Tensile behaviour of open-hole and bolted steel plates reinforced by CFRP strips

Accepted Manuscript Tensile behaviour of open-hole and bolted steel plates reinforced by CFRP strips Zhi-Yu Wang, Ning Zhang, Qing-Yuan Wang PII:

S1359-8368(16)30936-2

DOI:

10.1016/j.compositesb.2016.06.038

Reference:

JCOMB 4383

To appear in:

Composites Part B

Received Date: 17 February 2016 Revised Date:

5 May 2016

Accepted Date: 3 June 2016

Please cite this article as: Wang Z-Y, Zhang N, Wang Q-Y, Tensile behaviour of open-hole and bolted steel plates reinforced by CFRP strips, Composites Part B (2016), doi: 10.1016/ j.compositesb.2016.06.038. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Tensile behaviour of open-hole and bolted steel plates reinforced by CFRP strips Zhi-Yu Wang1,2, Ning Zhang1,2 and Qing-Yuan Wang2,3,* Department of Civil Engineering, Institute of Architecture and Environment, Sichuan University, PR China

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Sichuan Provincial Key Laboratory of Failure Mechanics and Engineering Disaster Prevention & Mitigation, Sichuan University, Chengdu, PR China

School of Architecture and Civil Engineering, Chengdu University, PR China Corresponding author: [email protected]

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Abstract

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The behaviours of the open-hole and bolted plates in tension are fundamental in the mechanical assessment of the bolted connections. Regarding the rehabilitation of steel structures, however, the combined effects of bolted washer clamp-up and CFRP reinforcement on the tensile behaviour of the connection with laser cut holes have not been fully understood. This investigation aims to fill the gap by carrying out experimental tests and developing analytical model accounting for these effects. The test results show that the CFRP reinforced plates are failed by the rupture of CFRP and the steel-adhesive interface failure accompanied by CFRP delamination. Both failure modes can be correlated with two load-deformation characterizing curves. It is also found that the increase of the nominal tensile strength of the specimens can be enhanced significantly by the increase of the number of the CFRP layers and further moderately improved with the combined effect of the bolted washer clamp-up. Moreover, the yield load and residual deformability of the specimens can be significantly increased with the bolted washer clamp-up and greater bolt torque respectively. An analytical model taking into account the bolt torque effect and interfacial stress equilibrium has been developed to predict the strength enhancement effects of washer clamp-up and CFRP reinforcement on the open-hole plates in different failure modes. The proposed model has been verified to be effective in providing satisfactory strength ratio in contrast to test data.

Keywords: E. Joints; A. Carbon fibre; A. plates; C. Analytical modelling; D. Mechanical testing

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1. Introduction

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Open-hole details are widely utilized in the connections of steel structural components, such as gusset plates and cross-frames. From the mechanical theoretical point of view, the presence of the hole introduces certain weakening effect on the section of the components in which the structural deficiency may arise. In the structural application, the fastened joints become a critical design issue even when the high strength and lightweight components are employed [1]. Moreover, the application of the hole fabrication methods is required in most design codes of structural engineering. The accurate analytical approaches and effective behavioural improvement of the structural components with holes are concerned in recent studies.

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The use of carbon fibre reinforced polymer (CFRP) to adhesively bond the damaged member for the purpose of enhancing the loading-carrying capacity has received excellent application in the civil engineering [2]. Their merits of high strength to weight ratios, good constructability and durability of non-metallic CFRP composites are quite promising for the strengthening of steel structures. Moreover, the flexible shape of CFRP composites eases their use in the reinforcement of the bolted or riveted steel members.

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The CFRP reinforced plates in tension are basic tests that are widely employed to provide the mechanical behaviour for the evaluation of structural CFRP retrofit. Considerable research efforts have been made on the bond behaviour between the steel plate and CFRP laminate. The ductile and brittle behaviour of the joints are directly influenced by the design parameters of CFRP laminates. One suggestion was made by Bocciarelli and Colombi [3] that high quality adhesive with high fracture energy and CFRP strips with a high axial stiffness in the design of steel-CFRP joints. To predict its typical failure modes and bond strength, some methods have been proposed accordingly with the use of the failure criteria related to the maximum stress in the bondline [4], the fracture mechanics [2,5] and the equivalent strain energy density [6]. Also, deformation harmony between the steel plate and CFRP laminate can be adopted in the study of integrate effect of laminates [7].

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On the other hand, it appears from the recent literature that the ease of tensile experimental testing has brought about a considerable amount of studies of open-hole and bolted joints. As such, this testing method for of composite laminates has been documented in recent codes, such as ASTM standards [8] for fastened parts in aerospace industry. It has also been shown [9-10] that the increase of notch size results in a decrease of the strength of CFRP laminates. One possible explanation [11-14] was the greater probability of having a large flaw in the highly stress area around the hole in larger size. In addition, the ultimate tensile stress of the open-hole plate is also influenced by the hole fabrication methods, such as punching [15, 16], drilling [17] and laser cutting [18, 19], to some extent. In contrast, the experimental studies on the tensile behaviour of steel elements with open-hole details strengthened by CFRP laminates are still limited. Different strengthening layouts have been chosen by different researchers. Colombi and Poggi [20] utilized CFRP plates to strengthen the bolted steel plates which exhibit insignificant effectiveness in the strengthening. Also, they found that the thin adhesive reduces the enhancement of the strength and pretension is suggested accordingly. Also, two-dimensional finite element models were adopted by Colombi et al. [21] in the 2

ACCEPTED MANUSCRIPT illustration of the influence of some parameters, such as composite strip stiffness, the pre-stress level, layer thickness and size of the debonded region, on the effectiveness of the reinforcement. Recently, Penagos-Sanchéz et al. [22] studied the double lap joints with various hole configurations through a series of tensile tests. Through a comparison, they found that the yielding load of the joints was increased with the number of layers and the contribution of CFRP was greater when the ratio between net and gross cross-sectional area of the steel was decreased, e.g. 56% gain when the aforementioned ratio was 52%.

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Despite valuable finding obtained from above mentioned studies, no further comments are available for the behaviour of bolted steel plates reinforced by the CFRP strips subjected to pure uniaxial tensile loads with the focus on the varied failure modes of CFRP. Moreover, as a general practice of the bolted connections, the flat washers are often placed beneath a nut or a joint to relieve friction, prevent leakage, or distribute pressure. After strengthening structurally deficient steel plates using CFRP, the square and rectangular washers can be installed with the centre bolt to form a reinforced bolted connection with great friction and fastening. In such a situation, the normal stress from the washer is applied directly on the surface of the steel plate and its reinforced CFRP laminates within the clamp-up area. Also, the pressure contact of the washer to some extent prevents the premature warping of the CFRP layer from local debonding. However, the tensile behaviour of the bolted connection allowing for the bolted washer clamp-up and CFRP reinforcement has not been clearly understood.

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For the purpose of evaluating the rehabilitation of steel structural components, the goal of this research work was to investigate the tensile behaviour of CFRP reinforced steel plates with open-hole and bolted details influenced by related parameters of CFRP and clamp-up condition. This paper will present the experimental results of reinforcement effects with varying the number of CFRP slayers, washer length and bolt torque. The typical failure modes with above influences are then discussed accordingly. Afterwards, an analytical model has been developed to predict the strength enhancement effects of washer clamp-up and CFRP reinforcement on the open-hole plates. This model takes into account the bolt torque effect and interfacial stress conditions. Through a contrast with related test data, the validity of the proposed model is discussed for exploitation in developing a useful but simple assessment for reinforcement of the structural details studied herein.

2. Experimental procedures 2.1 Configuration of test specimens Since the steel plate is expected to be vulnerable with the presence of the open-hole, the bolted washer and CFRP strips were adopted to cover the area centred at the bolt clearance hole. A number of 39 test specimens were prepared with different combination of washer length and/or the number of the layers of CFRP against bare steel counterparts. The basic geometry of the test specimens is shown in Table 1. The length and the width of the specimens were chosen as 300mm and 30mm respectively for all tests. The bolt clearance holes on the test specimens were cut using a standard laser cutter. During this cutting process, the initial kerf at the designed centre of the bolt clearance hole was made on the original metal in a confined area. This was performed as the local part of the metal is vaporized under the energy in the focused laser beam and blown through using 3

ACCEPTED MANUSCRIPT gas stream. The initial kerf was then enlarged properly to form a standard bolt clearance hole. The specimens containing manufacturing defects beyond the tolerance were discarded.

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The washer placed beneath the bolt head and nut was kept as 6mm thick to provide a uniform clamp-up pressure on its covered area. The square and rectangular washers were chosen in preference for their larger contact surface area than round washer to distribute pressure. All washer surfaces were flatten without rust and bevelled edge to ensure well contact condition of the washer surface to the steel plate or the CFRP strips. The carbon fibre sheets were cut to size of 200mm long and 30mm width using a scissor with very fine blade. The surface of steel plate in contact with CFRP was grounded with sandpaper by hand to remove roughs until the shiny surface of the metal was exposed over the area for strengthening. The surface was wiped with cotton cloth soaked in acetone to remove all grease and rust. The above surface preparation procure was applied and repeated to reduce the possibility of unexpected premature bond failure between steel and CFRP. Afterwards, the adhesive was mixed in accordance with the specifications suggested by the product and then applied over the surface with CFRP. The CFRP grips in the bonded regions were then applied with proper alignment and gently compressed with weights. The extra adhesive squeezed out from the edge of the CFRP was removed with caution to ensure proper and even bond condition. Subsequent to the preparation of CFRP strips, the test specimens were cured for 14 days under room temperature. 2.2 Test setup

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The experimental tests were carried out through a Shimadzu AG-100kNXplus STD universal testing machine of 100kN capacity. As shown in Fig. 1, the one end of the steel plate was gripped in the upper head of the test machine to apply direct tensile stress while the other end was gripped in the fixed bottom head of the test machine to provide reaction load. The specimens were cautiously installed to avoid eccentricity between two ends of the grip. The tensile deformation over the bolt clearance hole region was measured by fixing a SSG50-10 extensometer with 50mm gauge length centred at the middle of the test plate. Output and instant information from the testing machine were monitored and recorded by an automatic data acquisition system controlled by Shimadzu Trapezium X software. The loading rate of movement for the hydraulic jack of 0.02mm per second was applied until the rupture of the specimen. The actual measured cross-sectional dimensions were used for the calculation of nominal stress of testing specimens. 2.3 Test material and specimen index The steel materials used for test specimens with 3mm and 6mm thick. Both materials are chosen from different steel grade which conforms to the Chinese national standards GB/T700 [23] and GB/T1591 [24] respectively. The stress-strain relations of above materials obtained from coupon tests are summarized in Fig. 2. High performance carbon fibre UT70-30 with the thickness of 0.167mm produced by Toray Industries, Inc was employed. The values of the elastic modulus of the steel and carbon fibre are taken as 2.1×105 and 2.52×105 respectively in accordance with the manufacturer’s specifications. The Sikadur-330 epoxy resin matrix was used for the fabric reinforcement. It is a two part thixotropic epoxy based impregnating resin/adhesive. The measured properties at 7 days in accordance with the standard of DIN 53455 are: tensile strength-30 MPa, elastic modulus in tension-4.5GPa and elongation at break-0.9% [25]. Detailed technical data of 4

ACCEPTED MANUSCRIPT above constituent materials are listed in Table 2. The high strength and unidirectional carbon fibre fabric (UT70-30) was laminated using Sikadur-330 adhesive to form a carbon fibre reinforced polymer (CFRP) used to strengthen steel plates in this study. Standard samples of unidirectional carbon fibre reinforced polymer laminates with 1mm thick adhesive were prepared and tested according to ASTM: D3039. A value of 1438N/mm2 was used for the strength of laminates from the mean of four tensile tests.

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The test matrix is summarized in Table 3, which includes the index number together with the geometric parameters. These parameters were defined as: the thickness (tp) of the steel plate, the diameters of the bolt shank (dsh), the bolt clearance hole (dbh), the washer length (lw) and the layers of CFRP (nCFRP). In addition to the basic bolt torque value (Tin) of 80N·m, the other values of 60N·m and 120N·m are also taken for M14 bolt in comparison. For the sake of brevity, the specimen index is generally denoted as ‘T(tp)-H-P0-S0’ or ‘T(tp)-B-PR(lw)-SD(lCFRP) or NC-T(Tin)’, where, ‘H’ and ‘B’ represent two categories of specimens with open-hole only and with bolted washer clamp-up at double sides. The notations of ‘P0’ and ‘SD or NC’ correspond to these without washer and with washer at certain length or standard circular washer respectively. ‘T’ stands for the input torque value which is omitted for the specimens without bolted washer clamp-up. As an example in Table 1, the index of ‘T6-B-PR60- SD3L-T80’ can be taken as an specimens with 6mm thick steel plate double clamped with washers of 60mm lengths and reinforced with triple layer CFRP under the bolt toque of 80N·m.

3. Experimental results

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3.1 Failure modes

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By examining the damage photographs of test specimens, overall three primary failure modes and two combined failure modes were found for the specimens with open-hole, different CFRP strip layers and clamp-up conditions. As illustrated in Table 4, the failure mode C0 for the specimens with open-hole or bolted washer clamp-up but no CFRP strips is characterized by the fracture propagated from the bolt clearance hole region toward the steel plate free edge as a function of the applied load. The development of local plasticity at this location is evidenced by some discernible necking. Regarding the specimens with CFRP strips, on the other hand, two primary failure modes can be deduced as follows. Failure mode C1: completely rupture of adhesively bonded CFRP strips along with the fracture of steel plate at the edge of the bolt clearance hole. In this case, the strength of the steel-adhesive and carbon fibre-adhesive bonding at the failure location can be expected to be strong so that the steel plate and CFRP carry the predominant tensile loads. As such, both materials fracture nearly at the minimum net cross-sectional area through the centre of the bolt clearance hole where the maximum tensile stress takes place. Failure mode C2: completely debonding between the steel plate and the CFRP layers prior to the facture of the steel plate. This can be explained as the strength of the steel-adhesive interface becomes relatively lower than that of the CFRP and its interface with adhesive. In fact, the steel-adhesive interface may undergo pronounced enhancement of the shear strain as the steel plate behaves inelastically. At the ultimate stage of loading, the local interface failure 5

ACCEPTED MANUSCRIPT between the steel plate and the adhesive layers may lead to the debonding at the whole surface of the steel plate. This case mostly takes place for the specimens with multiple CFRP layers or long washers clamp-up. In addition, due to uneven interfacial stress distribution, two combined failure modes in relation with the modes C1 and C2 mentioned above can also be outlined as:

Failure mode C2”: in addition to the steel-adhesive interfacial failure at most part of the steel plate, local adhesive remnant in longitudinal direction still exists between two maximum stress locations accompanied by the delamination of CFRP nearby. Besides, CFRP layer is locally warped after the steel-adhesive interface becomes ineffective.

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Failure mode C1”: in addition to the failure behaviour represented in the mode C1, the longitudinal splitting and local debonding of CFRP from the maximum stress location at the edge of the bolt clearance hole.

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3.2 Load-deformation behaviour and notch sensitivity analysis

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The influences of CFRP and its clamp-up conditions on the strengths of bolted and CFRP reinforced steel plates can be indicated from their corresponding test load-deformation behaviours. As illustrated in Fig. 3, the behaviour of the specimen without CFRP reinforcement (Labelled as curve P0) was taken as the basis for comparison, in which the ultimate strength and deformation are denoted as Fn,uc and δn,uc respectively. The general behavioural trend of the CFRP reinforced specimen is started by an essentially linear range up to the yielding of the steel plate. Subsequent to yielding, the behaviour becomes increasingly nonlinear until the rupture of CFRP or the interface failure between steel and CFRP strip took place. The variables at this point are taken as the nominal tensile capacity, Fn,rc, and its corresponding deformation, δn,rc, respectively. Afterwards, the loss of CFRP reinforcement renders significant softening branch, indicating strength degradation, until the structural behaviour follows a similar trend to that of an unreinforced one, i.e. curve P0. The ultimate capacity of the behaviour is governed by the rupture of the open-hole steel plate. As plotted in Fig. 3, the curve P2 has moderate deformability with residual strength, Fr, and deformation, δr, prior to rupture while the curve P1 exhibits almost brittle rupture without residual behaviour. Based on the observation from the tests, the specimens with failure modes C1 and C2 are more likely to behave following curves P1 and P2 respectively. From a theoretical point of view, the presence of hole produces stress concentration and its ratio is often taken as 3.0 for notch sensitive isotropic materials. To examine the notch sensitivity of test materials, the nominal tensile capacities, Fk was obtained as Fn,uc or Fn,rc for notched (open-hole or bolted) plate and F0 was taken as test load of un-notched plate. And then, the test load ratios are calculated by dividing Fk by F0 as listed in Table 3. On the other hand, the effective cross-section ratio can be calculated as (b0-dbh)/b0, which is equal to 0.58 for the specimen of T6-H-P0-S0. In comparison, this ratio is very close to Fk/F0=0.64 which suggests that the test specimens are almost notch insensitive. Therefore, it is expected that the tensile stress is redistributed by yielding adjacent to the region between the bolt clearance hole and the free edge of the plate. On the other hand, the lower bound of nominal tensile capacities of the bolted washer clamp-up and CFRP reinforced steel plates, Fk, can be obtained from the product of (b0-dbh)/b0 and F0. 6

ACCEPTED MANUSCRIPT 3.3 Parameter variation analysis As indicated from Table 3 presented in the previous section, the load-deformation behaviour and the nominal tensile capacity of test specimens are subjected to different failure modes. To better understand related influences of bolted washer and CFRP strips, it is necessary to conduct parametric study through a comparison of the influences of the number of CFRP layers, the washer length and the bolt torque as follows.

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3.3.1 Effect of the number of CFRP layers

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Since the tensile stress is transferred from the steel to the CFRP strip, the increase of the number of CFRP layer is expected to enhance the stiffness of the layer itself. It is evident from Table 3, as the number of the CFRP layers is increased from single to triple, the open-hole and bolted steel plates mostly exhibit a transition from failure mode C1 or C2" to C2 (refer to Table 4), which means the interface failure between steel and CFRP strip is prone to occur. Visual inspection of Fig. 4 indicates that, with the increase of the number of CFRP layers, the nominal tensile capacity is enhanced whereas the deformation is reduced for the open-hole and bolted steel plates. This trend is similar for the specimens with 3mm thick and 6mm thick steel plates as shown in Fig. 4(a). For the purpose of comparing the strength enhancement and deformability reduction, the data of the specimen with open-hole only (i.e. without bolted washer clamp-up and CFRP reinforcement) was taken as the basic value with the suffix as “PR0, SD0”, and then the strength ratio, Kc, and deformation ratio, Dc, are represented by dividing the other data by the basic value. As shown in Fig. 5(a), the trend between Kc and the number of CFRP layers, nc, can be linearly correlated regardless of the size of the washer. The corresponding expression can be expressed as:

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(1) K c = 0.067 nc + 1.091 where, the strength ratios of 1.057 and 1.116 can be calculated for the cases when the number of CFRP layers are increased to double and triple respectively. On the other hand, regarding the trend of deformability in Fig. 5(b), the following second order polynomial regression can be given to correlate Dc and nc as:

Dc = 0.073nc2 − 0.354nc + 0.603

(2)

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3.3.2 Effect of washer length

As mentioned previously, the rectangular washers beneath the bolt head and nut distributes pressure on larger area than round washers. It can be observed from Fig. 6(a) and (b) that the yield loads of the specimens with bolted washer clamp-up are improved to some extent when comparing with that of the specimen with open-hole only (without bolted washer clamp-up and CFRP reinforcement). Likewise, the specimens with 6mm thick steel plates behave similarly with these with 3mm thick steel plates. It can be also indicated from Table 3 and Fig. 6(c) and (d) that the failure mode of C1 is likely to occur for the single CFRP layer reinforced specimens with larger washer length. This can be expected as the washer pressure lessens the CFRP declamination initiated at the edge of bolt clearance hole. For triple CFRP layered specimens, however, this effect is not obvious due to the presence of greater stiffness of CFRP layer itself. 7

ACCEPTED MANUSCRIPT The comparison of the ratio Kl of the strength of test specimens against that of the open-hole plate without CFRP reinforcement is shown in Fig. 7(a). It can be seen that the strengths of the specimens with CFRP reinforcement are further improved with the bolted washer clamp-up. The use of 30mm length washer greatly increases the strength of the specimen but the further strength enhancement becomes insignificant as the washer length increases from 30mm to 120mm. In addition, as shown in Fig. 7(b), the deformation ratio Dl exhibits a linear descending trend with the increase of the washer length as:

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(3) Dl = −0.005lw + 0.963 Such a decrease of the deformation ratio can be attributed to the fact that the greater washer length may limit the stress redistribution, resulting in lower deformability. However, this presumption may not be suitable for the specimen with 120mm washer in which the clamping effect becomes ineffective at the side of further length. 3.3.3 Effect of bolt torque

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Theoretically, the bolt clamp-up pressure is directly related to the bolt torque. As shown in Fig. 8, the enlargement of bolt torque moderately increases the strength of the specimens without CFRP reinforcement. Regarding the CFRP reinforced specimens, such increases are more significant especially for double layered specimens as shown in Fig. 9(a), which strength ratio can be linearly correlated with the input bolt torque value, Tin, as:

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(4) K t = 0.002Tin + 1.019 Likewise, the deformation ratio corresponding to the nominal tensile capacity is subjected to certain decrease with the increase of the bolt torque, as shown in Fig. 9(b). It is worthy of note that, however, the specimens seem to demonstrate notable residual behaviour for the specimens with higher bolt torque.

4. General analytical model for stress analysis

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The experimental results mentioned in the preceding sections indicate that a complex aspect of the CFRP strengthened tensile plates involves the interfacial failure mode between the carbon fibre strip and the steel plate. The interfacial failure is mainly defined for the failure mode C2 and C2”. In existing methods, such as Taljsten [26] and Smith and Teng [27], the general solutions are proposed by assuming that interfacial stresses do not vary across the adhesive layer thickness. Similarly, such an assumption is also introduced in the analytical model for the evaluation of the reinforcement effect of CFRP and bolt torque herein. Besides, regarding the loading condition by referring to Fig. 10, additional assumptions are made as follows: ·

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The plate has symmetry about longitudinal and transverse planes, i.e. planes passing the midline of plate thickness and the midline of longitudinal length. Hence, the external uniaxial loads are unable to induce bending moment about either x axis or y axis. Out-of-plane force and displacement perpendicular to the x-y plane are not applied so that the analytical model is simplified to a two dimensional problem. The adhesive layer is subjected to uniform shear stress condition between the carbon fibre strip 8

ACCEPTED MANUSCRIPT and the steel plate. ·

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The geometry of the carbon fibre strip, the adhesive and the steel plate are assumed to be of nominal values of thickness and length. The normal force (Fn) induced by the bolt preload renders identical compression distributed on the carbon fibre strip, the adhesive and the steel plate.

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Since the von-Mises yield theory generally gives results that are in good agreement with the test data for ductile materials, it was also employed as the failure criterion to correlate the yielding in uniaxial tests with that in the normal direction of loading. Considering the loads in shear and out-of-plane are disregarded in the analytical model, the expression in accordance with the von-Mises theory can be simplified as: (5)

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σ e2 = σ x2 + σ y2 − σ xσ y

σ x = 0.5σ y + (σ e2 − 0.75σ y2 )

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where, σe is material strength obtained from a uniaxial tension test. σx and σy are the stresses in the two orthogonal directions due to the tension load. When the stress (σy) is present, the stress in axial direction (σx) can be calculated following a transformation as: 0.5

(6)

Therefore, the strength enhancement ratio, Rn, to be introduced into the expression for the axial force allowing for the compression is: 2 0.5 (7) σn   σn   Rn = = 0.5   + 1 − 0.75    σ x σ =σ =0  σ e    σ e   y n where, σn is the normal stress and can be obtained as Fn/An. The compression area, An, can be determined as the clamp-up area of the rectangular washer in contact with the bolt head and nut. The general torque equation [28, 29] relating input bolt clamp-up torque value (Tin) to the preload (Fn) can be referred as: y =σ n ≠ 0

Tin = Fp Kdsh

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σx σ

(8)

5T Fn = in d sh

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where, K is the dimensionless nut factor, which can be taken as 0.2 for steel fasteners used in steel joints. Meanwhile, given the normal force is governed by the initial bolt tensioning, Fn can be regarded as equal to Fp, and then Fn can be recast into: (9)

As shown in Fig. 10, the steel plate is subjected to horizontal tensile force from the plate end, in addition to the compression that may occur from above mentioned bolt preload. The force equilibrium to the applied horizontal force pattern can be considered for the external tensile force, T, as: T = Fs + 2 Fc

(10) 9

ACCEPTED MANUSCRIPT where, Fs and Fc are tensile forces in steel plate and carbon fibre strip respectively. As the strip in a unit width, ds, is considered, the internal force equilibrium in the steel plate and its bonded carbon fibre strip can be expressed as:

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∂Fs (11) + 2τ a ds = 0 ∂x ∂Fc (12) − τ a ds = 0 ∂x where, τa is the shear stress of the adhesive layer. Similarly, the corresponding internal strain equilibrium can be given as:

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∂δ s F = s ∂x Es As

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∂δ c F = c ∂x Ec Ac

(13)

(14)

where, the symbols of δ, E and A denote the element displacement, elastic modulus and cross sectional area respectively while the suffixes s and c represent the steel plate and carbon fibre respectively. In light of uniform shear stress between the carbon fibre strip and the steel plate, the shear strain, γa, and its equilibrium relation [30] at the adhesive layer can be written as:

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δc − δs

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γa =

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(15)

where, Ga and ta are the shear modulus and thickness of the adhesive layer respectively. Eq. (15) can be further transformed into the form as: Ga (δ c − δ s ) ta

(16)

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τa =

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Substituting Eqs. (13) and (14) into Eq. (16) and differentiating the resulting equation once yields:

∂τ a Ga  Fc F  = − s   ∂x ta  Ec Ac Es As 

(17)

and then further substituting Eqs. (11) and (12) into Eq. (17) and differentiating the resulting equation once again yields:

∂ 2τ a Ga ds  1 2  − +  τ a = 0 2 ∂x ta  Ec Ac Es As 

(18)

The general solution to above linear second-order differential equation is:

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ACCEPTED MANUSCRIPT (19)

τ a = C1eλ x + C2 e− λ x where,

(20)

G ds  1 2  λ = a  +  ta  Ec Ac Es As  2

Fs = − Fc =

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(C e

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(C e λ

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− C2 e − λ x ) + Cs

− C2 e − λ x ) + Cc

(21) (22)

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Recalling Eq. (10) in relation with Eqs. (21) and (22) yields:

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By substituting Eq. (19) into Eqs. (11) and (12) and integrating them once gives:

T  1 2  Cs = +   Ec Ac  Ec Ac Es As  T  1 2  + Cc =   Es As  Ec Ac Es As 

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(23) T = Cs + 2Cc Applying the obtained relation of Eq. (23) into Eq. (21), the constant of Cs can be replaced by T-2Cc. Subsequently, substituting transformed Eq. (21) and Eq. (22) into the governing differential equation of Eq. (17), Cs and Cc can be obtained as: −1

−1

(24) (25)

Fs = −

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(C e

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− C2 e

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Therefore, Fs and Fc can be obtained by substituting Eqs. (24) and (25) into Eqs. (21) and (22) as:   ) + ETA  E 1A + E2A  c c  c c s s 

−1

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T  1 2  Fc = ( C1e − C2 e ) + + (27)   λ Es As  Ec Ac Es As  The constants C1 and C2 can be evaluated using two boundary conditions corresponding to the zero shear stress of the adhesive in shear at the centre of the steel plate and the zero tensile force of the carbon fibre strip at its end (lx=l0) as: λx

−λ x

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=0

(28)

Once the above boundary conditions are applied, the constants of integration can be obtained as follows:

λT

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 1 2  C1 = −C2 = − + (29)   2 Es As cosh(λ l0 )ds  Ec Ac Es As  Therefore, Fs, Fc and τa can be calculated by substituting Eq. (29) into Eqs. (26), (27) and (19) respectively as:

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 1 2   1 2 cosh(λ x)  Fs = T  + +     Ec Ac Es As   Ec Ac Es As cosh(λ l0 ) 

(30)

−1

−1

RI PT

T  1 2   cosh(λ x)  Fc = + (31)   1 −  Es As  Ec Ac Es As   cosh(λ l0 )  λT sinh(λ x) τa = (32)  2 + Es As ( Ec Ac ) −1  cosh(λ l0 )ds   The strength ratio, Rc2, between the CFRP reinforced steel part involved with interfacial deterioration and un-reinforced steel part prior to CFRP debonding can be obtained as:

SC

T  1 2  1 2 cosh(λ x)  Rc2 = =  + + (33)   Fs  Ec Ac Es As   Ec Ac Es As cosh(λ l0 )  The above expression for Rc2 can be determined in terms of the tensile strength Fs(0) at the centre of the steel plate where the bolt hole exists.

M AN U

Apart from the interfacial failure mode between the carbon fibre strip and the steel plate, aforementioned failure mode C1 is characterized by the rupture of adhesively bonded CFRP strips along with the fracture of steel plate at the edge of the bolt clearance hole. Regarding this case, the corresponding strength ratio, Rc1, between the CFRP reinforced steel part and un-reinforced counterpart can be given as: 2σ c Ac (34) σ s As where, σs and σc are normal stresses of steel plate and carbon fibre respectively. Therefore, with the ratio of Rc1 or Rc2, the influence of CFRP reinforcement on the strength variation for primary failure modes of C1 and C2 can then be determined.

TE D

Rc1 = 1 +

5. Comparison of analytical results

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The strength enhancement effect from bolted washer clamp-up induced compression and further reinforced by CFRP reinforcement is compared in this section. The specimens with washer length varying from 30mm to 120mm were classified into three groups, i.e. (1) dsh=12mm and tw=3mm, (2) dsh=12mm and tw=6mm, (3) dsh=14mm and tw=6mm. The test strength ratios were calculated by dividing the strengths of the specimens with bolted washer clamp-up or CFRP reinforced by these of the open-hole plate without bolted washer clamp-up and CFRP reinforcement. In the analytical model based strength ratio calculation, Eq. (34) is used for the failure mode C1, while the failure mode C1” is approximated as the average value related to modes C1 and C2, i.e. 0.5(Rc1+Rc2), due to the consideration of the effect of partly debonding. For the failure modes C2 and C2”, Eq. (33) is used in the calculation of the strength ratio of test specimens. Besides, two contact areas in compression, An, were taken into account for comparison: (1) overall washer area, i.e. An=bwlw-0.25π(dsh)2; (2) effective clamp-up area with 45̊ stress dispersal of the bolt head or nut through the washer, i.e. A’n=0.25π[(dhm+2tw)2-(dsh)2], as shown in Fig. 10. As such, the strength ratios of Rn and R’n were calculated using Eq. (7) with the variables of An and A’n respectively. Based on the relations given above, only the overall washer area, An, is positive associated with the washer 12

ACCEPTED MANUSCRIPT length, lw. Hence, it can be inferred that, with the increase of lw, the normal stress, σn, which is equal to Fn/An, is reduced to some extent. This also results in the reduction of the strength enhancement ratio, Rn, by referring to Eq. (7).

SC

RI PT

The comparison of the strength ratios from above calculation and test data for the specimens with only bolted washer clamp-up is described as “Case 1” as shown in Fig. 11 (a). In this graph, Rt denotes the ratio of the strength of the specimens with bolted washer clamp-up to that of the bare steel plate based on the experimental data. Overall, both predicted strength ratios represent lower bounds in contrast to the experimental results. It is worth-noting, however, the predictions involved with the effective clamp-up area, i.e. R’n, agree better with test data especially when the washer lengths are greater than 60mm. This indicates that the effective compressive area induced by the bolted washer clamp-up on the steel plate is limited and unable to cover the whole contact area of the washer with greater length. As a result, the use of full size washer area in the calculation of Rn demonstrates moderate agreements of strength predicted only for the specimens with short washer with the length of 30mm and underestimated results for these with long washers.

TE D

M AN U

With regard to the specimens with bolted washer clamp-up and CFRP reinforcement, two cases were analyzed. In the “Case 2”, the additional contribution of single layer of CFRP was considered as the part of the strength ratio expressed by Eq. (34), i.e. Rc1, for the failure mode C1. For the failure mode C2, similarly, Rc2 is given by Eq. (33). Assembling aforementioned effect of the bolted washer clamp-up, the strength ratios allowing for the combined effect of clamp-up and CFRP reinforcement are then analytically predicted by RnRc2 and R’nRc2 when the overall washer area and effective clamp-up area are taken as the contact areas respectively. In the “Case 3”, double layer of CFRP was taken into account by using the strength amplification coefficient calculated from Eq. (1), i.e. [Kc]=1.057 allowing for the CFRP varying from single layer to double layer. Therefore, the strength ratio in this case for the failure mode C1 can be expressed as [Kc]Rc1, while that for the failure mode C2 can be given as [Kc]RnRc2 and [Kc]R’nRc2 likewise. For the sake of comparison, the experimental ratio of the strength of the specimens with bolted washer clamp-up and CFRP reinforcement to that of the bare steel plate is denoted as Rt herein.

AC C

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As evidenced from Fig. 11(b) and (c), the predicted strength ratio for the failure mode C1 agrees well with test data. Regarding the failure mode C2 and C2”, the predicted strength ratios with R’nRc2 and [Kc]R’nRc2 involving with effective clamp-up area, shows less underestimated results with respect to these with RnRc2 and [Kc]RnRc2. Notwithstanding this, notable difference can be observed especially for the specimens with washer length of 60mm and 120mm. This can be, on the other hand, attributed to the difference existing for the nonlinear stress distribution with the bolted washer clamp-up condition under the long washer which still needs further investigation.

6. Summary and conclusion This paper presents an experimental programme to develop an insight into the tensile behaviour of CFRP reinforced open-hole and bolted steel plates. The fabrication of the hole in this study was involved with laser cutting, which differs from conventional punched and drilled holes. The combined effects of bolted washer clamp-up and CFRP reinforcement on the tensile behaviour of the plate has not yet been fully understood. The experimental test was performed to study the strength and deformability of the open-hole and bolted steel plates with varying the number of 13

ACCEPTED MANUSCRIPT CFRP slayers, washer length and bolt torque. Typical failure modes in relation with these mechanical characteristics are examined. An analytical model taking into account the bolted washer clamp-up and the interfacial stress equilibrium between steel and CFRP was proposed and its effectiveness was discussed accordingly. The following conclusions can be drawn from the present investigation:

In relation to two failure modes, the specimens with CFRP reinforcement demonstrate two types of load-deformation curves, i.e. P1, brittle rupture without residual behaviour, and P2, moderate deformability with residual behaviour. The configuration of open-hole details were shown to be notch insensitive so that the effective cross-section ratio can be taken as the reference in the calculation of the lower bound of nominal tensile capacities of the bolted washer clamp-up and CFRP reinforced steel plates.

·

The yield load of the specimen with bolted washer clamp-up is significantly improved in contrast with that with open-hole only. The bolted washer clamp-up effect acts beneficially in the further strength improvement of the specimens with CFRP strips. With the increase of the washer length under the limit of 120mm, the deformability of the specimens is reduced following a linear correlation. The increase of bolt torque has significant effect on the enhancement of nominal tensile capacity and residual behaviour of the specimens with bolted washer clamp-up and CFRP reinforcement. Besides, such an increase becomes more obvious for the specimens with increased number of CFRP layers.

·

AC C

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·

The increase of the number of the CFRP layers significantly enhances the nominal tensile strength of the specimens which can be linearly correlated accordingly. Meanwhile, the corresponding deformability is reduced following second order polynomial regression and the interface between steel and CFRP is prone to fail under applied tensile load.

TE D

·

M AN U

SC

·

The steel plates with open-hole only or bolted washer clamp-up but no CFRP strips exhibit apparent local plasticity development between the bolt clearance hole and the plate free edge. For the specimens with CFRP strips, on the other hand, the primary failure modes are the rupture of CFRP and the steel-adhesive interface failure accompanied by CFRP splitting or delamination.

RI PT

·

The proposed analytical model has demonstrated its good applicability in the evaluation of the strength ratio of the specimens with bolted washer clamp-up and CFRP reinforcement in relation with test failure modes. Also, the definition of effective clamp-up area instead of overall washer area has been verified in achieving less underestimated prediction when compared with the test strength ratios. Notwithstanding this, further studies are still needed for the differences induced by the clamp-up conditions of the specimens with the washers in enlarged sizes.

Acknowledgements The research presented was sponsored by the National Natural Science Foundation of PR China (No. 51308363 and No. 11327801), the Scientific Research Foundation for the Returned Overseas 14

ACCEPTED MANUSCRIPT Chinese Scholars (No. 2013-1792-9-4), the Program for Changjiang Scholars & Innovative Research Team in University (No. IRT14R37) and the Key Science and Technology Support Programs of Sichuan Province (No. 2015GZ0245 and No. 2015JPT0001).

References

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1. Chesson JE, Munse WH. Riveted and bolted joints: truss-type tensile connections. Journal of Structural Engineering, ASCE, 1963, 89(2): 67-107. 2. Zhao XL, Zhang L. State-of-the-art review on FRP strengthened steel structures. Engineering Structures. 2007(29): 1808-1823. 3. Bocciarelli M, Colombi P. Elasto-plastic debonding strength of tensile steel/CFRP joints. Engineering Fracture Mechanics, 2012(85): 59-72. 4. Cadei JMC, Stratford TJ, Hollaway LC, Duckett WG. Strengthening metallic structures using externally bonded fibre-reinforced polymers, CIRIA, London, UK, 2004. 5. Colombi P. Reinforcement delamination of metallic beams strengthened by FRP strips: fracture mechanics based approach. Engineering Fracture Mechanics, 2006(73):1980–95. 6. Chiew SP, Yu Y, Lee CK. Bond failure of steel beams strengthened with FRP laminates-Part 1: Model development. Composites Part B: Engineering, 2011(42): 1114-1121. 7. Teng JG. FRP-Strengthened RC Structures[M]. New York: Wiley, 2002 8. ASTM-D5766/D5766M-11, Standard test method for open-hole tensile strength of polymer matrix composite laminates, ASTM International, United States, 2011. 9. de Morais AB. Open-hole strength of quasi-isotropic laminates. Composite Science Technology. 2000(60):1997-2004. 10. Wang J, Callus PJ, Bannister MK. Experimental and numerical investigation of the tension and compression strength of un-notched and notched quasi isotropic laminates. Composite Structures. 2004(64): 297-306. 11. Prabhakaran R, Razzaq Z, Devara S. Load and resistance factor design (LRFD) approach for bolted joints in pultruded composites. Composites Part B: Engineering, 1996(27): 351-360. 12. Caminer, MA, Lopez-Pedrosa M, Pinna C, Soutis C. Damage monitoring and analysis of composite laminates with an open hole and adhesively bonded repairs using digital image correlation. Composites Part B: Engineering, 2013(53): 76-91. 13. Lee, Young-Geun; Choi, Eunsoo; Yoon, Soon-Jong. Effect of geometric parameters on the mechanical behavior of PFRP single bolted connection. Composites Part B: Engineering, 2015(75): 1-10. 14. Wang P, He R, Chen H, Zhu X, Zhao Q, Fang D. A novel predictive model for mechanical behaviour of single-lap GFRP composite bolted joint under static and dynamic loading. Composites Part B: Engineering, 2015(79): 322-330. 15. Chesson JE, Munse WH. Riveted and bolted joints: truss-type tensile connections. Journal of Structural Engineering, ASCE, 1963, 89(2): 67-107. 16. Rassati GA, Swanson JA, Yuan Q. Investigation of hole making practices in the fabrication of structural steel. American Institute of Steel Construction, 2004. 17. Frank KH. Influence of hole making process upon the tensile strength of steel plates. TxDOT Research Publication 2002(5): 1-9. 18. Yilbas BS, Akhtar SS, Keles O. Laser cutting of small diameter hole in aluminium foam. 15

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International Journal of Advanced Manufacture Technology, 2015(79): 101-111. 19. Brown JD, Lubitz DJ, Cekov YC, Frank KH, Keating PB. Evaluation of influence of hole making upon the performance of structural steel plates and connections. Report No. 0-4624-1, Center for Transportation Research, The University of Texas at Austin, 2007. 20. Colombi P, Poggi C. Strengthening of tensile steel members and bolted joints using adhesively bonded CFRP plates. Construction and Building Materials, 2006, 20(1-2): 22-33. 21. Colombi P, Bassetti A, Nussbaumer A. Analysis of cracked steel members reinforced by pre-stress composite patch. Fatigue Fracture of Engineering Materials Structures 2003(26): 59–66. 22. Penagos-Sanchéz DM, Légeron F, Demers M, Langlois S. Strengthening of the net section of steel elements under tensile loads with bonded CFRP strips. Journal of Composites for Construction, ASCE, 2015, 19(6): 67-107. 23. GB/T700-2006. Carbon structural steels. Beijing: Standards Press of China (in Chinese), 2007. 24. GB/T1591-2008. High strength low alloy structural steels. Beijing: Standards Press of China (in Chinese), 2009. 25. Product data sheet of Sikadur-330. Sika Limited. 26. Taljsten B. Strengthening of beams by plate bonding. Journal of Material Civil Engineering, ASCE, 1997, 9(4):206-12. 27. Smith ST, Teng JG. Interfacial stresses in plated beams. Engineering Structures. 2001(23): 857-871. 28. Bickford JH. Introduction to the design and behaviour of bolted joints. CRC Press, Taylor & Francis Group, Boca Raton, 2008. 29. Wang ZY, Wang QY. Yield and ultimate strengths determination of a blind bolted endplate connection to square hollow section column. Engineering Structures, 2016(111): 345-369. 30. Gaylord CN, Gaylord EH. Design of Steel Structures. New York: McGraw-Hill, 1972.

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ACCEPTED MANUSCRIPT Table 1 Illustration of test specimens Specimen index

Exampling graph

Basic geometry (mm)

T6-H-P0-S0

0

p

=30 0

=30

T6-B-PR30-S0-T80

w

sh

+

0

RI PT

+

=200

Bolt hole

1

=

=300

bh

T6-B-PR60-SD1L-T80

Bolt hole

T6-B-PR90-S0-T80

w

Bolt Washer plate

CFRP

M AN U

SC

T6-B-PR60- SD3L-T80

Loading

TE D

Extensometer

Reaction

Fig. 1 Test set-up

AC C

EP

Specimen

Table 2 Chemical compositions and mechanical properties of test materials

Chemical compositions (%) Mechanical properties (MPa) C Si Mn P S Yield stress Ultimate stress Steel (3mm thick plate) 0.12 0.18 0.38 0.025 0.023 272 341 Steel (6mm thick plate) 0.17 0.25 1.15 0.015 0.014 388 553 4216 Carbon fibre (UT70-30) Elastic Technical data Adhesive modulus strength (MPa) Mix ratio Density Pot life (MPa) Adhesive/epoxy resin 4500 30 A:B=4:1 1.3kg/l 30:90min=35:15ºC (Sikadur-330*) Materials

*

Note: Appearance contains resin part A in white colour and hardener part B in grey colour. 1

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Table 3 Test matrix

TE D

Test results δk Fr δr F /F (mm) (kN) (mm) k 0 2.08 - 0.81 1.45 - 0.90 1.38 - 0.93 1.03 - 0.94 0.61 19.85 2.52 1.19 0.39 - 1.20 0.13 - 1.19 3.44 - 0.64 1.33 - 0.75 0.76 48.66 1.08 0.79 0.61 45.69 0.88 0.82 2.59 - 0.69 0.80 59.39 2.00 0.75 0.66 59.28 2.24 0.78 0.56 58.15 2.89 0.82 2.28 - 0.69 0.62 - 0.75 0.46 53.38 0.59 0.79 0.37 60.23 2.29 0.81 2.18 - 0.68 0.58 - 0.75 0.39 - 0.79 0.30 61.24 1.86 0.83 2.13 - 0.70 0.94 61.69 2.11 0.76 0.81 61.74 1.83 0.78 0.63 59.78 1.74 0.79 2.38 - 0.59 2.72 - 0.59 2.29 - 0.56 2.43 - 0.54 2.19 - 0.58 2.47 - 0.61 0.73 44.25 2.23 0.61 0.84 48.49 1.94 0.66 0.94 - 0.76 1.06 47.94 2.24 0.81 0.64 49.34 1.30 0.64 0.95 59.02 1.91 0.79

SC

RI PT

Washer CFRP Failure layer lw Fk mode (mm) nCFRP (kN) C0 19.86 30 C0 22.18 60 C0 22.92 90 C0 23.12 1 C2" 29.32 30 1 C2 29.61 60 1 C2 29.29 C0 54.81 1 C1 64.33 2 C2" 68.06 3 C2" 70.15 30 C0 59.56 30 1 C2" 64.56 30 2 C2 67.01 30 3 C2 70.78 60 C0 59.00 60 1 C2" 64.29 60 2 C2" 68.02 60 3 C2" 70.01 90 C0 58.58 90 1 C1 65.82 90 2 C1" 67.80 90 3 C2 71.12 120 C0 60.47 120 1 C2 65.66 120 2 C2" 67.10 120 3 C2" 68.23 C0 50.60 C0 50.94 90 C0 48.51 90 C0 46.24 30 C0 49.95 30 C0 52.11 90 1 C2" 52.50 90 1 C2" 57.02 90 2 C1 65.53 90 2 C1 70.12 30 1 C2" 55.36 30 2 C1 67.61

M AN U

Bolt dbh dsh Torque (mm) (mm) (N·m) 12.5 12.5 12 80 12.5 12 80 12.5 12 80 12.5 12.5 12 80 12.5 12 80 12.5 12.5 12.5 12.5 12.5 12 80 12.5 12 80 12.5 12 80 12.5 12 80 12.5 12 80 12.5 12 80 12.5 12 80 12.5 12 80 12.5 12 80 12.5 12 80 12.5 12 80 12.5 12 80 12.5 12 80 12.5 12 80 12.5 12 80 12.5 12 80 15.1 14 60 15.1 14 120 15.1 14 60 16.0 14 120 15.1 14 60 15.0 14 120 16.0 14 60 15.9 14 120 15.9 14 60 16.0 14 120 16.2 14 120 16.1 14 120

AC C

T3-H-P0-S0 T3-B-PR30-S0-T80 T3-B-PR60-S0-T80 T3-B-PR90-S0-T80 T3-H-P0-SD1L T3-B-PR30-SD1L-T80 T3-B-PR60-SD1L-T80 T6-H-P0-S0 T6-H-P0-SD1L T6-H-P0-SD2L T6-H-P0-SD3L T6-B-PR30-S0-T80 T6-B-PR30-SD1L-T80 T6-B-PR30-SD2L-T80 T6-B-PR30-SD3L-T80 T6-B-PR60-S0-T80 T6-B-PR60-SD1L-T80 T6-B-PR60-SD2L-T80 T6-B-PR60-SD3L-T80 T6-B-PR90-S0-T80 T6-B-PR90-SD1L-T80 T6-B-PR90-SD2L-T80 T6-B-PR90-SD3L-T80 T6-B-PR120-S0-T80 T6-B-PR120-SD1L-T80 T6-B-PR120-SD2L-T80 T6-B-PR120-SD3L-T80 T6-B-NC-S0-T60 T6-B-NC-S0-T120 T6-B-PR90-S0-T60 T6-B-PR90-S0-T120 T6-B-PR30-S0-T60 T6-B-PR30-S0-T120 T6-B-PR90-SD1L-T60 T6-B-PR90-SD1L-T120 T6-B-PR90-SD2L-T60 T6-B-PR90-SD2L-T120 T6-B-PR30-SD1L-T120 T6-B-PR30-SD2L-T120

Plate tp (mm) 3 3 3 3 3 3 3 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

EP

Specimen index

Note: Fk and δk denote the nominal tensile strength and its corresponding deformation. Fk=Fn,rc and δk=δn,rc for tensile plates reinforced by CFRP strips while Fk=Fn,uc and δk=δn,uc for tensile plates un-reinforced by CFRP strips.

2

ACCEPTED MANUSCRIPT 800

6mm thick plate

Stress, σ (MPa)

600

400

0 0

0.1

0.2

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3mm thick pla te

200

0.3

Strain, (%)

Fig. 2 Stress-strain curves of steel materials Table 4 Illustration of test failure modes Exampling graph

SC

Failure mode C0

M AN U

C1

C2

k

=

n,rc

or

n,uc

n,rc

(kN)

P1 P2

P0

n,uc

Applied load,

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C2"

TE D

C1"

r

n,rc

Deformation,

r

n,uc

(mm)

Fig. 3 Definition of F-δ characterizing curves 3

ACCEPTED MANUSCRIPT T6-H-P0-SD1L

T6-H-P0-SD2L

T6-H-P0-SD3L

T3-H-P0-S0

T3-H-P0-SD1L

80

40

20

60

40 T6-B-PR30-S0-T80 T6-B-PR30-SD1L-T80 T6-B-PR30-SD2L-T80 T6-B-PR30-SD3L-T80

20

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Applied load, F (kN)

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Applied load, F (kN)

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Displacement, δ (mm)

(a) Group of un-reinforced specimens

T6-B-P60-S0-T80 T6-B-PR60-SD1L-T80 T6-B-PR60-SD2L-T80 T6-B-PR60-SD3L-T80

20

RI PT

60

T6-H-P0-S0

Applied load, F (kN)

Applied load, F (kN)

80

40

T6-B-PR90-S0-T80 T6-B-PR90-SD1L-T80 T6-B-PR90-SD2L-T80 T6-B-PR90-SD3L-T80

20

0

0 0

1

2

3

4

0

5

1

2

3

4

5

Displacement, δ (mm)

TE D

Displacement, δ (mm)

1.5 PR30

1.4

PR60

Kc = 0.067nc + 1.091

PR90

1.3

PR120

1.2 1.1 1

0

1

2

1

Deformation ratio, Dc=δPRi,SDi/δPR0,SD0

EP

P0

AC C

Strength ratio, Kc=FPRi,SDi/FPR0,SD0

(c) Group of PR60 washer clamp-up specimens (d) Group of PR90 washer clamp-up specimens Fig. 4 Comparison of F-δ relations of specimens reinforced with different CFRP layers

0.75

P0

PR30

PR60

PR90

PR120

0.5 D c = 0.073(nc)2 - 0.354nc + 0.603

0.25

0

3

Number of CFRP layers, nc

4

0

1

2

3

4

Number of CFRP layers, n c

(a) Comparison of strength ratio (b) Comparison of deformation ratio Fig. 5 Effect of the number of CFRP layers on the strength and deformation of test specimens

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ACCEPTED MANUSCRIPT 80

30

20

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0

60

40 T6-H-P0-S0 T6-B-PR30-S0-T80 T6-B-PR60-S0-T80 T6-B-PR90-S0-T80

20

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Applied load, F (kN)

40

0 0

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Displacement, δ (mm)

Applied load, F (kN)

T3-B-PR30-SD1L-T80 T3-B-PR60-SD1L-T80

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60

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80

T3-H-P0-SD1L

40

T6-H-P0-S0 T6-H-P0-SD1L-T80 T6-B-PR30-SD1L-T80

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(c) Group of specimens with single CFRP layer (3mm)

60

AC C

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20

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1

2

T6-H-P0-S0 T6-H-P0-SD2L-T80 T6-B-PR30-SD2L-T80 T6-B-PR60-SD2L-T80 T6-B-PR90-SD2L-T80

3

4

5

(d) Group of specimens with single CFRP layer (6mm) 80

Applied load, F (kN)

EP

80

2

Displacement, δ (mm)

Displacement, δ (mm)

Applied load, F (kN)

4

(b) Group of un-reinforced specimens (6mm)

T3-H-P0-S0

30

3

Displacement, δ (mm)

(a) Group of un-reinforced specimens (3mm) 40

2

60

40 T6-H-P0-S0 T6-H-P0-SD3L-T80 20

T6-B-PR30-SD3L-T80 T6-B-PR60-SD3L-T80 T6-B-PR90-SD3L-T80

0 3

Displacement, δ (mm)

4

5

0

1

2

3

4

5

Displacement, δ (mm)

(e) Group of specimens with double CFRP layer (f) Group of specimens with triple CFRP layer Fig. 6 Comparison of F-δ relations of specimens reinforced with different washer clamping condition

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1.2 1

0.6

P0

SD1

SD2

SD3

0.4 0

30

60

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120

150

P0

SD1

SD2

SD3

1.4 1.2 1 Dl= -0.005lw + 0.963

0.8 0.6 0.4 0

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1.4

0.8

1.6

Deformation ratio, Dl=δPRi,SDj/δPRj,SDj

Strength ratio, Kl=FPRi,SDj/FPR0,SD0

1.6

30

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Washer length, lw (mm)

80

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Applied load, F (kN)

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(a) Comparison of strength ratio (b) Comparison of deformation ratio Fig. 7 Effect of washer length on the strength and deformation of test specimens

T6-B-NC-S0-M14-60 T6-B-NC-S0-M14-120 T6-B-PR30-S0-M14-60 T6-B-PR30-S0-M14-120 T6-B-PR90-S0-M14-60 T6-B-PR90-S0-M14-120

20

60

40

T6-B-PR90-SD1L-M14-60 T6-B-PR90-SD1L-M14-120

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4

0

5

1

2

3

4

5

Displacement, δ (mm)

Displacement, δ (mm)

1.4 1.2 1 0.8

Deformation ratio, DtFTini,SDj/FTin0,SDj

EP

1.6

AC C

Strength ratio, Kt=FTini,SDj/FTin0,SDj

(a) Group of specimens without CFRP reinforcement (b) Group of specimens with CFRP reinforcement Fig. 8 Comparison of F-δ relations of specimens with different bolt torque

K t = 0.002Tin + 1.019

P0 SD1 SD2

0.6 0.4 0

30

60

90

Bolt torque, Tin (N· m)

120

150

1.4 P0

1.2

SD1 SD2

1 0.8 0.6 0.4 0.2 0

30

60

90

120

150

Bolt torque, Tin (N· m)

(a) Comparison of strength ratio (b) Comparison of deformation ratio Fig. 9 Effect of bolt torque on the strength and deformation of test specimens 6

ACCEPTED MANUSCRIPT

i

n

hm

Carbon fibre

i

ii

c

c

c

+d(

c

e

)

ii

hm

a

Adhesive

a

45

w

s

45

o

RI PT

a

o

sh

bh

0.5

0.5

Steel plate

s

s+

0.5d( s )

w

x

SC

Fig. 10 Differential segment of internal and external force on CFRP laminates

1.4

M AN U

1.4

Rn R'n Rt

1.1

1.25

Strength ratio

Strength ratio

1.25

1.1

RnRc2 or Rc1 R'nRc2 or Rc1 Rt

0.95

0.95

0.8

0

30

60

TE D

0.8 90

120

0

150

30

Washer length, lw (mm)

60

90

120

150

Washer length, lw (mm)

(a) Case 1: washer clamp-up and no CFRP reinforcement

(b) Case 2: washer clamp-up and single layered CFRP reinforcement

EP

1.4

AC C

Strength ratio

1.25

1.1

[Kc]RnRc2 or [Kc]Rc1 [Kc]R'nRc2 or [Kc]Rc1 Rt

0.95

0.8 0

30

60

90

120

150

Washer length, lw (mm)

(c) Case 3: washer clamp-up and double layered CFRP reinforcement Fig. 11 Comparison of predicted and experimental strength ratio of the group of specimens under clamp-up stress with or without CFRP reinforcement

7