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Load-carrying capacity of GFRP bars under combined axial force–transverse force loading
Composites: Part B 44 (2013) 167–171
Contents lists available at SciVerse ScienceDirect
Composites: Part B journal homepage: www.elsevier.com/locate/compositesb
Load-carrying capacity of GFRP bars under combined axial force–transverse force loading Andrin Herwig ⇑, Masoud Motavalli Empa, Swiss Federal Laboratories for Materials Science and Technology, Structural Engineering Laboratory, Ueberlandstrasse 129, CH-8600 Duebendorf, Switzerland
a r t i c l e
i n f o
Article history: Received 6 January 2012 Received in revised form 31 May 2012 Accepted 12 June 2012 Available online 21 June 2012 Keywords: A. Glass fibers B. Mechanical properties B. Strength D. Mechanical testing Combined loading
a b s t r a c t In several applications, glass fiber reinforced plastic (GFRP) bars are loaded with a transverse force while they simultaneously carry an axial force. Short-term tests of combined axial and transverse loading on assemblies consisting of one GFRP bar and two steel sleeves are described in this paper. The results show that the axial force capacity of the GFRP bar is affected only if the transverse force exceeds a certain threshold. A qualitative fracture criterion for combined axial force–transverse force loading is suggested. Further combined axial force–transverse force loading tests have been conducted on a specimen with a severe, forced 4° bending misalignment. These misaligned GFRP bars sustained more than 80% of the tensile resistance of the corresponding straight bars (without misalignment). Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction In the tunneling and mining industry, glass fiber reinforced plastic GFRP bars are used more frequently than steel for temporary rock anchors because they are more easily cut, which avoids damage to the tunnel drilling machine. GFRP bars are also used more frequently in the building industry because they are more resistant to corrosion, weigh less and have a lower heat conductivity than steel. In some of these applications, the application of an axial force to the GFRP bar is accompanied by a transverse force. Such transverse forces may appear with dislocation movements when rock bolts are used. The combined axial force–transverse force loading has not been investigated extensively. An experimental investigation of the pultruded GFRP elements of a cellular cross section is described in [1]. These GFRP elements have been built in a load carrying a ‘‘thermal insulation section’’ system for cantilevered balconies. Fig 1 shows the main elements of another type of thermal insulation section for overhanging balconies, including the ceiling slab, the insulation section and the balcony slab. The GFRP elements of [1] carried both compressive and transverse forces. However, the GFRP, as one component of the system, was not critical at the ultimate limit state. Therefore, no conclusions about the fracture behavior of the GFRP could be drawn from this study. However, there have been investigations of single GFRP elements. The investigation described in [2] describes the failure ⇑ Corresponding author. Tel.: +41 58 765 4791; fax: +41 58 765 44 55. E-mail address: [email protected] (A. Herwig). 1359-8368/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compositesb.2012.06.012
behavior of slender, pultruded GFRP laminates under axial compressive forces. Bending moments and transverse forces occur within these slender GFRP laminates because of the lateral deformations (buckling), and this interlaminar shear leads to failure. Short elements have also been extensively investigated. The transverse force behavior of GFRP and steel bars used as dowels in pavement joints with full scale static and cyclic tests is described in [3,4]. However, contrary to the present study, no axial force was applied to the GFRP bar because the pavement joints are designed as dilatation joints. One criterion of that study was the ‘‘joint effectiveness’’, which describes the stiffness as a function of the relative vertical movements between adjacent pavement slabs. Another criterion was the magnitude of the stress between the dowel and the concrete. This paper describes a mechanical component of a thermal insulation section (Fig. 1), which was developed in a collaborative operation between the Hitek Construction AG Company, Gstaad, Switzerland and Empa. The patent rights for the load-transferring GFRP elements are now in the possession of ERICO LENTON Concrete Reinforcement Products. The shear forces and bending moments are transferred exclusively through the GFRP bars and GFRP blocks, which cross vacuum insulation panels horizontally and are anchored in the adjacent concrete slabs. A detailed description of the entire investigation program can be found in [5]. This paper focuses on the tests of the upper GFRP element, as shown Fig. 1. Combined axial force–transverse force loading tests have also been conducted with a specimen with a forced 4° bending misalignment. Misalignment may occur because of inaccuracies during mounting in the field or may have to be considered in the
168
A. Herwig, M. Motavalli / Composites: Part B 44 (2013) 167–171
interior
exterior upper steel – GFRP element to be tested
GFRP in steel sleeve GFRP block façade insulation masonry reinforcing bar steel sleeve reinforcing bar GFRP bar
20 mm
Detail: upper steel – GFRP element Fig. 1. Load-transferring insulation section with horizontal steel–GFRP elements.
design of structures which should resist to damage scenarios leading to permanent deformations. The magnitude of the present forced misalignment may be considered as a severe case. A test set-up was designed to produce similar mechanical constraints for the upper GFRP element.
Transverse force (V)
no rotation around z-axis
2. Test specimen
Axial force compressive (C) or tensile (T)
The test specimen is shown in Fig. 2. The specimen consisted of a threaded GFRP bar with unidirectional E-glass fibers embedded in an epoxy resin matrix (glass fiber volume content, UV = 65 %). The GFRP bar is screwed 100 mm into two threaded steel sleeves that serve as anchorages. The void between the bar and the sleeve is injected with epoxy resin. The GFRP bar has a free length of 25 mm between the two sleeves. The axial force is introduced through a threaded connection at both ends of the specimen.
y
z
x
Fig. 3. Schematic loading system for the steel–GFRP element.
3.2. Experimental program and test results 3. Tests without forced misalignment 3.1. Loading system The loading system (Fig. 3) allows both sleeves to remain parallel to each other while translational movements between both sleeves remain possible. Both axial and transverse forces may be applied to the GFRP. The forces are produced by hydraulic jacks and measured by load cells.
Pure transverse force, axial force and combined axial–transverse force tests were conducted. The transverse and ultimate axial forces are listed in Table 1. The transverse force was increased until failure at a rate of 120 N/s for the pure transverse force tests (Nos. 1 and 2 in Table 1). The transverse forces in tests 1 and 2 reached V = 22.3 and 20.9 kN, respectively. The force was increased at a rate of 650 N/s for the pure tensile force tests (Nos. 3–6). The ultimate forces ranged from 235 to
Steel sleeve internal thread for axial force introduction injection fitting GFRP bar, A GFRP = 346 mm2 25
Cross section:
130
34
24 25
130
100
100
[mm] Fig. 2. Longitudinal section and cross section of the steel–GFRP element.
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Specimen no. 1 2
Transverse force V (kN) 22.3 20.9
Axial force T(+)/C() (kN)
Loading
– –
Transverse force increased until failure
3 4 5 6 7 8 9 10 11 12 13 14 15 16
– – – – 10 15 15 15 – – – 5 5 10
236 230 245 235 237 225 219 186 154 160 158 156 165 129
Axial force increased until failure
17 18 19 20
10 10 10 10
120 120 110 100
Time [s] at which failure occurred
10 40 10 300
21
10
70
No failure [s]
7200
22 23 24
15 15 15
70 70 50
Time [s] at which failure occurred
10 40 70
245 kN. The steel sleeves were reinforced by supplementary overscrewed sleeves to avoid a sleeve fracture because the short-term resistance of the GFRP bar was greater than that of the steel sleeve. For the combined tensile–transverse force tests (Nos. 7–10), the tensile force was increased at a rate of 650 N/s with a constant transverse force. The ultimate tensile forces obtained with a 15 kN transverse force (Nos. 8–10) were more varied than the forces obtained in the pure tensile tests (Nos. 3–6). The values ranged from 186 to 225 kN. The ultimate axial tensile force obtained with a 10 kN transverse force, corresponding to 50% of the pure transverse force resistance (No. 7), reached a value of 237 kN. This value corresponds to the average of the ultimate tensile forces obtained without a transverse force (Nos. 3–6). Because there was only one result for a 10 kN transverse force, attention was directed to the ultimate tensile forces of the next larger transverse force (15 kN, Nos. 8–10). The average of 210 kN for this group reached 90% of the average of the ultimate tensile forces that were obtained with 10 and 0 kN transverse forces. Thus, the ultimate tensile force was only slightly changed as the transverse force increased to 15 kN. Based on this result, we have concluded that there is no significant influence on the ultimate tensile force with transverse forces up to 10 kN. The compressive force was increased at a rate of 250 N/s for the pure compressive tests (Nos. 11–13). The ultimate resistance varied between 154 and 160 kN. The compressive force was increased at a rate of 650 N/s for the combined compression–transverse force tests (Nos. 14–17). While there was no decrease in the axial compressive force between transverse forces of 0 kN (Nos. 11–13) and 5 kN (Nos. 14 and 15), with mean values of 157 kN and 160 kN, respectively, the axial compressive force was reduced with a 10 kN transverse force (No. 16). The supplementary creep tests (Nos. 17–24) ascertained how the GFRP bars behave under a constant combined compression– transverse force loading. While a sudden fracture occurred with a
10 kN transverse force at an axial compressive force of 129 kN (No. 16), the creep specimens failed after several seconds under sustained axial compressive forces of 120 and 110 kN (Nos. 17– 19). Failure occurred only after 300 s with a 100 kN sustained axial compressive force (No. 20). No failure occurred after 7200 s for a 70 kN sustained axial compressive force (No. 21). For this force, which corresponds to 55% of the ultimate compressive force of test Nos. 16, the transverse deformation showed a typical exponential increase over time with an asymptotic tendency over the chosen period (Fig. 4). With application of a 15 kN transverse force, the specimens failed under 70 and 50 kN sustained axial compressive forces after several seconds (Nos. 22–24). As observed with the 10 kN transverse force (Nos. 17–20), creep deformation in the transverse direction led to instability and failure after delamination occurred in a direction parallel to the fibers. These creep tests showed that instability occurs with the application of a 10 kN transverse force even when the axial compressive force was smaller than 129 kN. 3.3. Fracture patterns Fig. 5 shows the fracture patterns of one specimen per loading mode. Delamination parallel to the fibers occurred under a pure transverse force (Fig. 5a). There were no broken glass fibers. The fibers broke along a craggy fracture surface under pure tensile loading (Fig. 5b). The same behavior was observed under combined tensile–transverse force loading, but the fracture surface was diagonal (Fig. 5c). The specimen failed completely, breaking into two parts, after the pure compressive test (Fig. 5d). For the combined compression–transverse force test (Fig. 5e), delamination occurred as in the pure transverse force tests (Fig. 5a), but in addition, there were buckled fibers. 3.4. Failure criteria Fig. 6 shows the results of the tests with axial tensile and transverse forces. The dots correspond to the test results, and the line represents a failure criterion. As stated above, the tensile resistance was not altered by transverse forces below a certain threshold. This threshold occurred at approximately 50% of the pure transverse force resistance. The first branch of the fracture criterion is therefore plotted as a horizontal line, while a second branch indicates a linear decrease of the ultimate tensile resistance with increasing transverse force. The fracture criterion is described by the following equations.
V k 6 gT V o;k :
T k ¼ T o;k
ð1aÞ
1.0
Transverse displacement [mm]
Table 1 Results of the combined axial force–transverse force tests.
0.9
C = -70 kN V = 10 kN
0.8
No. 21 0.7 0
0.5
1
1.5
2
time [h] Fig. 4. Creep deformation with the application of 70 kN compressive and 10 kN transverse forces (Specimen No. 21).
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Fig. 5. Fracture patterns: (a) pure transverse force, (b) pure tensile force, (c) combined tensile - transverse force, (d) pure compression, (e) combined compression–transverse force.
Ck is the characteristic value of the compressive resistance under the combined loading, Co,k is the characteristic value of the pure compressive resistance and gC is the fraction of the pure transverse force resistance, Vo,k, below which the compressive resistance is not altered. To develop the interaction diagrams shown in Figs. 6 and 7, the following values were used: gT = 0.5, Vo,k = 18 kN, To,k = 225 kN, c = 0 kN, Co,k = 150 kN, gC = 0.25, b = 728.6 and d = 0.545.
Ultimate tensile force T [kN]
300 ηΤ •Vo,k
To,k
250 200
test result
150 100 50 failure criterion Tk (Vk)
4. Tests with forced misalignment
Vo,k
0
0
5
10
15
20
25
4.1. Loading system
Transverse force V [kN] Fig. 6. Tensile – transverse force–interaction diagram.
V o;k > V k > gT V o;k :
T k ¼ T o;k 2
Vk ð1 gT ÞV o;k
þ c:
ð1bÞ
Vk and Tk are the characteristic values under combined loading of the transverse and the tensile resistances, respectively, To,k is the characteristic value of the pure tensile resistance and gT is the fraction of the pure transverse force resistance, Vo,k, below which the tensile resistance is not altered. Fig. 7 comprises the results of the tests using axial compressive forces. The lower values at V = 10 and 15 kN correspond to the creep tests, in which the loading was maintained at a constant value until failure occurred. As in the tests with axial tensile forces, there is a threshold for the transverse force, below which the compressive resistance is not influenced. As a result, transverse forces below 25% of the pure transverse force resistance do not affect the compressive resistance according to this criterion. For larger transverse forces the curve drops steeply. The criterion in Eq. (2a) and Eq. (2b) is proposed for the combined compression–transverse force loading:
V k 6 gC V o;k :
C k ¼ C o;k
V o;k > V k > gC V o;k :
4.2. Test program and results The forced 4° rotation led to a curvature of k = 1.5 103 mm1 for the free length of the specimen (Fig. 8). In this experiment, one steel sleeve was clamped in the test set up (Fig. 8a), and the other sleeve was tilted by 4°, applying a forced rotation. No rupture of
(a)
4o
ð2aÞ
C k ¼ C o;k þ b ðV k gc V o;k Þd
y
ð2bÞ
z
x
Transverse force (V)
-200
Ultimate compressive force C [kN]
To supplement the previous tests, the effect of a forced misalignment on the GFRP bar was examined with two additional specimens. These tests were motivated by the investigation of a possible damage scenario for the balcony system shown in Fig. 1. A forced 4° rotation was applied before testing (Fig. 8).
ηc •Vo,k
(b)
Co,k
no rotation around z - axis
-150
during transverse loading
-100
test result
Axial tensile force (T)
-50 failure criterion Ck (Vk)
0 0
5
10
y
Vo,k
15
20
-3
κ = 1.5 x 10 mm
25
-1
z
x
Transverse force V [kN] Fig. 7. Compressive – transverse force–interaction diagram.
Fig. 8. Schematic loading system for the steel–GFRP element, (a) clamped straight specimen, (b) misaligned specimen under combined loading.
A. Herwig, M. Motavalli / Composites: Part B 44 (2013) 167–171 Table 2 Results of the combined axial force–transverse force tests with forced curvature. Specimen no.
Trans-verse force V (kN)
Axial force (T/C) (kN)
Loading
25 26
– 10
212 199
Axial force increased until failure
Fig. 9. Fracture pattern with forced curvature: (a) without any transverse force and (b) with transverse force.
fibers could be observed during or after bending. Then, a combined tensile-transverse force test was conducted on the deformed specimen (Fig. 8b). Table 2 shows the forces at failure. The axial force reached 212 kN with a 0 kN transverse force (No. 25), 10% lower than the axial forces obtained in test Nos. 3–6, as shown in Table 1, which were loaded with the same load combination but without any forced misalignment. Specimen No. 26, with a 10 kN transverse force, failed at 199 kN, 16% lower than specimen No. 7 with the same loading, but without misalignment (Table 1). 4.3. Fracture pattern Fig. 9 shows the fracture pattern of the specimen with forced curvature. The fracture pattern exhibited similar characteristics to the patterns obtained in the tests without forced curvature, shown in Fig. 5b and c. 5. Results and discussion The load-carrying capacity of GFRP bars under combined axial force–transverse force loading was investigated, and a failure criterion was established. The findings that are described here are based on the particular product that was investigated and the applied boundary conditions. Additional testing should be conducted to more precisely determine the parameters of the failure criterion. The findings may lay the foundation for tests and characterizations for other types of GFRP bars that may be used in similar structures. The following conclusions were drawn: The axial tensile resistance of the investigated GFRP bars was not significantly altered by the application of a transverse force as long as the transverse force was not larger than 50% of the resistance under a pure transverse force. This can be explained by the flexibility of the matrix, which allows transverse deformations and a more direct force transfer through the fibers. The short term compressive resistance was not altered by the application of a transverse force as long as the transverse force was not larger than 25% of the resistance under a pure transverse force. For larger transverse forces, the transverse deformation increased over time, and a 2nd order effect appeared, leading to an instability failure. This may be explained by the direct force transfer along a steep diagonal path, which did not lead to significant tensile and shear forces in the matrix. Contrary to the tests per-
171
formed with an axial tensile force, the flexibility of the matrix destabilizes for larger transverse forces with an axial compressive force. The matrix is increasingly loaded over time, and the GFRP bar fails. Two axial tensile tests on specimens with a forced misalignment were conducted. The curvature in the GFRP bar amounted to 1.5 103 mm1. In the first test, in which there was no transverse force, 90% of the tensile resistance of straight bars under similar loading conditions could be supported. In the second test, in which a 10 kN transverse force was applied, 84% of the tensile resistance of straight bars under similar loading conditions could be supported. Because the fracture behavior for pure axial loading was brittle, one might expect that the ultimate tensile force should be dramatically reduced with a forced misalignment. Apparently, stress maxima are redistributed because of the flexibility of the matrix, which leads to a higher global resistance. Whilst design concepts [6] exist to account for forces acting parallel to the unidirectional glass fibers, no simple design concept is known to the author to account for loadings of bars in the transverse direction. Advanced composite failure theories, for example described in [7], may be applied to this or similar cases. This step requires further investigations with a non-linear numerical model considering geometrical non-linearities. 6. Conclusions 1. GFRP bars are well suited for combined transverse force–axial tensile force loading. 2. GFRP bars are well suited for short-term combined transverse force–axial compressive force loading. No conclusions may be drawn for the long-term behavior because of the limited number of results and maximal loading durations of only 7200 s. 3. Two tests indicated that the GFRP bar with a severe forced misalignment performs well under only axial force or combined transverse force–axial tensile force loading. Thus GFRP bars have the potential to also be used for structures in which forced deformations perpendicular to the bar axis appear. The accuracy during mounting in the field may lead to forced deformations.
Acknowledgements The author would like to thank the Swiss Federal Office for Energy (Project Number 101307) and Hitek Construction AG (Switzerland) for supporting this research. Furthermore, special thanks go to Mr. Daniel Reider, ERICO, for the useful corrections and suggestions. References [1] Keller T, Riebel F, Zhou A. Multifunctional hybrid GFRP/steel joint for concrete slab structures. J Compos Constr 2006;10(6):550–60. [2] Bai Y, Keller T. Shear failure of pultruded fiber-reinforced polymer composites under axial compression. J Compos Constr 2009;13(3):234–42. [3] Eddie D, Shalaby A, Rizkalla S. Glass Fiber-Reinforced Polymer Dowels for Concrete Pavements. ACI Struct J. 2001(March–April). [4] Porter ML. Alternative dowel bars. In: Proceedings of the 2003 mid-continent transportation research symposium, Ames, Iowa, August 2003. [5] Motavalli M, Ghazi Wakili K, Gsell D, Herwig A. Thermotragelemente (TTE) aus hochfestem Faserverbundstoff und integrierten Vakuumisolationspaneelen (VIP). BfE–Schlussbericht. 2008(July 11) [in German]. [6] Euro Comp 1996. Structural design of polymer composites. The European Structural Polym Compos Group. Clarke JL. editor. London; 1996. [7] Puck A, Schürmann H. Failure analysis of FRP laminates by means of physically based phenomenological models. Compos Sci Technol 62(12-13). pp. 16331662. [special issue].
Contents lists available at SciVerse ScienceDirect
Composites: Part B journal homepage: www.elsevier.com/locate/compositesb
Load-carrying capacity of GFRP bars under combined axial force–transverse force loading Andrin Herwig ⇑, Masoud Motavalli Empa, Swiss Federal Laboratories for Materials Science and Technology, Structural Engineering Laboratory, Ueberlandstrasse 129, CH-8600 Duebendorf, Switzerland
a r t i c l e
i n f o
Article history: Received 6 January 2012 Received in revised form 31 May 2012 Accepted 12 June 2012 Available online 21 June 2012 Keywords: A. Glass fibers B. Mechanical properties B. Strength D. Mechanical testing Combined loading
a b s t r a c t In several applications, glass fiber reinforced plastic (GFRP) bars are loaded with a transverse force while they simultaneously carry an axial force. Short-term tests of combined axial and transverse loading on assemblies consisting of one GFRP bar and two steel sleeves are described in this paper. The results show that the axial force capacity of the GFRP bar is affected only if the transverse force exceeds a certain threshold. A qualitative fracture criterion for combined axial force–transverse force loading is suggested. Further combined axial force–transverse force loading tests have been conducted on a specimen with a severe, forced 4° bending misalignment. These misaligned GFRP bars sustained more than 80% of the tensile resistance of the corresponding straight bars (without misalignment). Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction In the tunneling and mining industry, glass fiber reinforced plastic GFRP bars are used more frequently than steel for temporary rock anchors because they are more easily cut, which avoids damage to the tunnel drilling machine. GFRP bars are also used more frequently in the building industry because they are more resistant to corrosion, weigh less and have a lower heat conductivity than steel. In some of these applications, the application of an axial force to the GFRP bar is accompanied by a transverse force. Such transverse forces may appear with dislocation movements when rock bolts are used. The combined axial force–transverse force loading has not been investigated extensively. An experimental investigation of the pultruded GFRP elements of a cellular cross section is described in [1]. These GFRP elements have been built in a load carrying a ‘‘thermal insulation section’’ system for cantilevered balconies. Fig 1 shows the main elements of another type of thermal insulation section for overhanging balconies, including the ceiling slab, the insulation section and the balcony slab. The GFRP elements of [1] carried both compressive and transverse forces. However, the GFRP, as one component of the system, was not critical at the ultimate limit state. Therefore, no conclusions about the fracture behavior of the GFRP could be drawn from this study. However, there have been investigations of single GFRP elements. The investigation described in [2] describes the failure ⇑ Corresponding author. Tel.: +41 58 765 4791; fax: +41 58 765 44 55. E-mail address: [email protected] (A. Herwig). 1359-8368/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compositesb.2012.06.012
behavior of slender, pultruded GFRP laminates under axial compressive forces. Bending moments and transverse forces occur within these slender GFRP laminates because of the lateral deformations (buckling), and this interlaminar shear leads to failure. Short elements have also been extensively investigated. The transverse force behavior of GFRP and steel bars used as dowels in pavement joints with full scale static and cyclic tests is described in [3,4]. However, contrary to the present study, no axial force was applied to the GFRP bar because the pavement joints are designed as dilatation joints. One criterion of that study was the ‘‘joint effectiveness’’, which describes the stiffness as a function of the relative vertical movements between adjacent pavement slabs. Another criterion was the magnitude of the stress between the dowel and the concrete. This paper describes a mechanical component of a thermal insulation section (Fig. 1), which was developed in a collaborative operation between the Hitek Construction AG Company, Gstaad, Switzerland and Empa. The patent rights for the load-transferring GFRP elements are now in the possession of ERICO LENTON Concrete Reinforcement Products. The shear forces and bending moments are transferred exclusively through the GFRP bars and GFRP blocks, which cross vacuum insulation panels horizontally and are anchored in the adjacent concrete slabs. A detailed description of the entire investigation program can be found in [5]. This paper focuses on the tests of the upper GFRP element, as shown Fig. 1. Combined axial force–transverse force loading tests have also been conducted with a specimen with a forced 4° bending misalignment. Misalignment may occur because of inaccuracies during mounting in the field or may have to be considered in the
168
A. Herwig, M. Motavalli / Composites: Part B 44 (2013) 167–171
interior
exterior upper steel – GFRP element to be tested
GFRP in steel sleeve GFRP block façade insulation masonry reinforcing bar steel sleeve reinforcing bar GFRP bar
20 mm
Detail: upper steel – GFRP element Fig. 1. Load-transferring insulation section with horizontal steel–GFRP elements.
design of structures which should resist to damage scenarios leading to permanent deformations. The magnitude of the present forced misalignment may be considered as a severe case. A test set-up was designed to produce similar mechanical constraints for the upper GFRP element.
Transverse force (V)
no rotation around z-axis
2. Test specimen
Axial force compressive (C) or tensile (T)
The test specimen is shown in Fig. 2. The specimen consisted of a threaded GFRP bar with unidirectional E-glass fibers embedded in an epoxy resin matrix (glass fiber volume content, UV = 65 %). The GFRP bar is screwed 100 mm into two threaded steel sleeves that serve as anchorages. The void between the bar and the sleeve is injected with epoxy resin. The GFRP bar has a free length of 25 mm between the two sleeves. The axial force is introduced through a threaded connection at both ends of the specimen.
y
z
x
Fig. 3. Schematic loading system for the steel–GFRP element.
3.2. Experimental program and test results 3. Tests without forced misalignment 3.1. Loading system The loading system (Fig. 3) allows both sleeves to remain parallel to each other while translational movements between both sleeves remain possible. Both axial and transverse forces may be applied to the GFRP. The forces are produced by hydraulic jacks and measured by load cells.
Pure transverse force, axial force and combined axial–transverse force tests were conducted. The transverse and ultimate axial forces are listed in Table 1. The transverse force was increased until failure at a rate of 120 N/s for the pure transverse force tests (Nos. 1 and 2 in Table 1). The transverse forces in tests 1 and 2 reached V = 22.3 and 20.9 kN, respectively. The force was increased at a rate of 650 N/s for the pure tensile force tests (Nos. 3–6). The ultimate forces ranged from 235 to
Steel sleeve internal thread for axial force introduction injection fitting GFRP bar, A GFRP = 346 mm2 25
Cross section:
130
34
24 25
130
100
100
[mm] Fig. 2. Longitudinal section and cross section of the steel–GFRP element.
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A. Herwig, M. Motavalli / Composites: Part B 44 (2013) 167–171
Specimen no. 1 2
Transverse force V (kN) 22.3 20.9
Axial force T(+)/C() (kN)
Loading
– –
Transverse force increased until failure
3 4 5 6 7 8 9 10 11 12 13 14 15 16
– – – – 10 15 15 15 – – – 5 5 10
236 230 245 235 237 225 219 186 154 160 158 156 165 129
Axial force increased until failure
17 18 19 20
10 10 10 10
120 120 110 100
Time [s] at which failure occurred
10 40 10 300
21
10
70
No failure [s]
7200
22 23 24
15 15 15
70 70 50
Time [s] at which failure occurred
10 40 70
245 kN. The steel sleeves were reinforced by supplementary overscrewed sleeves to avoid a sleeve fracture because the short-term resistance of the GFRP bar was greater than that of the steel sleeve. For the combined tensile–transverse force tests (Nos. 7–10), the tensile force was increased at a rate of 650 N/s with a constant transverse force. The ultimate tensile forces obtained with a 15 kN transverse force (Nos. 8–10) were more varied than the forces obtained in the pure tensile tests (Nos. 3–6). The values ranged from 186 to 225 kN. The ultimate axial tensile force obtained with a 10 kN transverse force, corresponding to 50% of the pure transverse force resistance (No. 7), reached a value of 237 kN. This value corresponds to the average of the ultimate tensile forces obtained without a transverse force (Nos. 3–6). Because there was only one result for a 10 kN transverse force, attention was directed to the ultimate tensile forces of the next larger transverse force (15 kN, Nos. 8–10). The average of 210 kN for this group reached 90% of the average of the ultimate tensile forces that were obtained with 10 and 0 kN transverse forces. Thus, the ultimate tensile force was only slightly changed as the transverse force increased to 15 kN. Based on this result, we have concluded that there is no significant influence on the ultimate tensile force with transverse forces up to 10 kN. The compressive force was increased at a rate of 250 N/s for the pure compressive tests (Nos. 11–13). The ultimate resistance varied between 154 and 160 kN. The compressive force was increased at a rate of 650 N/s for the combined compression–transverse force tests (Nos. 14–17). While there was no decrease in the axial compressive force between transverse forces of 0 kN (Nos. 11–13) and 5 kN (Nos. 14 and 15), with mean values of 157 kN and 160 kN, respectively, the axial compressive force was reduced with a 10 kN transverse force (No. 16). The supplementary creep tests (Nos. 17–24) ascertained how the GFRP bars behave under a constant combined compression– transverse force loading. While a sudden fracture occurred with a
10 kN transverse force at an axial compressive force of 129 kN (No. 16), the creep specimens failed after several seconds under sustained axial compressive forces of 120 and 110 kN (Nos. 17– 19). Failure occurred only after 300 s with a 100 kN sustained axial compressive force (No. 20). No failure occurred after 7200 s for a 70 kN sustained axial compressive force (No. 21). For this force, which corresponds to 55% of the ultimate compressive force of test Nos. 16, the transverse deformation showed a typical exponential increase over time with an asymptotic tendency over the chosen period (Fig. 4). With application of a 15 kN transverse force, the specimens failed under 70 and 50 kN sustained axial compressive forces after several seconds (Nos. 22–24). As observed with the 10 kN transverse force (Nos. 17–20), creep deformation in the transverse direction led to instability and failure after delamination occurred in a direction parallel to the fibers. These creep tests showed that instability occurs with the application of a 10 kN transverse force even when the axial compressive force was smaller than 129 kN. 3.3. Fracture patterns Fig. 5 shows the fracture patterns of one specimen per loading mode. Delamination parallel to the fibers occurred under a pure transverse force (Fig. 5a). There were no broken glass fibers. The fibers broke along a craggy fracture surface under pure tensile loading (Fig. 5b). The same behavior was observed under combined tensile–transverse force loading, but the fracture surface was diagonal (Fig. 5c). The specimen failed completely, breaking into two parts, after the pure compressive test (Fig. 5d). For the combined compression–transverse force test (Fig. 5e), delamination occurred as in the pure transverse force tests (Fig. 5a), but in addition, there were buckled fibers. 3.4. Failure criteria Fig. 6 shows the results of the tests with axial tensile and transverse forces. The dots correspond to the test results, and the line represents a failure criterion. As stated above, the tensile resistance was not altered by transverse forces below a certain threshold. This threshold occurred at approximately 50% of the pure transverse force resistance. The first branch of the fracture criterion is therefore plotted as a horizontal line, while a second branch indicates a linear decrease of the ultimate tensile resistance with increasing transverse force. The fracture criterion is described by the following equations.
V k 6 gT V o;k :
T k ¼ T o;k
ð1aÞ
1.0
Transverse displacement [mm]
Table 1 Results of the combined axial force–transverse force tests.
0.9
C = -70 kN V = 10 kN
0.8
No. 21 0.7 0
0.5
1
1.5
2
time [h] Fig. 4. Creep deformation with the application of 70 kN compressive and 10 kN transverse forces (Specimen No. 21).
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Fig. 5. Fracture patterns: (a) pure transverse force, (b) pure tensile force, (c) combined tensile - transverse force, (d) pure compression, (e) combined compression–transverse force.
Ck is the characteristic value of the compressive resistance under the combined loading, Co,k is the characteristic value of the pure compressive resistance and gC is the fraction of the pure transverse force resistance, Vo,k, below which the compressive resistance is not altered. To develop the interaction diagrams shown in Figs. 6 and 7, the following values were used: gT = 0.5, Vo,k = 18 kN, To,k = 225 kN, c = 0 kN, Co,k = 150 kN, gC = 0.25, b = 728.6 and d = 0.545.
Ultimate tensile force T [kN]
300 ηΤ •Vo,k
To,k
250 200
test result
150 100 50 failure criterion Tk (Vk)
4. Tests with forced misalignment
Vo,k
0
0
5
10
15
20
25
4.1. Loading system
Transverse force V [kN] Fig. 6. Tensile – transverse force–interaction diagram.
V o;k > V k > gT V o;k :
T k ¼ T o;k 2
Vk ð1 gT ÞV o;k
þ c:
ð1bÞ
Vk and Tk are the characteristic values under combined loading of the transverse and the tensile resistances, respectively, To,k is the characteristic value of the pure tensile resistance and gT is the fraction of the pure transverse force resistance, Vo,k, below which the tensile resistance is not altered. Fig. 7 comprises the results of the tests using axial compressive forces. The lower values at V = 10 and 15 kN correspond to the creep tests, in which the loading was maintained at a constant value until failure occurred. As in the tests with axial tensile forces, there is a threshold for the transverse force, below which the compressive resistance is not influenced. As a result, transverse forces below 25% of the pure transverse force resistance do not affect the compressive resistance according to this criterion. For larger transverse forces the curve drops steeply. The criterion in Eq. (2a) and Eq. (2b) is proposed for the combined compression–transverse force loading:
V k 6 gC V o;k :
C k ¼ C o;k
V o;k > V k > gC V o;k :
4.2. Test program and results The forced 4° rotation led to a curvature of k = 1.5 103 mm1 for the free length of the specimen (Fig. 8). In this experiment, one steel sleeve was clamped in the test set up (Fig. 8a), and the other sleeve was tilted by 4°, applying a forced rotation. No rupture of
(a)
4o
ð2aÞ
C k ¼ C o;k þ b ðV k gc V o;k Þd
y
ð2bÞ
z
x
Transverse force (V)
-200
Ultimate compressive force C [kN]
To supplement the previous tests, the effect of a forced misalignment on the GFRP bar was examined with two additional specimens. These tests were motivated by the investigation of a possible damage scenario for the balcony system shown in Fig. 1. A forced 4° rotation was applied before testing (Fig. 8).
ηc •Vo,k
(b)
Co,k
no rotation around z - axis
-150
during transverse loading
-100
test result
Axial tensile force (T)
-50 failure criterion Ck (Vk)
0 0
5
10
y
Vo,k
15
20
-3
κ = 1.5 x 10 mm
25
-1
z
x
Transverse force V [kN] Fig. 7. Compressive – transverse force–interaction diagram.
Fig. 8. Schematic loading system for the steel–GFRP element, (a) clamped straight specimen, (b) misaligned specimen under combined loading.
A. Herwig, M. Motavalli / Composites: Part B 44 (2013) 167–171 Table 2 Results of the combined axial force–transverse force tests with forced curvature. Specimen no.
Trans-verse force V (kN)
Axial force (T/C) (kN)
Loading
25 26
– 10
212 199
Axial force increased until failure
Fig. 9. Fracture pattern with forced curvature: (a) without any transverse force and (b) with transverse force.
fibers could be observed during or after bending. Then, a combined tensile-transverse force test was conducted on the deformed specimen (Fig. 8b). Table 2 shows the forces at failure. The axial force reached 212 kN with a 0 kN transverse force (No. 25), 10% lower than the axial forces obtained in test Nos. 3–6, as shown in Table 1, which were loaded with the same load combination but without any forced misalignment. Specimen No. 26, with a 10 kN transverse force, failed at 199 kN, 16% lower than specimen No. 7 with the same loading, but without misalignment (Table 1). 4.3. Fracture pattern Fig. 9 shows the fracture pattern of the specimen with forced curvature. The fracture pattern exhibited similar characteristics to the patterns obtained in the tests without forced curvature, shown in Fig. 5b and c. 5. Results and discussion The load-carrying capacity of GFRP bars under combined axial force–transverse force loading was investigated, and a failure criterion was established. The findings that are described here are based on the particular product that was investigated and the applied boundary conditions. Additional testing should be conducted to more precisely determine the parameters of the failure criterion. The findings may lay the foundation for tests and characterizations for other types of GFRP bars that may be used in similar structures. The following conclusions were drawn: The axial tensile resistance of the investigated GFRP bars was not significantly altered by the application of a transverse force as long as the transverse force was not larger than 50% of the resistance under a pure transverse force. This can be explained by the flexibility of the matrix, which allows transverse deformations and a more direct force transfer through the fibers. The short term compressive resistance was not altered by the application of a transverse force as long as the transverse force was not larger than 25% of the resistance under a pure transverse force. For larger transverse forces, the transverse deformation increased over time, and a 2nd order effect appeared, leading to an instability failure. This may be explained by the direct force transfer along a steep diagonal path, which did not lead to significant tensile and shear forces in the matrix. Contrary to the tests per-
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formed with an axial tensile force, the flexibility of the matrix destabilizes for larger transverse forces with an axial compressive force. The matrix is increasingly loaded over time, and the GFRP bar fails. Two axial tensile tests on specimens with a forced misalignment were conducted. The curvature in the GFRP bar amounted to 1.5 103 mm1. In the first test, in which there was no transverse force, 90% of the tensile resistance of straight bars under similar loading conditions could be supported. In the second test, in which a 10 kN transverse force was applied, 84% of the tensile resistance of straight bars under similar loading conditions could be supported. Because the fracture behavior for pure axial loading was brittle, one might expect that the ultimate tensile force should be dramatically reduced with a forced misalignment. Apparently, stress maxima are redistributed because of the flexibility of the matrix, which leads to a higher global resistance. Whilst design concepts [6] exist to account for forces acting parallel to the unidirectional glass fibers, no simple design concept is known to the author to account for loadings of bars in the transverse direction. Advanced composite failure theories, for example described in [7], may be applied to this or similar cases. This step requires further investigations with a non-linear numerical model considering geometrical non-linearities. 6. Conclusions 1. GFRP bars are well suited for combined transverse force–axial tensile force loading. 2. GFRP bars are well suited for short-term combined transverse force–axial compressive force loading. No conclusions may be drawn for the long-term behavior because of the limited number of results and maximal loading durations of only 7200 s. 3. Two tests indicated that the GFRP bar with a severe forced misalignment performs well under only axial force or combined transverse force–axial tensile force loading. Thus GFRP bars have the potential to also be used for structures in which forced deformations perpendicular to the bar axis appear. The accuracy during mounting in the field may lead to forced deformations.
Acknowledgements The author would like to thank the Swiss Federal Office for Energy (Project Number 101307) and Hitek Construction AG (Switzerland) for supporting this research. Furthermore, special thanks go to Mr. Daniel Reider, ERICO, for the useful corrections and suggestions. References [1] Keller T, Riebel F, Zhou A. Multifunctional hybrid GFRP/steel joint for concrete slab structures. J Compos Constr 2006;10(6):550–60. [2] Bai Y, Keller T. Shear failure of pultruded fiber-reinforced polymer composites under axial compression. J Compos Constr 2009;13(3):234–42. [3] Eddie D, Shalaby A, Rizkalla S. Glass Fiber-Reinforced Polymer Dowels for Concrete Pavements. ACI Struct J. 2001(March–April). [4] Porter ML. Alternative dowel bars. In: Proceedings of the 2003 mid-continent transportation research symposium, Ames, Iowa, August 2003. [5] Motavalli M, Ghazi Wakili K, Gsell D, Herwig A. Thermotragelemente (TTE) aus hochfestem Faserverbundstoff und integrierten Vakuumisolationspaneelen (VIP). BfE–Schlussbericht. 2008(July 11) [in German]. [6] Euro Comp 1996. Structural design of polymer composites. The European Structural Polym Compos Group. Clarke JL. editor. London; 1996. [7] Puck A, Schürmann H. Failure analysis of FRP laminates by means of physically based phenomenological models. Compos Sci Technol 62(12-13). pp. 16331662. [special issue].