Stress concentration factors in FRP-strengthened offshore steel tubular T-joints under various brace loadings

Structures 20 (2019) 779–793

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Stress concentration factors in FRP-strengthened offshore steel tubular T-joints under various brace loadings

T

Alireza Sadat Hosseinia, Mohammad Reza Bahaaria, , Mohammad Lesanib ⁎

a b

School of Civil Engineering, College of Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran School of Civil Engineering, College of Engineering, Sadra University, P.O. Box 14875-314, Tehran, Iran

ARTICLE INFO

ABSTRACT

Keywords: Tubular T-joint Numerical analysis SCF FRP strengthening Fatigue life extension

The stress concentration factors (SCF) in FRP strengthened tubular T-joints subjected to brace axial loading, inplane and out-of-plane bending moments were investigated. The numerical analyses were performed using ABAQUS Finite Element software package. The benchmark joints were validated against the Lloyd's Register and API equations together with the experimental results. Six different types of FRP materials such as Glass/Vinyl ester, Glass/Epoxy (Scotch ply 1002), S-Glass/Epoxy, Aramid/Epoxy (Kevlar 49/Epoxy), Carbon/Epoxy (T3005208) and Carbon/Epoxy (AS/3501) were used as strengthening material in order to investigate the SCF values on the chord member of the tubular T-joints. Results derived from analyses are promising and show that the FRP strengthening method could be considered as an effective method to reduce the SCFs and consequently extend the fatigue life cycle of tubular T-joints. Results of the analyses for a 6 mm CFRP layup show that under axial loading (AX), the FRP strengthening decreases SCFs up to 30% and 50% at Crown and Saddle points on the chord, respectively. Moreover, under the action of in-plane bending (IPB) and out-of-plane bending (OPB) moments, SCF reductions of about 45% and 50% were observed, respectively.

1. Introduction

defined as the hot spot stress range (HSSR) divided by the nominal brace stress range”. In this research focus is made on the estimation of SCFs at Crown and Saddle points of the chord member in FRP strengthened tubular T-joints. Thus, the HSSR is the hot spot stress range on the chord which must be divided by the nominal direct stress in the brace member to reach the SCF. In this study, the relative SCF values (SCFs in the strengthened joint that are divided by the SCFs in the benchmark joint) were extracted from the numerical models and results were discussed in details. The numerical models consist of 152 steel tubular T-joints strengthened with a 6 mm FRP layup under the action of brace axial, IPB and OPB loads using Finite Element Method performed by general purpose ABAQUS software package. Six different FRP materials such as Glass/ Vinyl ester, Glass/Epoxy (Scotch ply 1002), S-Glass/Epoxy, Aramid/ Epoxy (Kevlar 49/Epoxy), Carbon/Epoxy (T300-5208) and Carbon/ Epoxy (AS/3501) were used to investigate the effect of FRP material properties on the SCF values at Crown and Saddle points of the chord member. Moreover, the effect of combined loads and fibers orientation of the FRP layup was investigated, and the results were presented. According to an earlier study [3], the most effective fiber orientations in the FRP layup, under axial loading proved to be 0° and 90°. Also, owing to the nature of the loading (AX, IPB and OPB), the FRP

Bottom founded offshore steel structures, such as jacket type platforms are constructed using circular hollow sections (CHS) due to their adequate structural performance, high strength-to-weight ratio, high buoyancy and lower drag coefficient [1]. An offshore jacket platform consists of several joints which are made by connecting CHSs. T-joint is the most common and basic joint configuration in these structures which is made by welding the cross-section of one tube (brace) perpendicular to the undisturbed exterior surface of the other tube (chord) by butt-welding. Typically, residual stresses attributed to welding are eliminated by post heating the joint-can (joint chord) before connecting to the offshore jacket structure. Generally, in a jacket type offshore structure, joints are the most susceptible parts to the fatigue phenomenon due to the cyclic nature of ocean waves loading. Hence, accurate fatigue life estimation and innovations for enhancing the fatigue life is of crucial importance. Practically, fatigue life of an offshore tubular joint can be estimated from stresses at the weld toe. In the design practice, in order to quantify the stress concentration at the weld toe, a parameter called the stress concentration factor (SCF) is used. According to API-Part 8.3.1 [2], “For each tubular joint configuration and each type of brace loading, SCF is ⁎

Corresponding author. E-mail addresses: [email protected] (A. Sadat Hosseini), [email protected] (M.R. Bahaari), [email protected] (M. Lesani).

https://doi.org/10.1016/j.istruc.2019.07.004 Received 8 October 2018; Received in revised form 30 April 2019; Accepted 5 July 2019 2352-0124/ © 2019 Published by Elsevier Ltd on behalf of Institution of Structural Engineers.

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materials were modeled such that the fibers placed in the two main cross directions would lead to the most appropriate FRP layup of 0° and 90° combination under IPB and OPB moments as well as axial loading. It is worth to note that the finite element models of the benchmark joints were verified against the experimental results extracted from HSE OTH 354 report [4] followed by comparing the results with the predictions of Lloyd's Register [4] and API [2] design equations. FRPs were applied on the verified benchmark joints. The results of analysis of strengthened finite element models addressed how FRP properties could affect the SCF values. In addition, more studies are being undertaken to investigate the combined effect of joint geometry and FRP layup properties.

Table 1 Values of the chord diameter and the other geometrical parameters of the benchmark joints. Reference JISSP joint 1.3 JISSP joint 1.13

D (mm) 508 508

α

β

γ

τ

10 6.2

0.8 0.8

20.3 20.3

0.99 1.07

Where D is the chord diameter; α = 2 L/D, L is the chord length; β = d/D, d is the brace diameter; γ = D/2 T, T is the chord thickness; τ = t/T, t is the brace thickness.

with GFRP [25]. Recently, Sadat Hosseini et al. [26] investigated the SCFs in FRP strengthened tubular T-joints subjected to brace axial loading, in-plane and out-of-plane bending moments using finite element analyses. Three FRP materials where used and SCF reduction of around 15% was observed for only a 1 mm thick CFRP layup. Besides, using a thicker FRP layup tends to increase its effectiveness significantly.

2. Literature review Several studies have been conducted on the SCF calculation in tubular joints since the 1970s. The main objective of these researches was to derive parametric equations for SCF calculation. Most of the researches were dedicated to derive SCF equations for the unstrengthened tubular joints; but owing to the new stricter code provisions, some joints of the existing tubular structures may not meet the code checks. Thus, reinforcing methods were presented to remove possible deficiencies. A variety of metallic and non-metallic external and internal, reinforcement schemes exist. For instance, one of the internal metallic schemes for strengthening is the use of steel rings welded to the internal surface of the chord member. In this regard, the effect of geometrical parameters on stress distribution along the brace/chord intersection and the SCFs in ring-stiffened tubular joints was studied by researchers and a set of parametric equations were presented for the prediction of the maximum values of SCFs under axial, IPB, and OPB loadings [5–10]. The static strength of tubular T-joints reinforced with collarplate under axial loading was investigated by Shao [11] through experimental investigation and finite element (FE) simulation. Recently, Ahmadi et al. [12] presented the probability density functions (PDFs) for probabilistic analysis of SCFs in tubular KT-joints reinforced with internal ring stiffeners under in-plane bending moments based on a finite element parametric study. As for non-metallic strengthening methods, the stress concentration factors of the concrete-filled chord and T-joints with grouted sleeves in circular joints were investigated [13–17]. The FRP strengthening technique is categorized as one of the external non-metallic reinforcement schemes. FRP wrapping method due to its convenience for application, corrosion resistance, light weight, potentially high overall durability, superior strength-to-weight ratio with respect to steel, could be an alternative for application in areas where conventional materials such as steel may encounter durability, weight or lack of design flexibility constraints. For example, Hollaway and Cadei [18], Zhao and Zhang [19] and Zhao [20] performed remarkable studies on FRP strengthened steel structures. FRP-strengthened CHSs with four layers of CFRP under tension loading was investigated by Jiao and Zhao [21]. Zhao et al. [22] studied the load bearing capacity of RHSs strengthened with CFRP sheets. Lesani et al. [23] numerically investigated the failure pattern, ultimate static strength and detailed behavior of steel tubular T-joints strengthened by GFRP (Glass/epoxy) under axial brace compressive loading. Remarkable increase in joint ultimate capacity due to the combined action of steel and composite against the compressive load was observed. In addition, critical deformations and ovalization of chord member showed a descending trend up to 50% of the un-strengthened joint. Lesani et al. [24] experimentally investigated the improvement of the ultimate capacity of T-joints wrapped with GFRP (Glass/vinyl ester) under static compressive loading and observed up to 50% increase in the ultimate load bearing capacity. A similar result and improvement was observed in their other numerical and experimental research program on T and Y shaped CHS steel tubular connections strengthened

3. Benchmark joint FE model verification Finite element models of the benchmark joints were developed and analyses were carried out. In order to verify the accuracy of the finite element modeling and analysis, T-joints JISSP joint 1.3 (for axial loading) and JISSP joint 1.13 (for IPB and OPB moments) were chosen among the test results published in HSE OTH 354 report [4]. The finite element geometries of the benchmark joints were exactly the same as the experimental models. Table 1 presents the benchmark joints properties and geometries employed in this study. ABAQUS [27] 3D brick elements (C3D20), defined by 20 nodes having three degrees of freedom per node were incorporated to model the joint geometry. Fig. 1(a) illustrates the isometric view of a benchmark T-joint numerical model used in this study. The mesh enlargement view of the T-joint is presented in Fig. 1(b). Different sub-zone mesh generation methods were used for the weld profile, hot spot stress region, FRP wrapping area and other regions of the joint. The mesh in the hot-spot stress region was much finer than the other zones since more computational precision was required in this area. FRP wrapping areas have coarser mesh but still fine enough to ensure computational accuracy. For the rest of the model, coarser mesh was used to lower the run time but still with acceptable accuracy which were obtained through mesh sensitivity analysis. As envisaged from Fig. 1(b), the weld profile at the brace-chord intersection was modeled in order to achieve stresses along the chordbrace intersection precisely. The weld profile along the brace-chord intersection shown in Fig. 1(c) satisfied the specifications addressed in AWS [28]. The weld profile was modeled with accurate dimensions as a sharp notch by using 3D brick 20 nodes elements. The weld material properties were assumed the same as those of the chord and brace members. Therefore, only the geometric effect of the weld profile was taken into account without considering any residual stresses. It was assumed that the joints were post-heated after the welding process, and there were no residual stresses in the joint. The boundary conditions were chosen in such a way to represent the actual boundary conditions of the experiments. In the analyses, chord ends were assumed to be fixed and the static monotonic loads were applied on the brace member as shown in Fig. 2. Determining the stress concentration factors in a tubular joint requires a linear-elastic numerical analysis to be carried out [29]. Thus, the stress values are kept quite small in order to stay at the linear part of the stress-strain range in the linear-elastic analysis. The Young's modulus and Poisson's ratio of steel were taken as 207 GPa and 0.3, respectively as found in the experimental model. In order to find the proper mesh size in the analysis, sensitivity analyses on stress distribution along the Crown and Saddle lines (Fig. 3) 780

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Fig. 1. The mesh generated for the T-joint using the sub-zone method; (a): Isometric view, (b): Mesh enlargement, (c): 3D view of the weld profile.

were performed for both of the un-strengthened benchmark T-joints. Fig. 4 shows the results of these studies. Five different mesh sizes ranged from 5 mm to 30 mm have been chosen for JISSP 1-3, while for JISSP 1-13, this range lies between 5 mm up to 40 mm. The proper mesh sizes for each T-joint was chosen as shown in Fig. 4. According to Fig. 4(a, b), the mesh dimensions would be 10 mm for JISSP joint 1.3 (axial loading), and 30 mm for JISSP joint 1.13 (IPB and OPB moments) as envisaged from Fig. 4(c, d).

In order to estimate the SCFs, the method introduced by IIW-XV-E [30] was implemented. In this method, the peak stress at the weld toe was calculated by linear extrapolation of the von-Mises stresses at distances of 0.4T and 1.4T from the weld toe; where T is the thickness of the chord member. In order to extract the stresses on the aforementioned points (0.4T and 1.4T), the hot spot region (ribbon with 1.5T width from the weld toe on the chord that can be seen in Fig. 1(b)) was divided into 15 equal ribbons with a dimension of 0.1T. Therefore,

Fig. 2. The loading conditions applied on the T-joints; a) Axial, b) In-plane bending, c) Out-of-plane bending. 781

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Fig. 3. Illustration of crown and saddle lines.

stresses were extracted from the fourth and the fourteenth elements measured from the weld toe. SCF was calculated by dividing the von Mises stresses at weld toe by the nominal stress on the brace member [31,32]. It is worth to note that SCFs could also be calculated using normal stresses, i.e. stresses perpendicular to the weld toe. Generally, it has been found that the difference between SCFs calculated from either primary stress or normal stress were minor, for K-joints, for instance, differences were found to be less than 10% [33].

Table 2 summarizes the verification results at the Saddle and Crown Points. In this table, e1 and e2 show the percentage of relative difference of Lloyd's Register [4] and API [2] equations with test results, respectively, and e3 denotes the percentage of the relative difference between the results of the present finite element model and the experiment results. According to Table 2, it is evident that the finite element model predicts the SCFs at Crown and Saddle points with better accuracy which is in good agreement with the test results and therefore, the FE

Fig. 4. Stress distribution along the Crown and Saddle lines; a) Axial loading-Crown line, b) Axial loading-Saddle line, c) In-Plane bending-Crown line, d) Out-ofplane bending-Saddle line. 782

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numerical modeling, the weld profile was modeled using AWS [28] recommendations. However, some simplifications were used to conceive a smooth and adequate weld profile [34,35]. To achieve more accurate and detailed stress distribution at the joint intersection zone, 3D brick elements (ABAQUS [27] element type C3D20 which is a 20-node quadratic brick element) were used to model the joint geometry and weld profile. Besides, FRP material was modeled as a layer covering the joint using ABAQUS [27] shell element type S4R, which is a 4-node doubly curved thin or thick shell with reduced integration, stretched on the tube surfaces as a skin by sharing interface nodes. Alike the numerical modeling of Lesani et al. [25], a perfect bond state was considered between steel and FRP. Hence, no cohesive/ adhesive element was modeled at the interface between FRP and the steel substrate. Moreover, in order to create a smooth transition around the chord/brace intersection for FRP application, just as in the experimental and numerical models, putty material was used [25]. FRP and putty properties are presented in Table 4. In a finite element analysis, the mesh generation process and mesh dimensions highly depend on the geometrical complexity of the model and the mesh size is of crucial importance. For instance, when the mesh is too coarse, the parametric distribution resolution may be inadequate, whereas choosing too fine a mesh brings about waste of computing time and possibly the user's time, and in some cases, won't even solve anyway. Similar to the benchmark specimens, and through sensitivity analyses, different sub-zone mesh generation methods were used for the weld profile, FRP wrapping area and the unwrapped regions of the joint which were far away from the weld and were not covered with FRP layers. FRP wrapped areas had coarser meshes compared to the weld profile but were still fine enough to sustain accuracy. The coarsest meshes were attributable to regions far away from the weld approaching chord/brace ends in which the mesh quality didn't have a remarkable effect on the finite element results and in particular the stress distribution along the weld toe. Fig. 7 shows the mesh generated for the strengthened tubular T-joint.

Table 2 Comparison of finite element results with experimental data [4] and predictions of Lloyd's Register [4] and API [2] equations. Load/position

Test

LR Eq.

API Eq.

FEM

e1 (%)

e2 (%)

e3 (%)

AX/crown AX/saddle IPB/crown OPB/saddle

5.4 11.4 3.9 12.2

3.94 10.54 4.07 18.2

3.85 12.13 4.85 15.3

5.3 11.1 3.92 10.1

27 7.5 4.4 49.2

28.7 6.4 24.4 25.4

1.9 2.6 0.5 −17.2

model is validated against the test results. 4. Verification of the strengthening method In this part of the study, FRP strengthening method in the finite element analysis is verified against an experimental as well as numerical model performed by Lesani et al. [25]. 4.1. Model geometry In addition to the verification of the benchmark model, application of FRP on the T-joint and the state of stresses have to be verified against an experimental modeling. The numerical model was built based on the characteristics of the reference study [25] and verified accordingly. In this way, the benchmark as well as the strengthened model of joint T2 was modeled precisely. The geometrical as well as material parameters of the T-joint are given in Table 3 and Fig. 5. Fig. 6 presents the tensile coupons and a typical stress-strain curve of the steel material obtained from the test coupons. 4.2. Finite element modeling The geometry of the numerical model was exactly the same as the experimental specimen [25]. To maintain accurate stresses at the chord-brace intersection and to achieve more precise results from the Table 3 The geometrical parameters of the T2 joint [25]. D (mm)

d (mm)

T (mm)

t (mm)

L (mm)

l (mm)

α

β

γ

τ

273.1 Fy (MPa) 385

114.3 Fu (MPa) 510

6.35 E (GPa) 200

8.56 ν 0.3

1845

573.45

13.5

0.4

21.5

1.35

L is the chord length and l is the Brace length.

Fig. 5. T2 specimen configuration [25]. 783

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Fig. 6. Typical steel stress-strain curve and test coupons [25].

4.3. Analysis methodology

Table 4 FRP and putty properties [25]. Glass/vinyl ester

A non-linear static analysis was carried out to study the behavior of the joints under axial brace compressive load. “Modified Riks method” [27] was used to consider both material and geometric non-linearity in the analysis. This method can include nonlinear materials and boundary conditions to predict unstable, geometrically nonlinear collapse of a structure. Sometimes in geometrically nonlinear static problems, the load–displacement response corresponding to buckling shows a negative stiffness. Among several approaches for modeling such behavior, the “Modified Riks Method” could find static equilibrium states during the unstable phase of the response. The loading during a Riks analysis is always proportional and a parameter named

Putty

Stress analysis E1 (Gpa) E2 (Gpa) 7 28

ν12 0.29

Failure analysis S1 (Gpa) S2 (Gpa) 410 55

S12 (Gpa) 46

G12 (Gpa) 4.5

G23 (Gpa) 2.54

E (Gpa) 2.5

ν 0.32

σf (Mpa) 70

E: Modulus of elasticity; G: Shear modulus; S: Strength; σf: Failure stress ν: Poisson ratio.

Fig. 7. The mesh generated for the T2 specimen configuration and FRP layups.

784

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load-displacement diagrams of Lesani et al. [25] experimental and numerical study versus that of this study. Comparing the diagrams of Load-displacement in Fig. 8, a good agreement between the two studies was observed. Therefore, the numerical model in this study could predict the relationship between the static loading and the displacements correctly, which shows that the states of stresses in the model were calculated precisely. The initial stiffness as the key role parameter of linear elastic modeling perfectly matches the results of the experiments. Overall, the solid model developed in this study could predict the load-displacement curve of the T2 joint more precise than the shell model. This was due to the extra ability of break elements to involve stresses in three dimensions. The other reason for obtaining more accurate and factual results in solid element modeling was the involvement of weld profile which is of crucial importance in making compatible numerical and experimental geometries to achieve robust results. To make sure of the authenticity of the analyzing procedure, another parameter called “ovalization” is also checked here. The ovalization phenomenon which is the horizontal deflection of the chord member circumference at the brace intersection on the hoop line is an important factor in tubular joint investigations. As the load is gradually applied, it forms a bulged chord surface. A comparison of the chord ovalization in both studies is demonstrated in Fig. 9. The deformed chord is illustrated at maximum ovalization for both studies in Fig. 9(a) and (b). It has been observed that maximum ovalization displacement occurs at Rφ/√DT = 4 [25]. Rφ is the curved surface along the hoop line. This

Fig. 8. Load–displacement diagram for present study versus Lesani et al. [25] experimental and numerical study.

load proportionality factor is found as part of the solution. The Newton method was used to solve the nonlinear equilibrium equations. In this method, the analysis will continue for the number of increments specified in the step definition. As the load proportionality factor reached a peak, the ultimate load was achieved. 4.4. Verification results Results of the analysis are presented hereunder. Fig. 8 shows the

Fig. 9. Chord ovalization in both studies; a) Ovalized chord in this study, b) Ozalized chord in Lesani et al. [25] study, c) Load-Ovalization diagram in this study versus Load-Ovalization diagram in Lesani et al. [25] study. 785

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Fig. 10. Hashin matrix compressive failure criterion corresponding to the peak load in FE analysis of the strengthened T2 joint (contours show the

location conforms to the point in which the maximum bulging/ovality had occurred. Moreover, in order to have a more perspicuous comparison of the results, the Load-Ovalization diagrams were extracted and given in Fig. 9(c) for this study and the reference study [25] respectively. The investigations show a very good correlation between the studies. It is worth to note that, the experimental behavior of the FRPstrengthened joint after peak in the reference study [25] was more realistic since the numerical model did not predict any delamination or debonding of the FRP plies whereas in reality and due to this phenomenon, sudden loss of the load bearing capacity was inevitable. However, in the experimental and numerical behavior of the strengthened joint in viewpoint of the initial stiffness, maximum load was compatible up to the peak load threshold. Beside the load-deformation figures, the importance of verifying the failure mode of the FRP is by no means negligible. Based on Lesani et al. [25], for the FRP, the Hashin damage criteria [36] were taken advantage of to consider the post-damage behavior of the FRP shell elements and for strength assessment and damage evolution. Hashin matrix damage criterion in FRP lay-up is illustrated in Fig. 10. Focusing on this figure, there was no sign of fiber or matrix failure of plies on the brace as was observed in Lesani et al. [25] study. In other words, the plies on the brace were all intact. Practically matrix compression failure as the major mode of failure occurred at the intersection zone and all plies around it, plus the saddle point region. These results matched with the failed zones in Lesani et al. [25] study. Based on the results of the verification analysis, the modeling procedure of this study was able to predict the deformations as well as stress distribution in the strengthened joint. Based on this verification analysis and the analyses performed on the benchmark specimen, the benchmark model was strengthened and analyzed in the following

section, and SCFs were extracted through a parametric study on FRP parameters. 5. FE modeling of the strengthened joint In this section, some key aspects of the FRP strengthened numerical model are presented. FRPs are composed of two distinct parts namely fibers and matrix. Thus, various compositions could be made. In this study, six types of common FRP materials namely, Glass/Vinyl ester, Glass/Epoxy (Scotch ply 1002), S-Glass/Epoxy, Aramid/Epoxy (Kevlar 49/Epoxy), Carbon/ Epoxy (T300-5208) and Carbon/Epoxy (AS/3501), were used as strengthening material on the T-joints to find out how different FRP materials affect the SCF values. Table 5 demonstrates the properties of the FRPs used in the analyses. In this table, subscripts “1” and “2” stand for the fiber longitudinal and transverse directions respectively. FRP material was modeled using shell elements defined as a skin layer on the 3D benchmark joint FE model. ABAQUS shell element type S4R was adopted, which is a 4-node doubly curved thin or thick shell with reduced integration. FRP meshed elements were tied to the external surface of the solid elements of the benchmark joint geometry. In other words, a perfect bond state was considered and no cohesive/adhesive element was modeled at the FRP and the steel substrate interface. This was because the bond between FRP layer and steel stayed undisturbed in the elastic range of loading according to the experimental and numerical analysis by Lesani et al. [24]. Fig. 11 shows an enlarged section of the strengthened T-joint. FRP fibers were considered in two major directions, namely 0° (Chord hoop direction and along the brace longitudinal axis) and 90°. Fig. 12 clarifies how these fiber orientations were being considered in the FRP modeling.

Table 5 FRP properties [23,37,38]. Mechanical properties E1 [GPa] E2 [GPa] ν12 G12 [GPa] G13 [GPa] G23 [GPa]

Glass/vinyl ester 28 7 0.29 4.5 4.5 2.54

Glass/epoxy (Scotch ply 1002) 38.6 8.27 0.26 4.14 4.14 3.1

S-glass/epoxy 43 8.9 0.27 4.5 3.18 3.18

Aramid/epoxy (Kevlar 49/ Epoxy) 76 5.5 0.34 2.3 2.3 2.01

Where E, modulus of elasticity; v, Poisson's ratio; G, shear modulus. 786

Carbon/epoxy (T3005208) 132 10.8 0.24 5.7 5.7 3.4

Carbon/epoxy (AS/ 3501) 138 8.96 0.3 7.1 7.1 2.82

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Fig. 11. Mesh enlargement around Crown Point of the numerical model of the FRP wrapped T-joint. Table 6 The abbreviations of the strengthening schemes and FRP materials. Strengthening scheme and FRP orientation Ch0 Ch90 Br0 Br90 Ch0&Br0 Ch0&Br90 Ch90&Br0 Ch90&Br90 FRP materials GV GE SGE AE T300 AS

Fig. 12. The FRP wrapped T-joint with definition of 0° and 90° fiber orientations in the FRP layup on Chord and Brace.

Chord strengthening with 0° fibers orientation Chord strengthening with 90° fibers orientation Brace strengthening with 0° fibers orientation Brace strengthening with 90° fibers orientation Chord and Brace strengthening with 0° fibers orientation on both chord and brace Chord and Brace strengthening with 0° fibers orientation on chord and 90° fibers orientation on brace Chord and Brace strengthening with 90° fibers orientation on chord and 0° fibers orientation on brace Chord and Brace strengthening with 90° fibers orientation on both chord and brace Glass/vinyl ester Glass/epoxy (Scotchply 1002) S-glass/epoxy Aramid/epoxy (Kevlar 49/Epoxy) Carbon/epoxy (T300-5208) Carbon/epoxy (AS/3501)

SCF values were extracted. In order to have a better insight towards the stress distribution on the joint, Fig. 13 shows the longitudinal stresses along the X-axis as well as the hoop stresses for the benchmark joint. The state of the stresses in this figure is used to interpret the results. Analyses were performed for all the six types of FRPs and results were given for different strengthening schemes. Figs. 14 and 15 show the relative SCFs (SCFs: SCF at the strengthened joint divided by SCFu: SCF at the benchmark joint) at Crown and Saddle points, respectively. Two major orientations (0° and 90°) were selected for the fibers in the FRP layups. As seen in Fig. 14, stiffer FRP material has more decreasing effect on the SCF values. According to this figure, fibers orientation on the chord member had a significant effect on SCFs. It is further seen that the decreasing effect of FRP wrapping on the chord member when the fibers are in 90°, is three fold the same FRP wrapping with 0° orientation on average. This is simply because the axial load is being transferred through the brace to the chord member along the X-axis on the Crown Point (Fig. 13). Thus, using fibers with 90° orientation has the best effect on lowering the stresses, because when fibers are placed along the load transfer direction, they efficiently contribute in load bearing as the steel substrate degrades. According to Fig. 14, applying FRP on the brace member only, has a negligible increasing effect on SCFs (black square and triangle in Fig. 14). Although brace strengthening had an undesirable effect on

For all analyses, the strengthening materials had a thickness of 6 mm and a wrapping length of equal to one diameter of the relative strengthened member (1D on the chord and 1d on the brace member). 6. Analyses and results In order to evaluate contribution from each component to the final result, analyses were carried out in three phases, strengthening the chord member only, strengthening the brace member only and finally strengthening both members. The details and results of the analyses on SCF values in strengthened T-joints for each type of loadings and strengthening schemes are presented in the following subsections. The abbreviations used in the subsequent Figures are explained in Table 6. 6.1. Axial loading The results of the analyses of FRP strengthened T-joints with six types of FRP materials are reported in this section to investigate the effect of FRP mechanical properties on SCF values at Crown and Saddle points, under brace axial loading. The joints were loaded by a 10 MT monotonic load applied on top of the brace member (See Fig. 2(a)). Stresses at the weld toe in Crown and Saddle points were calculated according to the IIW-XV-E [30] method as previously explained and 787

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Fig. 13. Stress distribution on the benchmark joint under a 10 MT axial load applied at top of the brace: a) Longitudinal stress, σx ( ± values); b) Hoop stress, σθ ( ± values); Unit of stresses: MPa.

thickness on both chord and brace members decreased the SCFs by 30% at the Crown Point. It was also observed that the decreasing effect of using stiffer composite material such as CFRP could be about 5 times more than the GFRP material. Considering the Saddle point on the chord of the T-joint when the chord member is strengthened (Fig. 15), it is seen that stiffer FRP material (Higher mechanical properties) shows more effectiveness in decreasing the SCF values. As clearly envisaged from this figure, using a 6 mm carbon-epoxy composite has about three times more effectiveness on SCF reduction than the GFRP material. In other words, CFRP strengthening decreases the SCFs about 50% at the Saddle point. The interesting point of this figure is that, in contrary to the Crown Point, using 0° fibers orientation in the Saddle point has the highest effect in reducing the stresses. This can be interpreted by considering that the fact that the main stresses on the Saddle point are the hoop stresses. Thus, using fibers on the 0° orientation (confining the chord member) is the most effective way of reducing stresses at this point. Alike the Crown Point, strengthening the brace member had an increasing effect on SCFs at the Saddle point. These effects were amplified by increasing the mechanical properties of FRP materials. As for the other orientations, using 90° fiber orientation had negligible increasing effect on SCFs. The increasing effect of higher modulus FRP materials, such as CFRP, on the brace member on SCFs was about maximum 5% at the Saddle point. The effect of different strengthening FRP materials on SCF values when the chord and brace members of the T-joint were strengthened simultaneously is also illustrated in Fig. 15. Based on this figure, the maximum effectiveness of the 6 mm FRP was

Fig. 14. Ratio of SCF values at the Crown Point of the FRP strengthened tubular T-joint with different FRP materials under brace axial load.

SCF, applying FRP on both Chord and Brace members increased the integrity of the strengthening. Moreover, brace strengthening provided a condition in which loads could be transferred through the brace FRP onto the Chord and thus lower stresses were observed in comparison to strengthening the chord alone. Regardless of the results and in practical applications, to achieve an integrated joint strengthening, both chord and brace members require to be wrapped. Focus on the effect of FRP materials regardless of the fiber orientations revealed that using Carbon/Epoxy (AS/3501) with a 6 mm 788

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Fig. 15. Ratio of SCF values at the Saddle point of the FRP strengthened tubular T-joint with different FRP materials under brace axial load.

Fig. 17. Ratio of SCF values in FRP strengthened tubular T-joint with different FRP materials under Out-of-plane bending moment.

observed for Carbon-epoxy material, when the chord was strengthened with 0° fiber orientation (Ch0). This layup could lower the SCFs up to 50% at the Saddle point. Based on Fig. 14, and considering the curve of Ch0, the SCF is reduced when Ch0Br0 or Ch0Br90 are used. However, in Fig. 15, the SCF is increased when FRP is applied on the brace. In fact, as mentioned earlier, the most effective results on Saddle point were observed when only chord was strengthened (Ch0) as depicted from Fig. 13. According to this figure the governing stress on the Crown is the longitudinal stress, while around the Saddle point the most dominant stress is the hoop stress. Strengthening the brace caused more stress transfer to the chord around the Saddle point and consequently increased the hoop stress. Thus, Chord and Brace strengthening was the best scheme for decreasing SCFs at the Crown Point while it did 'not act as the best on the Saddle point. Since it is impractical to strengthen the chord or brace individually, and due to the slight difference between Ch0 and Ch0Br90 schemes in Fig. 15, it is recommended to strengthen the chord and brace members to preserve structural integrity, achieve higher stiffness and higher load bearing capacity as previously addressed [25].

member, and both chord and brace members were strengthened with 0° and 90° fiber orientations were investigated. Results are presented in Figs. 16 and 17 for IPB and OPB moments respectively. In order to have a better understanding of the state of stresses on the T-joints under IPB and OPB moments, Figs. 18 and 19 show the longitudinal stresses along the X-axis as well as the hoop stresses for the benchmark joint under IPB and OPB moments, respectively. As depicted from Figs. 16 and 17, the effectiveness enhances by using stiffer composite material. Moreover, using carbon-epoxy material had higher effectiveness on SCF reduction in comparison to the GFRP material. In general, it was revealed that among four different schemes consisting of the composition of 0° and 90° fibers orientation, when the chord member was strengthened with 90° fibers and the brace member with 0° (Ch90&Br0) in the FRP system, the most reducing effect on SCF values was observed under IPB loading. Under OPB loading the most effective scheme was Ch0Br90. For instance, using this scheme with Carbon-epoxy FRP material decreased the SCF values by 40% for IPB moment and 50% for OPB moment. According to Fig. 16, under IPB moment, when only the chord member was strengthened with 90° fibers orientation, the SCF values were reduced effectively, while for OPB loading, the most decreasing effect on SCFs was observed when fibers were placed in 0° orientation on the chord member (Ref to Fig. 17). Brace strengthening had an increasing effect on SCF values. Moreover, change in FRP material properties showed more considerable alteration on SCF values when FRP fibers were laid in 90° and 0° directions under IPB and OPB moments respectively. These Figures reveal that the strengthened brace with 0° fibers had the highest increasing effect on the SCF amplitude. This was due to the fact that, the In-plane moment acting on the brace member was transferred through the Crown Point on the chord member as evident from the X-axis stress component (σx) (Fig. 18). Thus, using fibers with 90° orientation had the highest effectiveness on lowering the stresses under IBP moment. An adverse scenario exists for stresses under OPB moment. As seen in Fig. 19, the dominant stress on the chord member is the hoop stress (σθ) near the Saddle point. So, it could be concluded that 0° fibers orientation has the greatest effect on lowering the stresses. Having Figs. 14 to 17 along with the mechanical properties given in Table 1, one can find how the change in the value of each mechanical property in the two main extreme fiber orientations (0° and 90°) would affect the SCFs under three types of loadings (AX, IPB, and OPB). To sum up, according to Figs. 14 to 17 it is recommended to use the most effective orientation on the Crown and Saddle points. The most effective and integrated theoretical layup is as illustrated in Fig. 20. Owing to the importance of integrity in the wrapping procedure, the layup of Fig. 20 doesn't seem practical. So, in the next section, eight different practical layups of strengthening under the effect of all three

6.2. IPB and OPB moments The same analyses as mentioned in above Section 5.1 were conducted for the T-joints subjected to IPB and OPB moments (See Fig. 2(b, c)) in this subsection, and effects of using six FRP materials on SCF values at Crown and Saddle points were investigated. Similar to the Tjoint investigated under axial loading, the same strengthening schemes were used for the T-joint under bending moments. In other words, the effects of FRP material selection when the chord member, the brace

Fig. 16. Ratio of SCF values in FRP strengthened tubular T-joint with different FRP materials under In-plane bending moment. 789

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Fig. 18. Stress distribution on the benchmark joint under a 4 Ton-m IPB moment on the brace: a) Longitudinal stress, σx ( ± values); b) Hoop stress, σθ ( ± values); Unit of stresses: MPa.

loading types were investigated to find the most effective and integrated as well as practical layup for SCF reduction while the effect of combined loading was also taken into account.

In order to find the most effective layups in lowering the SCFs at Crown and Saddle points, analyses for all of the above layups were performed and results are presented in Fig. 21. In this figure, the vertical axis shows the relative SCF values (SCF in strengthened joints divided by the SCF in benchmark joints). The horizontal axis has two sides. The left side shows SCFs at the Crown Point and the right side corresponds to the SCFs at the Saddle point. According to this figure, joints in which lower values of SCFs were observed have the most effective layup. For instance, C2 (The orange plaid bar) is the most effective layup at the Saddle point but not necessarily at the Crown Point. The main point is that SCFs have to be decreased evenly on both Crown and Saddle points with the same fibers orientation in the layups. Therefore, by observing Fig. 21, it could be found out that the best layup is D2 (The aligned hatched brown bar), and B2 (white dotted black bar) stands next. So, the most effective layup on the chord is using 90° fibers in the first layer on the chord and 0° fibers in the first layer on the brace and the rest of the layers alternately. This layup decreased the SCFs up to 30% on both Crown and Saddle points. This study showed that the ply stacking sequence is highly effective on the SCFs. According to Table 7, although layup D1

6.3. Combined axial loading, IPB and OPB moments According to the results of this study which addressed the loadings individually, it was found that the best layup that could effectively reduce the SCFs was using 90° and 0° fibers orientations on the Crown and Saddle points, respectively. So, as long as unidirectional fabrics are used for FRP wrapping, it is inevitable to distinct the fibers orientation on Crown and Saddle points. Therefore, a combination of fibers orientation on every point should be considered. In this part, the numerical model is assumed to be under the action of combined Axial loading, IPB and OPB Moments. The ratio of axial force to bending moments is 12.5 N/N.m. The FRP layup consists of the combination of 0° and 90° fibers orientation using Carbon/Epoxy (T300-5208) material. Each layer's thickness is 1 mm and the total FRP layup thickness is 6 mm. Details of FRP layups for combined 0° and 90° fibers orientation are presented in Table 7.

790

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Fig. 19. Stress distribution on the benchmark joint under a 4 Ton-m OPB moment on the brace: a) Longitudinal stress, σx ( ± values); b) Hoop stress, σθ ( ± values); Unit of stresses: MPa.

(The gray vertical hatched bar) had the same material property, thickness and fibers orientation as layup D2, but, fibers were oriented in 0° direction for the first layer of D1. This affected the balance of SCF reduction at the Crown and Saddle points. Focusing on Figs. 14 and 15 reveals that under axial loading, the average decreasing effect of using 90° fibers is more than 0° fibers. This could also be interpreted from Figs. 16 and 17 for IPB and OPB moments respectively. Thus the results of Fig. 21 are justifiable when the results from each loading type were assessed individually. As observed in Table 7, the only difference among the lay-up schemes is the sequence of lay-up orientation, which has a considerable impact on the SCF. In order to interpret more clearly, some simpler layups are taken into account to examine the effect of ply stacking sequence. Table 7 reveals that the only difference between D1 and D2 schemes is the orientation of the first layer. Thus, complementary analyses were performed on four extra lay-ups as illustrated in Table 8. In all schemes, Brace lay-up remains the same. E1 and E2 consider the effect of the first layer on Chord under combined loading. F1 and F2

Fig. 20. The most effective layup obtained from the analysis.

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the benchmark model was strengthened using different FRP materials and a parametric study has been performed to investigate the FRP effectiveness under axial, IPB and OPB loadings. The following general and specific conclusions were derived from this study.

Table 7 FRP layups for combined 0° and 90° fibers orientations. Model number A1 A2 B1 B2 C1 C2 D1 D2

Chord layup

Brace layup

[03/903] [903/03] [0/90/0/90/0/90] [90/0/90/0/90/0] [03/903] [903/03] [0/90/0/90/0/90] [90/0/90/0/90/0]

[03/903] [903/03] [0/90/0/90/0/90] [90/0/90/0/90/0] [903/03] [03/903] [90/0/90/0/90/0] [0/90/0/90/0/90]

7.1. General conclusions

• Change of fiber and/or matrix material properties corresponds to • •

change in FRP mechanical properties. Generally, it was observed that use of FRP material with higher values of mechanical properties as the strengthening material had more efficiency in SCF reduction. In general, FRP strengthening showed more effective results on the Saddle point compared to the Crown Point. Further numerical and experimental investigations are necessary and some experimental tests are required for verification and interpretation.

7.2. Specific conclusions corresponding to different types of loading 7.2.1. Axial loading

• Among the six common composite materials investigated in this •

Fig. 21. Ratio of SCF values in an FRP strengthened tubular T-joint with various compositions of 0° and 90° FRP fibers under the three types of loading. Table 8 FRP complementary layups and the resulted SCFs for combined 0° and 90° fibers orientations.

⁎

Model number

Chord layup

E1 E2 F1 F2

[0] [90] [0/90] [90/0]

Brace layup [0] [0] [0] [0]

Crown point SCFs/u 0.995 0.895 0.878 0.867

•

Saddle point SCFs/u 0.900 1.024 0.892 0.863

paper, CFRP materials had effectiveness of about 3 and 2.5 times in SCF reduction than the GFRP materials at Crown and Saddle points respectively. CFRP strengthening could reduce the SCFs up to 30% and 50% at Crown and Saddle points respectively. According to the results, the most effective schemes under axial loading at the Crown Point were using 90° and 0° fibers on chord and brace respectively, and for the Saddle point using 0° and 90° fibers on chord and brace respectively. Moreover, in common practical applications, the joint would completely be wrapped with FRP (Both Chord and Brace strengthening). So, the fibers would be aligned in both longitudinal and hoop directions accordingly. Due to the better fatigue performance of CFRP materials in comparison to other composite materials, it is recommended to use CFRP composites as strengthening material for fatigue life extension of tubular joints.

7.2.2. IPB and OPB moments

SCFs/u = SCF after strengthening/SCF before strengthening.

• Brace strengthening had an unfavorable increasing effect on SCFs in

are chosen to examine the lay-up sequence effect for 2 layers. The analyses for the layups in Table 8 were performed and results are presented as SCF values in Crown and Saddle points. Based on Table 8, the first layer's orientation has a considerable effect on the state of the stresses. Comparing the E1 and E2 schemes, 0° fibers (E1) have a slightly decreasing effect on SCFs at both Crown and Saddle points. 90° fibers (E2) were the most effective at Crown point while they increased the SCFs at Saddle. As clearly seen, choosing 90° layer as the first layer (F2) which is directly adjacent to the steel substrate, provides slightly lower values of SCF rather than F1 scheme. This was due to the pattern of stress distribution on the chord member resulting from each type of loading, which was investigated in the previous sections. Thus, care must be taken when the combination of ply as well as the first layer orientations and the stacking sequence is chosen.

• • •

both IPB and OPB loading conditions, as when the fibers were in 0° orientation, the most adverse effect was observed. In case of IPB loading, the most decreasing effect on SCFs was observed when only the chord member was strengthened with 90° fibers orientation. But, since in practical applications, both chord and brace members are strengthened, the most effective applicable scheme under IPB moment was Ch90Br0 (see Table 2). In case of OPB moment, use of FRP wrapping with 0° fibers orientation on the chord member and 90° on the brace member had the most degrading effect on SCFs. Under in-plane and out-of-plane bending moments, CFRP material decreased the SCFs approximately two times more than that of the GFRP material.

7.2.3. Combined loading

• The most effective fibers layup on the chord was 90° fibers in the

7. Summary and conclusions In this paper, changes in SCF values at Crown and Saddle points on the chord member of the tubular T-joint due to change in FRP material used for wrapping the joint were investigated. The numerical models of the benchmark joints were verified based on existing experimental data. In addition, another analysis performed to verify the strengthening method against an experimental as well as numerical analysis. Finally,

• 792

first layer followed by 0° while for the brace it suits 0° fibers in the first layer followed by 90°. The rest of the layers to follow alternately. With this scheme, decrease of about 30% in SCF, on both Crown and Saddle points was observed. This study showed that the ply stacking sequence was extremely significant for the SCFs. Two layups with the same material property as well as thickness and fibers orientation showed different results due to the fibers orientation in the first layer.

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