2.1. Specimen Design
To investigate the distribution of the HSS in KK-joints in different combinations of loads, the creators of this study designed and fabricated a spatial CHS KK-joints. The dimensions of the specimen were obtained by scaling down the jacket foundation structure for offshore wind turbines, with a scaling ratio of 1:10. The notations used are given in
Table 1.
The diameter of the chord member
D is 219.1 mm, with a wall thickness
tc of 6.4 mm and a length
L of 2000 mm, approximately nine times the diameter of the chord member, while excluding the influence of end constraints on the joint region [
19]. The diameter of the brace member
d is 114.0 mm, with a wall thickness
tb of 6.0 mm, and the bracing member length
l is set at 700 mm (
Figure 2). Reinforcing ribs were installed at the ends of both the chord and brace members to enhance the end sections and prevent premature failure due to stress concentration.
The specimen is composed of four braces and one chord, with the brace ends cut into intersecting lines and directly welded to the surface of the chord. The axis of each brace forms a 45-degree angle with the axis of the chord, and the two planes formed by the braces have a 90-degree angle between them. The four braces axes intersect at a single point on the chord axis. In offshore wind turbine jacket structures, the quality requirements for welded joints are high due to long-term exposure to combined wind, wave, and current loads. The specimens in this study meet the welding requirements specified by the AWS code [
20].
As marine structures continue to evolve, the demands placed on structural steel are increasing. However, for the purposes of this study, commonly used low-carbon steel still suffices to meet the testing requirements for the HSS tests. The selected steel material in this study is Q355B steel. Additionally, to ensure the overall integrity of the structure and prevent the influence of unnecessary welds on the test results, seamless steel tubes are used for all the members. Material property tests were conducted on the steel samples, and the obtained characteristics (yield stress σ
y and Young modulus
E of the steel) of the specimens are presented in
Table 2.
2.2. Loading and Measurement System
To investigate the spatial interaction mechanism of spatial KK-joints, it is necessary to employ a loading method that combines multiple working conditions, specifically requiring the individual loading of the four braces. Therefore, a spatial loading test setup suitable for statically and dynamically loading spatial tube joints is developed in this study, as illustrated in
Figure 3. This test setup primarily consists of four independently controlled MTS loading actuators, supporting columns, oblique support devices, actuator supports, and specimen supports, among other components. The stability of the connections between the various parts is ensured using high-strength friction-type bolts. Additionally, all components placed on the reaction floor are connected to the floor with prestressed steel bars, preventing any relative slippage between the parts. During the installation of the specimen, it is necessary to first utilize a laser calibration instrument to position the specimen at the center of the loading device and align the axes of the braces and actuators, ensuring that the axes of the actuators and the braces coincide, thus preventing any additional loads during the loading process. Furthermore, prior to applying the load to the specimen, it is advisable to conduct a preliminary loading test, which serves to assess the alignment between the specimen and the test setup, as well as the stability of the measurement system.
Due to the effect of notching in the weld joint, direct measurement of stress at the weld toe is not feasible during testing. The prevailing approach commonly employed is the indirect method, which is currently known as the extrapolation method. In accordance with the recommendations provided by CIDECT [
5] and IIW codes [
21], the extrapolation method for tubular joints primarily encompasses linear extrapolation and quadratic extrapolation. Linear extrapolation involves linear calculations based on two measurement points in the extrapolation region to determine the stress at the weld toe, whereas quadratic extrapolation entails secondary calculations utilizing multiple measurement points. The codes suggest that the linear extrapolation method should be used for circular steel tubular joints. Consequently, the linear extrapolation method for measuring HSS is utilized in the tests for this study.
The arrangement of measurement points in the extrapolation region for the linear extrapolation method is illustrated in
Figure 4. As depicted in the diagram, the linear extrapolation method requires the placement of only two strain gauges in the extrapolation region of the weld toe. CIDECT [
5] has provided recommendations regarding the positioning of strain gauges, as shown in
Table 3. In the table,
rc represents the radius of the chord, while
rb denotes the radius of the brace. Finally, in welded tubular joints, the crown point refers to the highest point in the joints, while the saddle point refers to the lowest point in the joints.
In various international codes, there are some discrepancies regarding the stress (strain) component of SCFs. The question arises whether the principal stress (strain) or the stress (strain) perpendicular to the weld toe should be utilized. IIW [
21] argues in favor of adopting the maximum principal stress (strain), while AWS [
20] and API [
6] advocate for using the stress (strain) perpendicular to the weld toe. Although in theory, the fatigue crack propagation direction in tubular joints tends to expand towards the direction perpendicular to the maximum principal stress, the limitations of current testing techniques prevent the precise measurement of the maximum principal stress. Additionally, the direct superposition of maximum principal stress is not feasible under different combinations of loads. Moreover, it is more convenient to arrange the strain gauges perpendicular to the weld toe in experimental measurements. Furthermore, CIDECT [
5] suggests that the differences between these two types of stresses near the weld toe are not significant. Therefore, CIDECT [
5] recommends measuring the strain solely using strain gauges positioned perpendicular to the weld toe, without the need for employing strain gauges that measure the principal strain. In this study, the measurement of strain perpendicular to the weld is chosen.
Hence, the formula for calculating the hot spot strain at the weld toe based on linear extrapolation is as follows:
where
is the strain at the weld toe obtained by linear calculation;
and
represent the perpendicular strain measured at the first and second measurement points, respectively, in the extrapolation region, perpendicular to the weld toe;
Lr,min and
Lr,max denote the distances from the weld toe to the first and second extrapolation points in the extrapolation region, as specified in
Table 3. In the study,
Lr,min is set to 4 mm on both the chord side and the brace side.
Lr,max is determined to be 9.9 mm at the saddle point and 8.9 mm at the crown point on the chord side, while it is uniformly 12 mm on the brace side. Interpolation is employed for the points between the crown point and the brace point.
Furthermore, the strain concentration factor (SNCF) of the joints could be obtained by dividing the hot spot strain by the nominal strain.
where
εN is the nominal strain of the braces, which is mesured in this study by strain gauges.
Furthermore, according to Hooke’s Theorem, there exists a relationship between the SCF and the SNCF as expressed by the following equation:
where
represents the strain parallel to the weld toe, calculated using the same method as
, and
v denotes the Poisson’s ratio of the steel material.
where
and
represent the perpendicular strain measured at the first and second measurement points, respectively, in the extrapolation region, parallel to the weld toe.
Therefore, in order to obtain the SCF more accurately, this study employed a strain gauge parallel to the weld toe beside each strain gauge perpendicular to the weld toe. Additionally, due to the impracticality of measuring all positions along the weld toe during the experimental process, strategically positioned strain measurement points were selected in this study. In particular, the strain distribution around the weld toe of the joints under spatial effects needs to be considered. Hence, eight measurement points are placed for every brace region. The first measurement point is located at the 0° position, which is at the crown point near the side of the chord. Eight measurement points are distributed at 45° intervals along the weld toe, with the coordinate origin being the intersection of the brace axis and the surface of the chord. The positions of the four braces corresponded consistently to the strain gauges. The arrangement diagram and numbering of the strain gauges are illustrated in
Figure 5. It should be noted that the points at 0°/360° and 180° are referred to as the crown points of the joints, whereas the points at 90° and 270° are referred to as the saddle points of the joints. The actual arrangement of the gauges on the specimen is shown in
Figure 6.
In order to obtain the coefficient of hot spot stress, it is necessary to further measure the axial strain of the brace as a nominal strain. In this study, four uniformly distributed circumferential axial strain gauges are placed at the midpoint of the brace to avoid the influence of stress concentration at the node and end regions on the test results.
2.3. Load Design Rules
Four actuators on the test setup enable independent loading, providing various load combinations for the joints. Within the IIW code [
18], three reference combinations are provided for spatial KK-type joints: the first is force-symmetric loading, the second is unilateral loading, and the third is force anti-symmetric loading, as illustrated in
Figure 7.
To fully understand the stress conditions of spatial tubular joints, five loading conditions were proposed for HSS testing, as shown in
Table 4. Furthermore, to present a clearer depiction of the loading rules for each loading condition, the loading rules from the table are depicted in
Figure 8. It should be noted that the listed loading conditions in
Table 4 are implemented by first selecting a reference brace and applying the corresponding load condition to that reference brace. Given the symmetrical construction of the specimen, any brace can serve as the reference brace. Additionally, since the steel material remains in an elastic working state throughout the HSS tests, each brace is repeatedly subjected to the load conditions listed in
Table 4. It is important to note that in general, marine structures subjected to long-term loading rarely experience fatigue loads that cause the material to enter the plastic working stage. Therefore, it is necessary to ensure that the stress on the steel material during the HSS tests does not exceed the yield strength of the steel.