, minimal turbulence intensity, stable prevailing wind direction, and no need for land occupation. The gradual development of marine energy and resources towards deep-sea areas represents a crucial direction for China to promote energy transition [3] and an essential pathway to achieving the “2060 carbon peak and carbon neutrality” targets [4]. However, the service environment of the offshore wind jacket is complex and harsh, and the offshore structure is subjected to wind, waves, currents, and other alternating loads for a long-term period. The jacket joint performance is constantly deteriorating, and then fatigue failure occurs. In engineering, the S-N curve based on the hot spot stress method is often used to evaluate the fatigue life of joints [5,6]. The S-N curve illustrates the number of cycles a joint can withstand until fatigue failure occurs at various stress levels, plotting the logarithm of stress amplitude against the logarithm of the number of cycles to failure. This method is used to predict the fatigue life of the joint by obtaining the size of the hot spot stress amplitude along the weld by means of numerical or experimental methods [7].

STCSB connections have been widely applied in offshore jacket structures, which are characterized by high stiffness better seismic performance and ductility compared to steel tubular joints [8,9]. Many researchers have conducted experiments and numerical analyses on the column to connections. Korkmaz and Tankut [10] explored the seismic performance of precast connections, assessing the behavior of specimens with both conventional and enhanced connection details to develop a “moment-resistant precast concrete beam-to-beam joint.” Cao et al. [11] developed a novel seismic retrofitting technique for a precast reinforced concrete and ultra-high-performance concrete composite support frame, proposing a displacement-based design approach utilizing the stochastic capacity spectrum method (CSM). Lu et al. [12] and Kamba et al. [13] investigated the bearing capacity of the STCSB connections through experiments and numerical analyses; these studies revealed that the bearing capacity of joints is mainly affected by the ratio of beam flange width to column diameter and the column diameter to thickness ratio. When the column diameter to thickness ratio is greater than 27, the bearing capacity of the joints is less than the tensile capacity, and when the column diameter to thickness ratio is less than 22, the tensile and compressive capacities of the joints are almost the same. Using the results of parameter analysis, modified bearing capacity methods for STCSB connections were developed. Kim et al. [14] investigated the influences of the different steel plate-reinforced STCSB connections, and their investigations highlighted that the bearing capacity of the flange plate is higher than that of the cover plate. Meanwhile, Kosteski et al. [15] summarized the formulas of the bearing capacity of the STCSB connections. Further research was conducted by Kamba et al. [16], who found that the failure model of the STCSB connections is fracture failure at weld along the column wall on both sides of the beam flange. Moreover, the CIDECT design guide [17] provides a formula for calculating the welding STCSB connection considering the influence of the parameters of beam flange width to column diameter and column diameter to thickness ratio, and the corresponding failure mode is plastic failure of the column wall. Subsequently, many scholars also proposed an improved column-to-beam connection mode to improve the mechanical properties of the STCSB connections in view of the existing shortcomings of the connections [18,19]. Furthermore, many researchers have also conducted experiments on the seismic-resistant performance of STCSB connections. Dong et al. [20] proposed a novel connection of a concrete-filled steel tube column to an H-shaped beam with a slide plate, conducting six experiments under reversed cyclic loading, which indicated sufficient energy dissipation capacity and excellent ductility. Chen et al. [21] investigated the influence of cyclic hardening characteristics on the performance of a welded austenitic stainless steel H-section beam to column under combined uniaxial cyclic bending and constant compression. It was indicated that the cyclic strain hardening influenced the performance of the members under seismic loading. It can be found from the aforementioned analyses that the research on STCSB connections has mainly focused on static mechanical properties, stiffness, failure models, load-transferring mechanisms, seismic performance, and ductility. However, there are limited studies on the stress concentrations of STCSB connections. To provide a reliable design for an offshore jacket using STCSB connections, it is necessary to explore the fatigue performance of STCSB connections to support offshore structure design.

The existing literature on stress concentration and fatigue behavior of STCSB connections is limited. This research examines stress concentrations in STCSB connections via experimental and numerical methods, employing a hotspot stress approach-based numerical model to assess the influence of critical geometric parameters on the SCFs. Based on experimental investigation and parametric analysis, this study considers the impact of various geometric configurations on STCSB connections. We introduce targeted optimization strategies, such as stiffener augmentation and flange plate shape alteration, to reduce the stress concentration in the connection zone, contributing valuable insights to the field and offering enhanced design guidance for the engineering and implementation of offshore structures.

2. Materials and Methods

2.1. Specimens

Three STCSB connections with stiffening rings were fabricated using Q355 steel by Zhejiang Shengda Iron Tower Co., Ltd., a prominent manufacturer located in Zhejiang, China. The detailed dimensions of the tested STCSB connections with stiffening rings are given in Figure 1 and

Table 1. Geometric dimensions and dimensionless parameters of specimens.

Number	L	l	Dt	tc	hw	bf	tw	tf	bo	t0	Type of Stiffening Ring
	mm	mm	mm	mm	mm	mm	mm	mm	mm	mm
IB450 × 200-CC300-6-SRD20-14	2240	1800	300	6	450	200	9	14	20	14	Diamonds
IB450 × 200-CC300-5-SRD20-14	2240	1800	300	5	450	200	9	14	20	14	Diamonds
IB450 × 120-CC300-6-SRD20-14	2240	1800	300	6	450	120	9	14	20	14	Diamonds

Note: L is the length of the circular steel column, l is the length of the I-shape steel beam, D_t is the dimeter of the circular steel column, and t_c is the thickness of the circular steel column. h_w is the height of the web of the steel beam, b_f is the width of the steel beam flange, t_w is the thickness of the web of the steel beam, and t_f is the thickness of the steel beam flange. b_o is the width of the stiffening ring (the difference between the inner and outer diameters of the stiffening ring), and t₀ is the thickness of the stiffening ring.

. The I-shape steel beam, circular steel column, and stiffening ring were welded by means of submerged arc welding. For ease of specimen installation and loading apparatus setup, the dimensions L and l were designated as 2240 mm and 1800 mm, respectively. The steel column diameter D was uniformly set at 300 mm across all connections. The steel beams were specified with dimensions of 450 × 200 × 9 × 14 mm and 450 × 120 × 9 × 14 mm (h_w × b_f × t_w × t_f). The stiffening ring was of diamond type. All the specimens were labeled as IB450 × 200-CC300-6-SRA20-14, where IB, CC, and SR refer to the I-shape steel beam, circular steel column, and stiffening ring. The numbers and letters following IB, CC, and SR represent the dimensions of the beam, column, and stiffening ring, i.e., 450 is the height of the steel beam, 200 is the width of the steel beam, 300 is the outer diameter of the steel column, 6 is the thickness of the column, A is the type of the stiffening ring, 20 is the width of the stiffening ring, and 14 is the thickness of the stiffening ring.

Tensile tests were conducted utilizing a 100 kN-capable monotonic tensile testing machine at an ambient temperature of approximately 20 °C. Tensile coupons were extracted from the I-shaped steel beams and circular steel columns. The specific dimensions of these specimens, designed in accordance with ISO 6892-1 [22], are illustrated in Figure 2 and detailed in

Table 2. Detailed dimensions of the tensile coupon specimens for circular steel columns.

Member	Parameter	lt/mm	lr/mm	lg/mm	lc/mm	R/mm	t/mm	wg/mm	wc/mm	Rh/mm	lh/mm	Number
Circular steel column	300 × 5	214	15.0	64	60	15	5	16	45	6	30	2
	300 × 6	214	15.0	64	60	15	6	13	40	6	30	2

Note: l_t denotes the overall length of the tensile coupon specimens. The length of the transition arc segment is represented by l_r, with l_g designating the gauge length of the specimen. The clamping segment’s length is given by l_c. The radius of the transition arc is R, and the specimen’s thickness is denoted by t. The width of the gauge segment is w_g, while w_c signifies the width of the clamping segment. The radius of the holes within the specimens is R_h, and l_h measures the distance from the center of the hole to the end of the clamping segment. These dimensions are critical parameters in the design and analysis of tensile test specimens for material property evaluation.

, respectively. Throughout the loading procedure, deformation at the gauge length and the corresponding applied load were captured using an extensometer and the testing machinery, respectively. In compliance with ISO 6892-1 [22] and the methodology outlined by Huang and Young [23], the test was extensometer-controlled, with the specific loading protocol delineated in

Table 3. Strain rate of the tensile coupon test.

Stage	Strain Rate/s−1
Elastic stage	0.000017
Yield plateau stage	0.00005
Strain-hardening stage	0.0002
Necking stage	0.00033

. The strain rates were set at 0.000017 s⁻¹ for the elastic phase, 0.00005 s⁻¹ for the yield plateau, 0.0002 s⁻¹ for the strain-hardening phase, and 0.00033 s⁻¹ for the necking phase. The resulting engineering stress–strain curves are depicted in Figure 3, while the mechanical properties derived from the tensile coupons are enumerated in

Table 4. Mechanical properties of the tested Q355 steel.

Member	Specimen	Elastic Modulus/GPa	Yield Strength/MPa	Ultimate Strength/MPa
Circular steel column	300 × 5-1	220.72	435.79	582.86
	300 × 5-2	223.37	435.71	571.33
	300 × 6-1	200.76	405.37	559.31
	300 × 6-2	197.37	394.75	556.34
I-shape steel beam	Web-450 × 200-1	219.33	376.63	544.76
	Web-450 × 200-2	226.66	385.34	548.51
	Flange-450 × 200-1	207.64	357.10	552.03
	Flange-450 × 200-2	194.03	363.07	552.55

.

2.2. Test Setup

The schematic representation of the experimental setup for ascertaining the SCF of the STCSB connection is depicted in Figure 4. The I-shape steel beam was placed vertically, and the top end of the beam was hinged to the fatigue actuator with a loading capacity of 50 t. The other end of the actuator was fixed to the reaction wall. The circular steel column was horizontally placed, and both ends of it were hinged to the supports. Note that lateral supports were installed on both sides of the steel beam to avoid out-of-plane deformation of the steel beam during the loading process.

In the experimental procedure, a gradient strain gauge was deployed to ascertain the hot spot strain in proximity to the weld toe, as illustrated in Figure 5. This gradient strain gauge was composed of five biaxial strain gauges symmetrically positioned along the longitudinal axis with a uniform center-to-center spacing of 4 mm. The positioning of the gradient strain gauge’s extremity in relation to the weld toe’s terminus was prescribed by the guidelines of DNV [24] and CIDECT [25]. Furthermore, four uniaxial strain gauges were systematically positioned adjacent to the circular steel column’s periphery to measure the nominal column strain, thereby facilitating the computation of the actual load exerted on the specimens. The comprehensive layout of the strain gauges is delineated in Figure 6.

2.3. Measuring and Loading System

During this experimental assessment, the application of load was conducted in two phases: initial preloading and subsequent stress concentration evaluation. The preloading phase was essential to confirm that the specimen’s response remained within the linear elastic regime and to mitigate any effects arising from gaps present during setup. Displacement control was implemented at a rate of 0.02 mm/s using an actuator. For the stress concentration phase, force control was utilized, maintaining an actuator loading velocity of 1 N/min throughout the duration of the test. At specific load levels—6 kN, 12 kN, 18 kN, 24 kN, 27 kN, and 30 kN—the test was paused for two minutes to acquire ample strain measurements during periods of stable loading. Strain data were consistently recorded at a frequency of 20 Hz. As depicted in Figure 4a, due to the symmetrical nature of the STCSB connection about the beam’s web, strain gauges were applied to a single side only. The testing protocol encompassed two stages of loading: tensile and compressive.

3. Test Results and Discussion

When measuring the stress distribution around the welds of STCSB connections, strain gauges were placed at every 45° along the welds on both the steel column and the outer flange to measure the strains perpendicular (ε_⊥) and parallel (ε_//) to the welds. An additional strain gauge is placed in the area anticipated to have significant stress concentration prior to testing (at the 22.5° position). The arrangement of the strain gauges is detailed in Figure 6a. The hot spot strain at the weld was interpolated from the strain gauges, allowing for the calculation of the strain concentration factor (SNCF), which is the ratio of the hot spot strain to the corresponding nominal strain. The relationship between stress and strain, as per Hooke’s law for a 3D problem, was simply derived to establish the relationship between the stress concentration factor (SCF) and the SNCF [26].

$$\mathrm{SCF}=c\cdot \mathrm{SNCF}$$

(1)

$$c=\frac{\left(1+\upsilon \frac{{\epsilon }_{//}}{{\epsilon }_{\perp }}\right)}{\left(1-{\upsilon }^2\right)}$$

(2)

where υ is Poisson’s ratio and ε_// and ε_⊥ are the strains parallel and perpendicular to the weld, respectively.

In this study, the hot spot strain was calculated using the linear extrapolation method to determine the SNCF. Although the quadratic extrapolation method may be more efficient in data processing, it is more sensitive to data errors, potentially leading to an underestimation of the SNCF [27]. Therefore, considering its advantages in error control, the linear extrapolation method was chosen for calculating the SNCF [28].

The results of the stress concentration tests are presented in

Table 5. SCFs of the STCSB connections.

Member		Tensile Side						Compressive Side
		0°	22.5°	45°	90°	135°	180°	0°	22.5°	45°	90°	135°	180°
IB450 × 200-CC300-6-SRD20-14	Column	4.38	2.81	1.74	0.29	−1.85	−3.00	-	-	-	-	-	-
	Plate	-	-	-	-	-	-	-	-	-	-	-	-
IB450 × 200-CC300-5-SRD20-14	Column	4.76	3.77	1.70	0.35	−2.12	−3.96	−4.66	−3.69	−1.68	−0.36	2.08	3.79
	Plate	−0.47	−0.33	0.46	0.12	−0.42	−0.11	0.42	−1.24	−0.60	−0.18	0.06	0.02
IB450 × 120-CC300-6-SRD20-14	Column	3.17	0.77	0.96	0.38	−1.43	−2.62	−3.02	−0.77	−0.98	−0.41	1.36	2.54
	Plate	−0.21	0.17	0.24	0.09	−0.14	−0.11	0.03	−0.19	−0.27	−0.11	0.13	0.13

. For the specimen IB450 × 200-CC300-6-SRD20-14, strain gauge failure occurred, resulting in the acquisition of the SCF data only from the tensile side of the cylinder. As depicted in Figure 7, Figure 8 and Figure 9, the influence of the diameter-to-thickness ratio of the column and the width-to-diameter ratio of the beam to the column on the distribution and magnitude of the SCF at STCSB connections was analyzed. In the analysis, to distinguish between the compressive- and tensile-side SCFs, the compressive side is denoted with “-SCF” in the table. Additionally, the maximum SCF was determined by the maximum absolute value. It can be observed that the SCF distribution patterns on the tensile and compressive sides of the STCSB specimens under various parameters were similar. The maximum SCF on the tensile side was consistently located at the 0° position. For all specimens, the maximum SCF on the compressive side was at the 180° position. As the column wall thickness increased, i.e., the diameter-to-thickness ratio of column decreased, the maximum SCF gradually decreased, although this trend was not significant, as shown in Figure 7. Figure 8a suggests that reducing the flange width of the beam, i.e., the width-to-diameter ratio of the beam to the column, had a significant effect on the SCF distribution and maximum SCF, and a decrease in the maximum SCF was observed. Additionally, a sharp decrease in SCF from 0° to 22.5° on the tensile side of specimen IB450 × 120-CC300-6-SRD20-14 was observed, with a similar phenomenon on the compressive side, indicating that reducing the beam flange width may have altered the stress distribution near the 0° position at the weld.

4. Finite Element Analysis

4.1. FE Models

To devise rational and feasible optimization designs, this study investigated the impact of geometric configuration on stress concentration at connections. The finite element model employs a global modeling method where components are interconnected through shared nodes. This approach ensures consistency across the model, which is essential for maintaining accuracy and integrity throughout the analysis. The material’s constitutive relationship, which dictates the stress–strain behavior, is crucial for simulating the mechanical behavior of STCSB connections. The elastic modulus of Q355 steel was obtained using the material property test, and Poisson’s ratio was 0.3. The model’s boundary constraints and loading conditions were set in accordance with existing experimental loading and boundary constraints. Specifically, the column was pinned at the top and fixed at the bottom, with lateral constraints applied at the beam ends. The loading method was displacement-controlled. The finite element model and boundary conditions were defined as illustrated in Figure 9.

Mesh sensitivity analysis was conducted to select an appropriate mesh size that would balance computational efficiency with result accuracy. The analysis included three zones: non-refined, transition, and refined mesh areas. According to CCS specifications [29], the mesh size in the hot spot stress area, including the interpolation area, should not exceed the thickness t of the loaded component, with a recommended mesh size of t × t. The refined mesh area should extend at least 10 t in all directions from the hot spot. Preliminary analysis considered non-refined zone mesh sizes from 10 to 40 mm, a transition zone of 1.0 t, and a refined zone of 0.2 t to assess their impact on the hot spot stress concentration factor. Further analysis of mesh sizes ranging from 10 to 20 mm for points 1 to 4, as shown in Figure 10, yielded the results depicted in Figure 11a. The findings indicate that variations in the non-refined zone mesh size had minimal impact on the stress concentration; thus, a mesh size of 20 mm was selected. Subsequently, based on the 0.2 t refined zone mesh size and the 20 mm non-refined zone size, a sensitivity analysis of the transition zone mesh sizes from 0.5 t to 1.0 t was conducted, with the results shown in Figure 11b. The transition zone mesh size had a minor impact on the stress concentration, leading to the selection of 0.9 t as the transition zone mesh size. Finally, for the refined zone, the impact of mesh sizes from 0.15 t to 0.4 t on stress concentration at four selected points was analyzed, with the results illustrated in Figure 11c. It was found that mesh sizes of 0.15 t to 0.25 t in the refined zone significantly affected the stress concentration, which stabilized when the mesh size reached 0.3 t. Consequently, a refined zone mesh size of 0.3 t was chosen. The simulation employed C3D8I solid elements, which, under optimal mesh quality, yielded results comparable to a quadratic element (e.g., C3D20R), with the hot-spot stress and strain approximated to a quadratic element.

4.2. Validations

Experimental data from the current research were utilized to validate the findings.

Table 6. Comparison of results between SCF_FE and SCF_Test.

Member		SCFFE						SCFTest
Tensile Side		0°	22.5°	45°	90°	135°	180°	0°	22.5°	45°	90°	135°	180°
IB450 × 200-CC300-6-SRD20-14	Column	5.13	3.26	1.87	0.20	−2.03	−3.04	4.38	2.81	1.74	0.29	−1.85	−3.00
IB450 × 200-CC300-5-SRD20-14	Column	5.07	3.93	2.44	0.26	−2.47	−3.73	4.76	3.77	1.70	0.35	−2.12	−3.96
IB450 × 120-CC300-6-SRD20-14	Column	3.51	2.24	1.07	0.35	−1.40	−2.54	3.17	0.77	0.96	0.38	−1.43	−2.62
Compressive side
IB450 × 200-CC300-6-SRD20-14	Column	−5.10	−3.23	−1.89	−0.61	2.03	3.06	-	-	-	-	-	-
IB450 × 200-CC300-5-SRD20-14	Column	−5.02	−3.89	−2.45	−0.28	2.46	3.77	−4.66	−3.69	−1.68	−0.36	2.08	3.79
IB450 × 120-CC300-6-SRD20-14	Column	−3.49	−2.23	−1.08	−0.36	1.39	2.06	−3.02	−0.77	−0.98	−0.41	1.36	2.54

presents the computational results for the STCSB connections, where SCF_FE denotes the SCF obtained from finite element analysis and SCF_Test represents the data derived from experiments. It should be noted that the SCFs recorded on the flange plate were relatively low. To ensure the accuracy of the validation results, considering factors such as gauge placement errors and equipment precision, the comparative analysis was conducted solely on the SCF values from the column. This focused approach facilitated a more precise evaluation while mitigating potential sources of discrepancy in the analysis.

Figure 12 presents a comparative analysis between the experimental results and finite element (FE) simulations, demonstrating a high level of correlation between the empirical data and computational predictions. However, notable discrepancies were observed in specific data points, such as the specimen IB450 × 120-CC300-6-SRD20-14, where, at the 22.5° position, the FE-predicted SCF_FE were considerably higher than the experimentally determined ones (SCF_Test) for both the tension and compression sides. These deviations may be attributed to the differences between the calculated weld dimensions in the FE model and the actual specimens; variations in welding quality and bead appearance due to manual welding proficiency; and potential inaccuracies in the placement of strain gauges, leading to measurement errors.

For the purpose of substantiating the precision of numerical simulations and affirming the validity of the stress concentration factors obtained through the hot spot stress method,

Table 7. Comparison of errors between SCF_FE and SCF_Test results.

Member		SCFFE/SCFTest						Average	CoV
Tensile Side		0°	22.5°	45°	90°	135°	180°
IB450 × 200-CC300-6-SRD20-14	Column	1.17	1.16	1.07	0.69	1.10	1.01	1.03	0.12
IB450 × 200-CC300-5-SRD20-14	Column	1.07	1.04	1.44	0.74	1.17	0.94	1.07	0.16
IB450 × 120-CC300-6-SRD20-14	Column	1.11	2.91	1.11	0.92	0.98	0.97	1.02	0.07
Compressive side
IB450 × 200-CC300-6-SRD20-14	Column
IB450 × 200-CC300-5-SRD20-14	Column	1.08	1.05	1.46	0.78	1.18	0.99	1.09	0.15
IB450 × 120-CC300-6-SRD20-14	Column	1.16	2.90	1.10	0.88	1.02	0.81	0.99	0.12

delineates the ratios of finite element analysis results to experimental data (SCF_FE/SCF_Test) alongside their average values. Moreover, to account for data variability, the table includes the coefficient of variation (CoV) for the stress concentration factor ratios, which were ascertained by employing the hot spot stress approach. The average SCF_FE/SCF_Test ratio for the STCSB connections ranged from 0.99 to 1.09, indicating a general overestimation by the FE analysis. Upon meticulous review of each SCF_FE/SCF_Test ratio, it was observed that, aside from the significant discrepancy at the 22.5° position for the specimen IB450 × 120-CC300-6-SRD20-14, there was a substantial error at the 45° position across all specimens. This could be due to the minimal stress concentration effects at 45° and the challenges associated with accurately measuring the SCF at this position, influenced by factors such as strain gauge placement and the precision of measuring instruments.

In summary, while the mean ratios fell within an acceptable numerical range and the CoV values ranged from 0.07 to 0.16, indicating a low degree of variability and suggesting greater stability and predictability in the data, certain data points were excluded from the computation of the statistical mean and CoV. Specifically, the data points at the 45° position, which exhibited significantly lower SCF values, and the outlier at the 22.5° position for specimen IB450 × 120-CC300-6-SRD20-14 were not considered. This exclusion was a prudent approach to ensure the reliability and integrity of the statistical analysis, taking into account the inherent complexities of experimental and numerical stress concentration assessments.

5. Parametric Study

5.1. General

This study examines the effects of geometric configuration on the fatigue performance of structural connections by analyzing the influence of critical geometric parameters on SCF distribution. The abrupt geometric transition at the interface between the gusset outer flange plate and the column, which is prone to stress concentration, was targeted for analysis. SCFs were calculated along a path encircling the column–gusset plate junction. The parameters under investigation included the width-to-diameter ratio of the beam to the column, the diameter-to-thickness ratio of the column, the diameter-to-thickness ratio of the column to the beam, and the height-to-thickness ratio of the beam web, as outlined in

Table 8. Detailed dimensions of the STCSB connections.

Member	Geometrical Parameter	Column		Plate		Beam				Parameter Analysis Range
		D	tc	hs	ts	bf	tf	hw	tw
1	Width-to-diameter ratio of beam to column (bf/D)	300	6	200	12	130	12	440	6	0.43
2						160				0.53
3						190				0.63
4						220				0.73
5	Diameter-to-thickness ratio of column (D/tc)	300	4	200	12	160	12	440	6	30.0
6			6							37.5
7			8							50.0
8			10							72.0
9	Diameter-to-thickness ratio of column to beam (D/tf)	300	6	200	12	160	4	440	6	75.0
10							8			37.5
11							12			25.0
12							15			20.0
13	Height-to-thickness ratio of beam web (hw/tw)	300	6	200	12	160	12	280	6	46.67
14								360		60.00
15								440		73.33

. Given the relatively low SCFs observed for the beam, the analysis was concentrated on the SCF distribution of the steel tubular column.

5.2. Influence of the Width-to-Diameter Ratio of Beam to Column

The influence of the width-to-diameter ratio of the beam to the column on the stress concentration factor of the connections is delineated in Figure 13. The ratio was examined over a range from 0.43 to 0.73, with other parameters being held constant. Models 1 to 4, as per Table 8, were analyzed. Figure 13a illustrates the SCF distribution along the weld seam, and Figure 13b details the SCFs at specific points. Symmetry in SCF distribution was observed around the 90° position relative to the weld circumference. A significant rise in the SCF was noted beyond a width-to-diameter ratio of 0.63, with consistent trends across various measurement points.

5.3. Influence of the Diameter-to-Thickness Ratio of the Column

The influence of the column’s diameter-to-thickness ratio on the stress concentration factors of the connections is delineated in Figure 14. The ratio was examined from 30 to 72, with other parameters being unchanged. Models 4 to 8, as detailed in Table 8, were analyzed. Figure 14a shows the SCF distribution along the weld seam, and Figure 14b presents the SCFs at fixed points. The connection’s SCF increased significantly with the diameter-to-thickness ratio, with an accelerated growth rate at the 0° position beyond a ratio of 37.5. On the tensile side, a sharp decline in SCF values was observed from 0 to 22.5°, with a more gradual decrease between 22.5 and 45°, with the pattern becoming increasingly evident as the diameter-to-thickness ratio of the column increased.

5.4. Influence of Column Diameter-to-Beam Thickness Ratio

The influence of the column-to-beam diameter-to-thickness ratio on the stress concentration factor of the STCSB connections is detailed in Figure 15. The diameter-to-thickness ratio was examined across a range of 20 to 75, with other parameters being unchanged. Models 9 through 12, as depicted in Table 8, were analyzed. Figure 15a displays the SCF distribution along the weld seam, while Figure 15b shows the SCFs at discrete points. The connection’s SCF diminished with an increasing column-to-beam diameter-to-thickness ratio. Beyond a ratio of 25, the SCF exhibited a stabilizing trend after an initial reduction. Furthermore, thinner steel beams resulted in more pronounced geometric discontinuity at the gusset plate connection (with a constant flange plate thickness), causing increased stress concentration.

5.5. Influence of the Height-to-Thickness Ratio of the Beam Web

The influence of the height-to-thickness ratio of the beam web on the connection’s stress concentration factor is illustrated in Figure 16. The height-to-thickness ratio of the beam web varied from 46.67 to 73.33, with other variables held constant. Models 13 to 15, as listed in Table 8, were evaluated. Figure 16a presents the SCF distribution along the weld seam, while Figure 16b shows the SCFs at fixed points. The connection’s SCF increased with the height-to-thickness ratio of the beam web, yet the increment rate attenuated with an increasing ratio.

6. Optimization of STCSB Connections

Experimental and finite element analysis results indicate that the SCF distribution around the weld seam of these STCSB connections exhibited significant variation and was symmetrically distributed at 90° intervals. The maximum SCF was observed at either the 0° or 180° position, with notable disparities in the distribution near these peak stress locations. The shape of the outer flange may have also influenced the SCF distribution and magnitude. Stress concentration in welded connections is commonly attributed to geometric discontinuities at the weld locations. To alleviate stress concentration at the connections, the optimization of the outer flange configuration was attempted, and to ensure a smoother transition, the strategic placement of stiffeners was employed to reduce the SCFs. This section explores the enhancement of the overall SCF distribution at the connections through the modification of stiffener shapes as an optimization technique.

As depicted in Figure 17, significant stress concentrations were evident at the junction of the column with the outer flange and the contact area between the beam and the outer flange. Consequently, stress concentration could be mitigated by reinforcing the outer flange area with additional stiffeners and by optimizing the connection between the outer flange and the column to improve stress transfer pathways. Figure 18 illustrates two approaches. Method 1 involved the addition of stiffeners to the outer sides of the upper and lower outer flanges of the column, while Method 2 entailed the installation of a circular stiffener at the central position of the STCSB connection. The optimization of the outer flange is shown in Figure 18a,b. Analysis was conducted on three different parameters of diamond, arc, and circular shapes for the outer flange in order to determine the optimal form and parameters. The parameters for the stiffeners and outer flanges are detailed in

Table 9. Stiffener dimensions.

Member	Stiffener	bsti/mm	hsti/mm	tsti/mm	β1/°	β2/°
S1	Method 1	190.73	190.73	6	45	-
S2		190.73	190.73	12	45	-
S3		190.73	330.35	6	60	-
S4		190.73	330.35	12	60	-
S5		88.52	330.35	6	75	-
S6		147.51	147.51	6	45	45
S7	Method 2	100	-	6	-	-
S8		100	-	12	-	-

and

Table 10. Details of the outer flange.

Member	Outer Flange Configurations	bsti/mm	bf/mm	Rsti/mm	β1/°
S9	Diamond	200	200	-	45
S10	Arc	200	200	1167
S11		200	200	540	-
S12		200	200	365	-
S13		200	200	285	-
S14	Circle	200	200	-	--

, respectively.

The maximum SCFs for specimens S1–S14 are illustrated in Figure 19. Specimens S1–S6 incorporated stiffeners on the outer sides of the upper and lower outer ring plates of the column; S7–S8 featured circular stiffeners at the connection’s central position; S9 utilized the diamond-shaped ring plate, which is the standard STCSB connection; S10–S12 utilized arc-shaped ring plates; and S13–S14 employed circular ring plates. The computational results indicate that the addition of stiffeners at various locations and forms led to a fluctuating distribution of the maximum SCFs. Notably, specimen S4 exhibited the lowest maximum SCF, at 4.97, whereas specimen S2 recorded the highest SCF, reaching up to 7.05. This can be attributed to the stiffeners facilitating stress transfer at the connection between the ring plate and the column, significantly reducing the stress concentration effect at this location and causing a shift in the position of maximum stress concentration at the connection. Furthermore, the diamond and circular outer ring plates demonstrated better improvements in the maximum stress concentration effect. Collectively, these findings suggest that the addition of stiffeners can effectively mitigate stress concentration effects in the connection area and enhance the flexural performance of the STCSB connection.

7. Conclusions

This study presents a comprehensive investigation into the fatigue performance optimization of STCSB connections, which are pivotal in the construction of offshore structures. Through experimental testing and FE analysis, the research meticulously examined the impact of various geometrical parameters on SCFs. The study introduced optimization methods such as the addition of stiffeners and outer flange plates, demonstrating their efficacy in mitigating stress concentration and enhancing fatigue life.

(1) The stress concentration tests on welded STCSB connections revealed significant variations in the SCF distribution. The maximum SCF was consistently identified at the 0° or 180° position, highlighting the areas of peak stress.

(2) The developed FE models, incorporating detailed geometrical and material properties, were validated against the experimental results. The congruence between FE predictions and experimental data confirmed the accuracy and reliability of the numerical approach.

(3) A comprehensive parametric study was conducted to assess the impact of various geometrical parameters on the fatigue performance of STCSB connections. Key parameters such as the width-to-diameter ratio of the beam to column, the diameter-to-thickness ratio of the column, and the diameter-to-thickness ratio of the column to the beam were found to significantly influence the SCF distribution and magnitude. The SCF increased with both the width-to-diameter ratio of the beam to the column and the diameter-to-thickness ratio of the column. Conversely, it decreased as the diameter-to-thickness ratio of the column to the beam increased.

(4) The installation of a circular stiffener at the center of STCSB connections or the addition of stiffeners on the outer sides of the column’s upper and lower outer flanges effectively alleviated stress concentration. This optimization enhanced the connection’s bending resistance, highlighting the significance of flange plate design in the optimization of fatigue performance.

Currently, there is a scarcity of research on the stress concentration and fatigue performance of STCSB connections. This study analyzed the influence of various parameters on the stress concentration and proposed corresponding optimization schemes, thereby providing a reference for this field of research. While this study provides substantial contributions to the field, there are limitations. The research primarily focused on fatigue life assessment under uniaxial load, which may not encapsulate the full complexity of real loading scenarios. Future research could extend this study by incorporating multi-axial loading conditions. Moreover, long-term performance studies and further experimental validations could provide additional layers of reliability to the proposed optimization methods.