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Numerical study on girth weld of marine steel tubular piles
Applied Ocean Research 44 (2014) 112–118
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Technical note
Numerical study on girth weld of marine steel tubular piles Yi Lia , * , Xiao-Peng Zhoub , Zhao-Min Qic , 1 , Yi-Bo Zhangb a
National Inland Waterway Regulation Engineering Research Center and School of River and Ocean Engineering, Chongqing Jiaotong University, Chongqing 400074, China School of River and Ocean Engineering, Chongqing Jiaotong University, Chongqing, China c Southwest Guizhou Vocational and Technical College for Nationalities, Guizhou, China b
a r t i c l e
i n f o
Article history: Received 8 October 2012 Received in revised form 17 November 2013 Accepted 21 November 2013 Keywords: Marine steel piles Splice weld Stress concentration factor Finite element analysis Axial tension Bending moment
a b s t r a c t At a splice weld of marine steel tubular pile, the misalignments between two adjacent pile segments may cause significant stress concentrations. In structural analysis, the stress concentrations shall be properly addressed, normally by a stress concentration factor (SCF) in practice. Based on a flat-plate configuration, the SCF at pipe splice under either axial tension or in-plane bending moment has been theoretically derived. To verify the effectiveness of the flat-plate solutions, this paper investigated the SCFs with numerical modeling. Finite element models built by ANSYS were used to simulate pipe splices for different pile diameters and wall thicknesses, which are representative of practical marine applications. Axial tension and in-plane bending moment, as well as their combination were applied. The flat-plate solutions were compared with the numerical results. The results show that the flat-plate solutions are close to the numerical results, indicating that they are reasonably effective in practical applications under complex loading conditions. The findings will significantly help in the hot-spot analysis for splice welds of steel tubular members, particularly piles, in marine structures given complex loading effects. Additionally, an integrated formula including the effect of both axial tension and in-plane bending moment is formulated for the SCF at pile splice. c 2013 Elsevier Ltd. All rights reserved.
1. Introduction In many cases, especially deep-water applications, marine steel tubular piles are prefabricated in tubular segments, and the segments are connected on site or in shop by transversal splice welds, namely girth welds [1,2]. As usual, geometrical misalignments between two neighboring tubular segments remain at the transversal splice, due to various sources including concentricity, out of roundness, thickness difference, and center eccentricity, as schematically illustrated in detail by Det Norske Veritas (DNV) [3]. For example, if two pile segments with equal wall thicknesses and diameters are connected, out of roundness and center eccentricity may be the major sources leading to misalignments, and Fig. 1 demonstrates such an example which occurred during in-situ welding process. The misalignments may result in a considerable stress concentration effect on the hot spots at pile splice, thus increasing structural hot-spot stress and decreasing the fatigue strength of pile [4–6]. Hence the stress concentration effect should be appropriately considered in structural design. A practical way to estimate the structural hot-spot stress is to multiply the nominal stress at hot spot by a stress
1 Formerly, School of River and Ocean Engineering, Chongqing Jiaotong University, Chongqing, China * Corresponding author. Tel.: +86 23 62652714; fax: +86 23 62650204. E-mail address: [email protected] (Y. Li).
c 2013 Elsevier Ltd. All rights reserved. 0141-1187/$ - see front matter http://dx.doi.org/10.1016/j.apor.2013.11.005
Fig. 1. Splice weld of a marine steel tubular pile: (a) field welding of pile splice and (b) observed misalignment between two segments.
concentration factor (SCF). Because of the complex nature of the misalignments, i.e., uncertainties in on-site work and combined sources, analytic solutions to SCF are difficult to develop in most scenarios. Instead, approximate flat-plate solutions have provided a conservative, but robust method in practice for estimating SCF at pipe’s butt weld. The flat-plate solutions to SCF at pipe splices subjected to axial tension have been developed [7–9], and the wall thicknesses of connected segments can be equal or different in the solutions. More recently, Li et al. [10] derived a flat-plate solution given in-plane bending moment,
Y. Li et al. / Applied Ocean Research 44 (2014) 112–118
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Nomenclature d Ka Kam Km M N ri t
δ σa σ b1 σ b2 σ hs σi σn σo τ
outside diameter of pipe segment SCF at the outside maximum tension point (OMTP) under N SCF at the OMTP under both N and M SCF at the OMTP under in-plane bending moment bending moment applied on the cross section at splice weld axial tension applied on pile shaft inside radius of tubular pile wall thickness eccentricity between pipe segments nominal stress caused by N additional tensile stress at weld toe due to N additional tensile stress at weld toe due to M structural hot-spot stress nominal stress at the inside edge caused by M nominal stress nominal stress at the outside edge caused by M thickness ratio
which is applicable to the case of equal wall thicknesses of connected segments. The flat-plate solution [10] significantly supports the practical fatigue assessment for marine steel piles under complex loading conditions, which typify deep-water applications properly. However, the solution derived by Li et al. [10] has not been verified by physical or numerical models. With a series of numerical examples, this paper investigates the effectiveness of the flat-plate solutions, in particular that given inplane bending moment. The flat-plate solutions are compared with the numerical results of finite element models built by ANSYS [11]. The numerical examples adopt representative configurations of practical marine steel pile design, such as weld form, diameter, and wall thickness. The loading effects of in-plane bending moment and axial tension are considered in the examples. The remaining sections of this paper are organized as follows. In Section 2, both flat-plate solutions for axial tension and in-plane bending moment are reviewed, and an integrated formula combining both is derived. Then, the details of the numerical examples are described in Section 3. Numerical results are presented and analyzed in Section 4. Section 5 presents the conclusions. 2. Flat-plate solutions to SCF For large-diameter steel pipes in marine and offshore facilities, segments are often connected by transversal V-shape butt welds made from outside without an inside backing strip [3,12]. To help in guiding the positioning of segments and guarantee welding quality, the use of inside backing strip is normally recommended in practice. The strip is attached on the lower segment by weak welds, for instance intermittent welds [13], and thus may not work structurally like stiffeners. Generally speaking, therefore, the inside backing strip can be actually ignored in structural analysis of splice weld. Fig. 2 presents the typical configuration of a typical splice weld connecting two segments with equal wall thicknesses. A misalignment between two pipe segments is illustrated in Fig. 2(b), where t = wall thickness, and δ = the eccentricity between pipe walls. The pile diameters of both segments may be equal or different. Owing to the eccentricity, either the local tension around the weld or the global tension on the pipe shaft may introduce additional tensile stress in a certain region near the weld, i.e., stress concentration. The additional tensile stress reaches its maximum at the outside maximum tension point (OMTP). A weld toe of the butt weld, the OMTP is a critical
Fig. 2. Typical misalignment at splice weld: (a) splice and segments and (b) the misalignment between pipe walls.
Fig. 3. The in-plane misalignment considered for the stress concentration given bending moment.
structural hot spot in the fatigue design of the weld. Despite a large number of parametric formulas for the SCFs at the tubular joints of offshore structures as summarized by Ahmadi et al. [14], the SCFs at pile splices have not been extensively investigated so far, and pipe splices are essentially different from tubular joints [8,10]. In general, the piles of marine structures are subjected to different loadings. This paper considers an axial tension applied on pile shaft (N), as well as a bending moment applied on the cross section where splice weld is positioned (M), as illustrated in Fig. 2(a). Field observations have informed that the segment misalignments at a pile splice randomly distribute around pile cross section, as reported in detail by Dailey et al. [6,15]. A bending moment in a certain direction may be in-plane for some positions on pile perimeter, but out-of-plane for the others. So far, the impact of in-plane bending moment on stress concentration has been investigated [10]. Specifically, the wall misalignment to be considered is located at a crown, for which M is an in-plane bending moment and yields maximum tensile bending stress. As an example, Fig. 3 displays such an in-plane misalignment point for two segments in center eccentricity. For the case of equal wall thicknesses and pile diameters, Fig. 4 illustrates the stress distribution over wall thickness near the weld at in-plane misalignment point under N and M, where σ a = the nominal stress caused by N, σ o = the nominal stress at the outside edge caused by M, and σ i = the nominal stress at the inside edge caused by M. By the flat-plate assumption, the additional tensile stress at the OMTP due to N, σ b 1 , is expressed as follows [7–9]
σb1 =
3δσa t
(1)
While derived for double-side V-shape butt welds, Eq. (1) has been applied for single-side welds as a simple approximation. In Eq. (1), the nonlinear stress peak resulting from the local notch geometry of
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Fig. 4. Stress distribution over wall cross sections near in-plane misalignment point.
weld is ignored. Since the exact profile of an in-situ weld is almost unpredictable, it is difficult in reality to reflect the nonlinear stress peak directly in SCFs. Consequently, the nonlinear stress peak is normally excluded from the structural stress analysis [3,16]. Instead, the influence of the nonlinear stress may be implicitly reflected in experimental S-N curves. The SCF at the OMTP under axial tension, Ka , is hence written as 3δ Ka = 1 + t
(2)
The flat-plate solution is a benchmark for the approximation to SCF at pipe splice. In spite of the simple flat-plate assumption, it has exhibited its advantage in a practical sense. For the axial tension case, however, more complicated solutions have been also proposed, as summarized by Lotsberg [17]. In particular, Lotsberg [8,9] has developed a solution using cylindrical-shell theory Ka = 1 +
3δ −√t/d 3δ −√τ e =1+ e t t
(3)
where d = the outside diameter of the segments, and τ = thickness ratio (t/d). The cylindrical-shell solutions asymptotically approach the flat-plate solution in the thin-walled condition (τ → 0), as demonstrated in [8]. The thin-walled condition is a rather typical geometric feature of marine steel piles in practical installations. Ignoring the nonlinear stress peak, the additional tensile stress at the weld toe due to M, σ b 2 , can be estimated as [10]
σb2 =
3δ (σo + σi ) 2t
(4)
It should be noted that the additional tensile stress given by Eq. (4) is developed for the case of equal wall thicknesses and pile diameters. Strictly speaking, Eq. (4) is applicable to double-side V-shape butt welds, like Eq. (1). Moreover, Li et al. [10] formulated the SCF at the OMTP under in-plane bending moment, Km , 3δ 1 1+ Km = 1 + 2t 1 + (t/ ri ) 3δ 1 (5) 1+ =1+ 2t 1 + (t/ (0.5d − t)) 3δ 3δ =1+ (2 − 2 τ ) = 1 + (1 − τ ) 2t t where ri = the inside radius of the pile. Eqs. (4) and (5) are derived on the basis of a linear distribution of the nominal bending stress over the pipe cross section, as displayed in Fig. 5. The linear distribution is a reasonable assumption for regular design practice [16]. The linear distribution is also employed for the assumed plate. Eq. (5) has been applied in assessing fatigue reliability of steel berthing monopiles [10]. The derivative of Eq. (5) relative to d gives d Km 3δ = 2 dd d
(6)
In fact, Eq. (6) is a sensitivity measure relative to d. Since δ is quite small compared with d in regular circumstances, Km may not be so sensitive to the change of d, especially if d is relatively large.
Fig. 5. Nominal bending stress over pipe cross section.
In the case of combined axial tension and bending moment, International Institute of Welding (IIW) [16] suggests a generalized form of the structural hot-spot stress allowing for stress concentration:
σhs = K a σa + K mσo
(7)
where σ hs = the structural hot-spot stress. This paper examines the combined mode using the flat-plate assumptions. With Eqs. (2) and (5), one may formulate an integrated SCF in the following:
σhs K a σa + K mσo = σn σo + σa (1 + (3δ/ t)) σa + [1 + (3δ/ t) (1 − τ )] σo = σo + σa 3δ 1−τ 1 =1+ + t 1 + (σo /σa ) 1 + (σa /σo )
K am =
(8)
where Kam = the SCF at the OMTP under both N and M, and σ n = nominal stress. Both Eqs. (2) and (5) are irrelevant to nominal stresses (σ a and σ o ), or, in other words, acting loads (N and M). Unlike Eqs. (2) and (5), however, the combined SCF, Eq. (8), is related to σ a and σ o , implying that, under combined loading effects, acting loads also have an influence on stress concentration. This is an expectable result. It is clear that stress ratio (σ a /σ o ) plays an important role in the integrated SCF. When the pile splice is mainly subjected to axial tension (σ o /σ a → 0), Eq. (8) reduces to Eq. (2), indicating that the effect of bending moment is negligible. On the contrary, when the pile splice is mainly subjected to bending moment (σ o /σ a → ∞), Eq. (8) simply becomes Eq. (5), indicating that the effect of axial tension is negligible. 3. Finite element models At present, finite element analysis (FEA) is a useful tool for determining structural hot-spot stress and validating SCFs at weld joints [3,14,16,18]. For the axial tension case, it has been found that Eq. (2) is close to numerical results in certain scenarios [9]. However, Eq. (5) has not been examined with numerical examples. This paper conducts FEA with ANSYS [11] to study the effectiveness of Eqs. (2), (5), and (8) under different loading conditions and geometric configurations (d and t). The FEA examines a series of three-dimensional models. As shown in Fig. 6, each model contains two pile segments with equal wall thicknesses, both of which are connected by a splice weld. The models are built with 20-node solid elements (SOLID 95 in ANSYS). The Young’s modulus and Poisson’s ratio of pile material are 210 GPa and 0.30, respectively. The models cover the following geometric configurations of pile cross section: d = 0.8, 1.0, and 1.2 m (t = 16, 18, 20, and 22 mm), and d = 1.4 and 1.6 m (t = 22, 25, 28, and 31 mm). These diameters and thicknesses are very common in practical pile designs, and the general requirements for selecting minimum pile wall thickness recommended by American Petroleum Institute (API) [19] are also taken into consideration. The welds adopt the form shown in Fig.
Y. Li et al. / Applied Ocean Research 44 (2014) 112–118
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Fig. 8. An example for calibrating weld mesh: (a) weld details used in [22] and (b) calibrated weld mesh pattern. Fig. 6. A typical ANSYS model of two pile segments connected by a splice weld. Table 1 Calibration results for weld mesh pattern. Longitudinal surface stresses at different positions (MPa)
Mesh pattern in Fig. 8(b) Lotsberg and Holth [22] a b
Ao
Ai
Co
Ci
1.162
1.197
2.041
0.779
1.250a
1.188b
2.350b
0.760b
Read from Figs. 6 and 8 of Lotsberg and Holth [22]. Reported in Table 1 of Lotsberg and Holth [22].
Fig. 7. Weld details: (a) typical dimensions and (b) generated mesh.
7(a), which is determined in line with typical recommendations from various guidelines [3,9,20]. A fine mesh is implemented for the welds, as shown in Fig. 7(b). The two segments in each model are built in different lengths. The shorter one is always 1.0 m in length, and the longer one is 4d. The lengths are moderate, thus enhancing modeling efficiency. The end of the longer segments is fixed, while that of the shorter segments remains free. One should note that neither Eq. (2) nor Eq. (5) takes account of end boundary. A much longer pipe length is probably needed to eliminate the influence of the end condition entirely, for example 6d for chord members in jacket structures [21]. On the other hand, a much longer pipe length could require much heavier computational loads. The determination of pipe length is a tradeoff between accuracy and efficiency. The chosen length of the longer segments might be able to minimize the influence of end condition on the stress concentration at weld toe. In real situations, misalignments may result from different sources and even their combinations. The exact form of misalignments is almost impossible to predict. Therefore, it is impractical to model all of these complicated misalignments in FEA, particularly center eccentricity and out of roundness. For simplification, the concentricity between both segments is chosen as the only misalignment source in all ANSYS models. Specifically, the outside diameter of the shorter segment is larger than that of the longer segment by 2δ ; that is, the outside diameter of the longer segment is d, which is the nominal diameter in flat-plate solutions, while the outside diameter of the shorter segment is d + 2δ . Since δ is quite small (2 mm) compared with d in the models, the simplification will not cause significant errors. The following loads are to be considered for each case: N = 1000 kN, M = 1000 kN m, and their combination. Both M and N are imposed at the free end, and N is uniformly distributed over pile cross section so as to minimize the local effect. The self-weight of all structural components is ignored in the models. As usual, finite element (FE) modeling of weld requires a very fine mesh. The guidelines of DNV [3] and IIW [16] are properly adopted
herein. Furthermore, the present paper has calibrated the mesh pattern around weld using a numerical example provided by Lotsberg and Holth [22], as illustrated in Fig. 8(a). In the example, the pipe diameter at Co–Ci cross section was 1.067 m, wall thicknesses were 31 mm, and a 1.0-MPa nominal stress was imposed over Ao–Ai cross section. An ANSYS model was built by the methodology described above for the example, in which the weld details in Fig. 8(a) were applied. The calibration targets focused on the longitudinal surface stress at the four marked positions in Fig. 8(a). Note that Co is simply the OMTP. Different mesh patterns were examined, and the final choice is shown in Fig. 8(b). Table 1 presents the calibration results. At Ai and Ci, where the notch has a minor influence, the selected mesh pattern provides results close to [22]. Like Co, Ai experiences stress concentration effect due to tension. At Ao and Co, the selected mesh pattern slightly underestimates. The differences are likely due to the difference in element meshes at the notch region, as well as in weld details applied in the numerical models. A finer mesh may reduce the differences, but require a much larger computer capacity. It should be noted that, at Ao and Co, the surface stress reflects the notch stress that includes two parts, i.e., the nonlinear stress peak and the structural hot-spot stress. Consequently, the notch has a significant influence on the stress at Ao and Co. Theoretically, the segment misalignment will cause additional compressive stress at Ao, resulting in σ hs less than 1.0 MPa. Due to the influence of notch, the numerical solutions at that position were larger than 1.0 MPa. A much finer mesh pattern around both positions may increase the surface stresses there, but demand much heavier computational loads. However, an increase in the surface stresses by much finer mesh may only mean an enhanced modeling effect for the nonlinear stress peak at weld toe, and may not change σ hs significantly. In practice, σ hs can be effectively generated by either an extrapolation scheme based on stress read-out points at certain distances away from the toe, or the read out of stresses at Ai and Ci for comparison of hot spot stresses [3,16], as will be demonstrated in the next section, and thus a correct notch stress may not be required. Because it produces results close to [22], therefore, the selected mesh pattern is considered to be effective in modeling σ hs for this
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Fig. 11. SCF values (N = 1000 kN, d = 1.4 and 1.6 m).
Fig. 9. Linear extrapolation for hot-spot stress.
Fig. 12. SCF values (M = 1000 kN m, d = 0.8, 1.0, and 1.2 m).
Fig. 10. SCF values (N = 1000 kN, d = 0.8, 1.0, and 1.2 m).
example. The pattern is then applied for various model configurations described previously. 4. Results of analysis The ANSYS models generate actual stresses for the modeled welds and segments. As expected, under bending moment, the maximum longitudinal surface tensile stress along the weld toe occurs at the OMTP of the in-plane misalignment crown on the longer segment, implying that the misalignment yields the stress concentration at the hot spot under in-plane bending moment. Nominal stresses are also obtained using the selected pile diameters, wall thicknesses, and load cases, with no allowance for splice weld. Nominal stresses are tabulated in Table 2. Following the recommendation of DNV [3], the actual σ hs is developed by a linear extrapolation based on stress read-out points at 0.5t and 1.5t away from the toe, as shown in Fig. 9. An actual numerical solution to SCF is thereafter estimated for each modeling scenario by dividing the actual σ hs by the nominal stress at the same location. While normally recommended for plated structure [3], the procedure in Fig. 9 is considered appropriate for marine steel piles, given small thickness ratios in practical applications. There is a non-linearity in stress along the surface due to the circumferential stiffness of tubular, as illustrated in D.14 of [3]. This is a reason why the extrapolation like that in Fig. 9 should be used with caution at butt welds in tubulars, and normally the read-out of hot spot stresses at Ai and Ci in Fig. 8 is the preferred methodology at girth welds. In the meantime, the flat-plate solutions to SCFs are estimated by Eqs. (2), (5), and (8) along with nominal stresses. For comparative purposes, the cylindrical-shell solution by Eq. (3) is also provided for each axial tension case. The SCF results are presented in Figs. 10–15.
Fig. 13. SCF values (M = 1000 kN m, d = 1.4 and 1.6 m).
Fig. 14. SCF values (N = 1000 kN, M = 1000 kN m, d = 0.8, 1.0, and 1.2 m).
The results indicate that, in the examples, the segment misalignment causes a considerable stress concentration effect. In some cases, SCF may significantly increase the stress ratio at the hot spot, though nominal stress is well below the allowable limit. Here is a simple example. For the case with d = 0.8 m and t = 16 mm, the combined nominal stress under M = 1000 kN m and N = 1000 kN is 157.5 MPa, as
Y. Li et al. / Applied Ocean Research 44 (2014) 112–118
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Table 2 Nominal stresses under the imposed loads (MPa).
Loads
N = 1000
Stress
d = 0.8 m
d = 1.0 m
d = 1.2 m
d = 1.4 m
d = 1.6 m
t (mm)
t (mm)
t (mm)
t (mm)
t (mm)
16
18
20
22
16
18
20
22
16
18
20
22
22
25
28
31
22
25
28
31
σa
25.4
22.6
20.4
18.6
20.2
18.0
16.2
14.8
16.8
15.0
13.5
12.3
10.5
9.3
8.3
7.5
9.2
8.1
7.2
6.5
σo
132.1
118.3
107.3
98.2
83.5
74.7
67.6
61.8
57.5
51.4
46.5
42.5
31.0
27.4
24.6
22.4
23.6
20.9
18.7
17.0
kN M = 1000 kN m
Fig. 15. SCF values (N = 1000 kN, M = 1000 kN m, d = 1.4 and 1.6 m).
provided in Table 2. Assuming API 5L Grade X52 [19] for pile material, the combined nominal stress is well below the yield strength (360 MPa). With the numerical solution of SCF (1.325), the actual stress becomes 209 MPa. The stress amplification, hence, greatly reduces the safety level of pile materials, in particular base steel. It should be noted that the selected value of δ (2 mm) is moderate, and it is expected that higher values of δ will introduce stronger SCFs for the examples, as explained below. DNV [3] has a strict requirement on the misalignment tolerance, i.e., 0.1 t or maximum 3 mm. For the case with d = 0.8 m and t = 16 mm, when δ = 2 mm, the flat-plate solution of SCF under axial tension is estimated to be 1.375. When δ = 3 mm, the SCF increases to 1.563. In all cases, the numerical results confirm the overall trend of the flat-plate solutions relative to t; that is, as t increases, SCF decreases. Actually, both are almost parallel. Smaller thicknesses hereby introduce stronger stress concentrations at pile splice. Compared with numerical results, the SFC estimates by Eqs. (2), (5), and (8) slightly overestimate. The finding confirms that, as addressed by [3,8], the flat-plate solution is a conservative estimate for SCF. In general, the relative differences between flat-plate solutions and numerical results are small; that is, the maximum is merely 3.3%. Here a relative difference is defined as the absolute difference divided by numerical result. Perhaps the differences originate from several sources, such as the flat-plate assumption in the three formulas, the linear extrapolation scheme for σ hs , the concentricity configuration of FE models, the influence of fixed end on numerical results, and the mesh pattern of FE models. Despite the sources, the small relative differences imply a reasonably satisfactory global behavior of the flat-plate solutions in the numerical examples. From a practical point of view, therefore, the flat-plate solutions are effective in estimating SCFs. Interestingly, it is observed from Figs. 10 and 11 that, in axial tension cases, the numerical results are located between the flatplate and the cylindrical-shell solutions. The same conclusion can also be drawn based on [9,22]. The flat-plate and the cylindrical-shell solutions look like an upper bound and a lower bound, respectively. Since it is more conservative, the flat-plate solution by Eq. (2) may be a more appropriate option in practice for estimating SCFs.
Both Eqs. (2) and (5) produce very close results of SCF. As mentioned previously, both are dependent on the geometries of pile cross section and splice weld, and independent of loads and resultant stresses. According to Li et al. [10], upon the thin-walled condition, Eq. (5) eventually reduces to Eq. (2). In all of the examples, τ is rather small, so the SCF estimates of Eqs. (2) and (5) are close to each other, confirmed by numerical results. Consequently, the SCFs in combined cases (Figs. 14 and 15) are also close to those in tension and bending moments cases. In Figs. 12 and 13, the SCF estimates by Eq. (5) appear insensitive to the change of d, as explained by the sensitivity measure Eq. (6). In the examples, pile diameters are relatively large, so flat-plate solutions exhibit small scatters given different d values. As d increases, the sensitivity measure will further decrease, thus the scatters in Fig. 13 are smaller than those in Fig. 12. Since the sensitivity measure is independent of t, flat-plate solutions exhibit similar scatters for different t values. As a result, flat-plate solutions appear almost parallel as t changes. All of these phenomena are observed in FEA results. Generally speaking, the numerical results exhibit small scatters given different d values, and the scatters in Fig. 13 are much smaller than those in Fig. 12. Like flat-plate solutions, the numerical results appear parallel as t changes. These observations significantly validate the effectiveness of Eq. (5). Similar observations can also be obtained for cylindrical-shell solutions and related numerical results in tension cases (Figs. 10 and 11), by studying the sensitivity of Eq. (3) to d. The insensitiveness of SCFs to diameter indicates that, with the same t and δ , piles in different diameters may encounter similar stress concentration effects at splice. The finding is meaningful for practical fatigue assessment. Because of the insensitiveness, the SCF assessment may need to cover only representative diameters for a specific project, while SCFs for other diameters can thus be reasonably assumed. Hence data demand and analysis effort may be largely reduced in practice. 5. Conclusions Steel tubular piles have been widely installed in marine facilities as major foundation structures. For splice welds of marine steel pile, the stress concentration effect caused by segment misalignments is an important concern for practitioners in fatigue design [10,23,24]. The loading effects on marine piles are usually complex, for marine structures are exposed to various cyclic environmental loads (wave, wind, and current) and operational loads (berthing and mooring). Thus, the SCFs under these complex loading effects become one of the keys to analyzing the stress concentration effect at splice welds. As usual, the SCFs at butt weld exhibit considerable scatter from case to case [14]. Accordingly, it is always important to obtain effective and robust solutions to SCFs with thorough studies. In this paper, two existing flat-plate approximate solutions to the SCFs at pipe splice weld have been reviewed, one for the axial tension, and the other for in-plane bending moment. On the basis of both solutions, an integrated flat-plate solution incorporating the effects of both axial tension and in-plane bending moment has been formulated. The integrated flat-plate solution, Eq. (8), is applicable to splice
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welds that connect two pipe segments with equal wall thicknesses and diameters. The flat-plate solutions have been thoroughly tested in a series of numerical examples with representative geometrical configurations of practical pile design. In the numerical results of FE models built with ANSYS, the structural hot-spot stress is extracted from the notch stress, and used for estimating actual SCFs. Compared with the numerical results, the flat-plate solutions demonstrate a reasonably satisfactory global behavior in several aspects, such as the overall trend and the insensitivity to the change of pile diameters. The flat-plate solutions slightly overestimate, due to several sources. From a practical point of view, the flat-plate solutions are verified to be a simple, robust, and effective method in practice for estimating SCFs at splice weld under the thin-walled condition, which is fairly typical for marine steel piles. It is also realized that the numerical investigation only examined the case of concentricity, and other misalignment sources perhaps cause uncertainties. While slightly conservative, therefore, the flat-plate solutions are recommended in practical uses for conservative purposes. The numerical study indicates that SCFs are insensitive to the change of pile diameters. Accordingly, with the same t and δ , piles in different diameters may experience similar stress concentration effects at splice. In the future, the flat-plate solution given in-plane bending moment, Eq. (5), may need to be extended to the case of different wall thicknesses. This paper forms a strong basis for the further studies on estimating the SCFs at transversal splice welds of marine steel tubular pile, and even of other tubular members, under complex loading effects. The findings in this paper will be helpful in estimating structural hot-spot stress and studying mitigations for stress concentrations at transversal splice welds. Acknowledgments The authors would like to appreciate the insightful and constructive comments of three anonymous reviewers. This research was supported by the Natural Science Foundation Project of CQ CSTC (CSTC 2010BB7084), the Research Program of Chongqing Port Management Bureau (SW2013-27), the Innovative Research Program for Graduate Students at CQJTU (20130102), and CQJTU’s start-up research fund for new faculty members. References [1] Tomlinson MJ. Pile design and construction practice. London, UK: E & FN Spon;
1994. [2] Gerwick BC. Construction of marine and offshore structures. Boca Raton, FL: CRC Press; 2007. [3] Det Norske Veritas (DNV). DNV-RP-C203: Fatigue design of offshore steel structures; 2012. [4] Lotsberg I, Sigurdsson G, Arnesen K, Hall ME. Recommended design fatigue factors for reassessment of piles subjected to dynamic actions from driving. Journal of Offshore Mechanics and Arctic Engineering 2010;132:041603. [5] Tang Q, Holloway GL, Wade B. Pile driving fatigue damage—effective factors and reduction. In: Proceedings of the 2005 offshore technology conference, Houston, USA, May 2–5. 2005. [6] Dailey JE, Weidler JB, Hanna SY, Zedan MF, Yeung JY. Pile fatigue failures. II. Mechanism studies. Journal of Waterway, Port, Coastal, and Ocean EngineeringASCE 1987;113:215–32. [7] Boulton CF. Assessment of failures in deep sea terminal piles, Report LD 21914. Cambridge, England: The Welding Institute; 1975. [8] Lotsberg I. Stress concentration factors at circumferential welds in tubulars. Marine Structures 1998;11:207–30. [9] Lotsberg I. Stress concentration factors at welds in pipelines and tanks subjected to internal pressure and axial force. Marine Structures 2008;21:138–59. [10] Li Y, Lence BJ, Zhou S-L, Wu Q. Stochastic fatigue assessment for berthing monopiles in inland waterways. Journal of Waterway, Port, Coastal, and Ocean Engineering-ASCE 2011;137:43–53. [11] ANSYS. Structural analysis guide for ANSYS 12.1; 2010. [12] Lotsberg I. Stress concentration at butt welds in pipelines. Marine Structures 2009;22:335–7. [13] Ruukki. Splicing of Steel Pipe Piles by Welding, Update 05/2008. [14] Ahmadi H, Lotfollahi-Yaghin MA, Aminfar MH. Effect of stress concentration factors on the structural integrity assessment of multi-planar offshore tubular DKT-joints based on the fracture mechanics fatigue reliability approach. Ocean Engineering 2011;38:1883–93. [15] Dailey JE, Weidler JB, Hanna SY, Zedan MF, Yeung JY. Pile fatigue failures. IV. Fatigue description. Journal of Waterway, Port, Coastal, and Ocean EngineeringASCE 1987;113:251–63. [16] International Institute of Welding (IIW). Fatigue analysis of welded components: Designer’s guide to the structural hot-spot stress approach (IIW-1430– 00). Cambridge, UK: Woodhead Publishing Limited; 2006. [17] Lotsberg I. Stress concentrations due to misalignment at butt welds in plated structures and at girth welds in tubulars. International Journal of Fatigue 2009;31:1337–45. [18] Hamid A, Lotfollahi-Yaghin MA, Shao Y-B, Aminfar MH. Parametric study and formulation of outer-brace geometric stress concentration factors in internally ring-stiffened tubular KT-joints of offshore structures. Applied Ocean Research 2012;38:74–91. [19] American Petroleum Institute (API). API RP 2A-WSD: Recommended practice for planning, designing and constructing fixed offshore platforms-working stress design; 2000. [20] Ministry of Communications of PRC. JTJ 254–98: Technical codes for pile foundation in port engineering; 1998 [in Chinese]. [21] Efthymiou M. Development of SCF formulae and generalized influence functions for use in fatigue analysis. In: OTJ 88, Surrey, UK. 1988. [22] Lotsberg I, Holth PA. Stress concentration factors in welded tubular sections and pipelines. In: Proceedings of the 26th international conference on offshore mechanics and arctic engineering (OMAE 2007), San Diego, June 10–15. 2007. [23] Weidler JB, Dailey JE, Hanna SY, Zedan MF, Yeung JY. Pile fatigue failures. I. Damage appraisal. Journal of Waterway, Port, Coastal, and Ocean EngineeringASCE 1987;113:205–14. [24] Gaythwaite JW. Design of marine facilities for the berthing, mooring, and repair of vessels. New York: Van Nostrand Reinhold; 1990.
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Technical note
Numerical study on girth weld of marine steel tubular piles Yi Lia , * , Xiao-Peng Zhoub , Zhao-Min Qic , 1 , Yi-Bo Zhangb a
National Inland Waterway Regulation Engineering Research Center and School of River and Ocean Engineering, Chongqing Jiaotong University, Chongqing 400074, China School of River and Ocean Engineering, Chongqing Jiaotong University, Chongqing, China c Southwest Guizhou Vocational and Technical College for Nationalities, Guizhou, China b
a r t i c l e
i n f o
Article history: Received 8 October 2012 Received in revised form 17 November 2013 Accepted 21 November 2013 Keywords: Marine steel piles Splice weld Stress concentration factor Finite element analysis Axial tension Bending moment
a b s t r a c t At a splice weld of marine steel tubular pile, the misalignments between two adjacent pile segments may cause significant stress concentrations. In structural analysis, the stress concentrations shall be properly addressed, normally by a stress concentration factor (SCF) in practice. Based on a flat-plate configuration, the SCF at pipe splice under either axial tension or in-plane bending moment has been theoretically derived. To verify the effectiveness of the flat-plate solutions, this paper investigated the SCFs with numerical modeling. Finite element models built by ANSYS were used to simulate pipe splices for different pile diameters and wall thicknesses, which are representative of practical marine applications. Axial tension and in-plane bending moment, as well as their combination were applied. The flat-plate solutions were compared with the numerical results. The results show that the flat-plate solutions are close to the numerical results, indicating that they are reasonably effective in practical applications under complex loading conditions. The findings will significantly help in the hot-spot analysis for splice welds of steel tubular members, particularly piles, in marine structures given complex loading effects. Additionally, an integrated formula including the effect of both axial tension and in-plane bending moment is formulated for the SCF at pile splice. c 2013 Elsevier Ltd. All rights reserved.
1. Introduction In many cases, especially deep-water applications, marine steel tubular piles are prefabricated in tubular segments, and the segments are connected on site or in shop by transversal splice welds, namely girth welds [1,2]. As usual, geometrical misalignments between two neighboring tubular segments remain at the transversal splice, due to various sources including concentricity, out of roundness, thickness difference, and center eccentricity, as schematically illustrated in detail by Det Norske Veritas (DNV) [3]. For example, if two pile segments with equal wall thicknesses and diameters are connected, out of roundness and center eccentricity may be the major sources leading to misalignments, and Fig. 1 demonstrates such an example which occurred during in-situ welding process. The misalignments may result in a considerable stress concentration effect on the hot spots at pile splice, thus increasing structural hot-spot stress and decreasing the fatigue strength of pile [4–6]. Hence the stress concentration effect should be appropriately considered in structural design. A practical way to estimate the structural hot-spot stress is to multiply the nominal stress at hot spot by a stress
1 Formerly, School of River and Ocean Engineering, Chongqing Jiaotong University, Chongqing, China * Corresponding author. Tel.: +86 23 62652714; fax: +86 23 62650204. E-mail address: [email protected] (Y. Li).
c 2013 Elsevier Ltd. All rights reserved. 0141-1187/$ - see front matter http://dx.doi.org/10.1016/j.apor.2013.11.005
Fig. 1. Splice weld of a marine steel tubular pile: (a) field welding of pile splice and (b) observed misalignment between two segments.
concentration factor (SCF). Because of the complex nature of the misalignments, i.e., uncertainties in on-site work and combined sources, analytic solutions to SCF are difficult to develop in most scenarios. Instead, approximate flat-plate solutions have provided a conservative, but robust method in practice for estimating SCF at pipe’s butt weld. The flat-plate solutions to SCF at pipe splices subjected to axial tension have been developed [7–9], and the wall thicknesses of connected segments can be equal or different in the solutions. More recently, Li et al. [10] derived a flat-plate solution given in-plane bending moment,
Y. Li et al. / Applied Ocean Research 44 (2014) 112–118
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Nomenclature d Ka Kam Km M N ri t
δ σa σ b1 σ b2 σ hs σi σn σo τ
outside diameter of pipe segment SCF at the outside maximum tension point (OMTP) under N SCF at the OMTP under both N and M SCF at the OMTP under in-plane bending moment bending moment applied on the cross section at splice weld axial tension applied on pile shaft inside radius of tubular pile wall thickness eccentricity between pipe segments nominal stress caused by N additional tensile stress at weld toe due to N additional tensile stress at weld toe due to M structural hot-spot stress nominal stress at the inside edge caused by M nominal stress nominal stress at the outside edge caused by M thickness ratio
which is applicable to the case of equal wall thicknesses of connected segments. The flat-plate solution [10] significantly supports the practical fatigue assessment for marine steel piles under complex loading conditions, which typify deep-water applications properly. However, the solution derived by Li et al. [10] has not been verified by physical or numerical models. With a series of numerical examples, this paper investigates the effectiveness of the flat-plate solutions, in particular that given inplane bending moment. The flat-plate solutions are compared with the numerical results of finite element models built by ANSYS [11]. The numerical examples adopt representative configurations of practical marine steel pile design, such as weld form, diameter, and wall thickness. The loading effects of in-plane bending moment and axial tension are considered in the examples. The remaining sections of this paper are organized as follows. In Section 2, both flat-plate solutions for axial tension and in-plane bending moment are reviewed, and an integrated formula combining both is derived. Then, the details of the numerical examples are described in Section 3. Numerical results are presented and analyzed in Section 4. Section 5 presents the conclusions. 2. Flat-plate solutions to SCF For large-diameter steel pipes in marine and offshore facilities, segments are often connected by transversal V-shape butt welds made from outside without an inside backing strip [3,12]. To help in guiding the positioning of segments and guarantee welding quality, the use of inside backing strip is normally recommended in practice. The strip is attached on the lower segment by weak welds, for instance intermittent welds [13], and thus may not work structurally like stiffeners. Generally speaking, therefore, the inside backing strip can be actually ignored in structural analysis of splice weld. Fig. 2 presents the typical configuration of a typical splice weld connecting two segments with equal wall thicknesses. A misalignment between two pipe segments is illustrated in Fig. 2(b), where t = wall thickness, and δ = the eccentricity between pipe walls. The pile diameters of both segments may be equal or different. Owing to the eccentricity, either the local tension around the weld or the global tension on the pipe shaft may introduce additional tensile stress in a certain region near the weld, i.e., stress concentration. The additional tensile stress reaches its maximum at the outside maximum tension point (OMTP). A weld toe of the butt weld, the OMTP is a critical
Fig. 2. Typical misalignment at splice weld: (a) splice and segments and (b) the misalignment between pipe walls.
Fig. 3. The in-plane misalignment considered for the stress concentration given bending moment.
structural hot spot in the fatigue design of the weld. Despite a large number of parametric formulas for the SCFs at the tubular joints of offshore structures as summarized by Ahmadi et al. [14], the SCFs at pile splices have not been extensively investigated so far, and pipe splices are essentially different from tubular joints [8,10]. In general, the piles of marine structures are subjected to different loadings. This paper considers an axial tension applied on pile shaft (N), as well as a bending moment applied on the cross section where splice weld is positioned (M), as illustrated in Fig. 2(a). Field observations have informed that the segment misalignments at a pile splice randomly distribute around pile cross section, as reported in detail by Dailey et al. [6,15]. A bending moment in a certain direction may be in-plane for some positions on pile perimeter, but out-of-plane for the others. So far, the impact of in-plane bending moment on stress concentration has been investigated [10]. Specifically, the wall misalignment to be considered is located at a crown, for which M is an in-plane bending moment and yields maximum tensile bending stress. As an example, Fig. 3 displays such an in-plane misalignment point for two segments in center eccentricity. For the case of equal wall thicknesses and pile diameters, Fig. 4 illustrates the stress distribution over wall thickness near the weld at in-plane misalignment point under N and M, where σ a = the nominal stress caused by N, σ o = the nominal stress at the outside edge caused by M, and σ i = the nominal stress at the inside edge caused by M. By the flat-plate assumption, the additional tensile stress at the OMTP due to N, σ b 1 , is expressed as follows [7–9]
σb1 =
3δσa t
(1)
While derived for double-side V-shape butt welds, Eq. (1) has been applied for single-side welds as a simple approximation. In Eq. (1), the nonlinear stress peak resulting from the local notch geometry of
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Fig. 4. Stress distribution over wall cross sections near in-plane misalignment point.
weld is ignored. Since the exact profile of an in-situ weld is almost unpredictable, it is difficult in reality to reflect the nonlinear stress peak directly in SCFs. Consequently, the nonlinear stress peak is normally excluded from the structural stress analysis [3,16]. Instead, the influence of the nonlinear stress may be implicitly reflected in experimental S-N curves. The SCF at the OMTP under axial tension, Ka , is hence written as 3δ Ka = 1 + t
(2)
The flat-plate solution is a benchmark for the approximation to SCF at pipe splice. In spite of the simple flat-plate assumption, it has exhibited its advantage in a practical sense. For the axial tension case, however, more complicated solutions have been also proposed, as summarized by Lotsberg [17]. In particular, Lotsberg [8,9] has developed a solution using cylindrical-shell theory Ka = 1 +
3δ −√t/d 3δ −√τ e =1+ e t t
(3)
where d = the outside diameter of the segments, and τ = thickness ratio (t/d). The cylindrical-shell solutions asymptotically approach the flat-plate solution in the thin-walled condition (τ → 0), as demonstrated in [8]. The thin-walled condition is a rather typical geometric feature of marine steel piles in practical installations. Ignoring the nonlinear stress peak, the additional tensile stress at the weld toe due to M, σ b 2 , can be estimated as [10]
σb2 =
3δ (σo + σi ) 2t
(4)
It should be noted that the additional tensile stress given by Eq. (4) is developed for the case of equal wall thicknesses and pile diameters. Strictly speaking, Eq. (4) is applicable to double-side V-shape butt welds, like Eq. (1). Moreover, Li et al. [10] formulated the SCF at the OMTP under in-plane bending moment, Km , 3δ 1 1+ Km = 1 + 2t 1 + (t/ ri ) 3δ 1 (5) 1+ =1+ 2t 1 + (t/ (0.5d − t)) 3δ 3δ =1+ (2 − 2 τ ) = 1 + (1 − τ ) 2t t where ri = the inside radius of the pile. Eqs. (4) and (5) are derived on the basis of a linear distribution of the nominal bending stress over the pipe cross section, as displayed in Fig. 5. The linear distribution is a reasonable assumption for regular design practice [16]. The linear distribution is also employed for the assumed plate. Eq. (5) has been applied in assessing fatigue reliability of steel berthing monopiles [10]. The derivative of Eq. (5) relative to d gives d Km 3δ = 2 dd d
(6)
In fact, Eq. (6) is a sensitivity measure relative to d. Since δ is quite small compared with d in regular circumstances, Km may not be so sensitive to the change of d, especially if d is relatively large.
Fig. 5. Nominal bending stress over pipe cross section.
In the case of combined axial tension and bending moment, International Institute of Welding (IIW) [16] suggests a generalized form of the structural hot-spot stress allowing for stress concentration:
σhs = K a σa + K mσo
(7)
where σ hs = the structural hot-spot stress. This paper examines the combined mode using the flat-plate assumptions. With Eqs. (2) and (5), one may formulate an integrated SCF in the following:
σhs K a σa + K mσo = σn σo + σa (1 + (3δ/ t)) σa + [1 + (3δ/ t) (1 − τ )] σo = σo + σa 3δ 1−τ 1 =1+ + t 1 + (σo /σa ) 1 + (σa /σo )
K am =
(8)
where Kam = the SCF at the OMTP under both N and M, and σ n = nominal stress. Both Eqs. (2) and (5) are irrelevant to nominal stresses (σ a and σ o ), or, in other words, acting loads (N and M). Unlike Eqs. (2) and (5), however, the combined SCF, Eq. (8), is related to σ a and σ o , implying that, under combined loading effects, acting loads also have an influence on stress concentration. This is an expectable result. It is clear that stress ratio (σ a /σ o ) plays an important role in the integrated SCF. When the pile splice is mainly subjected to axial tension (σ o /σ a → 0), Eq. (8) reduces to Eq. (2), indicating that the effect of bending moment is negligible. On the contrary, when the pile splice is mainly subjected to bending moment (σ o /σ a → ∞), Eq. (8) simply becomes Eq. (5), indicating that the effect of axial tension is negligible. 3. Finite element models At present, finite element analysis (FEA) is a useful tool for determining structural hot-spot stress and validating SCFs at weld joints [3,14,16,18]. For the axial tension case, it has been found that Eq. (2) is close to numerical results in certain scenarios [9]. However, Eq. (5) has not been examined with numerical examples. This paper conducts FEA with ANSYS [11] to study the effectiveness of Eqs. (2), (5), and (8) under different loading conditions and geometric configurations (d and t). The FEA examines a series of three-dimensional models. As shown in Fig. 6, each model contains two pile segments with equal wall thicknesses, both of which are connected by a splice weld. The models are built with 20-node solid elements (SOLID 95 in ANSYS). The Young’s modulus and Poisson’s ratio of pile material are 210 GPa and 0.30, respectively. The models cover the following geometric configurations of pile cross section: d = 0.8, 1.0, and 1.2 m (t = 16, 18, 20, and 22 mm), and d = 1.4 and 1.6 m (t = 22, 25, 28, and 31 mm). These diameters and thicknesses are very common in practical pile designs, and the general requirements for selecting minimum pile wall thickness recommended by American Petroleum Institute (API) [19] are also taken into consideration. The welds adopt the form shown in Fig.
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115
Fig. 8. An example for calibrating weld mesh: (a) weld details used in [22] and (b) calibrated weld mesh pattern. Fig. 6. A typical ANSYS model of two pile segments connected by a splice weld. Table 1 Calibration results for weld mesh pattern. Longitudinal surface stresses at different positions (MPa)
Mesh pattern in Fig. 8(b) Lotsberg and Holth [22] a b
Ao
Ai
Co
Ci
1.162
1.197
2.041
0.779
1.250a
1.188b
2.350b
0.760b
Read from Figs. 6 and 8 of Lotsberg and Holth [22]. Reported in Table 1 of Lotsberg and Holth [22].
Fig. 7. Weld details: (a) typical dimensions and (b) generated mesh.
7(a), which is determined in line with typical recommendations from various guidelines [3,9,20]. A fine mesh is implemented for the welds, as shown in Fig. 7(b). The two segments in each model are built in different lengths. The shorter one is always 1.0 m in length, and the longer one is 4d. The lengths are moderate, thus enhancing modeling efficiency. The end of the longer segments is fixed, while that of the shorter segments remains free. One should note that neither Eq. (2) nor Eq. (5) takes account of end boundary. A much longer pipe length is probably needed to eliminate the influence of the end condition entirely, for example 6d for chord members in jacket structures [21]. On the other hand, a much longer pipe length could require much heavier computational loads. The determination of pipe length is a tradeoff between accuracy and efficiency. The chosen length of the longer segments might be able to minimize the influence of end condition on the stress concentration at weld toe. In real situations, misalignments may result from different sources and even their combinations. The exact form of misalignments is almost impossible to predict. Therefore, it is impractical to model all of these complicated misalignments in FEA, particularly center eccentricity and out of roundness. For simplification, the concentricity between both segments is chosen as the only misalignment source in all ANSYS models. Specifically, the outside diameter of the shorter segment is larger than that of the longer segment by 2δ ; that is, the outside diameter of the longer segment is d, which is the nominal diameter in flat-plate solutions, while the outside diameter of the shorter segment is d + 2δ . Since δ is quite small (2 mm) compared with d in the models, the simplification will not cause significant errors. The following loads are to be considered for each case: N = 1000 kN, M = 1000 kN m, and their combination. Both M and N are imposed at the free end, and N is uniformly distributed over pile cross section so as to minimize the local effect. The self-weight of all structural components is ignored in the models. As usual, finite element (FE) modeling of weld requires a very fine mesh. The guidelines of DNV [3] and IIW [16] are properly adopted
herein. Furthermore, the present paper has calibrated the mesh pattern around weld using a numerical example provided by Lotsberg and Holth [22], as illustrated in Fig. 8(a). In the example, the pipe diameter at Co–Ci cross section was 1.067 m, wall thicknesses were 31 mm, and a 1.0-MPa nominal stress was imposed over Ao–Ai cross section. An ANSYS model was built by the methodology described above for the example, in which the weld details in Fig. 8(a) were applied. The calibration targets focused on the longitudinal surface stress at the four marked positions in Fig. 8(a). Note that Co is simply the OMTP. Different mesh patterns were examined, and the final choice is shown in Fig. 8(b). Table 1 presents the calibration results. At Ai and Ci, where the notch has a minor influence, the selected mesh pattern provides results close to [22]. Like Co, Ai experiences stress concentration effect due to tension. At Ao and Co, the selected mesh pattern slightly underestimates. The differences are likely due to the difference in element meshes at the notch region, as well as in weld details applied in the numerical models. A finer mesh may reduce the differences, but require a much larger computer capacity. It should be noted that, at Ao and Co, the surface stress reflects the notch stress that includes two parts, i.e., the nonlinear stress peak and the structural hot-spot stress. Consequently, the notch has a significant influence on the stress at Ao and Co. Theoretically, the segment misalignment will cause additional compressive stress at Ao, resulting in σ hs less than 1.0 MPa. Due to the influence of notch, the numerical solutions at that position were larger than 1.0 MPa. A much finer mesh pattern around both positions may increase the surface stresses there, but demand much heavier computational loads. However, an increase in the surface stresses by much finer mesh may only mean an enhanced modeling effect for the nonlinear stress peak at weld toe, and may not change σ hs significantly. In practice, σ hs can be effectively generated by either an extrapolation scheme based on stress read-out points at certain distances away from the toe, or the read out of stresses at Ai and Ci for comparison of hot spot stresses [3,16], as will be demonstrated in the next section, and thus a correct notch stress may not be required. Because it produces results close to [22], therefore, the selected mesh pattern is considered to be effective in modeling σ hs for this
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Y. Li et al. / Applied Ocean Research 44 (2014) 112–118
Fig. 11. SCF values (N = 1000 kN, d = 1.4 and 1.6 m).
Fig. 9. Linear extrapolation for hot-spot stress.
Fig. 12. SCF values (M = 1000 kN m, d = 0.8, 1.0, and 1.2 m).
Fig. 10. SCF values (N = 1000 kN, d = 0.8, 1.0, and 1.2 m).
example. The pattern is then applied for various model configurations described previously. 4. Results of analysis The ANSYS models generate actual stresses for the modeled welds and segments. As expected, under bending moment, the maximum longitudinal surface tensile stress along the weld toe occurs at the OMTP of the in-plane misalignment crown on the longer segment, implying that the misalignment yields the stress concentration at the hot spot under in-plane bending moment. Nominal stresses are also obtained using the selected pile diameters, wall thicknesses, and load cases, with no allowance for splice weld. Nominal stresses are tabulated in Table 2. Following the recommendation of DNV [3], the actual σ hs is developed by a linear extrapolation based on stress read-out points at 0.5t and 1.5t away from the toe, as shown in Fig. 9. An actual numerical solution to SCF is thereafter estimated for each modeling scenario by dividing the actual σ hs by the nominal stress at the same location. While normally recommended for plated structure [3], the procedure in Fig. 9 is considered appropriate for marine steel piles, given small thickness ratios in practical applications. There is a non-linearity in stress along the surface due to the circumferential stiffness of tubular, as illustrated in D.14 of [3]. This is a reason why the extrapolation like that in Fig. 9 should be used with caution at butt welds in tubulars, and normally the read-out of hot spot stresses at Ai and Ci in Fig. 8 is the preferred methodology at girth welds. In the meantime, the flat-plate solutions to SCFs are estimated by Eqs. (2), (5), and (8) along with nominal stresses. For comparative purposes, the cylindrical-shell solution by Eq. (3) is also provided for each axial tension case. The SCF results are presented in Figs. 10–15.
Fig. 13. SCF values (M = 1000 kN m, d = 1.4 and 1.6 m).
Fig. 14. SCF values (N = 1000 kN, M = 1000 kN m, d = 0.8, 1.0, and 1.2 m).
The results indicate that, in the examples, the segment misalignment causes a considerable stress concentration effect. In some cases, SCF may significantly increase the stress ratio at the hot spot, though nominal stress is well below the allowable limit. Here is a simple example. For the case with d = 0.8 m and t = 16 mm, the combined nominal stress under M = 1000 kN m and N = 1000 kN is 157.5 MPa, as
Y. Li et al. / Applied Ocean Research 44 (2014) 112–118
117
Table 2 Nominal stresses under the imposed loads (MPa).
Loads
N = 1000
Stress
d = 0.8 m
d = 1.0 m
d = 1.2 m
d = 1.4 m
d = 1.6 m
t (mm)
t (mm)
t (mm)
t (mm)
t (mm)
16
18
20
22
16
18
20
22
16
18
20
22
22
25
28
31
22
25
28
31
σa
25.4
22.6
20.4
18.6
20.2
18.0
16.2
14.8
16.8
15.0
13.5
12.3
10.5
9.3
8.3
7.5
9.2
8.1
7.2
6.5
σo
132.1
118.3
107.3
98.2
83.5
74.7
67.6
61.8
57.5
51.4
46.5
42.5
31.0
27.4
24.6
22.4
23.6
20.9
18.7
17.0
kN M = 1000 kN m
Fig. 15. SCF values (N = 1000 kN, M = 1000 kN m, d = 1.4 and 1.6 m).
provided in Table 2. Assuming API 5L Grade X52 [19] for pile material, the combined nominal stress is well below the yield strength (360 MPa). With the numerical solution of SCF (1.325), the actual stress becomes 209 MPa. The stress amplification, hence, greatly reduces the safety level of pile materials, in particular base steel. It should be noted that the selected value of δ (2 mm) is moderate, and it is expected that higher values of δ will introduce stronger SCFs for the examples, as explained below. DNV [3] has a strict requirement on the misalignment tolerance, i.e., 0.1 t or maximum 3 mm. For the case with d = 0.8 m and t = 16 mm, when δ = 2 mm, the flat-plate solution of SCF under axial tension is estimated to be 1.375. When δ = 3 mm, the SCF increases to 1.563. In all cases, the numerical results confirm the overall trend of the flat-plate solutions relative to t; that is, as t increases, SCF decreases. Actually, both are almost parallel. Smaller thicknesses hereby introduce stronger stress concentrations at pile splice. Compared with numerical results, the SFC estimates by Eqs. (2), (5), and (8) slightly overestimate. The finding confirms that, as addressed by [3,8], the flat-plate solution is a conservative estimate for SCF. In general, the relative differences between flat-plate solutions and numerical results are small; that is, the maximum is merely 3.3%. Here a relative difference is defined as the absolute difference divided by numerical result. Perhaps the differences originate from several sources, such as the flat-plate assumption in the three formulas, the linear extrapolation scheme for σ hs , the concentricity configuration of FE models, the influence of fixed end on numerical results, and the mesh pattern of FE models. Despite the sources, the small relative differences imply a reasonably satisfactory global behavior of the flat-plate solutions in the numerical examples. From a practical point of view, therefore, the flat-plate solutions are effective in estimating SCFs. Interestingly, it is observed from Figs. 10 and 11 that, in axial tension cases, the numerical results are located between the flatplate and the cylindrical-shell solutions. The same conclusion can also be drawn based on [9,22]. The flat-plate and the cylindrical-shell solutions look like an upper bound and a lower bound, respectively. Since it is more conservative, the flat-plate solution by Eq. (2) may be a more appropriate option in practice for estimating SCFs.
Both Eqs. (2) and (5) produce very close results of SCF. As mentioned previously, both are dependent on the geometries of pile cross section and splice weld, and independent of loads and resultant stresses. According to Li et al. [10], upon the thin-walled condition, Eq. (5) eventually reduces to Eq. (2). In all of the examples, τ is rather small, so the SCF estimates of Eqs. (2) and (5) are close to each other, confirmed by numerical results. Consequently, the SCFs in combined cases (Figs. 14 and 15) are also close to those in tension and bending moments cases. In Figs. 12 and 13, the SCF estimates by Eq. (5) appear insensitive to the change of d, as explained by the sensitivity measure Eq. (6). In the examples, pile diameters are relatively large, so flat-plate solutions exhibit small scatters given different d values. As d increases, the sensitivity measure will further decrease, thus the scatters in Fig. 13 are smaller than those in Fig. 12. Since the sensitivity measure is independent of t, flat-plate solutions exhibit similar scatters for different t values. As a result, flat-plate solutions appear almost parallel as t changes. All of these phenomena are observed in FEA results. Generally speaking, the numerical results exhibit small scatters given different d values, and the scatters in Fig. 13 are much smaller than those in Fig. 12. Like flat-plate solutions, the numerical results appear parallel as t changes. These observations significantly validate the effectiveness of Eq. (5). Similar observations can also be obtained for cylindrical-shell solutions and related numerical results in tension cases (Figs. 10 and 11), by studying the sensitivity of Eq. (3) to d. The insensitiveness of SCFs to diameter indicates that, with the same t and δ , piles in different diameters may encounter similar stress concentration effects at splice. The finding is meaningful for practical fatigue assessment. Because of the insensitiveness, the SCF assessment may need to cover only representative diameters for a specific project, while SCFs for other diameters can thus be reasonably assumed. Hence data demand and analysis effort may be largely reduced in practice. 5. Conclusions Steel tubular piles have been widely installed in marine facilities as major foundation structures. For splice welds of marine steel pile, the stress concentration effect caused by segment misalignments is an important concern for practitioners in fatigue design [10,23,24]. The loading effects on marine piles are usually complex, for marine structures are exposed to various cyclic environmental loads (wave, wind, and current) and operational loads (berthing and mooring). Thus, the SCFs under these complex loading effects become one of the keys to analyzing the stress concentration effect at splice welds. As usual, the SCFs at butt weld exhibit considerable scatter from case to case [14]. Accordingly, it is always important to obtain effective and robust solutions to SCFs with thorough studies. In this paper, two existing flat-plate approximate solutions to the SCFs at pipe splice weld have been reviewed, one for the axial tension, and the other for in-plane bending moment. On the basis of both solutions, an integrated flat-plate solution incorporating the effects of both axial tension and in-plane bending moment has been formulated. The integrated flat-plate solution, Eq. (8), is applicable to splice
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welds that connect two pipe segments with equal wall thicknesses and diameters. The flat-plate solutions have been thoroughly tested in a series of numerical examples with representative geometrical configurations of practical pile design. In the numerical results of FE models built with ANSYS, the structural hot-spot stress is extracted from the notch stress, and used for estimating actual SCFs. Compared with the numerical results, the flat-plate solutions demonstrate a reasonably satisfactory global behavior in several aspects, such as the overall trend and the insensitivity to the change of pile diameters. The flat-plate solutions slightly overestimate, due to several sources. From a practical point of view, the flat-plate solutions are verified to be a simple, robust, and effective method in practice for estimating SCFs at splice weld under the thin-walled condition, which is fairly typical for marine steel piles. It is also realized that the numerical investigation only examined the case of concentricity, and other misalignment sources perhaps cause uncertainties. While slightly conservative, therefore, the flat-plate solutions are recommended in practical uses for conservative purposes. The numerical study indicates that SCFs are insensitive to the change of pile diameters. Accordingly, with the same t and δ , piles in different diameters may experience similar stress concentration effects at splice. In the future, the flat-plate solution given in-plane bending moment, Eq. (5), may need to be extended to the case of different wall thicknesses. This paper forms a strong basis for the further studies on estimating the SCFs at transversal splice welds of marine steel tubular pile, and even of other tubular members, under complex loading effects. The findings in this paper will be helpful in estimating structural hot-spot stress and studying mitigations for stress concentrations at transversal splice welds. Acknowledgments The authors would like to appreciate the insightful and constructive comments of three anonymous reviewers. This research was supported by the Natural Science Foundation Project of CQ CSTC (CSTC 2010BB7084), the Research Program of Chongqing Port Management Bureau (SW2013-27), the Innovative Research Program for Graduate Students at CQJTU (20130102), and CQJTU’s start-up research fund for new faculty members. References [1] Tomlinson MJ. Pile design and construction practice. London, UK: E & FN Spon;
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