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Experimental and analytical investigation of two- and six-plate bonded splice joints on serviceability limit deformations of pultruded GFRP beams
Composite Structures 111 (2014) 426–435
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Experimental and analytical investigation of two- and six-plate bonded splice joints on serviceability limit deformations of pultruded GFRP beams G.J. Turvey ⇑ Engineering Department, Lancaster University, Bailrigg, Lancaster LA1 4YR, UK
a r t i c l e
i n f o
Article history: Available online 27 December 2013 Keywords: Adhesive bonding Beams GFRP Pultrusion Splice joints
a b s t r a c t Six four-point flexure tests on 3 m span pultruded glass fibre reinforced polymer (GFRP) 152 152 6.4 mm Wide Flange (WF) beams with two- and six-plate mid-span bonded splice joints are described. The pultruded GFRP splice plates were 6.4 mm thick with two widths and three lengths and their rovings were parallel to their lengths. The beams were loaded to their deflection serviceability limit. Mid-span deflections, support rotations and splice joint end rotations were recorded. Their load versus deflection and support rotation responses were linear and repeatable. New shear-deformable beam equations were used to predict the spliced beam deformations. For major-axis flexure, deflections were predicted reasonably accurately for both joint layouts when the beam’s experimentally determined longitudinal elastic modulus was used. Major and minor-axis support rotations were predicted with maximum errors of 15% and 25% respectively. Generally, splice joint rotational stiffnesses were poorly predicted. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Splice joints are used to join standard length steel or aluminium beams end-to-end in order to form longer beams for use in continuous span bridges. Continuity greatly improves flexural stiffness compared to a series of simply supported, single-span beams. In continuous beams splice joints are generally located at or near to a point of contra-flexure (the point in the span where the bending moment is zero). Sometimes splice joints may be used at interior supports to create continuity between adjacent simply supported beams. In the latter situation, a stiffer/stronger splice joint would be required to resist the high bending moment at the support compared to the low moment close to or at a point of contra-flexure within the span. It should be appreciated that, in both situations, the splice plates may increase the flexural stiffness locally compared to that of the original unspliced beam. At first sight, it may appear somewhat perverse to locate a splice joint at a point of contra-flexure, especially as a pin joint should suffice. However, practical issues such as: the relative costs of pin and bolted splice joints, the consequences of failure within the joint types and the fact that the points of contra-flexure may vary for different loading situations, all work in favour of bolted splice joints. ⇑ Tel.: +44 (0)1524 593088. E-mail address: [email protected] 0263-8223/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compstruct.2013.12.022
Splice joints may also be used to repair beams which have suffered local damage due to impacts of various kinds. The damaged parts may be straightened or cut out and a spliced joint may be used to restore the beam’s structural integrity. In steel and aluminium beams the splice plates may be joined to the flanges and/or webs by means of welding or mechanical fastening, though the latter appears to be more common. At the present time structural grade pultruded glass fibre reinforced polymer (GFRP) composite beams are only available offthe-shelf with maximum depths of 300 mm. This depth limitation, combined with the relatively low flexural stiffness of GFRP, dictates that the use of pultruded GFRP beams in bridges is restricted to short, single-span, simply supported footbridges. By using splice joints to create continuity, pultruded GFRP beams could be used more efficiently in longer, multi-span footbridges. However, before this situation may be realised, it is not only necessary to develop knowledge and understanding of the stiffness and strength characteristics of splice joints, but also to determine how they affect the structural behaviour of pultruded GFRP spliced beams. It appears that the earliest flexural tests on splice-jointed pultruded GFRP beams were reported in 1998 by Nagaraj and Gangarao [1]. All of their tests were carried out on 102 102 6 mm Wide Flange (WF) and box-section beams with mid-span splice plates bolted or bolted and bonded to the flanges and web(s) by six, staggered 9.5 mm diameter bolts per splice plate. Eight splice
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plates were used to form the joint in the WF section and four to form the box-section joint. Each pultruded GFRP splice plate was 12.7 mm thick, i.e. more than twice the thickness of the flanges and webs of the WF and box-section profiles. Not all of the lengths and widths of the rectangular splice plates were specified, though the splice plates connecting the flanges of the WF section were 254 mm long. The web splice plates of the WF section were longer than the flange splice plates, whereas the reverse was the case for the box-section. The reasons for this are not explained in [1]. Likewise, the precise locations of the bolts in the splice plates are not given and the rationale for the asymmetric bolt stagger is not explained. Furthermore, there is no mention of any difficulties associated with bolting the splice plates to the webs and flanges of such a small box-section beam. All the spliced beam tests reported in [1] had a span of 1.828 m. Most of the beams were subjected to symmetric three-point cyclic loading in order to determine their fatigue strengths. However, a number of static three and four-point flexure tests were also carried out to provide benchmark strengths, so that the reduction in their flexural strengths due to fatigue could be quantified. Static analyses of the latter tests were also undertaken, but no generalised formulae were developed for the deflections of beams with bolted splice joints. In 2005 Keller and Castro [2] reported the results of several tests to failure on two-span unspliced and spliced 240 240 12 mm box-section pultruded GFRP beams. Both spans were 3.6 m long. A symmetrical loading arrangement was used, i.e. single vertical loads of equal magnitude were applied on opposite sides of the interior support at 1.2 m from it. In four of the beams continuity over the interior support was provided by splice plates bonded to the outer faces of the flanges. The overall lengths of the splice plates varied from 200 mm to 600 mm. The main thrust of the test work was to demonstrate that system ductility could be created in inherently brittle GFRP continuous beams by means of extensionally flexible bonded splice joints. In [2] a simplified approach was used to analyse the behaviour of the two-plate bonded splice joints at the interior support of the two-span box-section beams. The splice plate bonded to the top flange was modelled as a single-lap tension joint and expressions for the rotational and strength capacities of the box-section’s bonded splice joint were derived. This simplified approach worked reasonably well, but ignored the eccentric moment in the singlelap joint and the fact that the splice plate bonded to the soffit of the box-beam at the interior support was not only subjected to in-plane compression but also to normal compression from the support reaction. In addition, the model assumed that the centre of rotation was at the mid-depth of the box-section. Subsequently, the methodology, reported in [2], was formulated into a design procedure for Fibre-Reinforced Polymer (FRP) beams with ductile bonded splice joints [3]. In 2010 Turvey [4] reported three, major and minor-axis, fourpoint bending tests on pultruded GFRP 152 152 6.4 mm WF beams with two-plate bonded splice joints at their mid-spans. The 152 mm wide splice plates were cut out of 6.4 mm thick pultruded GFRP plate and had lengths of 210, 410 and 610 mm, i.e. a different length was used with each beam. The beams were loaded to produce mid-span deflections of span/200, i.e. slightly greater than the deflection serviceability limit given in [5]. More often than not, the latter limit state governs the design of pultruded GFRP beams. The purpose of the four-point flexure tests was not only to quantify the transverse stiffnesses and support rotations of the beams, but also to determine the moment – rotation characteristics of their mid-span bonded splice joints. At this location, the splice joints were subjected to pure bending. A spliced beam flexural analysis, based on classical shear-rigid small deflection beam theory, was developed in conjunction with
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the test work reported in [4]. Explicit formulae for the mid-span deflection, support rotations and splice joint end rotations were presented and it was shown that, provided measured rather than design manual [6] elastic moduli were used, reasonably good correlation between measured and predicted deflections, up to the deflection serviceability limit state, could be expected. More recently a three-point bending investigation of 152 152 6.4 mm pultruded GFRP beams with six 6.4 mm thick pultruded GFRP plates forming bonded splice joints at mid-span has been reported in [7]. In [7] it was also shown that deflections and support rotations up to the serviceability limit could be predicted adequately by analysis, provided test coupon values of the longitudinal elastic modulus of the beam were used. The closedform formulae for the spliced beam’s mid-span deflection and support rotations were derived from an analysis of a shear-deformable tip-loaded cantilever with a bonded splice joint at its built-in end. The analysis was extended by deriving equations to determine optimum and limiting splice plate lengths based on transverse stiffness considerations. The equations were also used in parameter studies to quantify the effects of specific splice joint properties, namely adhesive modulus and thickness, splice plate material (GFRP or CFRP) and splice plate length, on reducing mid-span deflections. In 2012 Hai and Mutsuyoshi [8] reported the results of two four-point flexure tests on pultruded hybrid fibre (HF) I-section beams with mid-span, double-lap, bolted and bonded splice joints. The HF flanges comprised both GFRP and Carbon Fibre Reinforced Polymer (CFRP) composite materials and the webs were all-GFRP. Furthermore, the flange and web splice plates were made of steel and their bonded surfaces were serrated to improve the bond strength. Two layouts of 10 mm diameter stainless steel bolts were used. The beams were tested to failure and their failure modes were recorded. A three-dimensional finite element model was used to simulate the tests and reasonable correlation was obtained with the experimental failure loads. It was only after completing the investigation, reported in [4], that it was appreciated that the beams with two-plate bonded splice joints at their mid-spans ought to have four additional splice plates bonded to the inner surfaces of their flanges to create sixplate bonded splice joints. The beams could then be re-tested in four-point flexure and the effects of the two joint configurations on the pultruded GFRP spliced beams’ responses could be compared. In addition, it was recognised that a generalised first-order shear-deformable, four-point flexure analysis of beams with midspan splice joints should also be undertaken. Completion of this work led to new closed-form equations for mid-span deflection, support rotations and splice joint end rotations. These equations have been used to predict (with varying degrees of accuracy) the deformations recorded in the spliced beam tests and new experimental and analytical results comparisons are reported. Elastic moduli of the pultruded GFRP beam and splice plate materials are introduced first. Details are then given of the beam and splice plate geometries and the splice joint layouts. This is followed by a description of the procedures used in the fabrication of the spliced beams. Thereafter, the beam test setup, instrumentation and test procedure are explained. Load – deflection, support rotation – load and moment – splice joint rotation data are presented to demonstrate the repeatability of the experimental procedure. An explanation is given of the new generalised closed-form equations, which take account of shear deformation, developed for four-point flexural analysis of the pultruded GFRP spliced beams. They are then used to predict mid-span deflections, support rotations and splice joint flexural stiffnesses observed in the fourpoint flexure tests and experimental – analytical results comparisons are presented and discussed. Finally, conclusions are drawn regarding the relative accuracy of these comparisons.
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2. Elastic moduli of the pultruded GFRP beams and splice plates In the present investigation, the pultruded GFRP beams were 152 152 6.4 mm WF profiles and the rectangular splice plates were cut out of 6.4 mm thick pultruded GFRP plate with their longer sides parallel to the pultrusion direction. The WF profiles and splice plates incorporate E-glass rovings (bundles of parallel fibres) stabilised in a thermoset polyester resin which usually contains a small quantity of chalk or clay filler (typically 5% to 10% by volume). In the WF profiles the rovings are closely packed transversely, whereas in the plate material they are discretely spaced transversely, so that the volume percentage of glass in the WF profiles (typically 40%) is higher than that in the 6.4 mm thick splice plates, which is about 30%. Rectangular coupons, cut out of the flanges and webs of the pultruded WF profiles and the plate, have been tested untabbed in tension to determine their longitudinal elastic moduli. Separate tests were not undertaken, as part of this investigation, to determine their in-plane shear moduli. However, in a previously unreported investigation such tests were undertaken and shear moduli were obtained for the WF profile, which were slightly higher than the shear moduli reported in the manufacturer’s design manual [6]. As similar data was not available for the pultruded plate, it was decided to use the value given in [6] for all of the subsequent calculations of spliced beam deflections. The average longitudinal elastic moduli obtained from the tension tests on the WF profile and the 6.4 mm thick plate coupons are given in Table 1, where they are compared with the manufacturer’s minimum values in [6]. It is evident that the average longitudinal elastic moduli are about 23% higher than the minimum values. 3. Spliced beam components and splice joint fabrication Fig. 1a shows the cross-sections of the two and six-plate bonded splice joints at the mid-span of a spliced beam and Fig. 1b shows a side elevation of a six-plate bonded splice joint. It was decided to fabricate three WF beams, each with a different length of bonded splice joint at mid-span. The overall length of each spliced beam was 3.1 m, sufficient to provide a 3 m simply supported span. The lengths of the splice joints were 210 mm, 410 mm and 610 mm, respectively. These dimensions allowed for a 10 mm gap at mid-span between the ends of each half-beam. As each beam was to be tested with both two and six-plate splice joints, it was also decided that the outer splice plates would extend over the full 152 mm width of the flanges of the WF profiles. The 68 mm width of the inner splice plates was determined by the requirement that their outer longitudinal edges were to be flush with the edges of the flanges of the WF profiles and their inner longitudinal edges were to be coincident with the start of the transition radii (between the flange and the web) on the inner surfaces of the flanges of the WF profiles.
Table 1 Average elastic longitudinal and shear moduli of the pultruded GFRP beam and splice plate material. Profile type
Longitudinal elastic modulus E (GPa)
In-plane shear modulus G (GPa)
WF beam
21.11a 17.2
2.93b 2.93
Splice plate
15.23 12.4
2.93 2.93
a The upper and lower longitudinal elastic moduli are the coupon test values and the minimum values given in [6] respectively. b The in-plane shear modulii are the minimum values given in [6].
Fig. 1a. Sketches of cross-sections of two and six-plate bonded splice joints at the mid-span of a pultruded GFRP WF beam [Note: transition radii between the web and flanges of the WF profiles are omitted.].
Fig. 1b. Sketch of side elevation of a six-plate bonded splice joint at the mid-span of a pultruded GFRP WF profile.
Beams with two-plate splice joints were fabricated first according to the following procedure. The three 3.1 m long WF profiles were cut in half to provide six half-beams, each 1.55 m long. The outer surfaces of the flanges at one end of each half-beam were abraded to remove their surface veils from the full width of the flanges over lengths slightly longer than the half-lengths of the splice plates to be used with each spliced beam. One face of each of the 152 mm wide splice plates was abraded to remove its surface veil. Plastic adhesive tape was then applied across the abraded flanges (at the extremities of the splice joints), along the flange edges and across the flanges at their cut ends. In this way, the plastic tape not only defined the flange areas over which the adhesive was to be applied, but also made it easier to remove excess adhesive. Adhesive tape was also applied along the edges of each splice plate. The two half-beams were then setup end-to-end on a table and clamped in position with a 10 mm gap between their cut ends. The abraded ends of the upper flanges and the abraded face of a 152 mm wide splice plate were cleaned and Araldite 2015 adhesive (see [9] for details of its physical and mechanical properties) was applied to the abraded faces of the flanges and the splice plate. Several wire spacers, approximately 1 mm in diameter, were placed transversely in the adhesive on the flanges in order to ensure a uniform bond thickness. The adhesive coated face of the splice plate was then placed on top of the flanges of the halfbeams, adjusted to the correct alignment and then clamped to the flanges to form one half of the two-plate splice joint. Between 30 and 60 min later the adhesive spew was cleaned off and the splice joint was left to cure at room temperature. Twenty-four hours later the clamps were removed, the beam was rotated carefully through 180° and then whole process was repeated to complete the fabrication of the other half of the two-plate bonded splice joint at the centre of the pultruded GFRP WF beam.
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Fig. 2. Test setup for a four-point flexure test on a pultruded GFRP WF beam with a six-plate bonded splice joint at mid-span.
After completing the serviceability deflection limit tests on the beams with two-plate splice joints, the same procedure was used to bond pairs of splice plates to the inner faces of the flanges to form beams with six-plate bonded splice joints at their centres. These beams were then subjected to deflection serviceability limit tests. 4. Test setup, instrumentation and test procedure The three spliced beams were tested in turn as 3 m span simply supported beams subjected to symmetric four-point bending with respect to their major and minor flexural axes. In all of the tests the two, symmetrically distributed loads were actually line loads positioned outside the splice joints. Fig. 2 is a sketch of the major-axis test setup which shows the principal dimensions of the beam, the splice plates and the load spacing. The sketch also shows the locations of the instrumentation (four electronic clinometers and a dial gauge; the strain gauges on the outer surfaces of the splice plates are not shown). A photograph of part of the test rig is shown in
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Fig. 3. The line loads were applied to the beam’s top flange by a transverse steel rod at each end of a steel box-section loading bar. The centre of the loading bar was attached to the lower end of a 50 KN capacity load cell, the upper end of which was connected to the ram of a manually operated hydraulic jack. The jack was bolted to a giant meccano reaction frame. The ends of the beam were supported by fixed transverse steel rods that were tack welded to flat steel plates, which, in turn, were supported by sections of giant meccano. During each four-point major-axis flexure test the load was increased gradually to produce 1 mm mid-span deflection increments until the deflection reached 15 mm (span/200). (It should be appreciated that in the EUROCOMP Design Code and Handbook [5] a smaller serviceability deflection limit is recommended.). After each deflection increment, the load was kept constant for the short period of time required to note the deflection, rotations and strains. Mid-span deflections were recorded by a 50 mm travel dial gauge with a displacement resolution of 0.01 mm. Rotations at the supports and at the ends of the splice joints were recorded by electronic clinometers fixed at the mid-depth of the beam’s web over the supports and in line with the ends of the splice joints, respectively. The clinometers were very accurate for rotations less than 5o, their angular resolution being about 0.001°. Four uniaxial strain gauges, bonded to the outer faces of the 152 mm wide splice plates, recorded the strains at mid-span. The internal resistance of the gauges was 120 ohms and their gauge lengths were 10 mm. The longitudinal axes of the gauges were parallel to the longitudinal edges of the splice plates and inset therefrom by about 10 mm. After the centre deflection reached 15 mm and the deflection, rotations and strains had been noted, the beam was unloaded in 1 mm decrements and the deflection, rotations and strains were noted after each decrement. This load – unload procedure was applied three times to each beam.
Fig. 3. View of the test rig showing a pultruded GFRP WF beam with a 210 mm long two-plate bonded splice joint at its mid-span being set up for testing in four-point flexure.
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The test setup for the minor-axis four-point flexure tests differed in a few minor respects from that shown in Fig. 2. Two small, recessed timber bars spanning between the upper edges of the flanges were used to transmit the line loads to the beam. The mid-span deflection was measured from above rather than below the beam and L-shaped aluminium plates, attached to the beam’s web, supported the clinometers. The test procedure for the minor-axis tests was similar to that for the major-axis tests. However, as the beam’s minor-axis flexural rigidity was significantly lower than that of its major-axis, it was decided to limit the maximum deflection to 10 mm. It should be appreciated that the present investigation was aimed specifically at quantifying the stiffness characteristics of the pultruded GFRP spliced beams and their bonded splice joints up to the deflection serviceability limit, especially as this criterion generally dominates their design. Nevertheless, the failure characteristics of these beams are also of considerable interest. However, the test setup was not suitable for carrying out failure tests, especially if the lateral buckling mode of failure were to precede debonding of the splice plates or local buckling of the flanges or web, because the line loads would prevent lateral displacement of the top flange and inhibit the development of lateral buckling in a single half-wave mode. For this reason, no failure testing was attempted. 5. Repeatability of the spliced beam test data It is convenient first to demonstrate the repeatability of the measurements obtained from the four-point flexure tests. The load – mid-span deflection response of the three major-axis flexure tests on the beam with a 610 mm long six-plate splice joint is shown in Fig. 4. It is evident that the response repeatability is excellent. Similar response repeatability was obtained for the same beam tested in minor-axis flexure. It was noted, however, that, in general, there was rather more variability in the linearity of the deformation responses recorded in the minor-axis tests as the number and length of the splice plates reduced. The repeatability of the rotation at the support A is shown in Fig. 5 for the three four-point major-axis flexure tests on the beam with a 610 mm long two-plate splice joint at mid-span. The repeatability is clearly very good. Similar repeatability of support rotations was obtained for the other spliced beams. Fig. 6 shows the repeatability of the splice joint’s total rotation for the three major-axis four-point flexure tests on the beam with a 410 mm long two-plate splice joint. It is evident that the repeatability is not as good as those obtained for the mid-span deflections
Fig. 5. Repeatability of rotation at support A versus load recorded in three majoraxis four-point flexure tests on a pultruded GFRP WF beam with a 610 mm long two-plate bonded splice joint at mid-span [span = 3 m].
and support rotations. Nevertheless, the test data in Figs. 4–6 indicate that the deflection and rotation responses of the spliced beams are linear. Furthermore, very good estimates of the beams’ transverse stiffness and reasonable estimates of the splice joints’ rotational stiffness may be obtained from straight line fits to the test data. 6. Serviceability deflection response of beams with mid-span bonded splice joints Having shown that the load – deformation responses of simply supported, pultruded GFRP WF beams with mid-span bonded splice joints are linear and repeatable, it is of interest to show the effects of the number of splice plates and their lengths on the beams’ major and minor-axis load - mid-span deflection responses. The effects of splice joint length for major-axis flexure of the beams with two and six-plate splice joints are shown in Figs. 7 and 8 respectively. Although the results presented in these figures look very similar, for a given value of the load the mid-span deflections of the beams with six-plate splice joints are slightly smaller than those with two-plate splice joints. As expected, for a given load the mid-span deflections reduce with increasing splice joint length. The load – deflection graphs for minor-axis four-point flexure of pultruded GFRP WF beams with two and six-plate splice joints are depicted in Figs. 9 and 10 respectively. These two figures show that the minor-axis deflection response is not as consistently linear as that observed in the major-axis tests. It is also evident that, for a given load and splice joint length, the mid-span deflection of the beam with a two-plate splice joint is noticeably larger than the corresponding beam with a six-plate splice joint. Thus, the four splice plates bonded to the inner faces of the WF profiles flanges have a much greater influence on deflections for minor than major-axis flexure. 7. Experimental transverse beam stiffnesses and splice joint rotational stiffnesses
Fig. 4. Repeatability of load versus mid-span deflection responses recorded in three major-axis four-point flexure tests on a pultruded GFRP WF beam with a 610 mm long six-plate bonded splice joint at mid-span [span = 3 m].
As noted earlier, the load – mid-span deflection responses of the WF beams with bonded mid-span splice joints were repeatable and linear. Hence, it was decided to quantify their transverse stiffnesses by fitting straight lines through the data derived from their third repeat tests. However, the load – splice end rotation responses obtained from each repeat test showed rather more variability, especially for minor-axis flexure. Consequently, it was decided to determine the rotational stiffnesses of the splice joints from straight lines fitted to the data of all three repeat tests.
G.J. Turvey / Composite Structures 111 (2014) 426–435
Fig. 6. Repeatability of end moment versus total splice joint rotation recorded in three major-axis four-point flexure tests on a pultruded GFRP WF beam with a 410 mm long two-plate bonded splice joint at mid-span [span = 3 m].
Fig. 7. Simply supported pultruded GFRP WF beams with two-plate bonded splice joints at mid-span subjected to major-axis four-point flexure: Effect of splice joint length on mid-span deflections [Test 3 data, span = 3 m].
Fig. 8. Simply supported pultruded GFRP WF beams with six-plate bonded splice joints at mid-span subjected to major-axis four-point flexure: Effect of splice joint length on mid-span deflections [Test 3 data, span = 3 m].
The beam transverse stiffnesses for both major and minor-axis flexure are given in Table 2. As expected, both sets of transverse stiffnesses increase with splice joint length and the major-axis stiffnesses are roughly three times greater than the corresponding minor-axis stiffnesses. Also in Table 2 values are given for the ratio of the transverse stiffness of beams with six-plate splice joints relative to those with two-plate splice joints. For major-axis flexure, it
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Fig. 9. Simply supported pultruded GFRP WF beams with two-plate bonded splice joints at mid-span subjected to minor-axis four-point flexure: Effect of splice joint length on mid-span deflections [Test 3 data, span = 3 m].
Fig. 10. Simply supported pultruded GFRP WF beams with six-plate bonded splice joints at mid-span subjected to minor-axis four-point flexure: Effect of splice joint length on mid-span deflections [Test 3 data, span = 3 m].
is evident that the additional four splice plates bonded to the inner surfaces of the flanges only increase the transverse stiffness by between 2% and 6%. For minor-axis flexure the additional splice plates produce a slightly greater increase in transverse stiffness, i.e. between 7% and 12%. It seems, therefore, that there is little to be gained in terms of transverse stiffness by using six-plate instead of two-plate bonded splice joints. Rotational stiffnesses and rotational stiffnesses per unit length of the two and six-plate bonded splice joints are also included in Table 2. The rotational stiffnesses of two-plate splice joints for major-axis flexure are of the order of three to four times greater than those for minor-axis flexure. For six-plate splice joints the corresponding range of values is three to seven. Moreover, it appears that the rotational stiffnesses of the two-plate splice joints decrease as the length of the splice joint increases, but the rotational stiffnesses of the six-plate splice joints do not. Furthermore, adding four extra plates appears to reduce the minor-axis rotational stiffness of the 210 mm long splice joint. This counter-intuitive result is most probably a consequence of the variability of the moment – splice joint end rotation measurements. In the last column of Table 2, which shows the ratios of the rotational stiffness of the sixplate to that of the corresponding two-plate bonded splice joint, it is evident that adding four extra splice plates increases the majoraxis rotational stiffness by between 19% and 62%. On the other hand, and discounting the value for the 210 mm long splice plate, the minor-axis rotational stiffness increases are somewhat smaller at 8% to 51%.
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Table 2 Transverse and rotational stiffnesses of pultruded GFRP WF beams with two- and six-plate mid-span bonded splice joints in four-point bending. Bending axis
Number of splice plates
Splice joint length (mm)
Transverse beam stiffness (kN/mm)
Ratio of six-plate to twoplate transverse stiffness
Rotational joint stiffness (kNm/ mrad)
Rotational stiffness per unit length (kNm/mrad/ m)
Ratio of six-plate to twoplate rotational stiffness
Major
2 6 2 6 2 6
210
0.461a 0.482 0.504 0.532 0.569 0.582
1.046
0.767b 1.070 0.699 1.130 0.626 0.747
3.652 5.095 1.705 2.756 1.026 1.225
1.40
2 6 2 6 2 6
210
0.139 0.149 0.153 0.172 0.186 0.205
1.072
0.255 0.175 0.153 0.165 0.144 0.217
1.214 0.833 0.373 0.402 0.236 0.356
0.69
Minor
a b
410 610
410 610
1.056 1.023
1.124 1.102
1.62 1.19
1.08 1.51
The transverse beam stiffnesses were obtained from the slope of the best fit straight line through the data points obtained from the third repeat test on each beam. The rotational stiffnesses of the splice joints were obtained from the slope of the best fit straight line through the data points of the three repeat tests.
8. Analysis of shear-deformable simply supported beams with mid-span bonded splice joints A number of methods may be used to analyse the serviceability deformations of pultruded GFRP beams with mid-span bonded splice joints and subjected to symmetric four-point flexure depicted in Fig. 11. In this paper, new closed-form formulae for the mid-span deflection, support rotations and splice joint end rotations, derived using the Method of Influence Coefficients [10] and Transformed Sections [11], have been used. Classical shear-rigid beam formulae were used in [2], but the new formulae presented here are based on first-order shear-deformable beam theory. The mid-span deflection at E may be expressed as:
dE ¼
WL3 qð2 qÞ ð1 kÞ 2 þ kð2 kÞ 3qð2 qÞ þ 3 þ 24a ð1 þ /I Þ 96EI ð1Þ
jhc j ¼ jhD j ¼
WL2 qð1 kÞ 8EI ð1 þ /I Þ
ð3Þ
The equation for /I has been derived by considering the transformed section of the splice joint cross-section and determining the ratio of the second moment of area of the splice plates (and adhesive, if thought necessary) to the second moment of area I of the WF profile. Figs. 12 and 13 show how the cross-section geometry of a six-plate splice joint is transformed for major and minoraxis flexure, respectively. The cross-section geometry of the splice joint is defined in terms of the depth d of the WF profile and the geometric parameters, ki ði ¼ b; f ; wÞ, ai, bj (j = i, o) and baj (j = i, o). For the transformed splice cross-section an additional parameter ci (i = a, p) defines the ratio of the longitudinal elastic modulus of the adhesive and the splice plate respectively to the longitudinal elastic modulus of the WF profile. Hence, for the six-plate splice joint in major-axis flexure, the equation for /I may be expressed as:
2 2 2 2 þ ai b3i 1 þ 3 1 þ 2 bbai þ b2 b 1k þ cca b3ao 1 þ 3 1 þ bao1k þ cca ai b3ai 1 þ 3 1 þ b2 b 1k b30 1 þ 3 1 þ 2 bbaoo þ bo1k f i i i f f ai ai f p p h i /I ¼ 2cp k3f 3 kw 1 1 k ð1 2kf Þ b
ð4Þ
In Eq. (1) k and q are factors which define the distance between the symmetric point loads W2 and the length of the splice joint, respec EI tively, in terms of the beam’s span L. The symbols: a ¼ GAL 2 , E, G, I and A define the shear flexibility, longitudinal elastic modulus, transverse shear modulus, second moment of area and cross-sectional area of the WF profile, respectively. The symbol /I defines the increase in second moment of area due to the bonded splice plates relative to the second moment of area I of the WF profile. The equations for the support rotations are given as:
jhA j ¼ jhB j ¼
WL2 q ð1 kÞ ð1 þ k 2qÞ þ 2 16EI ð1 þ /I Þ
ð2Þ
Likewise, the equations for the end rotations of the splice joint are:
and, for minor-axis flexure, it simplifies to:
h
/I ¼
2 c c c cp 4 bo þ cpa bao þ a3i bi þ cpi bai þ 3ai bi þ cpa bai ð2 ai Þ
i
3 1 1 2k1 kkw
4
f
b
ð5Þ Clearly, the major and minor-axis transformed sections for the twoplate bonded splice joints are obtained by setting ai = bi = bai = 0 in Eqs. (4) and (5). For the 152 152 6.4 mm pultruded GFRP WF profile and the 6.4 mm thick pultruded GFRP plate the parameters for determining /I in Eqs. (4) and (5) have been set to: kb ¼ 1;
kf ¼ kw ¼ 0:042;
ai ¼ 0:895; bo ¼ bi ¼ 1; cp ¼ 0:721
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Table 3 Values of the additional second moment of area ratio /I for two and six-plate bonded splice joints.
Fig. 11. A simply supported beam with a six-plate bonded splice joint at mid-span subjected to major-axis four-point flexure: definitions of the loading and geometric parameters.
Flexural axis
Beam longitudinal elastic modulus (kN/mm2)
Splice plate longitudinal elastic modulus (kN/mm2)
Number of plates in splice joint
Additional second moment of area ratio (/I)
Major
21.11
15.23
17.2
12.4
2 6 2 6
0.7482 1.2202 0.7477 1.2193
21.11
15.23
17.2
12.4
2 6 2 6
0.72088 1.4409 0.72035 1.4399
Minor
Fig. 13. (a) Cross-section of a six-plate bonded splice joint (minor-axis flexure) and (b) transformed cross-section.
Fig. 12. (a) Cross-section of a six-plate bonded splice joint (major-axis flexure) and (b) transformed cross-section.
Furthermore, it has been assumed that the contribution of the adhesive may be neglected, so that ca = 0. Values of /I have been computed for two and six-plate splice joints with respect to their major and minor-axes using both values of the longitudinal elastic moduli given in Table 1. The values are given in the last column of Table 3. It is evident that, regardless of which of the elastic moduli given in Table 1 is used, the /I values obtained are very similar for a specific number of splice plates and flexural axis. For major-axis flexure the ratio of /I for a six-plate
splice joint to that of a two-plate joint is about 1.6, whereas for minor-axis flexure the corresponding ratio is 2. 9. Comparison of analysis predictions and test data for pultruded GFRP WF beams with mid-span bonded splice joints The experimental data, derived from the major and minor-axis four-point flexure tests on pultruded GFRP WF beams with two and six-plate bonded splice joints at their mid-spans, have been predicted using Eqs. (1)–(5) above. It has been convenient to use the experimental data corresponding to the maximum serviceability mid-span deflections of 15 mm and 10 mm for major and minor-axis flexure respectively.
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Table 4 Comparison of experimental and predicted mid-span deflections of simply supported pultruded GFRP WF beams in four-point bending with two- and six-plate mid-span bonded splice joints. Flexural axis
Splice plate length (mm)
Number of splice plates
Total load (kN)
Experimental deflection (mm)
Predicted deflection (mm) Gross cross-sectional area
Web cross-sectional areaa
Major
210
2
6.9
15
6
7.3
2
7.6
6
8.0
2
8.5
6
8.8
13.676b (0.91)c 16.681 (1.11) 14.168 (0.94) 17.278 (1.15) 14.087 (0.94) 17.175 (1.15) 14.206 (0.95) 17.315 (1.15) 14.745 (0.98) 17.97 (1.20) 14.284 (0.95) 17.4 (1.16)
14.68 (0.98) 17.685 (1.18) 15.23 (1.02) 18.341 (1.22) 15.193 (1.01) 18.281 (1.22) 15.37 (1.02) 18.48 (1.23) 15.982 (1.07) 19.207 (1.28) 15.565 (1.04) 18.68 (1.25)
2
1.4
10
6
1.6
2
1.5
6
1.8
2
1.9
6
2.1
8.523 (0.85) 10.44 (1.04) 9.449 (0.94) 11.573 (1.16) 8.540 (0.85) 10.459 (1.05) 9.628 (0.96) 11.791 (1.18) 10.124 (1.01) 12.397 (1.24) 10.153 (1.02) 12.431 (1.24)
8.566 10.483 9.498 11.622 8.586 10.505 9.683 11.846 10.182 12.455 10.217 12.495
410
610
Minor
210
410
610
(0.86) (1.05) (0.95) (1.16) (0.86) (1.05) (0.97) (1.18) (1.02) (1.25) (1.02) (1.25)
a
For minor-axis flexure the web area is the cross-sectional area of the two flanges. The upper and lower values of the predicted deflections in each row have been calculated using longitudinal elastic modulus values of 21.11 kN/mm2 and 17.2 kN/mm2 respectively. c The values in brackets in each row are the ratios of the predicted mid-span deflections relative to the corresponding experimental deflections. b
Table 5 Comparison of average experimental and predicted rotations at the end supports and rotational stiffnesses of the joints of simply supported pultruded GFRP WF beams in fourpoint bending with two- and six-plate mid-span bonded splice joints. Flexural axis
Splice plate length (mm)
Number of splice plates
Total load (kN)
Experimental support rotationa (mrad)
Predicted support rotation (mrad)
Ratio of predicted to experimental support rotation
Experimental rotational stiffnessb (kN/ mrad)
Predicted rotational stiffness (kN/ mrad)
Ratio of predicted to experimental rotational stiffness
Major
210
2
6.9
16.301
7.3
16.747
2
7.6
16.179
6
8.0
16.3185
2
8.5
16.7115
6
8.8
16.6245
0.85 1.05 0.87 1.07 0.90 1.11 0.92 1.12 0.93 1.14 0.94 1.13
0.767
6
13.9363c 17.1048 14.5362 17.8411 14.624 17.9491 14.9485 18.3475 15.5447 19.0796 15.6351 18.8594
2.052c 1.672 2.606 2.122 1.051 0.856 1.334 1.087 0.665 0.575 0.897 0.731
2.68 2.18 2.44 1.98 1.50 1.22 1.18 0.96 1.06 0.92 1.20 0.98
2
1.4
11.842
6
1.6
12.453
2
1.5
12.252
6
1.8
12.6365
2
1.9
14.137
6
2.1
13.1335
8.884 10.904 9.952 12.2145 9.079 11.143 10.4513 12.8277 10.9428 13.4312 11.3258 13.9014
0.75 0.92 0.80 0.98 0.74 0.93 0.83 1.02 0.77 0.95 0.86 1.06
0.643 0.524 0.913 0.743 0.329 0.268 0.467 0.381 0.222 0.180 0.314 0.255
2.52 2.05 5.22 4.25 2.15 1.75 2.83 2.31 1.54 1.25 1.48 1.18
410
610
Minor
210
410
610
a
1.070 0.699 1.130 0.626 0.747 0.255 0.175 0.153 0.165 0.144 0.217
The experimental support rotations have been determined from the best fit straight line through the test data obtained from the third repeat tests. The experimental rotational stiffnesses have been determined from the best fit straight lines through the test data obtained from the three repeat tests. The upper and lower values of the predicted support rotations and rotational stiffnesses in each row have been calculated using the longitudinal elastic modulus values of 21.11 kN/mm2 and 17.2 kN/mm2 respectively. b
c
G.J. Turvey / Composite Structures 111 (2014) 426–435
The analytically predicted mid-span deflections are given in Table 4. Two sets of predicted deflections are given – one based on the beam’s gross cross-sectional area and the other on its web cross-sectional area. It should be appreciated that for minor-axis flexure the web cross-sectional area has been assumed equal to the cross-sectional area of two flanges. In each of the last two columns of Table 4 the upper and lower values correspond to the upper and lower longitudinal elastic modulus values given in Table 1. The values in brackets are the ratios of the predicted deflections to the experimental values. It is evident that, for major-axis flexure, deflections are predicted more accurately when the measured longitudinal elastic modulus is used in conjunction with the web cross-sectional area. However, for minor-axis flexure the situation is more complicated. First of all, there is practically no difference between the deflections based on the gross and web cross-sectional areas. This is unsurprising, because the web of the WF profile makes a negligible contribution to the second moment of area for minor-axis flexure. The second point is that deflections are predicted more accurately for the longer splice joints using the longitudinal elastic modulus derived from coupon tests, whereas for the shorter splice lengths the more accurate predictions were obtained using the manufacturer’s minimum value of the longitudinal elastic modulus (see Table 1). The comparison of predicted and experimental average support rotations corresponding to the mid-span deflection serviceability limits are shown in Table 5. For major-axis flexure, it is evident that the support rotations are more accurately predicted for the longer splice joints when the measured longitudinal elastic modulus is used. For the shorter splice joints, the more accurate predictions are obtained with the manufacturer’s minimum longitudinal elastic modulus [6]. For the minor-axis support rotations, irrespective of splice joint length, more accurate predictions were obtained when the longitudinal elastic modulus given in [6] was used. The final set of results predictions, i.e. for the rotational stiffnesses of the splice joints, are also given in Table 5. For the major-axis rotational stiffnesses, it appears that more accurate predictions of the experimental rotational stiffnesses are obtained when the manufacturer’s minimum longitudinal elastic modulus is used. The same is true for the minor-axis rotational stiffnesses of the splice joints. However, it is obvious that, in general, the rotational stiffnesses are poorly predicted, especially for the shortest splice joints. In addition, the minor-axis rotational stiffnesses are less accurately predicted than the major-axis rotational stiffnesses. 10. Concluding remarks Four-point flexure tests have been carried out on three 3 m span pultruded GFRP WF beams with mid-span bonded splice joints. The splice joints consisted of pultruded GFRP plates 6.4 mm thick which were bonded first to the outer surfaces of the flanges to form two-plate joints. Subsequently, a further four plates were bonded to the inner surfaces of the flanges to create six-plate joints. The splice joints were of three lengths, namely 210 mm, 410 mm and 610 mm. The spliced beams were tested several times with respect to both flexural axes up to their approximate deflection serviceability limits and mid-span deflections, support rotations and splice joint rotations were recorded.
435
A new closed-form splice joint analysis, based on first-order shear-deformable beam theory has been used to predict the experimental behaviour – in particular, mid-span deflections, support rotations and splice joint rotational stiffnesses. It has been shown that major-axis mid-span deflections are predicted to within a few percent provided the longitudinal elastic modulus used in the calculations is derived from coupon tests. For minor-axis flexure, the predicted mid-span deflections appear to be more accurate for shorter splice lengths when the manufacturer’s minimum longitudinal elastic modulus is used. Support rotations appear, for the most part, better predicted when the minimum modulus is used. Splice joint rotational stiffnesses appear to be the least well predicted characteristics with the present closed-form analysis. The major-axis rotational stiffnesses of short splices, in particular, are over-predicted by more than a factor of two and the corresponding minor-axis rotational stiffnesses are over-estimated to an even greater extent. However, for the longest two and six-plate splice joints, the major-axis rotational stiffness predictions are reasonable (8% and 2% low respectively) when the minimum longitudinal elastic modulus is used. Finally, it is perhaps worth remarking that, from a practical standpoint, it is the major-axis mid-span deflections of the spliced beams that are most important and it has been demonstrated that the new closed-form analysis is able to predict these deflections with good accuracy, for the range of splice joint lengths considered, when the measured longitudinal elastic modulus is used. Acknowledgements The author wishes to acknowledge the contribution of Mr. A. Echegut who carried out the four-point flexure tests as part of his Internship in the Engineering Department. He also wishes to acknowledge the contribution of the Engineering Department’s Technicians who assisted with the beam test setup and instrumentation. References [1] Nagaraj V, Gangarao HVS. Fatigue behaviour and connection efficiency of pultruded GFRP beams. J Compos Constr 1998;2(1):57–65. [2] Keller T, de Castro J. System ductility and redundancy of FRP beam structures with ductile adhesive joints. Compos B Eng 2005;36(8):586–96. [3] de Castro J, Keller T. Design of robust and ductile FRP structures incorporating ductile adhesive joints. Compos B Eng 2010;41(2):148–56. [4] Turvey GJ. Effects of bonded splice joints on the flexural response of pultruded fibre reinforced polymer beams. Appl Mech Mater 2010;24–25:401–6. [5] Clarke JL, editor. Structural design of polymer composites: EUROCOMP design code and handbook. London: E & FN Spon; 1996. [6] Anon. EXTREN fiberglass structural shapes design manual. Bristol, VA: Strongwell; 1989. [7] Turvey GJ. Flexure of pultruded GFRP beams with bonded splice joints. Proc Inst Civil Eng: Struct Build 2011;164(SB5):333–44. [8] Hai N, Mutsuyoshi H. Structural behaviour of double-lap joints of steel splice plates bolted/bonded to pultruded hybrid CFRP/GFRP laminates. Constr Build Mater 2012;30:347–59. [9] Huntsman. Araldite adhesives: strength in bonding 2000+: Adhesive Selector Guide; 2012.. [10] Morice PB. Linear structural analysis: an introduction to the influence coefficient method applied to statically indeterminate structures. London: Thames and Hudson; 1969. [11] Case J, Chilver AH. Strength of materials. London: Edward Arnold; 1959.
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Experimental and analytical investigation of two- and six-plate bonded splice joints on serviceability limit deformations of pultruded GFRP beams G.J. Turvey ⇑ Engineering Department, Lancaster University, Bailrigg, Lancaster LA1 4YR, UK
a r t i c l e
i n f o
Article history: Available online 27 December 2013 Keywords: Adhesive bonding Beams GFRP Pultrusion Splice joints
a b s t r a c t Six four-point flexure tests on 3 m span pultruded glass fibre reinforced polymer (GFRP) 152 152 6.4 mm Wide Flange (WF) beams with two- and six-plate mid-span bonded splice joints are described. The pultruded GFRP splice plates were 6.4 mm thick with two widths and three lengths and their rovings were parallel to their lengths. The beams were loaded to their deflection serviceability limit. Mid-span deflections, support rotations and splice joint end rotations were recorded. Their load versus deflection and support rotation responses were linear and repeatable. New shear-deformable beam equations were used to predict the spliced beam deformations. For major-axis flexure, deflections were predicted reasonably accurately for both joint layouts when the beam’s experimentally determined longitudinal elastic modulus was used. Major and minor-axis support rotations were predicted with maximum errors of 15% and 25% respectively. Generally, splice joint rotational stiffnesses were poorly predicted. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Splice joints are used to join standard length steel or aluminium beams end-to-end in order to form longer beams for use in continuous span bridges. Continuity greatly improves flexural stiffness compared to a series of simply supported, single-span beams. In continuous beams splice joints are generally located at or near to a point of contra-flexure (the point in the span where the bending moment is zero). Sometimes splice joints may be used at interior supports to create continuity between adjacent simply supported beams. In the latter situation, a stiffer/stronger splice joint would be required to resist the high bending moment at the support compared to the low moment close to or at a point of contra-flexure within the span. It should be appreciated that, in both situations, the splice plates may increase the flexural stiffness locally compared to that of the original unspliced beam. At first sight, it may appear somewhat perverse to locate a splice joint at a point of contra-flexure, especially as a pin joint should suffice. However, practical issues such as: the relative costs of pin and bolted splice joints, the consequences of failure within the joint types and the fact that the points of contra-flexure may vary for different loading situations, all work in favour of bolted splice joints. ⇑ Tel.: +44 (0)1524 593088. E-mail address: [email protected] 0263-8223/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compstruct.2013.12.022
Splice joints may also be used to repair beams which have suffered local damage due to impacts of various kinds. The damaged parts may be straightened or cut out and a spliced joint may be used to restore the beam’s structural integrity. In steel and aluminium beams the splice plates may be joined to the flanges and/or webs by means of welding or mechanical fastening, though the latter appears to be more common. At the present time structural grade pultruded glass fibre reinforced polymer (GFRP) composite beams are only available offthe-shelf with maximum depths of 300 mm. This depth limitation, combined with the relatively low flexural stiffness of GFRP, dictates that the use of pultruded GFRP beams in bridges is restricted to short, single-span, simply supported footbridges. By using splice joints to create continuity, pultruded GFRP beams could be used more efficiently in longer, multi-span footbridges. However, before this situation may be realised, it is not only necessary to develop knowledge and understanding of the stiffness and strength characteristics of splice joints, but also to determine how they affect the structural behaviour of pultruded GFRP spliced beams. It appears that the earliest flexural tests on splice-jointed pultruded GFRP beams were reported in 1998 by Nagaraj and Gangarao [1]. All of their tests were carried out on 102 102 6 mm Wide Flange (WF) and box-section beams with mid-span splice plates bolted or bolted and bonded to the flanges and web(s) by six, staggered 9.5 mm diameter bolts per splice plate. Eight splice
G.J. Turvey / Composite Structures 111 (2014) 426–435
plates were used to form the joint in the WF section and four to form the box-section joint. Each pultruded GFRP splice plate was 12.7 mm thick, i.e. more than twice the thickness of the flanges and webs of the WF and box-section profiles. Not all of the lengths and widths of the rectangular splice plates were specified, though the splice plates connecting the flanges of the WF section were 254 mm long. The web splice plates of the WF section were longer than the flange splice plates, whereas the reverse was the case for the box-section. The reasons for this are not explained in [1]. Likewise, the precise locations of the bolts in the splice plates are not given and the rationale for the asymmetric bolt stagger is not explained. Furthermore, there is no mention of any difficulties associated with bolting the splice plates to the webs and flanges of such a small box-section beam. All the spliced beam tests reported in [1] had a span of 1.828 m. Most of the beams were subjected to symmetric three-point cyclic loading in order to determine their fatigue strengths. However, a number of static three and four-point flexure tests were also carried out to provide benchmark strengths, so that the reduction in their flexural strengths due to fatigue could be quantified. Static analyses of the latter tests were also undertaken, but no generalised formulae were developed for the deflections of beams with bolted splice joints. In 2005 Keller and Castro [2] reported the results of several tests to failure on two-span unspliced and spliced 240 240 12 mm box-section pultruded GFRP beams. Both spans were 3.6 m long. A symmetrical loading arrangement was used, i.e. single vertical loads of equal magnitude were applied on opposite sides of the interior support at 1.2 m from it. In four of the beams continuity over the interior support was provided by splice plates bonded to the outer faces of the flanges. The overall lengths of the splice plates varied from 200 mm to 600 mm. The main thrust of the test work was to demonstrate that system ductility could be created in inherently brittle GFRP continuous beams by means of extensionally flexible bonded splice joints. In [2] a simplified approach was used to analyse the behaviour of the two-plate bonded splice joints at the interior support of the two-span box-section beams. The splice plate bonded to the top flange was modelled as a single-lap tension joint and expressions for the rotational and strength capacities of the box-section’s bonded splice joint were derived. This simplified approach worked reasonably well, but ignored the eccentric moment in the singlelap joint and the fact that the splice plate bonded to the soffit of the box-beam at the interior support was not only subjected to in-plane compression but also to normal compression from the support reaction. In addition, the model assumed that the centre of rotation was at the mid-depth of the box-section. Subsequently, the methodology, reported in [2], was formulated into a design procedure for Fibre-Reinforced Polymer (FRP) beams with ductile bonded splice joints [3]. In 2010 Turvey [4] reported three, major and minor-axis, fourpoint bending tests on pultruded GFRP 152 152 6.4 mm WF beams with two-plate bonded splice joints at their mid-spans. The 152 mm wide splice plates were cut out of 6.4 mm thick pultruded GFRP plate and had lengths of 210, 410 and 610 mm, i.e. a different length was used with each beam. The beams were loaded to produce mid-span deflections of span/200, i.e. slightly greater than the deflection serviceability limit given in [5]. More often than not, the latter limit state governs the design of pultruded GFRP beams. The purpose of the four-point flexure tests was not only to quantify the transverse stiffnesses and support rotations of the beams, but also to determine the moment – rotation characteristics of their mid-span bonded splice joints. At this location, the splice joints were subjected to pure bending. A spliced beam flexural analysis, based on classical shear-rigid small deflection beam theory, was developed in conjunction with
427
the test work reported in [4]. Explicit formulae for the mid-span deflection, support rotations and splice joint end rotations were presented and it was shown that, provided measured rather than design manual [6] elastic moduli were used, reasonably good correlation between measured and predicted deflections, up to the deflection serviceability limit state, could be expected. More recently a three-point bending investigation of 152 152 6.4 mm pultruded GFRP beams with six 6.4 mm thick pultruded GFRP plates forming bonded splice joints at mid-span has been reported in [7]. In [7] it was also shown that deflections and support rotations up to the serviceability limit could be predicted adequately by analysis, provided test coupon values of the longitudinal elastic modulus of the beam were used. The closedform formulae for the spliced beam’s mid-span deflection and support rotations were derived from an analysis of a shear-deformable tip-loaded cantilever with a bonded splice joint at its built-in end. The analysis was extended by deriving equations to determine optimum and limiting splice plate lengths based on transverse stiffness considerations. The equations were also used in parameter studies to quantify the effects of specific splice joint properties, namely adhesive modulus and thickness, splice plate material (GFRP or CFRP) and splice plate length, on reducing mid-span deflections. In 2012 Hai and Mutsuyoshi [8] reported the results of two four-point flexure tests on pultruded hybrid fibre (HF) I-section beams with mid-span, double-lap, bolted and bonded splice joints. The HF flanges comprised both GFRP and Carbon Fibre Reinforced Polymer (CFRP) composite materials and the webs were all-GFRP. Furthermore, the flange and web splice plates were made of steel and their bonded surfaces were serrated to improve the bond strength. Two layouts of 10 mm diameter stainless steel bolts were used. The beams were tested to failure and their failure modes were recorded. A three-dimensional finite element model was used to simulate the tests and reasonable correlation was obtained with the experimental failure loads. It was only after completing the investigation, reported in [4], that it was appreciated that the beams with two-plate bonded splice joints at their mid-spans ought to have four additional splice plates bonded to the inner surfaces of their flanges to create sixplate bonded splice joints. The beams could then be re-tested in four-point flexure and the effects of the two joint configurations on the pultruded GFRP spliced beams’ responses could be compared. In addition, it was recognised that a generalised first-order shear-deformable, four-point flexure analysis of beams with midspan splice joints should also be undertaken. Completion of this work led to new closed-form equations for mid-span deflection, support rotations and splice joint end rotations. These equations have been used to predict (with varying degrees of accuracy) the deformations recorded in the spliced beam tests and new experimental and analytical results comparisons are reported. Elastic moduli of the pultruded GFRP beam and splice plate materials are introduced first. Details are then given of the beam and splice plate geometries and the splice joint layouts. This is followed by a description of the procedures used in the fabrication of the spliced beams. Thereafter, the beam test setup, instrumentation and test procedure are explained. Load – deflection, support rotation – load and moment – splice joint rotation data are presented to demonstrate the repeatability of the experimental procedure. An explanation is given of the new generalised closed-form equations, which take account of shear deformation, developed for four-point flexural analysis of the pultruded GFRP spliced beams. They are then used to predict mid-span deflections, support rotations and splice joint flexural stiffnesses observed in the fourpoint flexure tests and experimental – analytical results comparisons are presented and discussed. Finally, conclusions are drawn regarding the relative accuracy of these comparisons.
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2. Elastic moduli of the pultruded GFRP beams and splice plates In the present investigation, the pultruded GFRP beams were 152 152 6.4 mm WF profiles and the rectangular splice plates were cut out of 6.4 mm thick pultruded GFRP plate with their longer sides parallel to the pultrusion direction. The WF profiles and splice plates incorporate E-glass rovings (bundles of parallel fibres) stabilised in a thermoset polyester resin which usually contains a small quantity of chalk or clay filler (typically 5% to 10% by volume). In the WF profiles the rovings are closely packed transversely, whereas in the plate material they are discretely spaced transversely, so that the volume percentage of glass in the WF profiles (typically 40%) is higher than that in the 6.4 mm thick splice plates, which is about 30%. Rectangular coupons, cut out of the flanges and webs of the pultruded WF profiles and the plate, have been tested untabbed in tension to determine their longitudinal elastic moduli. Separate tests were not undertaken, as part of this investigation, to determine their in-plane shear moduli. However, in a previously unreported investigation such tests were undertaken and shear moduli were obtained for the WF profile, which were slightly higher than the shear moduli reported in the manufacturer’s design manual [6]. As similar data was not available for the pultruded plate, it was decided to use the value given in [6] for all of the subsequent calculations of spliced beam deflections. The average longitudinal elastic moduli obtained from the tension tests on the WF profile and the 6.4 mm thick plate coupons are given in Table 1, where they are compared with the manufacturer’s minimum values in [6]. It is evident that the average longitudinal elastic moduli are about 23% higher than the minimum values. 3. Spliced beam components and splice joint fabrication Fig. 1a shows the cross-sections of the two and six-plate bonded splice joints at the mid-span of a spliced beam and Fig. 1b shows a side elevation of a six-plate bonded splice joint. It was decided to fabricate three WF beams, each with a different length of bonded splice joint at mid-span. The overall length of each spliced beam was 3.1 m, sufficient to provide a 3 m simply supported span. The lengths of the splice joints were 210 mm, 410 mm and 610 mm, respectively. These dimensions allowed for a 10 mm gap at mid-span between the ends of each half-beam. As each beam was to be tested with both two and six-plate splice joints, it was also decided that the outer splice plates would extend over the full 152 mm width of the flanges of the WF profiles. The 68 mm width of the inner splice plates was determined by the requirement that their outer longitudinal edges were to be flush with the edges of the flanges of the WF profiles and their inner longitudinal edges were to be coincident with the start of the transition radii (between the flange and the web) on the inner surfaces of the flanges of the WF profiles.
Table 1 Average elastic longitudinal and shear moduli of the pultruded GFRP beam and splice plate material. Profile type
Longitudinal elastic modulus E (GPa)
In-plane shear modulus G (GPa)
WF beam
21.11a 17.2
2.93b 2.93
Splice plate
15.23 12.4
2.93 2.93
a The upper and lower longitudinal elastic moduli are the coupon test values and the minimum values given in [6] respectively. b The in-plane shear modulii are the minimum values given in [6].
Fig. 1a. Sketches of cross-sections of two and six-plate bonded splice joints at the mid-span of a pultruded GFRP WF beam [Note: transition radii between the web and flanges of the WF profiles are omitted.].
Fig. 1b. Sketch of side elevation of a six-plate bonded splice joint at the mid-span of a pultruded GFRP WF profile.
Beams with two-plate splice joints were fabricated first according to the following procedure. The three 3.1 m long WF profiles were cut in half to provide six half-beams, each 1.55 m long. The outer surfaces of the flanges at one end of each half-beam were abraded to remove their surface veils from the full width of the flanges over lengths slightly longer than the half-lengths of the splice plates to be used with each spliced beam. One face of each of the 152 mm wide splice plates was abraded to remove its surface veil. Plastic adhesive tape was then applied across the abraded flanges (at the extremities of the splice joints), along the flange edges and across the flanges at their cut ends. In this way, the plastic tape not only defined the flange areas over which the adhesive was to be applied, but also made it easier to remove excess adhesive. Adhesive tape was also applied along the edges of each splice plate. The two half-beams were then setup end-to-end on a table and clamped in position with a 10 mm gap between their cut ends. The abraded ends of the upper flanges and the abraded face of a 152 mm wide splice plate were cleaned and Araldite 2015 adhesive (see [9] for details of its physical and mechanical properties) was applied to the abraded faces of the flanges and the splice plate. Several wire spacers, approximately 1 mm in diameter, were placed transversely in the adhesive on the flanges in order to ensure a uniform bond thickness. The adhesive coated face of the splice plate was then placed on top of the flanges of the halfbeams, adjusted to the correct alignment and then clamped to the flanges to form one half of the two-plate splice joint. Between 30 and 60 min later the adhesive spew was cleaned off and the splice joint was left to cure at room temperature. Twenty-four hours later the clamps were removed, the beam was rotated carefully through 180° and then whole process was repeated to complete the fabrication of the other half of the two-plate bonded splice joint at the centre of the pultruded GFRP WF beam.
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Fig. 2. Test setup for a four-point flexure test on a pultruded GFRP WF beam with a six-plate bonded splice joint at mid-span.
After completing the serviceability deflection limit tests on the beams with two-plate splice joints, the same procedure was used to bond pairs of splice plates to the inner faces of the flanges to form beams with six-plate bonded splice joints at their centres. These beams were then subjected to deflection serviceability limit tests. 4. Test setup, instrumentation and test procedure The three spliced beams were tested in turn as 3 m span simply supported beams subjected to symmetric four-point bending with respect to their major and minor flexural axes. In all of the tests the two, symmetrically distributed loads were actually line loads positioned outside the splice joints. Fig. 2 is a sketch of the major-axis test setup which shows the principal dimensions of the beam, the splice plates and the load spacing. The sketch also shows the locations of the instrumentation (four electronic clinometers and a dial gauge; the strain gauges on the outer surfaces of the splice plates are not shown). A photograph of part of the test rig is shown in
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Fig. 3. The line loads were applied to the beam’s top flange by a transverse steel rod at each end of a steel box-section loading bar. The centre of the loading bar was attached to the lower end of a 50 KN capacity load cell, the upper end of which was connected to the ram of a manually operated hydraulic jack. The jack was bolted to a giant meccano reaction frame. The ends of the beam were supported by fixed transverse steel rods that were tack welded to flat steel plates, which, in turn, were supported by sections of giant meccano. During each four-point major-axis flexure test the load was increased gradually to produce 1 mm mid-span deflection increments until the deflection reached 15 mm (span/200). (It should be appreciated that in the EUROCOMP Design Code and Handbook [5] a smaller serviceability deflection limit is recommended.). After each deflection increment, the load was kept constant for the short period of time required to note the deflection, rotations and strains. Mid-span deflections were recorded by a 50 mm travel dial gauge with a displacement resolution of 0.01 mm. Rotations at the supports and at the ends of the splice joints were recorded by electronic clinometers fixed at the mid-depth of the beam’s web over the supports and in line with the ends of the splice joints, respectively. The clinometers were very accurate for rotations less than 5o, their angular resolution being about 0.001°. Four uniaxial strain gauges, bonded to the outer faces of the 152 mm wide splice plates, recorded the strains at mid-span. The internal resistance of the gauges was 120 ohms and their gauge lengths were 10 mm. The longitudinal axes of the gauges were parallel to the longitudinal edges of the splice plates and inset therefrom by about 10 mm. After the centre deflection reached 15 mm and the deflection, rotations and strains had been noted, the beam was unloaded in 1 mm decrements and the deflection, rotations and strains were noted after each decrement. This load – unload procedure was applied three times to each beam.
Fig. 3. View of the test rig showing a pultruded GFRP WF beam with a 210 mm long two-plate bonded splice joint at its mid-span being set up for testing in four-point flexure.
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The test setup for the minor-axis four-point flexure tests differed in a few minor respects from that shown in Fig. 2. Two small, recessed timber bars spanning between the upper edges of the flanges were used to transmit the line loads to the beam. The mid-span deflection was measured from above rather than below the beam and L-shaped aluminium plates, attached to the beam’s web, supported the clinometers. The test procedure for the minor-axis tests was similar to that for the major-axis tests. However, as the beam’s minor-axis flexural rigidity was significantly lower than that of its major-axis, it was decided to limit the maximum deflection to 10 mm. It should be appreciated that the present investigation was aimed specifically at quantifying the stiffness characteristics of the pultruded GFRP spliced beams and their bonded splice joints up to the deflection serviceability limit, especially as this criterion generally dominates their design. Nevertheless, the failure characteristics of these beams are also of considerable interest. However, the test setup was not suitable for carrying out failure tests, especially if the lateral buckling mode of failure were to precede debonding of the splice plates or local buckling of the flanges or web, because the line loads would prevent lateral displacement of the top flange and inhibit the development of lateral buckling in a single half-wave mode. For this reason, no failure testing was attempted. 5. Repeatability of the spliced beam test data It is convenient first to demonstrate the repeatability of the measurements obtained from the four-point flexure tests. The load – mid-span deflection response of the three major-axis flexure tests on the beam with a 610 mm long six-plate splice joint is shown in Fig. 4. It is evident that the response repeatability is excellent. Similar response repeatability was obtained for the same beam tested in minor-axis flexure. It was noted, however, that, in general, there was rather more variability in the linearity of the deformation responses recorded in the minor-axis tests as the number and length of the splice plates reduced. The repeatability of the rotation at the support A is shown in Fig. 5 for the three four-point major-axis flexure tests on the beam with a 610 mm long two-plate splice joint at mid-span. The repeatability is clearly very good. Similar repeatability of support rotations was obtained for the other spliced beams. Fig. 6 shows the repeatability of the splice joint’s total rotation for the three major-axis four-point flexure tests on the beam with a 410 mm long two-plate splice joint. It is evident that the repeatability is not as good as those obtained for the mid-span deflections
Fig. 5. Repeatability of rotation at support A versus load recorded in three majoraxis four-point flexure tests on a pultruded GFRP WF beam with a 610 mm long two-plate bonded splice joint at mid-span [span = 3 m].
and support rotations. Nevertheless, the test data in Figs. 4–6 indicate that the deflection and rotation responses of the spliced beams are linear. Furthermore, very good estimates of the beams’ transverse stiffness and reasonable estimates of the splice joints’ rotational stiffness may be obtained from straight line fits to the test data. 6. Serviceability deflection response of beams with mid-span bonded splice joints Having shown that the load – deformation responses of simply supported, pultruded GFRP WF beams with mid-span bonded splice joints are linear and repeatable, it is of interest to show the effects of the number of splice plates and their lengths on the beams’ major and minor-axis load - mid-span deflection responses. The effects of splice joint length for major-axis flexure of the beams with two and six-plate splice joints are shown in Figs. 7 and 8 respectively. Although the results presented in these figures look very similar, for a given value of the load the mid-span deflections of the beams with six-plate splice joints are slightly smaller than those with two-plate splice joints. As expected, for a given load the mid-span deflections reduce with increasing splice joint length. The load – deflection graphs for minor-axis four-point flexure of pultruded GFRP WF beams with two and six-plate splice joints are depicted in Figs. 9 and 10 respectively. These two figures show that the minor-axis deflection response is not as consistently linear as that observed in the major-axis tests. It is also evident that, for a given load and splice joint length, the mid-span deflection of the beam with a two-plate splice joint is noticeably larger than the corresponding beam with a six-plate splice joint. Thus, the four splice plates bonded to the inner faces of the WF profiles flanges have a much greater influence on deflections for minor than major-axis flexure. 7. Experimental transverse beam stiffnesses and splice joint rotational stiffnesses
Fig. 4. Repeatability of load versus mid-span deflection responses recorded in three major-axis four-point flexure tests on a pultruded GFRP WF beam with a 610 mm long six-plate bonded splice joint at mid-span [span = 3 m].
As noted earlier, the load – mid-span deflection responses of the WF beams with bonded mid-span splice joints were repeatable and linear. Hence, it was decided to quantify their transverse stiffnesses by fitting straight lines through the data derived from their third repeat tests. However, the load – splice end rotation responses obtained from each repeat test showed rather more variability, especially for minor-axis flexure. Consequently, it was decided to determine the rotational stiffnesses of the splice joints from straight lines fitted to the data of all three repeat tests.
G.J. Turvey / Composite Structures 111 (2014) 426–435
Fig. 6. Repeatability of end moment versus total splice joint rotation recorded in three major-axis four-point flexure tests on a pultruded GFRP WF beam with a 410 mm long two-plate bonded splice joint at mid-span [span = 3 m].
Fig. 7. Simply supported pultruded GFRP WF beams with two-plate bonded splice joints at mid-span subjected to major-axis four-point flexure: Effect of splice joint length on mid-span deflections [Test 3 data, span = 3 m].
Fig. 8. Simply supported pultruded GFRP WF beams with six-plate bonded splice joints at mid-span subjected to major-axis four-point flexure: Effect of splice joint length on mid-span deflections [Test 3 data, span = 3 m].
The beam transverse stiffnesses for both major and minor-axis flexure are given in Table 2. As expected, both sets of transverse stiffnesses increase with splice joint length and the major-axis stiffnesses are roughly three times greater than the corresponding minor-axis stiffnesses. Also in Table 2 values are given for the ratio of the transverse stiffness of beams with six-plate splice joints relative to those with two-plate splice joints. For major-axis flexure, it
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Fig. 9. Simply supported pultruded GFRP WF beams with two-plate bonded splice joints at mid-span subjected to minor-axis four-point flexure: Effect of splice joint length on mid-span deflections [Test 3 data, span = 3 m].
Fig. 10. Simply supported pultruded GFRP WF beams with six-plate bonded splice joints at mid-span subjected to minor-axis four-point flexure: Effect of splice joint length on mid-span deflections [Test 3 data, span = 3 m].
is evident that the additional four splice plates bonded to the inner surfaces of the flanges only increase the transverse stiffness by between 2% and 6%. For minor-axis flexure the additional splice plates produce a slightly greater increase in transverse stiffness, i.e. between 7% and 12%. It seems, therefore, that there is little to be gained in terms of transverse stiffness by using six-plate instead of two-plate bonded splice joints. Rotational stiffnesses and rotational stiffnesses per unit length of the two and six-plate bonded splice joints are also included in Table 2. The rotational stiffnesses of two-plate splice joints for major-axis flexure are of the order of three to four times greater than those for minor-axis flexure. For six-plate splice joints the corresponding range of values is three to seven. Moreover, it appears that the rotational stiffnesses of the two-plate splice joints decrease as the length of the splice joint increases, but the rotational stiffnesses of the six-plate splice joints do not. Furthermore, adding four extra plates appears to reduce the minor-axis rotational stiffness of the 210 mm long splice joint. This counter-intuitive result is most probably a consequence of the variability of the moment – splice joint end rotation measurements. In the last column of Table 2, which shows the ratios of the rotational stiffness of the sixplate to that of the corresponding two-plate bonded splice joint, it is evident that adding four extra splice plates increases the majoraxis rotational stiffness by between 19% and 62%. On the other hand, and discounting the value for the 210 mm long splice plate, the minor-axis rotational stiffness increases are somewhat smaller at 8% to 51%.
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Table 2 Transverse and rotational stiffnesses of pultruded GFRP WF beams with two- and six-plate mid-span bonded splice joints in four-point bending. Bending axis
Number of splice plates
Splice joint length (mm)
Transverse beam stiffness (kN/mm)
Ratio of six-plate to twoplate transverse stiffness
Rotational joint stiffness (kNm/ mrad)
Rotational stiffness per unit length (kNm/mrad/ m)
Ratio of six-plate to twoplate rotational stiffness
Major
2 6 2 6 2 6
210
0.461a 0.482 0.504 0.532 0.569 0.582
1.046
0.767b 1.070 0.699 1.130 0.626 0.747
3.652 5.095 1.705 2.756 1.026 1.225
1.40
2 6 2 6 2 6
210
0.139 0.149 0.153 0.172 0.186 0.205
1.072
0.255 0.175 0.153 0.165 0.144 0.217
1.214 0.833 0.373 0.402 0.236 0.356
0.69
Minor
a b
410 610
410 610
1.056 1.023
1.124 1.102
1.62 1.19
1.08 1.51
The transverse beam stiffnesses were obtained from the slope of the best fit straight line through the data points obtained from the third repeat test on each beam. The rotational stiffnesses of the splice joints were obtained from the slope of the best fit straight line through the data points of the three repeat tests.
8. Analysis of shear-deformable simply supported beams with mid-span bonded splice joints A number of methods may be used to analyse the serviceability deformations of pultruded GFRP beams with mid-span bonded splice joints and subjected to symmetric four-point flexure depicted in Fig. 11. In this paper, new closed-form formulae for the mid-span deflection, support rotations and splice joint end rotations, derived using the Method of Influence Coefficients [10] and Transformed Sections [11], have been used. Classical shear-rigid beam formulae were used in [2], but the new formulae presented here are based on first-order shear-deformable beam theory. The mid-span deflection at E may be expressed as:
dE ¼
WL3 qð2 qÞ ð1 kÞ 2 þ kð2 kÞ 3qð2 qÞ þ 3 þ 24a ð1 þ /I Þ 96EI ð1Þ
jhc j ¼ jhD j ¼
WL2 qð1 kÞ 8EI ð1 þ /I Þ
ð3Þ
The equation for /I has been derived by considering the transformed section of the splice joint cross-section and determining the ratio of the second moment of area of the splice plates (and adhesive, if thought necessary) to the second moment of area I of the WF profile. Figs. 12 and 13 show how the cross-section geometry of a six-plate splice joint is transformed for major and minoraxis flexure, respectively. The cross-section geometry of the splice joint is defined in terms of the depth d of the WF profile and the geometric parameters, ki ði ¼ b; f ; wÞ, ai, bj (j = i, o) and baj (j = i, o). For the transformed splice cross-section an additional parameter ci (i = a, p) defines the ratio of the longitudinal elastic modulus of the adhesive and the splice plate respectively to the longitudinal elastic modulus of the WF profile. Hence, for the six-plate splice joint in major-axis flexure, the equation for /I may be expressed as:
2 2 2 2 þ ai b3i 1 þ 3 1 þ 2 bbai þ b2 b 1k þ cca b3ao 1 þ 3 1 þ bao1k þ cca ai b3ai 1 þ 3 1 þ b2 b 1k b30 1 þ 3 1 þ 2 bbaoo þ bo1k f i i i f f ai ai f p p h i /I ¼ 2cp k3f 3 kw 1 1 k ð1 2kf Þ b
ð4Þ
In Eq. (1) k and q are factors which define the distance between the symmetric point loads W2 and the length of the splice joint, respec EI tively, in terms of the beam’s span L. The symbols: a ¼ GAL 2 , E, G, I and A define the shear flexibility, longitudinal elastic modulus, transverse shear modulus, second moment of area and cross-sectional area of the WF profile, respectively. The symbol /I defines the increase in second moment of area due to the bonded splice plates relative to the second moment of area I of the WF profile. The equations for the support rotations are given as:
jhA j ¼ jhB j ¼
WL2 q ð1 kÞ ð1 þ k 2qÞ þ 2 16EI ð1 þ /I Þ
ð2Þ
Likewise, the equations for the end rotations of the splice joint are:
and, for minor-axis flexure, it simplifies to:
h
/I ¼
2 c c c cp 4 bo þ cpa bao þ a3i bi þ cpi bai þ 3ai bi þ cpa bai ð2 ai Þ
i
3 1 1 2k1 kkw
4
f
b
ð5Þ Clearly, the major and minor-axis transformed sections for the twoplate bonded splice joints are obtained by setting ai = bi = bai = 0 in Eqs. (4) and (5). For the 152 152 6.4 mm pultruded GFRP WF profile and the 6.4 mm thick pultruded GFRP plate the parameters for determining /I in Eqs. (4) and (5) have been set to: kb ¼ 1;
kf ¼ kw ¼ 0:042;
ai ¼ 0:895; bo ¼ bi ¼ 1; cp ¼ 0:721
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Table 3 Values of the additional second moment of area ratio /I for two and six-plate bonded splice joints.
Fig. 11. A simply supported beam with a six-plate bonded splice joint at mid-span subjected to major-axis four-point flexure: definitions of the loading and geometric parameters.
Flexural axis
Beam longitudinal elastic modulus (kN/mm2)
Splice plate longitudinal elastic modulus (kN/mm2)
Number of plates in splice joint
Additional second moment of area ratio (/I)
Major
21.11
15.23
17.2
12.4
2 6 2 6
0.7482 1.2202 0.7477 1.2193
21.11
15.23
17.2
12.4
2 6 2 6
0.72088 1.4409 0.72035 1.4399
Minor
Fig. 13. (a) Cross-section of a six-plate bonded splice joint (minor-axis flexure) and (b) transformed cross-section.
Fig. 12. (a) Cross-section of a six-plate bonded splice joint (major-axis flexure) and (b) transformed cross-section.
Furthermore, it has been assumed that the contribution of the adhesive may be neglected, so that ca = 0. Values of /I have been computed for two and six-plate splice joints with respect to their major and minor-axes using both values of the longitudinal elastic moduli given in Table 1. The values are given in the last column of Table 3. It is evident that, regardless of which of the elastic moduli given in Table 1 is used, the /I values obtained are very similar for a specific number of splice plates and flexural axis. For major-axis flexure the ratio of /I for a six-plate
splice joint to that of a two-plate joint is about 1.6, whereas for minor-axis flexure the corresponding ratio is 2. 9. Comparison of analysis predictions and test data for pultruded GFRP WF beams with mid-span bonded splice joints The experimental data, derived from the major and minor-axis four-point flexure tests on pultruded GFRP WF beams with two and six-plate bonded splice joints at their mid-spans, have been predicted using Eqs. (1)–(5) above. It has been convenient to use the experimental data corresponding to the maximum serviceability mid-span deflections of 15 mm and 10 mm for major and minor-axis flexure respectively.
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Table 4 Comparison of experimental and predicted mid-span deflections of simply supported pultruded GFRP WF beams in four-point bending with two- and six-plate mid-span bonded splice joints. Flexural axis
Splice plate length (mm)
Number of splice plates
Total load (kN)
Experimental deflection (mm)
Predicted deflection (mm) Gross cross-sectional area
Web cross-sectional areaa
Major
210
2
6.9
15
6
7.3
2
7.6
6
8.0
2
8.5
6
8.8
13.676b (0.91)c 16.681 (1.11) 14.168 (0.94) 17.278 (1.15) 14.087 (0.94) 17.175 (1.15) 14.206 (0.95) 17.315 (1.15) 14.745 (0.98) 17.97 (1.20) 14.284 (0.95) 17.4 (1.16)
14.68 (0.98) 17.685 (1.18) 15.23 (1.02) 18.341 (1.22) 15.193 (1.01) 18.281 (1.22) 15.37 (1.02) 18.48 (1.23) 15.982 (1.07) 19.207 (1.28) 15.565 (1.04) 18.68 (1.25)
2
1.4
10
6
1.6
2
1.5
6
1.8
2
1.9
6
2.1
8.523 (0.85) 10.44 (1.04) 9.449 (0.94) 11.573 (1.16) 8.540 (0.85) 10.459 (1.05) 9.628 (0.96) 11.791 (1.18) 10.124 (1.01) 12.397 (1.24) 10.153 (1.02) 12.431 (1.24)
8.566 10.483 9.498 11.622 8.586 10.505 9.683 11.846 10.182 12.455 10.217 12.495
410
610
Minor
210
410
610
(0.86) (1.05) (0.95) (1.16) (0.86) (1.05) (0.97) (1.18) (1.02) (1.25) (1.02) (1.25)
a
For minor-axis flexure the web area is the cross-sectional area of the two flanges. The upper and lower values of the predicted deflections in each row have been calculated using longitudinal elastic modulus values of 21.11 kN/mm2 and 17.2 kN/mm2 respectively. c The values in brackets in each row are the ratios of the predicted mid-span deflections relative to the corresponding experimental deflections. b
Table 5 Comparison of average experimental and predicted rotations at the end supports and rotational stiffnesses of the joints of simply supported pultruded GFRP WF beams in fourpoint bending with two- and six-plate mid-span bonded splice joints. Flexural axis
Splice plate length (mm)
Number of splice plates
Total load (kN)
Experimental support rotationa (mrad)
Predicted support rotation (mrad)
Ratio of predicted to experimental support rotation
Experimental rotational stiffnessb (kN/ mrad)
Predicted rotational stiffness (kN/ mrad)
Ratio of predicted to experimental rotational stiffness
Major
210
2
6.9
16.301
7.3
16.747
2
7.6
16.179
6
8.0
16.3185
2
8.5
16.7115
6
8.8
16.6245
0.85 1.05 0.87 1.07 0.90 1.11 0.92 1.12 0.93 1.14 0.94 1.13
0.767
6
13.9363c 17.1048 14.5362 17.8411 14.624 17.9491 14.9485 18.3475 15.5447 19.0796 15.6351 18.8594
2.052c 1.672 2.606 2.122 1.051 0.856 1.334 1.087 0.665 0.575 0.897 0.731
2.68 2.18 2.44 1.98 1.50 1.22 1.18 0.96 1.06 0.92 1.20 0.98
2
1.4
11.842
6
1.6
12.453
2
1.5
12.252
6
1.8
12.6365
2
1.9
14.137
6
2.1
13.1335
8.884 10.904 9.952 12.2145 9.079 11.143 10.4513 12.8277 10.9428 13.4312 11.3258 13.9014
0.75 0.92 0.80 0.98 0.74 0.93 0.83 1.02 0.77 0.95 0.86 1.06
0.643 0.524 0.913 0.743 0.329 0.268 0.467 0.381 0.222 0.180 0.314 0.255
2.52 2.05 5.22 4.25 2.15 1.75 2.83 2.31 1.54 1.25 1.48 1.18
410
610
Minor
210
410
610
a
1.070 0.699 1.130 0.626 0.747 0.255 0.175 0.153 0.165 0.144 0.217
The experimental support rotations have been determined from the best fit straight line through the test data obtained from the third repeat tests. The experimental rotational stiffnesses have been determined from the best fit straight lines through the test data obtained from the three repeat tests. The upper and lower values of the predicted support rotations and rotational stiffnesses in each row have been calculated using the longitudinal elastic modulus values of 21.11 kN/mm2 and 17.2 kN/mm2 respectively. b
c
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The analytically predicted mid-span deflections are given in Table 4. Two sets of predicted deflections are given – one based on the beam’s gross cross-sectional area and the other on its web cross-sectional area. It should be appreciated that for minor-axis flexure the web cross-sectional area has been assumed equal to the cross-sectional area of two flanges. In each of the last two columns of Table 4 the upper and lower values correspond to the upper and lower longitudinal elastic modulus values given in Table 1. The values in brackets are the ratios of the predicted deflections to the experimental values. It is evident that, for major-axis flexure, deflections are predicted more accurately when the measured longitudinal elastic modulus is used in conjunction with the web cross-sectional area. However, for minor-axis flexure the situation is more complicated. First of all, there is practically no difference between the deflections based on the gross and web cross-sectional areas. This is unsurprising, because the web of the WF profile makes a negligible contribution to the second moment of area for minor-axis flexure. The second point is that deflections are predicted more accurately for the longer splice joints using the longitudinal elastic modulus derived from coupon tests, whereas for the shorter splice lengths the more accurate predictions were obtained using the manufacturer’s minimum value of the longitudinal elastic modulus (see Table 1). The comparison of predicted and experimental average support rotations corresponding to the mid-span deflection serviceability limits are shown in Table 5. For major-axis flexure, it is evident that the support rotations are more accurately predicted for the longer splice joints when the measured longitudinal elastic modulus is used. For the shorter splice joints, the more accurate predictions are obtained with the manufacturer’s minimum longitudinal elastic modulus [6]. For the minor-axis support rotations, irrespective of splice joint length, more accurate predictions were obtained when the longitudinal elastic modulus given in [6] was used. The final set of results predictions, i.e. for the rotational stiffnesses of the splice joints, are also given in Table 5. For the major-axis rotational stiffnesses, it appears that more accurate predictions of the experimental rotational stiffnesses are obtained when the manufacturer’s minimum longitudinal elastic modulus is used. The same is true for the minor-axis rotational stiffnesses of the splice joints. However, it is obvious that, in general, the rotational stiffnesses are poorly predicted, especially for the shortest splice joints. In addition, the minor-axis rotational stiffnesses are less accurately predicted than the major-axis rotational stiffnesses. 10. Concluding remarks Four-point flexure tests have been carried out on three 3 m span pultruded GFRP WF beams with mid-span bonded splice joints. The splice joints consisted of pultruded GFRP plates 6.4 mm thick which were bonded first to the outer surfaces of the flanges to form two-plate joints. Subsequently, a further four plates were bonded to the inner surfaces of the flanges to create six-plate joints. The splice joints were of three lengths, namely 210 mm, 410 mm and 610 mm. The spliced beams were tested several times with respect to both flexural axes up to their approximate deflection serviceability limits and mid-span deflections, support rotations and splice joint rotations were recorded.
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A new closed-form splice joint analysis, based on first-order shear-deformable beam theory has been used to predict the experimental behaviour – in particular, mid-span deflections, support rotations and splice joint rotational stiffnesses. It has been shown that major-axis mid-span deflections are predicted to within a few percent provided the longitudinal elastic modulus used in the calculations is derived from coupon tests. For minor-axis flexure, the predicted mid-span deflections appear to be more accurate for shorter splice lengths when the manufacturer’s minimum longitudinal elastic modulus is used. Support rotations appear, for the most part, better predicted when the minimum modulus is used. Splice joint rotational stiffnesses appear to be the least well predicted characteristics with the present closed-form analysis. The major-axis rotational stiffnesses of short splices, in particular, are over-predicted by more than a factor of two and the corresponding minor-axis rotational stiffnesses are over-estimated to an even greater extent. However, for the longest two and six-plate splice joints, the major-axis rotational stiffness predictions are reasonable (8% and 2% low respectively) when the minimum longitudinal elastic modulus is used. Finally, it is perhaps worth remarking that, from a practical standpoint, it is the major-axis mid-span deflections of the spliced beams that are most important and it has been demonstrated that the new closed-form analysis is able to predict these deflections with good accuracy, for the range of splice joint lengths considered, when the measured longitudinal elastic modulus is used. Acknowledgements The author wishes to acknowledge the contribution of Mr. A. Echegut who carried out the four-point flexure tests as part of his Internship in the Engineering Department. He also wishes to acknowledge the contribution of the Engineering Department’s Technicians who assisted with the beam test setup and instrumentation. References [1] Nagaraj V, Gangarao HVS. Fatigue behaviour and connection efficiency of pultruded GFRP beams. J Compos Constr 1998;2(1):57–65. [2] Keller T, de Castro J. System ductility and redundancy of FRP beam structures with ductile adhesive joints. Compos B Eng 2005;36(8):586–96. [3] de Castro J, Keller T. Design of robust and ductile FRP structures incorporating ductile adhesive joints. Compos B Eng 2010;41(2):148–56. [4] Turvey GJ. Effects of bonded splice joints on the flexural response of pultruded fibre reinforced polymer beams. Appl Mech Mater 2010;24–25:401–6. [5] Clarke JL, editor. Structural design of polymer composites: EUROCOMP design code and handbook. London: E & FN Spon; 1996. [6] Anon. EXTREN fiberglass structural shapes design manual. Bristol, VA: Strongwell; 1989. [7] Turvey GJ. Flexure of pultruded GFRP beams with bonded splice joints. Proc Inst Civil Eng: Struct Build 2011;164(SB5):333–44. [8] Hai N, Mutsuyoshi H. Structural behaviour of double-lap joints of steel splice plates bolted/bonded to pultruded hybrid CFRP/GFRP laminates. Constr Build Mater 2012;30:347–59. [9] Huntsman. Araldite adhesives: strength in bonding 2000+: Adhesive Selector Guide; 2012.