Investigation of fatigue resistance of fillet-welded tube connection details for sign support structures

Abstract

Stiffened and unstiffened fillet-welded tube-to-transverse plate connection details are widely used for mast-arm and base-plate connections for highway sign structures. However, due to repetitive wind loads, cyclic fatigue stresses are induced and they are the primary source of failure in welded connections at these locations. The resistance of fatigue critical details has been an on-going research topic because of limited experimental results and the variability in existing fatigue testing results. The main objective of this study is to evaluate fatigue resistance of fillet-welded tube connection details by utilizing the advanced fatigue tool in ANSYS Workbench platform. Finite Element (FE) models development and model validation using existing test data was presented. The resulting fatigue resistance from FE analysis was expressed in terms of fatigue life, fatigue damage, and fatigue safety factor to determine the fatigue performance of fillet-welded connections. Existing fatigue test data was grouped to perform a synthetic analysis and then analysis results were provided to determine input data and fatigue limit for the fatigue module. The local stress level at fatigue critical locations was evaluated using a static FE model for different number of stiffeners and boundary conditions. The results of this investigation provides fatigue resistance of fillet-welded connection details in the form of fatigue life, fatigue damage and safety factor for various connection parameters and structural conditions.

Keywords

fatigue / weld connections / base plate / fillet welds

Introduction

In highway transportation systems, sign structures play an important role in transportation safety and in providing useful information to the public. A potential or unexpected fatigue failure at a critical connection detail can cause injuries, property damage, disruption to traffic and accidents [¹]. The damage raises the safety concern with respect to the highway system and can cost up to several thousands of dollars per occurrence. Across the United States, several support structures can be found in every single mile along a major highway. Failure investigations and published reports concluded that fatigue is the main cause of failure in sign structures [²–⁶]. Localized fatigue failure have occurred around fatigue critical locations such as at the toe of fillet welds and at the tip of stiffeners in stiffened tube-to-transverse plate connections. However, due to the easiness of fabrication and the cost-effectiveness, fillet-welded connection details are widely used for mast-arms and for base-plate to tube connection. In New Jersey, tube-to-transverse plate connection details with longitudinal stiffeners are designed and detailed following New Jersey Department of Transportation standard drawings [⁷]. These type of connections are also extensively used for cantilevered and overhead sign structures. According to a recent study [⁸], these connections are determined as the most fatigue critical detail as compared to groove-weld connections. To minimize the stress level at the at the fillet weld toe base, a stiffened fillet-welded connection was developed to decrease out-of-plane distortion at the pole wall [⁸]. However, the termination at the tip of stiffeners also became a critical potential fatigue crack location [⁹].

To investigate the fatigue resistance of both unstiffened and stiffened connection details, several experimental studies were performed in past decades. The fatigue provision of the American Association of State Highway and Transportation Officials Specification (AASHTO) specifications [⁹] has been modified and updated by following findings from the recent fatigue testing and research work. However, because of the fact that the test specimen and test matrix were designed by following the state’s own design specification and own interests, it becomes necessary to perform additional studies to determine fatigue resistance for critical connection details.

Recent fatigue tests on galvanized unstiffened specimens under Federal Highway Administration (FHWA) research program [¹⁰] found that there are significant influences in the workmanship which causes scatters in testing results due to the quality of welding and inherent defects in welding from manufactures. Thus, fatigue resistance for both analysis and design needs to be determined by minimizing risks from unknown effects or parameters. Further, the variation in crack length was attributed to the difficulty in observing the initial crack while cyclic loadings are applied in fatigue testing. Many experimental studies provide no information for the first crack length. Additional variation can be observed in the light of considering the fatigue failure criteria defined as a 305 mm (12 inch) long crack [¹⁰] and ten percent loss in overall stiffness [¹¹].

The main objective of this study is to perform analytical investigation of fatigue resistance of fillet-welded tube connection details for structural supports following stress life analysis using ANSYS. By utilizing the advanced fatigue tool in ANSYS Workbench 17 platform, Finite Element (FE) models are developed and then validated using existing experimental data [¹²]. A synthetic fatigue testing data analysis is also performed to employ more reliable information that is utilized as input data into the fatigue module. The fatigue resistance of fillet-welded details is determined in terms of fatigue life, fatigue damage, and safety factor. Impacts on fatigue resistance due to the number of stiffeners and boundary conditions are also evaluated.

Background

AASHTO-LTS specification

In the light of fatigue design and analysis of structural supports, most of state DOT’s follow the AASHTO standard specifications for Structural Supports for Highway Signs, Luminaires, and Traffic Signals. The fourth edition of specification [¹³] was the first specification that includes the fatigue design provisions (Chapter 11). In this Specification, fatigue design criteria are introduced to resist the equivalent static wind load effects. Due to the uncertainty of stress fluctuations and the corresponding number of cycles, the category-based infinite fatigue life design methodology is recommended for each fatigue critical connection detail. However, many studies [¹⁴–¹⁶] revealed that there are inconsistencies in this provision.

The first AASHTO-LTS edition [⁹] that adopts the Load Resistance Factored Design (LRFD) concept for structural supports was introduced. Significant changes to the fatigue provisions were made based on the findings from NCHRP Project 10-70 [⁸]. This specification also provides the curve for stress range versus number cycles with the fatigue design category but categories are no longer used to determine the Constant Amplitude Fatigue Threshold (CAFT). The CAFT for infinite life design is determined from Table 11.9.3.1-1 for specific fatigue connection details. Stress Concentration Factors (SCF) are functions of geometry of connection details and it indicates that the fatigue design limits on S-N curve depends on SCF factors. The stress induced by wind load components such as galloping, natural-wind gusts and truck-induced gusts \mathit{\gamma }{\left(\mathrm{\Delta }f\right)}_n should be below the CAFT for an infinite fatigue life. This is given in Eq. (1):

(1)

where {\left(\mathrm{\Delta }f\right)}_n is the wind-induced nominal stress range (ksi), {\left(\mathrm{\Delta }F\right)}_n is the fatigue resistance for the various connection details and \varphi {\left(\mathrm{\Delta }F\right)}_{\mathrm{TH}} is the CAFT, respectively. \mathit{\gamma } is the load factor per Fatigue I limit state defined in the load combination and load factors table, and \varphi is the resistance factor equal to 1.0.

The fatigue details of support structures tested in the laboratory (Table C11.9.3.1-1) provide both a fatigue constant of A and the CAFT. However, there are certain limitations when determining the fatigue resistance because there are no considerations for the factors such as inherent defects in welding, the quality of welding, peening, galvanization, and mean stress and residual stress effect. The CAFT is only applicable where geometries of the connection are within a certain range of dimensions.

Socket connection detail: tube-to-transvers plate connection

A socket connection is a fillet-welded connection or referred to as tube-to-transverse plate connection, was classified as a category E’ [¹³]. This category has a CAFT equal to 17.9 MPa for steel and of 6.9 MPa for aluminum. A typical fillet-welded socket connection is shown in Fig. 1. The term ‘socket’ refers ‘to the way the baseplate is cutout to allow the pole to fit inside’ [¹⁶]. There are two fillet welds in this connection detail. The first welding is applied at the top of the base plate and the second fillet weld is applied inside the cut-out in the base plate, between the bottom surface of the pole and the sides of the base plate. The first fillet welding is more structurally significant components than the second one as it resists shear and tensile stresses [¹⁶]. With respect to the infinite life design requirement where no crack is anticipated, the stress range must be below CAFT.

Although there have been several previous research efforts to evaluate fatigue resistance of sign structure details, there is a need to understand the fatigue performance of unstiffened connection detail. With regard to a synthetic fatigue testing data analysis, known factors that affect fatigue resistance are considered. Based on base plate thickness, galvanization, peening, and tube geometry, the existing experimental fatigue tests are then grouped by assuming the log-normal distribution for the parameter A, or called fatigue coefficient. A statistical analysis is conducted in this study to set a fatigue design threshold for the commercial FEA software, ANSYS Workbench 17.

Stiffened socket connection detail: tube-to-transverse plate connection with longitudinal stiffeners

Stiffened tube-to-transverse plate detail are typically designed to increase the stiffness of the fillet weld toe at the base plate and to decrease out-of-plane distortion behavior of the tube wall [⁸,¹⁷]. The fatigue design of this detail was first introduced in the AASHTO specification in its first edition [¹³]. In this edition, the fatigue design category for weld terminations at the ends of longitudinal stiffener varied from Category C to E depending on the length of stiffeners (short, medium, and long). Figure 2 shows fillet-welded socket connection with longitudinal attachment (stiffeners).

Galvanized stiffened tube-to-transverse plate connections which represent multi-sided high level luminaire support structure were tested for fatigue at Lehigh University [⁸]. It was discussed that increasing the stiffness of the transverse plate is the most cost-effective means of improving the fatigue resistance of this connection [⁸]. This study introduced an optimized tube-to-transverse plate connections detail that included longitudinal stiffener and a ratio of stiffener thickness to tube thickness of 1.25, a ratio of stiffener height to stiffener spacing of 1.6 and a stiffener termination angle of 15 degree.

An adequately designed and optimized stiffened tube-to-transverse plate fillet-welded connection provides a CAFT of 48.3 MPa which is AASHTO Category D while the prior specification [¹³,¹⁸] defines the CAFT of this connection as 17.9 MPa (Category E′). Based on the results of this experimental study, proposed recommendations were adopted for approved fatigue details in the AASHTO 2015 Specification [⁹]. However, the recommendations were made mainly from the testing result with only ten specimens. Possible scatters of data due to workmanship was not investigated and considered. Therefore, there is a need in additional research work to take account these factors.

Fatigue module in ANSYS workbench

In ANSYS Workbench 17 platform, fatigue analysis is performed based on linear static analysis and fatigue calculations that support only solid and surface bodies. In stress life analysis, the fatigue module requires an S-N curve (stress range versus number of cycle) as input material properties of the Engineering Data set. In this study, the required S-N curves were obtained from synthetic fatigue test analysis results. Young’s modulus and Poisson’s ratio are also necessary for fatigue analysis. The terms for fatigue output will be addressed in herein.

Fatigue life

The contour plot of fatigue life results represent the available life for the given fatigue analysis. Under constant stress amplitude loading, the fatigue life represents the number of cycles until the part will fail due to fatigue. The fatigue module finds cycles to failure from the S-N curves input data and mean stress correction theory is not considered for this study.

Fatigue damage

The term ‘fatigue damage’ is determined as the available life divided by the design life. If the fatigue damage values is greater than 1, it indicates the failure was reached before the design life is reached. Determining accurate fatigue design life from existing fatigue data analysis is the major tasks for this study.

(2)Fatigue\mathrm{\hspace{0.17em}}Damage={\displaystyle \frac{Available\mathrm{\hspace{0.17em}}life}{Design\mathrm{\hspace{0.17em}}life}}.

Fatigue safety factor

The fatigue safety factor is another form of contour plot that represents the fatigue resistance. The value of safety factor is determined by a fatigue failure at a given design life. If output are less than one, it indicates that failure before the design life is reached and the maximum factor of safety is set as 15. Similar with fatigue damage, fatigue design life value is defined as the same cycle ranges for infinite fatigue life.

Synthetic fatigue data analysis

As discussed earlier, analysis results of fatigue testing data will be utilized as an input parameters in fatigue module in ANSYS Workbench 17. Based on parameters which significantly affect fatigue performance or has different treatment types, the collected test data was grouped to eliminate the variability and then statistical analysis is performed to establish the fatigue design limit.

Statistical analysis of fatigue test data

In stress life analysis, the S-N curve is constructed on log-log scale with key parameters such as the stress range under constant-amplitude and the number of cycles to failure. The linear regression on S-N curve represents the relationship between stress-range and the number of cycles. According to the Miner’s rule [¹⁹], the fatigue life curve is generally expressed by the following equation:

(3)N·S_{\mathrm{R}}^m=A,

where m represents the slope of the linear line in log-log scale and A is the value of the intercept on the x-axis (horizontal axis). The fatigue coefficient, A, is assumed to be a log-normal random variable according to the recommendation from previous studies [²⁰]. The variance of A is calculated as follows:

(4){\sigma }_A^{\mathrm{2}}={\displaystyle \frac{{\displaystyle {\sum }_{i=\mathrm{1}}^{k}i}{(A_i-{\overline{A}}_i)}^{\mathrm{2}}}{k-\mathrm{2}}},

where k is the number of test specimen and the (k≠2) term in the denominator is used instead of k to make the variance of A an unbiased estimator of the normal population variance [²¹].

Least square regression analysis on fatigue data

In this paper, a least square regression analysis was performed by following the procedures in ASTM Standard E739-91 [²¹]. In a linear form, the regression equation, can be written as,

(5)Y=a+b·X.

The value a and b in the linear form represent the value at the x-intercept and slope of the regression fit, respectively. In stress life fatigue analysis for lognormal random variables, Eq. (5) can be rewritten in logarithmic form [²⁰] with a slope of 3 as shown in Eq. (6):

(6)\log N=\log A-\mathrm{3}\log S_{\mathrm{R}},

where N is the number of cycles. A and S_{\mathrm{R}} are the fatigue coefficient and stress range, respectively. The terms can be evaluated [²⁰],

(7)\widehat{a}=\overline{Y}-\mathrm{3}·\overline{X}.

\widehat{a} and \widehat{b} are the predicted value of a and b, respectively, and \overline{X} and \overline{Y} represents the sample mean value. Hence, the least squares line for stress life fatigue data analysis is given as,

(8)\widehat{Y}=\widehat{a}+\mathrm{3}·X.

Fatigue coefficient A and fatigue design life

To take account the residuals from regression fit, the fatigue coefficient, A, can be determined as lognormal random variable. It can be expressed as,

(9)Y=\ln A.

If A is lognormally distributed, Y is a normal distribution where A is greater than zero [²²]. Since Y is normally distributed, standard normal function can be written,

(10)F_A\left(a\right)=F_Y\left(y\right)=\varphi \left({\displaystyle \frac{y-u_Y}{{\sigma }_Y}}\right),

where u_Y=u_{\ln A} is a mean value of \ln A and {\sigma }_Y={\sigma }_{\ln A} is a standard deviation of \ln A, respectively. The variance and mean of \ln A can be expressed [²²],

(11){\sigma }_{\ln A}^{\mathrm{2}}=\ln \left[\mathrm{1}+{\left({\displaystyle \frac{{\sigma }_A}{u_A}}\right)}^{\mathrm{2}}\right],

(12)u_{\ln A}=\ln u_A-{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}·{\sigma }_{\ln A}^{\mathrm{2}}.

To establish the fit lines for the fatigue experimental data, a regression analysis was performed for existing testing data for both unstiffened and stiffened fillet-welded socket connections. By utilizing listed equations above, the mean minus two standard deviation regression lines were established from the regression fit. The linear regression line for the mean minus two standard deviation was shifted down slightly to establish a lower bound and this approach is commonly used for design purposes and is associated with a 2.3 % probability of failure assuming the life logarithms to be normally distributed [²³,²⁴]. In addition, the fatigue design life which is used for the calculation of fatigue damage and safety factor is considered as the fatigue design life corresponding to the number of cycle that ranges from 10 million to 20 million cycles for infinite fatigue life [²⁵].

Socket connection detail: tube-to-transvers plate connection

Several researchers performed fatigue tests on unstiffened fillet-welded socket connections [⁸,¹⁰,¹¹,¹⁴,¹⁵,²⁶]. This unstiffened fillet-welded socket connection is similar to the fillet-welded tube-to transverse plate connection given in Table 11.9.3.1-1 in the LRFD specifications [⁹]. These fatigue tests were performed after the fourth edition of AASHTO fatigue provisions were published [¹³]. Figure 3 shows a plot of the existing test data from the above mentioned researchers along with Category E′. As can be observed in Fig. 3, there is a large scatter in the test data.

Due to the many significant parameters that influence fatigue resistance, the test data were divided into eight groups for base plate thickness, peening, galvanizing, and the shape of tube as shown in Table 1. Table 1 also shows the fatigue coefficient, A from the regression line representing the mean minus two standard deviation. For instance, the fatigue data listed under Group 1, the base plate thickness was greater than 50.8 mm and the tube had a round shape. For the tested specimens in Group 1, there was no peening and no galvanization. The tests in Group 2 were tested under the same conditions as in Group 1 but the test specimens were galvanized. Figure 4 shows the fatigue test data for both Groups 1 and 2 with category E′ and with the fatigue limit which represents the mean minus two standard deviation regression line. The reduction of fatigue limit is found with a galvanization for Group 2. A detail of geometric parameters for post, base plate and fillet welding of unstiffened fillet-welded socket connection are also summarized in Table 2.

To evaluate the fatigue damage and safety factor using the fatigue module in ANSYS Workbench, fatigue design limit in terms of stress range was calculated for both 10 million cycles and 20 million cycles which were established for infinite fatigue life [²⁵].

In Fig. 5, a bar chart represents the fatigue coefficient A, for the mean minus two standard deviation regression line for the eight groups of test data compared to the AASTHO limits (Group 9). The right axis in Fig. 5 represents the fatigue design limit. Group 9 which represents the values from the AASHTO specification [⁹] was added in Fig. 5 to show comparisons between AASHTO and the eight test data groups.

With respect to galvanization, the reduction in fatigue design life is observed for Groups 1 and 2. Also, for Groups 4 and 6 where plate thickens is less than 2 inch with a round tube and no peening, the fatigue coefficient and fatigue design limit have decreased significantly compared to other test data in Fig. 5. The tube geometry was another important parameter investigated in the data analysis in this study. For Groups 1 and 3, Groups 4 and 5 as well as Groups 7 and 8, there is a reduction in fatigue design life with multisided tube due to the stress concentration at the corner of the tube. Group 5 shows the worst fatigue performance with base plate thickness of 54.6 mm (1.25 inch).

With regard to an effect of surface treatment, there is an improvement in fatigue resistance with the peening treatment. It can be observed by comparing Groups 5 and 7 as well as Groups 4 and 8. As illustrated in the bar chart in Fig. 5, the highest fatigue coefficient is found in the data in Groups 8. Although this group has a base plate thickness less than 2 inch, the peening treatment seems to have improved fatigue resistance substantially. It is worth noting that there were only four tests in Group 8 compared to the groups which have more tests per group.

According to the previous studies [¹¹,²⁷], it is believed that base plate thickness is one of the most critical factors that affect fatigue performance of socket connections. In this study, Groups 1 and 4, Groups 2 and 6, and Groups 3 and 5 are compared and it is observed that there are reductions in fatigue design limit for a thin base plate except Group 4 where has 38.1 mm (1.5 inch) of plate thickness.

Regarding fatigue design life for 10 million and 20 million cycles, this study represents that there are considerable discrepancies for each case. According to Section 5.4 in Table 11.9.1-1 in the AASHTO specifications [⁹], the CAFT’s are determined by K_I and those vary from 17.9 MPa to 48.3 MPa as illustrated in Fig. 5. The fatigue coefficient is defined as 3.9 × 10⁸ when K_F is less than 3.2. It is observed that in terms of fatigue coefficient and CAFT fatigue performance of unstiffened socket connection details is overly predicted with a mean minus two standard deviation regression lines. Each group represents significant disparity in fatigue performance. The results of the fatigue test data analysis evaluated for the eight groups earlier will be further discussed in light of the FE analysis results in the next sections.

Stiffened socket connection detail: tube-to-transvers plate connection with longitudinal stiffeners

The fatigue test results for stiffened fillet-welded socket connection detail from several researchers [⁸,¹⁴,¹⁵,²⁶] were analyzed in this section. The detail is also named tube-to-transverse plate connections stiffened by longitudinal attachments with fillet-weld. In this detail the tube is subjected to longitudinal loading and the welds are wrapped around the stiffener termination [⁹]. This detail was defined as category E′ for a CAFT of 17.9 MPa in the fourth edition of specification [¹³]. Figure 2 shows a typical stiffened socket connection detail tube-to-transverse plate connection with longitudinal stiffeners. Modifications were made to this detail in the LRFD specification [⁹]. By considering two potential fatigue crack locations: at the weld location at the base and at the weld location at the tip of stiffeners, a CAFT of 48.3 MPa is introduced when the stress intensity factor, K_I, is less than 5.5. Based on the fatigue crack location, collected data are sorted out into two groups and the testing data are plotted on S-N curve with fatigue categories as shown in Fig. 6.

From the test data analysis procedure, significant differences were observed in the fatigue resistance at crack location at the tip of stiffener due to the geometric effects of stiffeners. Because of that, the fatigue data are further sorted into another two groups: the socket connection with eight stiffeners [⁸,¹⁴] and the socket connection with four stiffeners [¹⁴,²⁶]. Except for two testing results [¹⁴], the first group presents a CAFT of 48.3 MPa and it was defined as an optimized stiffened tube-to-transverse connection detail [¹⁷] with eight stiffeners.

A statistical regression analysis was performed on the test data to establish fatigue limits and design life. Figure 7 shows mean minus two standard deviation lines from the least square regression analysis for the two test data groups. The connection with eight stiffeners shows higher fatigue resistance. In addition, the test groups are summarized in Table 3 with failure location, number of stiffeners, fatigue coefficient, and number of testing data. The geometric parameters for the post, the base plate and the thickness of fillet welds are shown in Table 4. The stiffener parameters are summarized in Table 5.

As was done in the test data analysis for the socket connection-tube-to-transvers plate connection in the previous section, the fatigue design life is calculated with a lower range of 10 million cycles and an upper range of 20 million cycles. In Fig. 8, a bar chart represents the fatigue coefficient, A, from obtained from the mean minus two standard deviation regression analysis line of the test data. Figure 8 also shows fatigue design limit on the right hand vertical axis. As presented in Table 3, Group 1 represents a fatigue failure at base, Groups 2 and 3 are for tests with four stiffeners and eight stiffeners respectively. In addition, Group 4 was added to Table 3 to show comparisons of the test data from Groups 1, 2, and 3 to the limits given in the AASHTO (2015) Specifications [⁹] represented in Group 4. The fatigue resistance at the base which is represented by Group 1 tests in Table 3, is the lowest fatigue performance compared to Groups 2 and 3. This indicates that local stress was higher at base toe than at tip of stiffeners and failure was observed at base toe only. Because of the geometric parameters, the stiffeners fail to reduce or minimize the level of stress at the toe. On the other hand, Group 3 tests which has eight stiffeners represents the best fatigue resistance in terms of fatigue coefficient, A, and design life.

According to the Section 6.2 in the Table 11.9.1-1 of the AASHTO specifications, the CAFT of 48.3 MPa can be used when K_I is less than 5.5. The fatigue coefficient, A, for this case is given as 11 × 10⁸ when K_F is less than 2.5. For a fatigue design life range between 10 million and 20 million cycles and using a mean minus two standard deviation regression line, the analysis of the test data from Group 3 and comparing them to AAHSTO (Group 4) shows that the CAFT values from AASHTO is conservative for eight stiffeners (Group 3). However, for Group 2 (four stiffeners) and Group 1 (At base failure with various number of stiffeners), the data analysis shows that the AASHTO fatigue limit (Group 4) is overestimated.

FE investigation

A three-dimensional FE model is developed to perform advanced fatigue evaluation of the stiffened connection details for sign support structures. The geometry of this model was originally constructed using SOLIDWORK 2010, then it was exported to the commercial Finite Element Analysis (FEA) software ANSYS Workbench 17. In this study, a static structural option was chosen for an imported solid model then the model was regenerated into a design module. After that, contact regions, boundary conditions, and meshes were determined. According to the previous study [²⁷], element size with 0.25 inch length along the weld toe area is acceptable. A tube-to-transverse plate connection detail stiffened with eight longitudinal welded stiffeners was developed to perform a comprehensive fatigue analysis. The model was validated using experimental data and also compared to the nominal stresses from basic mechanics. Since Workbench does not support shell elements for fatigue analysis, ANSYS Solid 187 elements that are relatively tolerant of irregular shapes were selected for FE models in this study.

FE model development

The round tube is 3.7 m long and 7.9 mm thick and was attached to the base plate with fillet welds on top and bottom as shown in Fig. 9. The fillet welds were equal leg welds with 9.5 mm × 9.5 mm. For the FE model validation, the acceptable maximum gap between the tube and the base plate was deliberately set at 1.6 mm. The round shape base plate is 50.8 mm thick with eight f30 mm anchor rods equally spaced around the circumference of the base plate such that there is one anchor rod between two adjacent stiffeners. Each stiffener is 457.2 mm long and 9.5 mm thick with a 15 degree stiffener termination angle on the tube. Stiffeners are attached to both the round tube and the base plate with 12.7 mm thick fillet welds. The round tube and the stiffeners are welded at the top and along the side of stiffeners and the base plate were also connected by enclosed fillet welds. A 508 mm × 508 mm × 50.8 mm square plate was add on the top of the round tube for load application to simulate both static and cyclic loading.

FE model validation

For FE model validation, a FE model of the tube-to-transverse plate connection detail with identical dimensions and geometry of tested specimen [¹²] was developed. Based on static test results, the load versus stress plot was constructed for the fatigue critical location at the top of stiffeners. To obtain the stress values at a specific location, a node was defined. Figure 10 shows the load versus maximum principle stress from the FE model and from test data. The plot in Fig. 10 shows good agreements between experimental results [¹²] and FE results.

SCF for the fatigue critical locations were obtained using an additional FE model validation procedure. In Fig. 11, a SCF (approximately 2.5) was observed at the top of stiffeners then gradually decrease along the tube as expected. Overall, the SCF pattern for FEM results shows higher stress level but good agreements between test results. The SCF at the base weld connecting the base plate to the post is shown in Fig. 10. It was observed that the SCF at the base weld was about 3.0 from FE model compared to SCF of about 3.7 from experimental results. As shown in Fig. 11, both stress patterns along the tube gradually decreased as distance from the base weld toe increased as expected.

FE analysis results

In static FE model, the local principle stresses at the fatigue critical locations are evaluated by altering the base plate thickness, the number of stiffeners and the boundary conditions. The plate thickness varied from 38.1 to 76.2 mm. The number of stiffeners evaluated were: eight, four, two, and no stiffeners. With respect to the boundary conditions, two boundary conditions were investigated: a fixed boundary at the base plate and partially fixed boundary at the plate. The fixed condition was modeled as mast-arm connection and the partially fixed boundary was simulated as representing the base connection with fixed support condition on the bottom and side of the bolts.

The input data into the ANSYS FE model include the following: the stress range and number of cycles of the detail under the constant amplitude stress life analysis, the fatigue design life. The proposed S-N curve for fatigue design was obtained from the synthetic fatigue testing data analysis by considering the characterics of the connection such as the base plate thickness, galvanization, peening, and tube shape. Due to the fact that FE model developed with a round tube, testing results for multi-sided tube (Groups 3, 5, 7) are not considered as S-N data input into FE model. Base plate thickness for FE model was adjusted to 38.1 mm for Group 4, 6, and 8, respectively. An average plate thickness of 30 specimen was 56.6 mm for Group 2 and 40.1 mm for Group 6. Table 6 shows base plate thickness for experiments and FE model.

For each run of the model, the following output was obtained: the fatigue damage, the factor of safety, and the fatigue life. It is noted that the fatigue damage and safety factor has a range due to the range of design life of 10 to 20 million cycles. The advantage in use of two fatigue resistance terms is the simplicity in representing fatigue performance while stress range and number of cycles needs log-log space. These were used to compare the performance of the details for the various cases as explained in the next section. The results will be presented in the form of contour plot and tabulated format.

Results and discussions from the static FE analysis

Effect of base plate thickness

The first developed FE model has partially fixed boundary condition, 50.8 mm thick base plates and no stiffeners. The effect of the base plate thickness was evaluated for unstiffened fillet-welded connections by varying the thickness from 38.1 to 76.2 mm. Under the constant applied force, the FE model results showed that there is a decrease in the local principal stress as the thickness of the base plate increased. The effect of the base plate thickness, the number of stiffeners, and boundary condition are summarized in Fig. 12.

Effect of the number of stiffeners

For a connection with eight stiffeners, the maximum local principal stress dropped by 42% compared to the case with no stiffeners. The maximum principal stress in the unstiffened socket connection was at base toe while the stiffened connections showed the maximum principal stress at the tip of stiffeners. It is important to note that this FE model was developed with an optimized stiffener configuration that was introduced in LRFD AASHTO Specification [⁹] and also can minimize the local stress level at base. For the case of the connection with four stiffeners, Table 7 shows that the local principal stress at the base and the tip of stiffener were similar. Figure 13 shows the local principal stress at the base toe and at the tip of the stiffener for stiffened connections with different number of stiffener.

Effect of boundary conditions

As discussed earlier the two boundary conditions were investigated: fixed and partially fixed conditions. It was observed that fully fixed condition mitigated the significant level of local principal stress at base by enhancing the rigidity of the base plate as shown in Tables 7 and 8. The FE model of the stiffened connection with eight stiffeners showed a similar level of principal stress at the tip of stiffeners for both partially fixed and fully fixed condition. At the base toe, the model showed the principal stress at the base toe was significantly less than that at the tip of the stiffener.

The analysis results of the FE model of the stiffened connection with four stiffeners a partially fixed boundary condition showed similar local principal stresses at both, the tip of stiffeners and at the base. When the boundary conditions are changed to fully fixed boundary conditions, the principal stresses decreased at both locations with significantly less stress at the base toe as shown in Table 7. Table 7 also shows a comparison of the principal stresses of stiffened connection with two stiffeners and unstiffened connection (zero stiffeners). The results show that the local principal stress at the base toe for the fixed condition is about 37% less than that of the partially fixed boundary condition for both connections.

Results and discussions from the fatigue FE analysis

As discussed earlier, the S-N curve from synthetic data regression analysis and fatigue design life were used as input variables for fatigue module in the ANSYS Workbench platform. In this study, only test groups that have a round shape tube were considered. The base plate thickness was 38.1 mm for test Groups 4, 6, and 8, respectively. For a constant applied force of 4.45 kN at the top of the round tube, the resulting local principal stresses and fatigue resistances were determined. Figures 14(a), 14(b), and 14(c) show the contour plots of fatigue resistance outputs for fatigue life, fatigue damage, and fatigue safety factor for the unstiffened connection, respectively. The fatigue life represents the number of cycles corresponding to the local principal stress while fatigue damage represents the ratio of the design life to the available life. When the fatigue damage is greater than 1.0, this indicates that fatigue failure has occurred before its intended design life. The fatigue safety factor represents the factor of safety for fatigue failure at a given design life. When the safety factor is less then 1.0, that means failure has occurred before reaching its intended design life.

Effect of galvanization

To evaluate an effect of galvanizations on fatigue resistance, the S-N curve from the synthetic analysis of the test data of Groups 1 and 2 were used for model input. Groups 1 and 2 have plate thicknesses greater than 50.8 mm with a round tube and no peening treatment. Results from the FE analysis showed that without galvanization (Group 1 input data), a fatigue life of 1.53E+ 05 cycles was achieved with stress of 53.1 MPa compared 9.70E+ 04 cycles was obtained with galvanization (Group 2 input data). This shows that the fatigue resistance (fatigue life, damage, and safety factor) was reduced due to the galvanization and fatigue design life of 10 million cycles for Groups 1 and 2 was increased from 6.52 to 10.31. On the other hand, the safety factor decreased from 0.54 to 0.46. Similar trend was observed for Group 4 and 6 which has the plate thinness of 38.1 mm. The FE results using input data from Groups 4 and 6 showed a fatigue life of 2.53E+ 05 and 3.31E+ 04, respectively. Table 8 shows the stress range and fatigue resistance of each group.

In the light of fatigue resistance without any corrosion effect, it was observed that there is a reduction in the fatigue resistance of the hot-dip galvanized fillet-welded tube connection for support structures. However, it can be beneficial to achieve a better fatigue resistance with formed zinc patina which provides cathodic protection under the severe corrosive environment.

Effect of peening treatment

The peening surface treatment as the proven method having compressive stressed layer by progressively repeated impacts showed an improvement of fatigue resistance of the socket connection details. The analysis results was compared with Group 4 and 8 which have plate thickness less than 2 inch with a round tube and not galvanized. With a stress of 56.9 MPa, fatigue life of 2.53E+ 05 and 2.81E+ 05 cycles were obtained, respectively. As such, fatigue damage and safety factor value also showed that peening treatment enhanced the fatigue resistance.

Effect of base plate thickness and boundary conditions

The base plate thickness was an important parameter that affects fatigue performance of socket connections. The thickness of base plate was adjusted for FE model for the sake of comparing Groups 1 and 4, and Groups 2 and 6. It was anticipated that there are reductions in fatigue resistance for the specimen that has a thin base plate. However, Group 4 showed a higher fatigue resistance in terms of fatigue life, damage, and safety factor compared to Group 1 which has a larger thickness. This result was unexpected and may be attributed to workmanship, weld quality, inherent defects, and others. Future tests and analyses may be needed to verify this result. For Group 6, which has galvanized connections, a lower fatigue resistance was observed with base plate thickness of 38.1 mm as compared to Group 2.

For fully fixed boundary condition, fatigue resistance of all groups improved by achieving a lower stress range. In the case of Group 6, a fatigue life of (3.31E+ 04) was obtained with partially fixed condition while a higher fatigue life (3.99E+ 05) was observed with fully fixed condition. In addition to the effect of base plate thickness, this result also can be compared to fatigue life of 9.70E+ 04 where base plate thickness was increased to 50.8 mm. Table 8 summarizes the effects of the base plate, number of stiffeners, and boundary conditions on fatiue life, fatigue damage, and safety factor.

Summary and recommendations

In this study, the fatigue resistance of unstiffened and stiffened fillet-welded connection details was investigated by utilizing fatigue module platform in ANSYS Workbench. A synthetic fatigue testing data analysis, FE model development, and validation were performed. For the static FE analysis, FE models were utilized to evaluate an effect of base plate thickness, the number of stiffeners, boundary conditions. To evaluate fatigue resistance, the stress range, number of cycles, and the fatigue design life were used as input data from synthetic data analysis. Based on the results of this study, the following conclusions can be drawn:

1) A synthetic fatigue data analysis of fatigue test results was performed to provide input data in which the fatigue test data were sorted into eight groups based on base plate thickness, galvanization, peening treatment, and tube shape.

2) Regression analysis for mean minus two standard deviations was performed to establish a lower bound that is associated with a 2.3% probability of failure. The regression results were used as fatigue input data into the ANSYS FE fatigue module.

3) Results from the static FE model analysis showed that the local principal stress decreases with the increase in the base plate thickness. As expected, adding stiffeners, reduced the stress level compared to unstiffened connection. The fully fixed boundary condition reduced the local principal stress at the base toe compared to partially fixed conditions.

4) As the proven method having compressive stressed layer by progressively repeated impacts, the FE analysis showed that peening surface treatment enhanced the fatigue resistance of the socket connection details.

5) Without any corrosion effect, a reduction in the fatigue resistance was observed for the hot-dip galvanized fillet-welded tube connection for support structures. However, formed zinc patina that provides cathodic protection can be beneficial under the severe corrosive environment.

6) There is a need for additional fatigue testing of stiffened and unstiffened connections to validate the results from this study such as the effects of various weld and stiffener geometries, galvanizations, and surface treatments on the fatigue performance of these connections.

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