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Web crippling behaviour of pultruded glass fibre reinforced polymer sections
Composite Structures 108 (2014) 789–800
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Web crippling behaviour of pultruded glass fibre reinforced polymer sections Chao Wu ⇑, Yu Bai 1 Department of Civil Engineering, Monash University, Clayton, VIC 3800, Australia
a r t i c l e
i n f o
Article history: Available online 15 October 2013 Keywords: Fibre-reinforced composite Pultrusion Web crippling Concentrated bearing load Web–flange junction Shear failure
a b s t r a c t We investigated the web crippling behaviour of pultruded GFRP sections under concentrated loading, employing four square hollow sections of different sizes. End-two-flange (ETF) and interior-two-flange (ITF) loading conditions were adopted, with specimens seated on a bearing plate. Specimens were also placed on the ground with end or interior bearing load to simulate the loading conditions of floor joist members. The observed failure initiated at web–flange junctions and was followed by buckling or crushing in the webs, and these modes were quite different from metallic sections. Correspondingly, two load limits were defined according to the progressive failure process. The effects of the loading positions (end loading or interior loading) as well as the supporting conditions (on a bearing plate or on the ground) on the web crippling behaviour are discussed. An effective web area in the pultrusion direction is identified to characterize the load transfer path within the web. Finally, a simple mechanism based design equation is proposed to estimate the strength of such pultruded GFRP sections subjected to web crippling. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Pultruded glass fibre reinforced polymer (GFRP) composites have attracted extensive research attention as promising alternatives to conventional construction materials (steel and concrete) for civil infrastructure applications [1], due to their advantages of light weight, ease of installation, low maintenance, and resistance to harsh environmental conditions [2–4]. Because of the inherent orthotropic behaviour of the material, it is preferable for pultruded GFRP sections to carry loading in their pultrusion direction. Inevitably, however, there are situations when concentrated loading is applied and transferred in both longitudinal (pultrusion) and transverse directions [5–7], with reaction force and load from support or other structural members like joists, purlins and rafters. The term of ‘‘web crippling’’ was commonly used to describe the failure behaviour of metallic sections under such concentrated bearing load conditions [8,9], including web yielding and web buckling. For orthotropic pultruded GFRP sections under the same loading conditions, the failure mechanism may be different from that of metallic sections. The terminology of ‘‘web crippling’’ is extended in this paper to describe potential failure behaviour in general for pultruded GFRP sections under concentrated bearing load conditions.
⇑ Corresponding author. Tel.: +61 3 9905 4967. 1
E-mail addresses: [email protected] (C. Wu), [email protected] (Y. Bai). Tel.: +61 3 9905 4987.
0263-8223/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compstruct.2013.10.020
Extensive experimental research has been conducted on web crippling strength of thin-walled metallic sections [9–14], including cold-formed steel sections [11,15–17] and aluminium sections [18,19]. Four loading conditions have been specified according to existing design rules [20–24] of metallic sections, namely endone-flange (EOF), interior-one-flange (IOF), end-two-flange (ETF) and interior-two-flange (ITF). These loading conditions are classified based on the concentrated load acting on one flange only or both flanges as well as the location of the applied load [18]. However, these four loading conditions do not directly represent floor joist members seated on a solid foundation subjected to concentrated bearing load [13]. Zhao and Hancock [10,25], Young and Hancock [26] and Zhou and Young [13] conducted a series of tests on cold-formed steel sections subjected to concentrated bearing load, where the specimens were seated on a fixed solid steel base-plate. The same experimental setup was adopted for sharp corner aluminium tubular sections in [14]. In this way, the supporting condition of the floor joist members seated on solid foundations was realistically presented. In general, both web yielding and web buckling failure modes were observed for metallic sections under various loading conditions. The key parameters which affect web crippling strength include loading position (end or interior loading), supporting condition (section on bearing plate or on the ground), corner radius and web slenderness ratio (web height divided by web thickness) of a section, bearing plate size and material properties. Unlike isotropic steel and aluminium materials, pultruded GFRP sections have reduced material properties in the transverse
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Nomenclature B bplate fs H L Le PE Pi Pmax rext
total width of GFRP section width of the bearing plate interlaminar shear strength total height of GFRP section length of GFRP specimen effective length of GFRP specimen experimental web crippling strength elastic limit load ultimate load exterior corner radius of GFRP section
direction and tend to fail in interlaminar shear under compression loading [27,28], making the web crippling more critical when transverse concentrated loading is applied. However, experimental study of pultruded GFRP profiles subjected to web crippling is still limited. The web buckling strength of multi-cellular FRP bridge deck modules was experimentally investigated by Prachasaree and GangaRao [29]. FRP multi-cellular box sections of dimensions 76.2 73.7 cm were placed on a flat solid foundation. Truck loading was represented by applying compression over the top flange through a plate with dimensions 25.4 50.8 cm. With increase of the compression load, crack initiated at the web–flange junction and propagated along the longitudinal direction of the beam. In terms of web buckling strength per web, it was found that single web specimens performed better than multi-web specimens. This is because, for the single web section, the web was aligned with the centre line of the concentrated loading, and therefore load eccentricity effect was minimized. For multi-web specimens, however, certain webs were distant from the centre line of the concentrated loading, resulting in bending stress at the web–flange junction. The finding was further supported by the premature failure observed at the web–flange junction of multi-web specimens. Borowicz and Bank [5] investigated the behaviour of simply supported pultruded GFRP beams subjected to three-point bending through concentrated loads applied on the top flange in the plane of the web. Twenty pultruded GFRP I beams with nominal depths from 152.4 to 304.8 mm were examined, with a span-to-depth ratio of 4.0. Eight beams were mounted with bearing plates under the loading head; the other twelve beams were without bearing plates. Lateral supports were provided to prevent global stability failure of the specimens. All specimens failed with a wedgelike shear failure at the upper web–flange junction. The experimental results showed that the introduction of bearing plates increased the ultimate capacity of the beams by at least 35%. A design equation was proposed with parameters identified from experiments or selected from the design equations of metallic sections. The predicted capacities agreed well with the experimental results. That study covered only the IOF loading condition; other loading conditions such as ITF, EOF and ETF have not yet been examined and therefore no corresponding web crippling design approaches have been developed. In another study by Charoenphan et al. [30], the progressive tearing failure was identified as a typical damage mechanism in single-cell, thin-walled, rectangular pultruded composite material tubes subjected to transverse (bending) loads. This progressive failure occurred along the corners of the tube at the junction between the cell walls and propagated in a stable fashion as the transverse load was increased. The response was credited for enhancing load-carrying capacity in the tube and providing energy absorption during the failure. However, the work was also based on IOF loading condition, and no design method was proposed.
rin RN tf tplate tw D ETF ITF EG IG
interior corner radius of GFRP section nominal web crippling capacity flange thickness of GFRP section thickness of the bearing plate web thickness of GFRP section spacing between strain gauges in longitudinal direction end-two-flange loading condition interior-two-flange loading condition end loading condition with specimen on the ground interior loading condition with specimen on the ground
This paper addresses this knowledge gap by presenting an experimental study of the web crippling behaviour of pultruded GFRP profiles with square hollow sections (SHS) subjected to different loading conditions. Four GFRP square sections were chosen so that the effect of web slenderness ratio on web crippling behaviour could be investigated. Both ETF and ITF loading conditions were adopted, with concentrated loading applied simultaneously and symmetrically on the top and bottom flanges of GFRP sections. Specimens were also placed on a solid foundation with end or interior concentrated loading to simulate the supporting condition of floor joist members. The web crippling failure mechanisms of pultruded GFRP SHS sections were revealed by load–displacement curves as well as by the progressive failure process recorded by a video photogrammetry system. Finally, existing design approaches for web crippling failure of pultruded GFRP SHS sections were evaluated and a new mechanism-based design equation is proposed. 2. Experimental program 2.1. Materials Four pultruded GFRP SHS sections were examined in the experimental program. The measured section dimensions are presented in Table 1 using the symbols given in Fig. 1. The section ID is given by the initial S (square hollow section). Tensile coupon tests were carried out to determine the properties including the Young’s modulus and ultimate tensile strength in the pultrusion direction. Three-point bending short beam tests were also conducted to obtain interlaminar shear strength. The coupons were taken from the centre of the section webs and tested according to ASTM D 3039 [31] for tensile properties and ASTM D 2344 [32] for shear properties. The measured tensile modulus and strength in the pultrusion direction were 25 GPa and 283 MPa, respectively. The interlaminar shear strength was 28.05 MPa. 2.2. Specimens A total of 31 specimens were tested as listed in Table 2. The label of each specimen is comprised of three parts. The first part, S1–S4, is the section name (see Table 1). The second part is the loading condition (see Fig. 2), i.e. ETF for end-two-flange, ITF for interior-two-flange, EG for end bearing load with ground support and IG for interior bearing load with ground support. The third part is the ID of repeating specimens. The length of the specimen, L, was chosen to be much longer than the length required (1.5 times the total height of the web) in ASCE Specification [21] and the AS/NZS 4673 [22] for steel members, and the resulting lengthto-depth ratios were in a range of 3–8.
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C. Wu, Y. Bai / Composite Structures 108 (2014) 789–800 Table 1 Measured section dimensions. Section ID
Width B (mm)
Depth H (mm)
Flange thickness tf (mm)
Web thickness tw (mm)
Exterior corner radius rext (degree)
Interior corner radius rin (degree)
S1 S2 S3 S4
102.3 102.5 50.2 51.1
102.1 102.7 50.3 51.3
5.4 10.2 4.0 6.3
5.3 10.4 4.1 6.5
2.1 2.8 1.0 1.5
2.9 2.9 1.0 1.9
Fig. 1. Section shapes and symbols for SHS section. Table 2 Specimen length and gauge spacing and experimental results for all specimens. Specimens Specimen Gauge length spacing L (mm) D (mm)
Elastic Ultimate Predicted limit load load strength Pi (kN) Pmax (kN) RN (kN)
RN/Pi
S1-ETF-1 S1-ETF-2 S1-ITF-1 S1-ITF-2 S2-ETF-1 S2-ETF-2 S2-ITF-1 S2-ITF-2 S2-EG-1 S2-EG-2 S2-IG-1 S2-IG-2 S3-ETF-1 S3-ETF-2 S3-ITF-1 S3-ITF-2 S3-EG-1 S3-EG-2 S3-EG-3 S3-IG-1 S3-IG-2 S4-ETF-1 S4-ETF-2 S4-ETF-3 S4-ITF-1 S4-ITF-2 S4-EG-1 S4-EG-2 S4-EG-3 S4-IG-1 S4-IG-2 Average SD COV
10.64 15.12 26.88 26.58 19.68 26.06 42.81 40.14 20.84 18.81 48.63 47.61 12.18 12.88 16.42 15.78 11.02 11.72 11.42 12.54 15.78 13.57 22.75 18.73 20.41 27.09 14.58 16.36 19.96 29.46 24.81
1.14 0.81 0.84 0.85 1.22 0.92 1.03 1.10 1.15 1.27 0.91 0.93 0.77 0.73 1.06 1.10 0.86 0.80 0.82 1.39 1.10 1.10 0.66 0.80 1.35 1.02 1.03 0.91 0.75 0.94 1.11 0.98 0.18 0.19
300 300 600 600 300 300 600 600 300 300 600 600 200 200 400 400 200 200 200 400 400 200 200 200 400 400 200 200 200 400 400
65 65 70 70 65 65 70 70 65 65 70 70 40 40 45 45 40 40 40 45 45 40 40 40 45 45 40 40 40 45 45
14.21 15.41 30.26 29.90 26.22 26.79 45.32 48.47 32.41 32.20 52.28 50.53 15.53 13.85 21.24 19.44 14.43 15.43 16.40 22.32 23.39 15.14 25.53 21.86 32.02 28.82 21.66 21.04 21.50 31.82 28.96
12.19 12.19 22.50 22.50 23.93 23.93 44.14 44.14 23.93 23.93 44.14 44.14 9.43 9.43 17.40 17.40 9.43 9.43 9.43 17.40 17.40 14.96 14.96 14.96 27.59 27.59 14.96 14.96 14.96 27.59 27.59
2.3. Experimental set-up and instrumentation All tests were performed on a Baldwin Universal testing machine. Two loading conditions, ETF and ITF, were adopted for
S1–S4 sections (see Fig. 2a and b). Furthermore, to represent the loading condition of floor joist members, end bearing load and interior bearing load were also applied on S2–S4 by placing them on a fixed rigid steel base as shown in Fig. 2c and d. The load was applied through a rigid steel bearing plate 10 mm thick. The bearing length, bplate, seen in Fig. 2, was 50 mm for all the specimens. The width of the bearing plate (200 mm) was sufficient to act across the full flange widths of all GFRP sections. The compressive loading was applied in displacement control at a loading rate of 0.5 mm/min for all the specimens. The tests were stopped when the bearing plate displacement exceeded at least 15% the depth of the section. An ARAMIS photogrammetry system was used to monitor the progressive failure of specimens. The surface of web on one side was speckled (flat, white background with flat, black dots) to create a unique ‘‘fingerprint’’ for the ARAMIS software analysis (similar to that reported in [5]). Seven strain gauges, G1–G7, were attached on the web surface of the other side as shown in Fig. 3, where G1–G3 were vertically attached along the centre line of the bearing plates, and G4–G7 were attached in the pultrusion direction along the neutral axis of the web. The spacing (d in Fig. 3) of strain gauges G1–G3 was equal to half the depth of the corresponding section (2d = H) and the spacing of strain gauges G4–G7, D, is listed in Table 2 for different specimens. A video camera was also set up to record the progressive failure of all the specimens. The experimental set-up is shown in Fig. 4. 3. Experimental results and discussion 3.1. Failure modes The progressive failure process of each specimen was recorded using a video camera (see Fig. 4). From the experimental observations, the initial cracking at 45° occurred at web–flange junction of S1, with the two fracture surfaces sliding against each other as shown in Fig. 5a. From fracture mechanics point of view, this crack was attributed to Mode III shear failure. Subsequent bending cracks due to web buckling (similar to the buckling failure of composite plates in [33]) were identified as presented in the final failure mode in Fig. 5b. When the load was moved to the middle of the specimen, S1-ITF, similar initial crack was captured at the web– flange junction, as shown in Fig. 5c (the failure was captured from inside the specimen), followed by the steel bearing plate punching into the two webs. Finally the flanges tore off from the webs, while the other parts of the specimen away from the loading point remained intact (see Fig. 5d). This particular failure process, from the initial web–flange junction failure to the subsequent web failure modes, was observed for all the S1 specimens. For specimens with S2, very similar failure modes were identified from the two loading conditions ETF and ITF. Under ETF (see Fig. 6a), cracks initiated at the four web–flange junctions, followed by crushing of the webs. When the specimens were loaded with ITF (see Fig. 6b), the failure was also very localised within the loading zone where the flange was separated from the web and then the longitudinal fibres of the webs were broken by the steel bearing plate. When the section was seated on the ground (EG and IG), it
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Fig. 2. Illustration of loading conditions: (a) ETF; (b) ITF; (c) end bearing with solid ground (EG); and (d) interior bearing with solid ground (IG). S1 was only subjected to (a and b).
Fig. 3. Strain gauge arrangement: (a) end loaded specimen; and (b) interior loaded specimen.
was noticed that the upper part of the section experienced more serious damage than the lower part, as shown in Fig. 6(c and d) for the corresponding failure modes. As with S1 and S2, 45° cracks were observed at all web–flange junctions of S3 subjected to ETF, as shown in Fig. 7a. This resulted in separation of the webs and flanges, and finally both webs failed in buckling. The failure modes are shown in Fig. 7b for S3 loaded under ITF, where the two webs are crushed at the top and bottom flanges and buckling cracks are also observed in the middle of the webs. When seated on the solid ground under loading condition EG, specimens S3-EG (Fig. 7c) experienced the same 45° separation at the top two web–flange junctions, and subsequently the two
webs of S3-EG failed by shear. This shear failure modes in the webs were capture clearly by the video camera as in Fig. 7c, which was credited to the lower shear strength comparing to the compressive strength of pultruded GFRP laminate as explained in [27,28]. When the loading was applied in the middle of S3 (i.e. IG), the top flange of the specimens S3-IG separated from the webs and the two webs were crushed with the bearing plate punched into the webs. It was also noticed that the lower part of the specimen placed on solid ground experienced little damage (see Fig. 7c and d). The failure modes of Section S4 were very similar to those of S2, as shown in Fig. 8. The webs failed mainly by crushing rather than by buckling or shear as observed for Sections S1 and S3 (see Figs. 5
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the traditional terminology in existing international standards for the design of structural sections under concentrated bearing load conditions. For metallic sections, ‘‘web crippling’’ may comprise web yielding or web buckling failure modes. For pultruded GFRP square hollow sections, ‘‘web buckling’’ is characterized by a series of new failure mechanisms including web–flange junction separation, web buckling, web shearing and/or web crushing. Because of the web–flange junction separation, the concentrated loading was consequently carried by the webs, resulting in shearing, buckling and/or crushing failure of the webs. These subsequent failure modes of the webs appeared dependent on the web slenderness ratio: buckling and/or shearing failure occurred for Sections S1 and S3 with slenderness ratios ranging from 12.3 to 19.5 whereas web crushing occurred for Sections S2 and S4 with lower slenderness ratios from 7.9 to 9.9. 3.2. Load–displacement curves Fig. 4. Experimental set-up and instrumentation.
and 7). This may be because the web slenderness ratios of S2 and S4 were relatively lower than those of the other two sections (S1 and S3). In summary, a progressive failure process was observed as an initial 45° web–flange junction failure followed by individual web failure modes. These failure mechanisms were not observed in metallic sections. However, the term of ‘‘web crippling’’, as used to describe the failure behaviour of metallic sections, is extended to pultruded GFRP sections. This is to maintain a consistence with
The curves of applied concentrated load versus the vertical displacement of the bearing plate are presented in Fig. 9a for S1 subjected to ETF and ITF. The load–displacement curves are categorized into two groups for S2–S4, i.e. ‘‘on the ground’’ and ‘‘on the bearing plate’’. These two groups are presented in the same graph for better comparison, as shown in Fig. 9(b–d). Several common aspects appeared in the load–displacement responses of all the sections, as demonstrated in Fig. 9. Firstly, the displacement was increased linearly with load until a certain limit was reached, after which failure initiated and progressively developed. This limit corresponded to the elastic limit of such sections
Fig. 5. Typical failure modes of section S1: (a) initial failure of S1-ETF-2; (b) final failure of S1-ETF-2; (c) initial failure of S1-ITF-1; and (d) final failure of S1-ITF-1.
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(a)
(b)
(c)
(d)
Fig. 6. Typical failure modes of section S2: (a) S2-ETF-1; (b) S2-ITF-2; (c) S2-EG-1; and (d) S2-IG-1.
Fig. 7. Typical failure modes of section S3: (a) S3-ETF-1; (b) S3-ITF-2; (c) S3-EG-2; and (d) S3-IG-2.
subjected to ITF, ETG, IG and EG loading conditions. Therefore the load at this point is defined as the ‘‘elastic limit load or capacity’’ of the sections. It should be noted that the load applied on the sections could increase in the progressive failure process, for example as shown in Fig. 9d for specimen S4-ITF-2. As a result,
the maximum load achieved during the entire loading process is defined as the ‘‘ultimate load or capacity’’ of the sections. In relation to the progressive failure process identified in Section 3.1, a two-system load-carrying mechanism can be proposed for the two corresponding load limits. The elastic limit load was
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(a)
(b)
(c)
(d)
795
Fig. 8. Typical failure modes of section S4: (a) S4-ETF-3; (b) S4-ITF-2; (c) S4-EG-2; and (d) S4-IG-2.
associated with the initial failure at the top and/or bottom web– flange junctions of the sections. After the web–flange junction separation, the second load-carrying mechanism, the web system, then took effect, and the applied load was therefore sustained or developed further. The ultimate load was achieved when the subsequent web failure modes occurred. Such a two-system load-carrying mechanism represents a sectional redundancy [32,35] and therefore introduces sectional pseudo-ductility as shown in Fig. 9. This pseudo-ductility, which exhibited non-linear, decreasing stiffness with increasing load, similar to the behaviour of ductile structures, could be achieved by the progressive failure of brittle components or connections at system level [34–36]. Due to this progressive failure process, energy was dissipated as represented by the area under the load–displacement curve in Fig. 9. It can be seen that the energy dissipation was considerably affected by the loading position (end loading or interior loading). For specimens with the same section, when the load was moved from the end to the middle of the specimen (i.e. from ETF/EG to ITF/IG), both elastic limit load and ultimate load were substantially increased, resulting in a larger area under the load–displacement curve, i.e. higher energy dissipation during the progressive failure. 3.3. Elastic limit load and ultimate load The elastic limit load and ultimate load of each section identified from the load–displacement curves are listed in the last two columns of Table 2. The average values of repeating specimens are used for each section and presented in Fig. 10 for all loading conditions. The effects of three key parameters on the elastic limit load and ultimate load are discussed in this section, including supporting condition (on a bearing plate or on solid ground), loading position (end loading or interior loading) and web slenderness ratio. As indicated in Fig. 10, the elastic limit load was not greatly affected by the supporting conditions. For example, the average elastic limit load of S3-ETF (see Table 2) was 12.53 kN, which is
quite close (10% difference) to the elastic limit load of S3-EG of 11.39 kN. This is mainly because the elastic limit load was associated with the first failure mode at the web–flange junction under the bearing plate and could hardly be affected by the supporting condition. On the other hand, the loading position had considerable effect on the elastic limit load. For example, an increase by up to 107.5% was found for specimens with S1 on a bearing plate, when the load was moved from the end (S1-ETF) to the middle of the specimen (S1-ITF). Again, such an improvement in elastic limit load may be linked to the failure at web–flange junction. The effect of loading position on the ultimate load is also identified from Fig. 10. The largest increase of 103.1% in ultimate load was achieved by S1 on a bearing plate when the load was moved from end (S1-ETF) to middle of the specimen (S1-ITF). As shown in Fig. 10, the ultimate load also exhibited a general increasing trend when the supporting condition was changed from bearing plate to solid ground. For example, the increase in ultimate load ranged from 2.7% to 21.9% for end loaded specimens, and from 9.6% to 12.4% for interior loaded specimens. According to the previous discussion, the ultimate load was mainly associated with the web failure modes. When the specimens supported on solid ground were subjected to interior load, the concentrated load could be transferred to a larger web area and spread to a larger supporting area, thereby resulting in higher ultimate capacity. Fig. 11 shows the out-of-plane displacement of the web measured by ARAMIS for S2 supported on the bearing plate (S2-ETF) and for S2 supported on the ground (S2-EG). These measurements were made within the progressive failure process of the webs (i.e. after the failure of web–flange separation but before ultimate failure). The out-of-plane displacement field was normalised against the maximum value (4.50 mm for S2-EG and 10.11 mm for S2-ETF) to show the range of the web area contributing to the load transfer mechanism. It is clear in Fig. 11 that only a certain range of web was engaged in the deformation as a result of load transfer from the bearing plate to the web, and beyond this range the web deformation was negligible (for example the deep blue areas). This range of the web is therefore considered as the effective web
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Fig. 9. Load–displacement curves for all specimens: (a) Section S1; (b) Section S2; (c) Section S3; and (d) Section S4.
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Fig. 10. Elastic limit load and ultimate load of each section under various loading conditions.
area when the section is subjected to a concentrated bearing load. The effective area of S2 on the ground (S2-EG) is obviously larger than that of S2 on the bearing plate (S2-ETF), resulting in a 21.9% increase in ultimate load. Similarly, the effect of loading position on the ultimate load can also be explained by the concept of effective web area. When the load was moved from the end to the middle of the specimen, the load could be transferred to a larger effective web area due to the symmetric loading condition about the bearing plate. Finally, the web slenderness ratio of square sections had a significant effect on the ultimate load of those sections. For example, the ultimate load was improved by 79.0% under loading condition ETF when the web slenderness ratio was reduced from 19.2 (specimens S1-ETF) to 10.2 mm (specimens S2-ETF). It was also interesting to find that the improvement in elastic limit load correlated well with the increase of web thickness. For example, a 78% improvement in elastic limit load was found from the comparison between S1-ETF and S2-ETF, corresponding to a 96% increase of web thickness (from 5.3 mm for S1 to 10.4 mm for S2), and a 46% improvement in elastic limit load was identified when the web thickness increased by 51% from 4.1 mm for S3-ETF to 6.5 mm for S4-ETF. 4. Comparisons 4.1. Comparison to design methods for metallic sections An insight into the web crippling behaviour of pultruded GFRP sections can be achieved by comparison to previous research [10,12,13,18,19,25,26,37] on metallic sections subjected to concentrated bearing loads. Generally, the web crippling failures of metallic sections were characterized by web failure modes including web buckling and web yielding [38]. In contrast, due to the typical anisotropic material behaviour of pultruded GFRP sections, more complex failure modes were encountered, including web shearing, web buckling, web crushing and especially web–flange junction separation, the last of which was never experienced by metallic sections. Since section integrity is already invalidated after web– flange separation, this failure mode becomes more important for the design limit state. Therefore, the associated elastic limit load can be considered as the design web crippling capacity of pultruded GFRP sections under concentrated loading conditions. Because the design web crippling capacity of pultruded GFRP sections was determined by the corresponding failure mode, equations developed for the design of metallic sections may not
be directly applicable to pultruded GFRP sections. This contention is further justified by comparison between the experimental results from this study and the predictions using design models of cold-formed steel members. The design equation used in AS 4100 [38] was adopted as an example. Interlaminar shear capacity of GFRP section was used in the calculation to account for the shear failure mechanism. The comparison yields a mean of 1.83 for RN/ Pi, where RN is the predicted web crippling capacity using the design equation in AS 4100 [38] and Pi is the experimental elastic limit load. The standard deviation (SD) and coefficient of variation (COV) are 0.53 and 0.29, respectively. 4.2. Comparison to design methods for pultruded GFRP sections Studies of web crippling behaviour of pultruded GFRP sections are very limited. Borowicz and Bank (2010) [5] studied the behaviour of pultruded FRP I beams subjected to concentrated loads in the plane of the web. By studying design standards for web crippling capacity of metallic sections, Borowicz and Bank (2010) [5] proposed a nominal web crippling capacity for the interlaminar shear failure at the web–flange junction of pultruded GFRP I beams:
RN ¼ 0:7dtw fs 1 þ ð2k þ 6t plate þ bplate Þ=d
ð1Þ
where RN is the design web crippling capacity; bplate is the width of the bearing plate; tplate denotes the thickness of the bearing plate; d is the overall depth of the member; tw is the web thickness; k is the distance from top of the flange to the web toe of the fillet; and fs is the interlaminar shear strength of the web material. Eq. (1) was used in [5] to estimate the web crippling capacity of pultruded FRP I beams under a three-point bending condition and good agreement was reported, with an average ratio of 1.12 for the experimental results to the predictions. The SD and the COV were 0.11 and 0.10, respectively. Eq. (1) was used to predict the web crippling capacity of the specimens tested in the current study. The predicted results are compared with both the experimental elastic limit load and the ultimate load in Table 3. The parameters used for calculation can be found in Table 1 and k used in Eq. (1) is max{tf + rext; tf + rin}. As can be seen from Table 3, the predicted web crippling capacities are highly overestimated for all specimens. This is because Eq. (1) was developed based on a three-point bending set-up, which corresponds to the IOF loading condition and is not capable of considering failure mechanisms of the different loading conditions investigated in the current study. Therefore, it is necessary to
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Damage due to web– flange junction failure
102 mm
(a)
Damage due to web– flange junction failure
102 mm
(b) Fig. 11. Identification of effective web area through ARAMIS measurements: (a) specimen S2-ETF supported by bearing plate; and (b) specimen S2-EG supported by the ground.
Table 3 Predictions of experimental web crippling capacity using Eq. (1). Specimens
Elastic limit load Pi (kN)
Ultimate load Pmax (kN)
Predicted strength RN (kN)
R N/ Pi
RN/ Pmax
S1-ETF S1-ITF S2-ETF S2-ITF S2-EG S2-IG S3-ETF S3-ITF S3-EG S3-IG S4-ETF S4-ITF S4-EG S4-IG Average SD COV
12.88 26.73 22.87 41.48 19.83 48.12 12.53 16.10 11.39 14.16 18.35 23.75 16.97 27.14
14.81 30.08 26.51 46.90 32.31 51.41 14.69 20.34 15.42 22.86 20.84 30.42 21.40 30.39
49.52 49.52 102.05 102.05 102.05 102.05 28.69 28.69 28.69 28.69 47.09 47.09 47.09 47.09
3.84 1.85 4.46 2.46 5.15 2.12 2.29 1.78 2.52 2.03 2.57 1.98 2.77 1.73 2.68 1.02 0.38
3.34 1.65 3.85 2.18 3.16 1.99 1.95 1.41 1.86 1.25 2.26 1.55 2.2 1.55 2.16 1.23 0.57
Fig. 12. Illustration of Ashear under the bearing plate.
shear plane at the web–flange junction was observed from the failure modes. Therefore, Ashear can be expressed as
Ashear ¼ 2 tw bplate =cosð45 Þðtwo webs for square sectionÞ develop a new method to estimate the web crippling behaviour of pultruded GFRP sections under loading conditions of ETF, ITF, EG and IG, based on the failure mechanisms observed in the current experimental study. 4.3. Proposed web crippling design method for pultruded GFRP sections As discussed previously, the design web crippling capacity of pultruded GFRP sections is developed for their elastic limit loads. According to the observed Mode III shear failure mechanism at the web–flange junction, the nominal elastic limit load, RN, should be a function of the interlaminar shear strength (fs) [5], the shear area (Ashear) under the bearing plate, and the shear stress distribution within the area. Ashear is illustrated in Fig. 12 where the 45°
ð2Þ
Also as discussed previously, the elastic limit load was considerably affected by the loading position (end loading or interior loading). Therefore, the experimental results of elastic limit load are plotted against the shear areas (Ashear) in Fig. 13(a) for the end loaded specimens and in Fig. 13(b) for the interior loaded specimens. As seen from Fig. 13, a linear relationship can be identified between the elastic limit load and shear area Ashear for both end loading and interior loading conditions. It is interesting to find that the slope coefficient for the interior loading condition is 29.81 MPa, corresponding to 106.3% of the interlaminar shear strength fs (28.05 MPa); and that of the end loading condition is 16.38 Mpa, corresponding to 58.4% of the interlaminar shear strength. This finding implies that the shear stress distribution within the shear
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bearing force. In the study, 31 specimens were tested up to failure, with four pultruded GFRP square hollow sections. Four loading conditions were investigated: ETF, ITF, EG and IG. Based on the experimental study, the effects of loading position (end loading or interior loading) and the effects of supporting conditions (on bearing plate or on the ground) on the web crippling behaviour of pultruded GFRP sections were clarified. Failure modes, different from those of metallic counterparts under the same loading conditions, were observed for pultruded GFRP specimens under different loading conditions. A simple mechanism-based model was proposed for the web crippling strength of pultruded GFRP sections. The following specific conclusions can be drawn from this work:
Fig. 13. Relationship between experimental elastic limit load and Ashear: (a) end loading condition; and (b) interior loading condition.
area under the bearing plate may be more uniform for interior loaded specimens, i.e. the entire shear area under the bearing plate contributes to the load-carrying capacity. However, shear stress distribution may be highly non-uniform within the shear area for the end loading condition, with the result that only approximately half of the shear area (58.4%) contributes to the section capacity. Considering the linear relationship identified in Fig. 13, the following two equations are proposed for estimating the nominal web crippling capacity of pultruded GFRP sections:
RN ¼ ae fs Ashear ðend loading conditionÞ
ð3aÞ
RN ¼ ai fs Ashear ðinterior loading conditionÞ
ð3bÞ
where a value of 0.58 is fitted for ae under the end loading condition and 1.07 for ai under the interior loading condition. The elastic limit load calculations using Eq. (3) are compared with the experimental results from the current study in Table 2. It can be seen that the calculated RN based on the shear failure mechanism at the web–flange junction generally agrees well with the elastic limit load for both end loaded and interior loaded specimens. A mean of 0.98 with a COV of 0.19 is achieved for all specimens. 5. Conclusion This paper presents an experimental study of web crippling behaviour of pultruded GFRP sections subjected to a concentrated
(1) Web–flange junction failure was observed first for all square sections under various loading conditions. Subsequent web failure modes included shearing, buckling and crushing, depending on the web slenderness ratio: slender webs experienced buckling failure whereas stocky webs experienced crushing. It was also found that the initial web–flange junction failure and subsequent web failures concentrated at the upper portion of the section when the specimens were seated on the ground. (2) Elastic limit load and ultimate load were defined according to the failure modes and load–displacement responses. Both could be greatly improved when the loading position was changed from end loading to interior loading. However, the elastic limit load was not greatly affected by the supporting conditions, as it was dominated by the web–flange junction failure mechanism. In contrast, the ultimate load could be marginally increased when the section was seated on the ground rather than on a bearing plate, since it was dominated by the web failure mechanism. (3) An effective web area was identified for understanding of the effects of loading position and supporting condition on the ultimate load. When the concentrated bearing load was applied in the middle of the sections seated on the ground, the load could be transferred through a larger effective web area, which contributed to the load-carrying capacity. As a result, higher ultimate loads were found from the specimens seated on the ground with the load applied in the middle (IG). (4) Compared with metallic sections under concentrated bearing load, the pultruded GFRP section behaved very differently. Web–flange junction failure of pultruded GFRP sections invalidated the integration of the section and therefore the elastic limit load was considered as the web crippling capacity in design. Predictions of experimental results in this study using the design model in AS 4100 for cold-formed steel sections largely overestimated the elastic limit load, because of the different failure mechanisms of steel and pultruded GFRP sections. The web crippling model developed in the literature for pultruded GFRP sections was based on the IOF condition, and it also overestimated the experimental results. A new mechanism-based equation was therefore developed considering the web–flange junction shear failure mechanism. This design equation showed satisfactory agreement with experimental results. The new design equation for web crippling strength was established based on the limited experimental results presented in this paper. More experimental validation is expected to cover more section sizes and geometries. Nevertheless, because of the considerably reduced web crippling strength of pultruded GFRP sections subjected to concentrated loading in comparison to metallic sections, special attention must be paid when pultruded GFRP sections are used to sustain concentrated loading in the transverse direction at web positions. Possible strengthening approaches to
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improve the bearing capacity of pultruded GFRP sections are necessary as those proposed in [39]. Acknowledgements The authors gratefully acknowledge the financial support provided by the Australian Research Council through the Discovery Early Career Researcher Award scheme and Monash University. The authors also wish to thank Mr Xiang Ji and Mr Patric Morgan for preparation of specimens. Mr Kevin Nievaart and Mr Long Goh are acknowledged for their assistance in carrying out the experimental testing in the Civil Engineering Laboratory at Monash University. References [1] Keller T. Use of fiber reinforced polymers in bridge construction. Structural engineering documents 7. Zurich, Switzerland: International Association for Bridge and Structural Engineering (IABSE); 2003. [2] Hollaway L. Polymer composites for civil and structural engineering. London: Chapman & Hall; 1993. [3] Hollaway LC. Polymer composites in construction: a brief history. Proc ICE – Eng Comput Mech 2009;162(3):107–18. [4] Pendhari SS, Kant T, Desai YM. Application of polymer composites in civil construction: a general review. Compos Struct 2008;84(2):114–24. [5] Borowicz DT, Bank LC. Behavior of pultruded fiber-reinforced polymer beams subjected to concentrated loads in the plane of the web. J Comp Construction 2010;15(2):229–38. [6] Bai Y, Keller T, Wu C. Pre-buckling and post-buckling failure at web–flange junction of pultruded GFRP beams. Mater Struct 2013;46(7):1143–54. [7] Gao Y, Chen J, Zhang Z, Fox D. An advanced FRP floor panel system in buildings. Compos Struct 2013;96:683–90. [8] Wu C, Zhao XL, Duan WH. Design rules for web crippling of CFRP strengthened aluminium rectangular hollow sections. Thin-Walled Struct 2011;49(10):1195–207. [9] Packer JA. Web crippling of rectangular hollow sections. J Struct Eng 1984; 110(10):2357–73. [10] Zhao XL, Hancock GJ. Square and rectangular hollow sections subject to combined actions. J Struct Eng 1992;118(3):648–67. [11] Young B, Hancock GJ. Design of cold-formed channels subjected to web crippling. J Struct Eng 2001;127(10):1137–44. [12] Zhou F, Young B. Cold-formed stainless steel sections subjected to web crippling. J Struct Eng 2006;132(1):134–44. [13] Zhou F, Young B. Experimental and numerical investigations of cold-formed stainless steel tubular sections subjected to concentrated bearing load. J Constr Steel Res 2007;63(11):1452–66. [14] Zhou F, Young B, Zhao XL. Tests and design of aluminum tubular sections subjected to concentrated bearing load. J Struct Eng 2009;135(7):806–17. [15] Winter G, Pian RHJ. Crushing strength of thin steel webs. Cornell Bulletin 35, Part 1. Ithaca, N.Y.: Cornell University; 1946.
[16] Hancock GJ. Cold-formed steel structures. J Constr Steel Res 2003;59(4):473–87. [17] Zhao XL, Wilkinson T, Hancock GJ. Cold-formed tubular members and connections. Oxford, UK: Elsevier; 2005. [18] Zhou F, Young B. Aluminum tubular sections subjected to web crippling–Part I: tests and finite element analysis. Thin-Walled Struct 2008;46(4):339–51. [19] Young B, Zhou F. Aluminum tubular sections subjected to web crippling–Part II: proposed design equations. Thin-Walled Struct 2008;46(4):352–61. [20] AS/NZS 4600–2005. Cold-formed steel structures. Sydney, Australia: Standards Association of Australia; 2005. [21] Specification for the design of cold-formed stainless steel structural members. American Society of Civil Engineers. SEI/ASCE-8-02. Reston, VA; 2002. [22] AS/NZS 4673–2001. Cold-formed stainless steel structures. Sydney, Australia: Standards Association of Australia; 2001. [23] NAS. North American specification for the design of cold-formed steel structural members. Washington, DC: American Iron and Steel Institute; 2001. [24] NAS. Commentary on North American Specification for the design of coldformed steel structural members. Washington, DC: American Iron and Steel Institute; 2001. [25] Zhao XL, Hancock GJ. Square and rectangular hollow sections under transverse end-bearing force. J Struct Eng 1995;121(9):1323–9. [26] Young B, Hancock GJ. Cold-formed steel channels subjected to concentrated bearing load. J Struct Eng 2003;129(8):1003–10. [27] Bai Y, Keller T. Shear failure of pultruded fiber-reinforced polymer composites under axial compression. J Comp Construction 2009;13(3):234–42. [28] Bai Y, Vallée T, Keller T. Delamination of pultruded glass fiber-reinforced polymer composites subjected to axial compression. Compos Struct 2009;91(1):66–73. [29] Prachasaree W, GangaRao HVS. Web buckling strength evaluation of multicellular FRP bridge deck module. In: 4th international conference on engineering technologies. Novi Sad, Serbia; 2009. [30] Charoenphan S, Bank LC, Plesha ME. Progressive tearing failure in pultruded composite material tubes. Compos Struct 2004;63(1):45–52. [31] ASTM D3039/D3039M-08. Standard test method for tensile properties of polymer matrix composite materials. West Conshohocken, PA; 2008. [32] ASTM D2344/D2344M- 00. Standard test method for short-beam strength of polymer matrix composite materials and their laminates. West Conshohocken, PA; 2006. [33] Boyle MP, Roberts JC, Wienhold PD, Bao G, White GJ. Experimental, numerical, and analytical results for buckling and post-buckling of orthotropic rectangular sandwich panels. Compos Struct 2001;52(3–4):375–80. [34] Keller T, Castro JD. System ductility and redundancy of FRP beam structures with ductile adhesive joints. Compos B Eng 2005;36(8):586–96. [35] Castro JD, Keller T. Design of robust and ductile FRP structures incorporating ductile adhesive joints. Compos B Eng 2010;41(2):148–56. [36] Bai Y, Zhang C. Capacity of nonlinear large deformation for trusses assembled by brittle FRP composites. Compos Struct 2012;94(11):3347–53. [37] Prabakaran K, Schuster PM. Web crippling of cold-formed steel members. In: 14th International specialty conference on cold-formed steel structures. St. Louis, Missouri: University of Missouri-Rolla; 1998. p. 151–164. [38] AS 4100–1998. Steel structures. Sydney, Australia: Standards Association of Australia; 1998. [39] Crosky A, Kelly D, Li R, Legrand X, Huong N, Ujjin R. Improvement of bearing strength of laminated composites. Compos Struct 2006;76:260–71.
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Composite Structures journal homepage: www.elsevier.com/locate/compstruct
Web crippling behaviour of pultruded glass fibre reinforced polymer sections Chao Wu ⇑, Yu Bai 1 Department of Civil Engineering, Monash University, Clayton, VIC 3800, Australia
a r t i c l e
i n f o
Article history: Available online 15 October 2013 Keywords: Fibre-reinforced composite Pultrusion Web crippling Concentrated bearing load Web–flange junction Shear failure
a b s t r a c t We investigated the web crippling behaviour of pultruded GFRP sections under concentrated loading, employing four square hollow sections of different sizes. End-two-flange (ETF) and interior-two-flange (ITF) loading conditions were adopted, with specimens seated on a bearing plate. Specimens were also placed on the ground with end or interior bearing load to simulate the loading conditions of floor joist members. The observed failure initiated at web–flange junctions and was followed by buckling or crushing in the webs, and these modes were quite different from metallic sections. Correspondingly, two load limits were defined according to the progressive failure process. The effects of the loading positions (end loading or interior loading) as well as the supporting conditions (on a bearing plate or on the ground) on the web crippling behaviour are discussed. An effective web area in the pultrusion direction is identified to characterize the load transfer path within the web. Finally, a simple mechanism based design equation is proposed to estimate the strength of such pultruded GFRP sections subjected to web crippling. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction Pultruded glass fibre reinforced polymer (GFRP) composites have attracted extensive research attention as promising alternatives to conventional construction materials (steel and concrete) for civil infrastructure applications [1], due to their advantages of light weight, ease of installation, low maintenance, and resistance to harsh environmental conditions [2–4]. Because of the inherent orthotropic behaviour of the material, it is preferable for pultruded GFRP sections to carry loading in their pultrusion direction. Inevitably, however, there are situations when concentrated loading is applied and transferred in both longitudinal (pultrusion) and transverse directions [5–7], with reaction force and load from support or other structural members like joists, purlins and rafters. The term of ‘‘web crippling’’ was commonly used to describe the failure behaviour of metallic sections under such concentrated bearing load conditions [8,9], including web yielding and web buckling. For orthotropic pultruded GFRP sections under the same loading conditions, the failure mechanism may be different from that of metallic sections. The terminology of ‘‘web crippling’’ is extended in this paper to describe potential failure behaviour in general for pultruded GFRP sections under concentrated bearing load conditions.
⇑ Corresponding author. Tel.: +61 3 9905 4967. 1
E-mail addresses: [email protected] (C. Wu), [email protected] (Y. Bai). Tel.: +61 3 9905 4987.
0263-8223/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compstruct.2013.10.020
Extensive experimental research has been conducted on web crippling strength of thin-walled metallic sections [9–14], including cold-formed steel sections [11,15–17] and aluminium sections [18,19]. Four loading conditions have been specified according to existing design rules [20–24] of metallic sections, namely endone-flange (EOF), interior-one-flange (IOF), end-two-flange (ETF) and interior-two-flange (ITF). These loading conditions are classified based on the concentrated load acting on one flange only or both flanges as well as the location of the applied load [18]. However, these four loading conditions do not directly represent floor joist members seated on a solid foundation subjected to concentrated bearing load [13]. Zhao and Hancock [10,25], Young and Hancock [26] and Zhou and Young [13] conducted a series of tests on cold-formed steel sections subjected to concentrated bearing load, where the specimens were seated on a fixed solid steel base-plate. The same experimental setup was adopted for sharp corner aluminium tubular sections in [14]. In this way, the supporting condition of the floor joist members seated on solid foundations was realistically presented. In general, both web yielding and web buckling failure modes were observed for metallic sections under various loading conditions. The key parameters which affect web crippling strength include loading position (end or interior loading), supporting condition (section on bearing plate or on the ground), corner radius and web slenderness ratio (web height divided by web thickness) of a section, bearing plate size and material properties. Unlike isotropic steel and aluminium materials, pultruded GFRP sections have reduced material properties in the transverse
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Nomenclature B bplate fs H L Le PE Pi Pmax rext
total width of GFRP section width of the bearing plate interlaminar shear strength total height of GFRP section length of GFRP specimen effective length of GFRP specimen experimental web crippling strength elastic limit load ultimate load exterior corner radius of GFRP section
direction and tend to fail in interlaminar shear under compression loading [27,28], making the web crippling more critical when transverse concentrated loading is applied. However, experimental study of pultruded GFRP profiles subjected to web crippling is still limited. The web buckling strength of multi-cellular FRP bridge deck modules was experimentally investigated by Prachasaree and GangaRao [29]. FRP multi-cellular box sections of dimensions 76.2 73.7 cm were placed on a flat solid foundation. Truck loading was represented by applying compression over the top flange through a plate with dimensions 25.4 50.8 cm. With increase of the compression load, crack initiated at the web–flange junction and propagated along the longitudinal direction of the beam. In terms of web buckling strength per web, it was found that single web specimens performed better than multi-web specimens. This is because, for the single web section, the web was aligned with the centre line of the concentrated loading, and therefore load eccentricity effect was minimized. For multi-web specimens, however, certain webs were distant from the centre line of the concentrated loading, resulting in bending stress at the web–flange junction. The finding was further supported by the premature failure observed at the web–flange junction of multi-web specimens. Borowicz and Bank [5] investigated the behaviour of simply supported pultruded GFRP beams subjected to three-point bending through concentrated loads applied on the top flange in the plane of the web. Twenty pultruded GFRP I beams with nominal depths from 152.4 to 304.8 mm were examined, with a span-to-depth ratio of 4.0. Eight beams were mounted with bearing plates under the loading head; the other twelve beams were without bearing plates. Lateral supports were provided to prevent global stability failure of the specimens. All specimens failed with a wedgelike shear failure at the upper web–flange junction. The experimental results showed that the introduction of bearing plates increased the ultimate capacity of the beams by at least 35%. A design equation was proposed with parameters identified from experiments or selected from the design equations of metallic sections. The predicted capacities agreed well with the experimental results. That study covered only the IOF loading condition; other loading conditions such as ITF, EOF and ETF have not yet been examined and therefore no corresponding web crippling design approaches have been developed. In another study by Charoenphan et al. [30], the progressive tearing failure was identified as a typical damage mechanism in single-cell, thin-walled, rectangular pultruded composite material tubes subjected to transverse (bending) loads. This progressive failure occurred along the corners of the tube at the junction between the cell walls and propagated in a stable fashion as the transverse load was increased. The response was credited for enhancing load-carrying capacity in the tube and providing energy absorption during the failure. However, the work was also based on IOF loading condition, and no design method was proposed.
rin RN tf tplate tw D ETF ITF EG IG
interior corner radius of GFRP section nominal web crippling capacity flange thickness of GFRP section thickness of the bearing plate web thickness of GFRP section spacing between strain gauges in longitudinal direction end-two-flange loading condition interior-two-flange loading condition end loading condition with specimen on the ground interior loading condition with specimen on the ground
This paper addresses this knowledge gap by presenting an experimental study of the web crippling behaviour of pultruded GFRP profiles with square hollow sections (SHS) subjected to different loading conditions. Four GFRP square sections were chosen so that the effect of web slenderness ratio on web crippling behaviour could be investigated. Both ETF and ITF loading conditions were adopted, with concentrated loading applied simultaneously and symmetrically on the top and bottom flanges of GFRP sections. Specimens were also placed on a solid foundation with end or interior concentrated loading to simulate the supporting condition of floor joist members. The web crippling failure mechanisms of pultruded GFRP SHS sections were revealed by load–displacement curves as well as by the progressive failure process recorded by a video photogrammetry system. Finally, existing design approaches for web crippling failure of pultruded GFRP SHS sections were evaluated and a new mechanism-based design equation is proposed. 2. Experimental program 2.1. Materials Four pultruded GFRP SHS sections were examined in the experimental program. The measured section dimensions are presented in Table 1 using the symbols given in Fig. 1. The section ID is given by the initial S (square hollow section). Tensile coupon tests were carried out to determine the properties including the Young’s modulus and ultimate tensile strength in the pultrusion direction. Three-point bending short beam tests were also conducted to obtain interlaminar shear strength. The coupons were taken from the centre of the section webs and tested according to ASTM D 3039 [31] for tensile properties and ASTM D 2344 [32] for shear properties. The measured tensile modulus and strength in the pultrusion direction were 25 GPa and 283 MPa, respectively. The interlaminar shear strength was 28.05 MPa. 2.2. Specimens A total of 31 specimens were tested as listed in Table 2. The label of each specimen is comprised of three parts. The first part, S1–S4, is the section name (see Table 1). The second part is the loading condition (see Fig. 2), i.e. ETF for end-two-flange, ITF for interior-two-flange, EG for end bearing load with ground support and IG for interior bearing load with ground support. The third part is the ID of repeating specimens. The length of the specimen, L, was chosen to be much longer than the length required (1.5 times the total height of the web) in ASCE Specification [21] and the AS/NZS 4673 [22] for steel members, and the resulting lengthto-depth ratios were in a range of 3–8.
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C. Wu, Y. Bai / Composite Structures 108 (2014) 789–800 Table 1 Measured section dimensions. Section ID
Width B (mm)
Depth H (mm)
Flange thickness tf (mm)
Web thickness tw (mm)
Exterior corner radius rext (degree)
Interior corner radius rin (degree)
S1 S2 S3 S4
102.3 102.5 50.2 51.1
102.1 102.7 50.3 51.3
5.4 10.2 4.0 6.3
5.3 10.4 4.1 6.5
2.1 2.8 1.0 1.5
2.9 2.9 1.0 1.9
Fig. 1. Section shapes and symbols for SHS section. Table 2 Specimen length and gauge spacing and experimental results for all specimens. Specimens Specimen Gauge length spacing L (mm) D (mm)
Elastic Ultimate Predicted limit load load strength Pi (kN) Pmax (kN) RN (kN)
RN/Pi
S1-ETF-1 S1-ETF-2 S1-ITF-1 S1-ITF-2 S2-ETF-1 S2-ETF-2 S2-ITF-1 S2-ITF-2 S2-EG-1 S2-EG-2 S2-IG-1 S2-IG-2 S3-ETF-1 S3-ETF-2 S3-ITF-1 S3-ITF-2 S3-EG-1 S3-EG-2 S3-EG-3 S3-IG-1 S3-IG-2 S4-ETF-1 S4-ETF-2 S4-ETF-3 S4-ITF-1 S4-ITF-2 S4-EG-1 S4-EG-2 S4-EG-3 S4-IG-1 S4-IG-2 Average SD COV
10.64 15.12 26.88 26.58 19.68 26.06 42.81 40.14 20.84 18.81 48.63 47.61 12.18 12.88 16.42 15.78 11.02 11.72 11.42 12.54 15.78 13.57 22.75 18.73 20.41 27.09 14.58 16.36 19.96 29.46 24.81
1.14 0.81 0.84 0.85 1.22 0.92 1.03 1.10 1.15 1.27 0.91 0.93 0.77 0.73 1.06 1.10 0.86 0.80 0.82 1.39 1.10 1.10 0.66 0.80 1.35 1.02 1.03 0.91 0.75 0.94 1.11 0.98 0.18 0.19
300 300 600 600 300 300 600 600 300 300 600 600 200 200 400 400 200 200 200 400 400 200 200 200 400 400 200 200 200 400 400
65 65 70 70 65 65 70 70 65 65 70 70 40 40 45 45 40 40 40 45 45 40 40 40 45 45 40 40 40 45 45
14.21 15.41 30.26 29.90 26.22 26.79 45.32 48.47 32.41 32.20 52.28 50.53 15.53 13.85 21.24 19.44 14.43 15.43 16.40 22.32 23.39 15.14 25.53 21.86 32.02 28.82 21.66 21.04 21.50 31.82 28.96
12.19 12.19 22.50 22.50 23.93 23.93 44.14 44.14 23.93 23.93 44.14 44.14 9.43 9.43 17.40 17.40 9.43 9.43 9.43 17.40 17.40 14.96 14.96 14.96 27.59 27.59 14.96 14.96 14.96 27.59 27.59
2.3. Experimental set-up and instrumentation All tests were performed on a Baldwin Universal testing machine. Two loading conditions, ETF and ITF, were adopted for
S1–S4 sections (see Fig. 2a and b). Furthermore, to represent the loading condition of floor joist members, end bearing load and interior bearing load were also applied on S2–S4 by placing them on a fixed rigid steel base as shown in Fig. 2c and d. The load was applied through a rigid steel bearing plate 10 mm thick. The bearing length, bplate, seen in Fig. 2, was 50 mm for all the specimens. The width of the bearing plate (200 mm) was sufficient to act across the full flange widths of all GFRP sections. The compressive loading was applied in displacement control at a loading rate of 0.5 mm/min for all the specimens. The tests were stopped when the bearing plate displacement exceeded at least 15% the depth of the section. An ARAMIS photogrammetry system was used to monitor the progressive failure of specimens. The surface of web on one side was speckled (flat, white background with flat, black dots) to create a unique ‘‘fingerprint’’ for the ARAMIS software analysis (similar to that reported in [5]). Seven strain gauges, G1–G7, were attached on the web surface of the other side as shown in Fig. 3, where G1–G3 were vertically attached along the centre line of the bearing plates, and G4–G7 were attached in the pultrusion direction along the neutral axis of the web. The spacing (d in Fig. 3) of strain gauges G1–G3 was equal to half the depth of the corresponding section (2d = H) and the spacing of strain gauges G4–G7, D, is listed in Table 2 for different specimens. A video camera was also set up to record the progressive failure of all the specimens. The experimental set-up is shown in Fig. 4. 3. Experimental results and discussion 3.1. Failure modes The progressive failure process of each specimen was recorded using a video camera (see Fig. 4). From the experimental observations, the initial cracking at 45° occurred at web–flange junction of S1, with the two fracture surfaces sliding against each other as shown in Fig. 5a. From fracture mechanics point of view, this crack was attributed to Mode III shear failure. Subsequent bending cracks due to web buckling (similar to the buckling failure of composite plates in [33]) were identified as presented in the final failure mode in Fig. 5b. When the load was moved to the middle of the specimen, S1-ITF, similar initial crack was captured at the web– flange junction, as shown in Fig. 5c (the failure was captured from inside the specimen), followed by the steel bearing plate punching into the two webs. Finally the flanges tore off from the webs, while the other parts of the specimen away from the loading point remained intact (see Fig. 5d). This particular failure process, from the initial web–flange junction failure to the subsequent web failure modes, was observed for all the S1 specimens. For specimens with S2, very similar failure modes were identified from the two loading conditions ETF and ITF. Under ETF (see Fig. 6a), cracks initiated at the four web–flange junctions, followed by crushing of the webs. When the specimens were loaded with ITF (see Fig. 6b), the failure was also very localised within the loading zone where the flange was separated from the web and then the longitudinal fibres of the webs were broken by the steel bearing plate. When the section was seated on the ground (EG and IG), it
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Fig. 2. Illustration of loading conditions: (a) ETF; (b) ITF; (c) end bearing with solid ground (EG); and (d) interior bearing with solid ground (IG). S1 was only subjected to (a and b).
Fig. 3. Strain gauge arrangement: (a) end loaded specimen; and (b) interior loaded specimen.
was noticed that the upper part of the section experienced more serious damage than the lower part, as shown in Fig. 6(c and d) for the corresponding failure modes. As with S1 and S2, 45° cracks were observed at all web–flange junctions of S3 subjected to ETF, as shown in Fig. 7a. This resulted in separation of the webs and flanges, and finally both webs failed in buckling. The failure modes are shown in Fig. 7b for S3 loaded under ITF, where the two webs are crushed at the top and bottom flanges and buckling cracks are also observed in the middle of the webs. When seated on the solid ground under loading condition EG, specimens S3-EG (Fig. 7c) experienced the same 45° separation at the top two web–flange junctions, and subsequently the two
webs of S3-EG failed by shear. This shear failure modes in the webs were capture clearly by the video camera as in Fig. 7c, which was credited to the lower shear strength comparing to the compressive strength of pultruded GFRP laminate as explained in [27,28]. When the loading was applied in the middle of S3 (i.e. IG), the top flange of the specimens S3-IG separated from the webs and the two webs were crushed with the bearing plate punched into the webs. It was also noticed that the lower part of the specimen placed on solid ground experienced little damage (see Fig. 7c and d). The failure modes of Section S4 were very similar to those of S2, as shown in Fig. 8. The webs failed mainly by crushing rather than by buckling or shear as observed for Sections S1 and S3 (see Figs. 5
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the traditional terminology in existing international standards for the design of structural sections under concentrated bearing load conditions. For metallic sections, ‘‘web crippling’’ may comprise web yielding or web buckling failure modes. For pultruded GFRP square hollow sections, ‘‘web buckling’’ is characterized by a series of new failure mechanisms including web–flange junction separation, web buckling, web shearing and/or web crushing. Because of the web–flange junction separation, the concentrated loading was consequently carried by the webs, resulting in shearing, buckling and/or crushing failure of the webs. These subsequent failure modes of the webs appeared dependent on the web slenderness ratio: buckling and/or shearing failure occurred for Sections S1 and S3 with slenderness ratios ranging from 12.3 to 19.5 whereas web crushing occurred for Sections S2 and S4 with lower slenderness ratios from 7.9 to 9.9. 3.2. Load–displacement curves Fig. 4. Experimental set-up and instrumentation.
and 7). This may be because the web slenderness ratios of S2 and S4 were relatively lower than those of the other two sections (S1 and S3). In summary, a progressive failure process was observed as an initial 45° web–flange junction failure followed by individual web failure modes. These failure mechanisms were not observed in metallic sections. However, the term of ‘‘web crippling’’, as used to describe the failure behaviour of metallic sections, is extended to pultruded GFRP sections. This is to maintain a consistence with
The curves of applied concentrated load versus the vertical displacement of the bearing plate are presented in Fig. 9a for S1 subjected to ETF and ITF. The load–displacement curves are categorized into two groups for S2–S4, i.e. ‘‘on the ground’’ and ‘‘on the bearing plate’’. These two groups are presented in the same graph for better comparison, as shown in Fig. 9(b–d). Several common aspects appeared in the load–displacement responses of all the sections, as demonstrated in Fig. 9. Firstly, the displacement was increased linearly with load until a certain limit was reached, after which failure initiated and progressively developed. This limit corresponded to the elastic limit of such sections
Fig. 5. Typical failure modes of section S1: (a) initial failure of S1-ETF-2; (b) final failure of S1-ETF-2; (c) initial failure of S1-ITF-1; and (d) final failure of S1-ITF-1.
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(a)
(b)
(c)
(d)
Fig. 6. Typical failure modes of section S2: (a) S2-ETF-1; (b) S2-ITF-2; (c) S2-EG-1; and (d) S2-IG-1.
Fig. 7. Typical failure modes of section S3: (a) S3-ETF-1; (b) S3-ITF-2; (c) S3-EG-2; and (d) S3-IG-2.
subjected to ITF, ETG, IG and EG loading conditions. Therefore the load at this point is defined as the ‘‘elastic limit load or capacity’’ of the sections. It should be noted that the load applied on the sections could increase in the progressive failure process, for example as shown in Fig. 9d for specimen S4-ITF-2. As a result,
the maximum load achieved during the entire loading process is defined as the ‘‘ultimate load or capacity’’ of the sections. In relation to the progressive failure process identified in Section 3.1, a two-system load-carrying mechanism can be proposed for the two corresponding load limits. The elastic limit load was
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(b)
(c)
(d)
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Fig. 8. Typical failure modes of section S4: (a) S4-ETF-3; (b) S4-ITF-2; (c) S4-EG-2; and (d) S4-IG-2.
associated with the initial failure at the top and/or bottom web– flange junctions of the sections. After the web–flange junction separation, the second load-carrying mechanism, the web system, then took effect, and the applied load was therefore sustained or developed further. The ultimate load was achieved when the subsequent web failure modes occurred. Such a two-system load-carrying mechanism represents a sectional redundancy [32,35] and therefore introduces sectional pseudo-ductility as shown in Fig. 9. This pseudo-ductility, which exhibited non-linear, decreasing stiffness with increasing load, similar to the behaviour of ductile structures, could be achieved by the progressive failure of brittle components or connections at system level [34–36]. Due to this progressive failure process, energy was dissipated as represented by the area under the load–displacement curve in Fig. 9. It can be seen that the energy dissipation was considerably affected by the loading position (end loading or interior loading). For specimens with the same section, when the load was moved from the end to the middle of the specimen (i.e. from ETF/EG to ITF/IG), both elastic limit load and ultimate load were substantially increased, resulting in a larger area under the load–displacement curve, i.e. higher energy dissipation during the progressive failure. 3.3. Elastic limit load and ultimate load The elastic limit load and ultimate load of each section identified from the load–displacement curves are listed in the last two columns of Table 2. The average values of repeating specimens are used for each section and presented in Fig. 10 for all loading conditions. The effects of three key parameters on the elastic limit load and ultimate load are discussed in this section, including supporting condition (on a bearing plate or on solid ground), loading position (end loading or interior loading) and web slenderness ratio. As indicated in Fig. 10, the elastic limit load was not greatly affected by the supporting conditions. For example, the average elastic limit load of S3-ETF (see Table 2) was 12.53 kN, which is
quite close (10% difference) to the elastic limit load of S3-EG of 11.39 kN. This is mainly because the elastic limit load was associated with the first failure mode at the web–flange junction under the bearing plate and could hardly be affected by the supporting condition. On the other hand, the loading position had considerable effect on the elastic limit load. For example, an increase by up to 107.5% was found for specimens with S1 on a bearing plate, when the load was moved from the end (S1-ETF) to the middle of the specimen (S1-ITF). Again, such an improvement in elastic limit load may be linked to the failure at web–flange junction. The effect of loading position on the ultimate load is also identified from Fig. 10. The largest increase of 103.1% in ultimate load was achieved by S1 on a bearing plate when the load was moved from end (S1-ETF) to middle of the specimen (S1-ITF). As shown in Fig. 10, the ultimate load also exhibited a general increasing trend when the supporting condition was changed from bearing plate to solid ground. For example, the increase in ultimate load ranged from 2.7% to 21.9% for end loaded specimens, and from 9.6% to 12.4% for interior loaded specimens. According to the previous discussion, the ultimate load was mainly associated with the web failure modes. When the specimens supported on solid ground were subjected to interior load, the concentrated load could be transferred to a larger web area and spread to a larger supporting area, thereby resulting in higher ultimate capacity. Fig. 11 shows the out-of-plane displacement of the web measured by ARAMIS for S2 supported on the bearing plate (S2-ETF) and for S2 supported on the ground (S2-EG). These measurements were made within the progressive failure process of the webs (i.e. after the failure of web–flange separation but before ultimate failure). The out-of-plane displacement field was normalised against the maximum value (4.50 mm for S2-EG and 10.11 mm for S2-ETF) to show the range of the web area contributing to the load transfer mechanism. It is clear in Fig. 11 that only a certain range of web was engaged in the deformation as a result of load transfer from the bearing plate to the web, and beyond this range the web deformation was negligible (for example the deep blue areas). This range of the web is therefore considered as the effective web
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Fig. 9. Load–displacement curves for all specimens: (a) Section S1; (b) Section S2; (c) Section S3; and (d) Section S4.
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Fig. 10. Elastic limit load and ultimate load of each section under various loading conditions.
area when the section is subjected to a concentrated bearing load. The effective area of S2 on the ground (S2-EG) is obviously larger than that of S2 on the bearing plate (S2-ETF), resulting in a 21.9% increase in ultimate load. Similarly, the effect of loading position on the ultimate load can also be explained by the concept of effective web area. When the load was moved from the end to the middle of the specimen, the load could be transferred to a larger effective web area due to the symmetric loading condition about the bearing plate. Finally, the web slenderness ratio of square sections had a significant effect on the ultimate load of those sections. For example, the ultimate load was improved by 79.0% under loading condition ETF when the web slenderness ratio was reduced from 19.2 (specimens S1-ETF) to 10.2 mm (specimens S2-ETF). It was also interesting to find that the improvement in elastic limit load correlated well with the increase of web thickness. For example, a 78% improvement in elastic limit load was found from the comparison between S1-ETF and S2-ETF, corresponding to a 96% increase of web thickness (from 5.3 mm for S1 to 10.4 mm for S2), and a 46% improvement in elastic limit load was identified when the web thickness increased by 51% from 4.1 mm for S3-ETF to 6.5 mm for S4-ETF. 4. Comparisons 4.1. Comparison to design methods for metallic sections An insight into the web crippling behaviour of pultruded GFRP sections can be achieved by comparison to previous research [10,12,13,18,19,25,26,37] on metallic sections subjected to concentrated bearing loads. Generally, the web crippling failures of metallic sections were characterized by web failure modes including web buckling and web yielding [38]. In contrast, due to the typical anisotropic material behaviour of pultruded GFRP sections, more complex failure modes were encountered, including web shearing, web buckling, web crushing and especially web–flange junction separation, the last of which was never experienced by metallic sections. Since section integrity is already invalidated after web– flange separation, this failure mode becomes more important for the design limit state. Therefore, the associated elastic limit load can be considered as the design web crippling capacity of pultruded GFRP sections under concentrated loading conditions. Because the design web crippling capacity of pultruded GFRP sections was determined by the corresponding failure mode, equations developed for the design of metallic sections may not
be directly applicable to pultruded GFRP sections. This contention is further justified by comparison between the experimental results from this study and the predictions using design models of cold-formed steel members. The design equation used in AS 4100 [38] was adopted as an example. Interlaminar shear capacity of GFRP section was used in the calculation to account for the shear failure mechanism. The comparison yields a mean of 1.83 for RN/ Pi, where RN is the predicted web crippling capacity using the design equation in AS 4100 [38] and Pi is the experimental elastic limit load. The standard deviation (SD) and coefficient of variation (COV) are 0.53 and 0.29, respectively. 4.2. Comparison to design methods for pultruded GFRP sections Studies of web crippling behaviour of pultruded GFRP sections are very limited. Borowicz and Bank (2010) [5] studied the behaviour of pultruded FRP I beams subjected to concentrated loads in the plane of the web. By studying design standards for web crippling capacity of metallic sections, Borowicz and Bank (2010) [5] proposed a nominal web crippling capacity for the interlaminar shear failure at the web–flange junction of pultruded GFRP I beams:
RN ¼ 0:7dtw fs 1 þ ð2k þ 6t plate þ bplate Þ=d
ð1Þ
where RN is the design web crippling capacity; bplate is the width of the bearing plate; tplate denotes the thickness of the bearing plate; d is the overall depth of the member; tw is the web thickness; k is the distance from top of the flange to the web toe of the fillet; and fs is the interlaminar shear strength of the web material. Eq. (1) was used in [5] to estimate the web crippling capacity of pultruded FRP I beams under a three-point bending condition and good agreement was reported, with an average ratio of 1.12 for the experimental results to the predictions. The SD and the COV were 0.11 and 0.10, respectively. Eq. (1) was used to predict the web crippling capacity of the specimens tested in the current study. The predicted results are compared with both the experimental elastic limit load and the ultimate load in Table 3. The parameters used for calculation can be found in Table 1 and k used in Eq. (1) is max{tf + rext; tf + rin}. As can be seen from Table 3, the predicted web crippling capacities are highly overestimated for all specimens. This is because Eq. (1) was developed based on a three-point bending set-up, which corresponds to the IOF loading condition and is not capable of considering failure mechanisms of the different loading conditions investigated in the current study. Therefore, it is necessary to
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Damage due to web– flange junction failure
102 mm
(a)
Damage due to web– flange junction failure
102 mm
(b) Fig. 11. Identification of effective web area through ARAMIS measurements: (a) specimen S2-ETF supported by bearing plate; and (b) specimen S2-EG supported by the ground.
Table 3 Predictions of experimental web crippling capacity using Eq. (1). Specimens
Elastic limit load Pi (kN)
Ultimate load Pmax (kN)
Predicted strength RN (kN)
R N/ Pi
RN/ Pmax
S1-ETF S1-ITF S2-ETF S2-ITF S2-EG S2-IG S3-ETF S3-ITF S3-EG S3-IG S4-ETF S4-ITF S4-EG S4-IG Average SD COV
12.88 26.73 22.87 41.48 19.83 48.12 12.53 16.10 11.39 14.16 18.35 23.75 16.97 27.14
14.81 30.08 26.51 46.90 32.31 51.41 14.69 20.34 15.42 22.86 20.84 30.42 21.40 30.39
49.52 49.52 102.05 102.05 102.05 102.05 28.69 28.69 28.69 28.69 47.09 47.09 47.09 47.09
3.84 1.85 4.46 2.46 5.15 2.12 2.29 1.78 2.52 2.03 2.57 1.98 2.77 1.73 2.68 1.02 0.38
3.34 1.65 3.85 2.18 3.16 1.99 1.95 1.41 1.86 1.25 2.26 1.55 2.2 1.55 2.16 1.23 0.57
Fig. 12. Illustration of Ashear under the bearing plate.
shear plane at the web–flange junction was observed from the failure modes. Therefore, Ashear can be expressed as
Ashear ¼ 2 tw bplate =cosð45 Þðtwo webs for square sectionÞ develop a new method to estimate the web crippling behaviour of pultruded GFRP sections under loading conditions of ETF, ITF, EG and IG, based on the failure mechanisms observed in the current experimental study. 4.3. Proposed web crippling design method for pultruded GFRP sections As discussed previously, the design web crippling capacity of pultruded GFRP sections is developed for their elastic limit loads. According to the observed Mode III shear failure mechanism at the web–flange junction, the nominal elastic limit load, RN, should be a function of the interlaminar shear strength (fs) [5], the shear area (Ashear) under the bearing plate, and the shear stress distribution within the area. Ashear is illustrated in Fig. 12 where the 45°
ð2Þ
Also as discussed previously, the elastic limit load was considerably affected by the loading position (end loading or interior loading). Therefore, the experimental results of elastic limit load are plotted against the shear areas (Ashear) in Fig. 13(a) for the end loaded specimens and in Fig. 13(b) for the interior loaded specimens. As seen from Fig. 13, a linear relationship can be identified between the elastic limit load and shear area Ashear for both end loading and interior loading conditions. It is interesting to find that the slope coefficient for the interior loading condition is 29.81 MPa, corresponding to 106.3% of the interlaminar shear strength fs (28.05 MPa); and that of the end loading condition is 16.38 Mpa, corresponding to 58.4% of the interlaminar shear strength. This finding implies that the shear stress distribution within the shear
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bearing force. In the study, 31 specimens were tested up to failure, with four pultruded GFRP square hollow sections. Four loading conditions were investigated: ETF, ITF, EG and IG. Based on the experimental study, the effects of loading position (end loading or interior loading) and the effects of supporting conditions (on bearing plate or on the ground) on the web crippling behaviour of pultruded GFRP sections were clarified. Failure modes, different from those of metallic counterparts under the same loading conditions, were observed for pultruded GFRP specimens under different loading conditions. A simple mechanism-based model was proposed for the web crippling strength of pultruded GFRP sections. The following specific conclusions can be drawn from this work:
Fig. 13. Relationship between experimental elastic limit load and Ashear: (a) end loading condition; and (b) interior loading condition.
area under the bearing plate may be more uniform for interior loaded specimens, i.e. the entire shear area under the bearing plate contributes to the load-carrying capacity. However, shear stress distribution may be highly non-uniform within the shear area for the end loading condition, with the result that only approximately half of the shear area (58.4%) contributes to the section capacity. Considering the linear relationship identified in Fig. 13, the following two equations are proposed for estimating the nominal web crippling capacity of pultruded GFRP sections:
RN ¼ ae fs Ashear ðend loading conditionÞ
ð3aÞ
RN ¼ ai fs Ashear ðinterior loading conditionÞ
ð3bÞ
where a value of 0.58 is fitted for ae under the end loading condition and 1.07 for ai under the interior loading condition. The elastic limit load calculations using Eq. (3) are compared with the experimental results from the current study in Table 2. It can be seen that the calculated RN based on the shear failure mechanism at the web–flange junction generally agrees well with the elastic limit load for both end loaded and interior loaded specimens. A mean of 0.98 with a COV of 0.19 is achieved for all specimens. 5. Conclusion This paper presents an experimental study of web crippling behaviour of pultruded GFRP sections subjected to a concentrated
(1) Web–flange junction failure was observed first for all square sections under various loading conditions. Subsequent web failure modes included shearing, buckling and crushing, depending on the web slenderness ratio: slender webs experienced buckling failure whereas stocky webs experienced crushing. It was also found that the initial web–flange junction failure and subsequent web failures concentrated at the upper portion of the section when the specimens were seated on the ground. (2) Elastic limit load and ultimate load were defined according to the failure modes and load–displacement responses. Both could be greatly improved when the loading position was changed from end loading to interior loading. However, the elastic limit load was not greatly affected by the supporting conditions, as it was dominated by the web–flange junction failure mechanism. In contrast, the ultimate load could be marginally increased when the section was seated on the ground rather than on a bearing plate, since it was dominated by the web failure mechanism. (3) An effective web area was identified for understanding of the effects of loading position and supporting condition on the ultimate load. When the concentrated bearing load was applied in the middle of the sections seated on the ground, the load could be transferred through a larger effective web area, which contributed to the load-carrying capacity. As a result, higher ultimate loads were found from the specimens seated on the ground with the load applied in the middle (IG). (4) Compared with metallic sections under concentrated bearing load, the pultruded GFRP section behaved very differently. Web–flange junction failure of pultruded GFRP sections invalidated the integration of the section and therefore the elastic limit load was considered as the web crippling capacity in design. Predictions of experimental results in this study using the design model in AS 4100 for cold-formed steel sections largely overestimated the elastic limit load, because of the different failure mechanisms of steel and pultruded GFRP sections. The web crippling model developed in the literature for pultruded GFRP sections was based on the IOF condition, and it also overestimated the experimental results. A new mechanism-based equation was therefore developed considering the web–flange junction shear failure mechanism. This design equation showed satisfactory agreement with experimental results. The new design equation for web crippling strength was established based on the limited experimental results presented in this paper. More experimental validation is expected to cover more section sizes and geometries. Nevertheless, because of the considerably reduced web crippling strength of pultruded GFRP sections subjected to concentrated loading in comparison to metallic sections, special attention must be paid when pultruded GFRP sections are used to sustain concentrated loading in the transverse direction at web positions. Possible strengthening approaches to
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improve the bearing capacity of pultruded GFRP sections are necessary as those proposed in [39]. Acknowledgements The authors gratefully acknowledge the financial support provided by the Australian Research Council through the Discovery Early Career Researcher Award scheme and Monash University. The authors also wish to thank Mr Xiang Ji and Mr Patric Morgan for preparation of specimens. Mr Kevin Nievaart and Mr Long Goh are acknowledged for their assistance in carrying out the experimental testing in the Civil Engineering Laboratory at Monash University. References [1] Keller T. Use of fiber reinforced polymers in bridge construction. Structural engineering documents 7. Zurich, Switzerland: International Association for Bridge and Structural Engineering (IABSE); 2003. [2] Hollaway L. Polymer composites for civil and structural engineering. London: Chapman & Hall; 1993. [3] Hollaway LC. Polymer composites in construction: a brief history. Proc ICE – Eng Comput Mech 2009;162(3):107–18. [4] Pendhari SS, Kant T, Desai YM. Application of polymer composites in civil construction: a general review. Compos Struct 2008;84(2):114–24. [5] Borowicz DT, Bank LC. Behavior of pultruded fiber-reinforced polymer beams subjected to concentrated loads in the plane of the web. J Comp Construction 2010;15(2):229–38. [6] Bai Y, Keller T, Wu C. Pre-buckling and post-buckling failure at web–flange junction of pultruded GFRP beams. Mater Struct 2013;46(7):1143–54. [7] Gao Y, Chen J, Zhang Z, Fox D. An advanced FRP floor panel system in buildings. Compos Struct 2013;96:683–90. [8] Wu C, Zhao XL, Duan WH. Design rules for web crippling of CFRP strengthened aluminium rectangular hollow sections. Thin-Walled Struct 2011;49(10):1195–207. [9] Packer JA. Web crippling of rectangular hollow sections. J Struct Eng 1984; 110(10):2357–73. [10] Zhao XL, Hancock GJ. Square and rectangular hollow sections subject to combined actions. J Struct Eng 1992;118(3):648–67. [11] Young B, Hancock GJ. Design of cold-formed channels subjected to web crippling. J Struct Eng 2001;127(10):1137–44. [12] Zhou F, Young B. Cold-formed stainless steel sections subjected to web crippling. J Struct Eng 2006;132(1):134–44. [13] Zhou F, Young B. Experimental and numerical investigations of cold-formed stainless steel tubular sections subjected to concentrated bearing load. J Constr Steel Res 2007;63(11):1452–66. [14] Zhou F, Young B, Zhao XL. Tests and design of aluminum tubular sections subjected to concentrated bearing load. J Struct Eng 2009;135(7):806–17. [15] Winter G, Pian RHJ. Crushing strength of thin steel webs. Cornell Bulletin 35, Part 1. Ithaca, N.Y.: Cornell University; 1946.
[16] Hancock GJ. Cold-formed steel structures. J Constr Steel Res 2003;59(4):473–87. [17] Zhao XL, Wilkinson T, Hancock GJ. Cold-formed tubular members and connections. Oxford, UK: Elsevier; 2005. [18] Zhou F, Young B. Aluminum tubular sections subjected to web crippling–Part I: tests and finite element analysis. Thin-Walled Struct 2008;46(4):339–51. [19] Young B, Zhou F. Aluminum tubular sections subjected to web crippling–Part II: proposed design equations. Thin-Walled Struct 2008;46(4):352–61. [20] AS/NZS 4600–2005. Cold-formed steel structures. Sydney, Australia: Standards Association of Australia; 2005. [21] Specification for the design of cold-formed stainless steel structural members. American Society of Civil Engineers. SEI/ASCE-8-02. Reston, VA; 2002. [22] AS/NZS 4673–2001. Cold-formed stainless steel structures. Sydney, Australia: Standards Association of Australia; 2001. [23] NAS. North American specification for the design of cold-formed steel structural members. Washington, DC: American Iron and Steel Institute; 2001. [24] NAS. Commentary on North American Specification for the design of coldformed steel structural members. Washington, DC: American Iron and Steel Institute; 2001. [25] Zhao XL, Hancock GJ. Square and rectangular hollow sections under transverse end-bearing force. J Struct Eng 1995;121(9):1323–9. [26] Young B, Hancock GJ. Cold-formed steel channels subjected to concentrated bearing load. J Struct Eng 2003;129(8):1003–10. [27] Bai Y, Keller T. Shear failure of pultruded fiber-reinforced polymer composites under axial compression. J Comp Construction 2009;13(3):234–42. [28] Bai Y, Vallée T, Keller T. Delamination of pultruded glass fiber-reinforced polymer composites subjected to axial compression. Compos Struct 2009;91(1):66–73. [29] Prachasaree W, GangaRao HVS. Web buckling strength evaluation of multicellular FRP bridge deck module. In: 4th international conference on engineering technologies. Novi Sad, Serbia; 2009. [30] Charoenphan S, Bank LC, Plesha ME. Progressive tearing failure in pultruded composite material tubes. Compos Struct 2004;63(1):45–52. [31] ASTM D3039/D3039M-08. Standard test method for tensile properties of polymer matrix composite materials. West Conshohocken, PA; 2008. [32] ASTM D2344/D2344M- 00. Standard test method for short-beam strength of polymer matrix composite materials and their laminates. West Conshohocken, PA; 2006. [33] Boyle MP, Roberts JC, Wienhold PD, Bao G, White GJ. Experimental, numerical, and analytical results for buckling and post-buckling of orthotropic rectangular sandwich panels. Compos Struct 2001;52(3–4):375–80. [34] Keller T, Castro JD. System ductility and redundancy of FRP beam structures with ductile adhesive joints. Compos B Eng 2005;36(8):586–96. [35] Castro JD, Keller T. Design of robust and ductile FRP structures incorporating ductile adhesive joints. Compos B Eng 2010;41(2):148–56. [36] Bai Y, Zhang C. Capacity of nonlinear large deformation for trusses assembled by brittle FRP composites. Compos Struct 2012;94(11):3347–53. [37] Prabakaran K, Schuster PM. Web crippling of cold-formed steel members. In: 14th International specialty conference on cold-formed steel structures. St. Louis, Missouri: University of Missouri-Rolla; 1998. p. 151–164. [38] AS 4100–1998. Steel structures. Sydney, Australia: Standards Association of Australia; 1998. [39] Crosky A, Kelly D, Li R, Legrand X, Huong N, Ujjin R. Improvement of bearing strength of laminated composites. Compos Struct 2006;76:260–71.