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Flexural behavior of GFRP-reinforced concrete encased steel composite beams
Construction and Building Materials 28 (2012) 255–262
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Flexural behavior of GFRP-reinforced concrete encased steel composite beams Xian Li ⇑, Henglin Lv, Shuchun Zhou State Key Laboratory for Geomechanics & Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221006, China
a r t i c l e
i n f o
Article history: Received 10 May 2011 Received in revised form 16 August 2011 Accepted 16 August 2011 Available online 13 October 2011 Keywords: Flexural strength FRP reinforcement Concrete encased steel beams Ductility Corrosion
a b s t r a c t To improve the ductility and meanwhile ensure satisfactory corrosion-resistant performance, a new type of FRP-reinforced concrete encased steel (FRP-RCS) composite beams comprised of ductile structural steel shapes in combination with corrosion-resistant FRP-reinforced concrete was proposed and studied. An experimental investigation on flexural behavior of the proposed FRP-RCS beams was conducted by testing a total of seven simply supported beam specimens subjected to four-point bending loads. The test specimens included one FRP-reinforced concrete (FRP-RC) beam reinforced with GFRP bars only and six FRP-RCS beams reinforced with both GFRP bars and encased structural steel shapes. The main parameters considered in this study were concrete compressive strength, amounts of GFRP reinforcement as well as ratio and configuration of encased structural steel shapes. The test results indicate that using encased steel shapes can provide a significant enhancement in load carrying capacity, stiffness, ductility and energy absorption capacity of tested beams. The tested FRP-RC beam suffered a brittle failure caused by the sudden fracture of tensile GFRP bars whereas the proposed FRP-RCS beams behaved in a ductile manner mainly due to the beneficial residual strength of encased steel shapes following concrete crushing. In addition, an analytical method was suggested to predict the load carrying capacity of the proposed FRP-RCS beams. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Corrosion of steel reinforcement has become a major concern for reinforced concrete structures in aggressive and corrosive environments, reducing service life of the structures and resulting in a substantial increase of maintenance and repair costs. Fiber reinforced polymers (FRP) bars have gradually gained the acceptance as an attractive substitute of steel reinforcement in the last decades thanks to their well-known advantageous properties such as high strength, light weight and corrosion resistance. Extensive studies [3,5,17,19] on FRP-reinforced concrete (FRP-RC) members were conducted to evaluate their flexural and shear performance. As a result, some guidelines [1,11] were developed to aid the design and construction of FRP-RC members. However, these studies also implied that FRP-RC members exhibited limited ductility under bending since FRPs possess some mechanical properties quite different from those of conventional steel bars, including elastic brittle stress–strain relationship. To compensate the lack of ductility, the design of FRP-RC members was suggested by Mufti and co-workers [14,19] to be based on the concept of deformability, rather than the usual concept of ductility used in steel-reinforced concrete members. The margin of ⇑ Corresponding author. Tel./fax: +86 516 83590601. E-mail address: [email protected] (X. Li). 0950-0618/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2011.08.058
safety against failure was also suggested to be higher than that used in steel-reinforced concrete design. Therefore, upcoming collapse of the members can be observed by some warning in forms of extensive cracking and ample deflection. This design concept was adopted by ACI-440-1R [1]; however, it can not be applied to cases such as seismic application where the internal force redistribution is very important. Alternative techniques using FRP hybrid rods or combinations of FRP rods with different material characteristics in an effort to develop an inelastic behavior are being realized to be favorable. Since the reinforcing fibers such as glass, aramid, carbon fibers and steel core have different stiffness and ultimate strains, hybrid FRP bar consisting of more than one reinforcing material behaves in an elastic-pseudo ductile manner. Results of some experimental studies [7,10,15] indicated that the use of the hybrid FRP bars can increase the flexural capacity and ductility of FRP-RC members. However, such efforts have thus far resulted in limited practical developments. Research conducted by Lau and Pam [13] demonstrated that the ductility of FRP-RC beams could be improved by adding a certain amount of conventional steel reinforcement since yielding of the steel bars resulted in significant inelastic deformation. Meanwhile, several investigations [6,18] on concrete encased steel members verified their desirable ductility and energy-dissipating capacity for seismic application. However, to date, no research information can be found related to the flexural behavior of FRP-RC members with encased structural steel shapes.
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Table 1 Cross sectional details of tested beams. Sectional typea
Cross section B D (mm)
Top bars
Bottom bars
fcu (MPa)
Steel shape ds bf tw tf (mm)
B1 B2 B3 B4 B5 B6 B7
A B B B B C D
160 250 160 250 160 250 160 250 160 250 160 300 160 300
2U6 2U6 2U6 2U6 2U6 2U6 2U12 + U8
3U12 3U12 2U12 2U8 3U12 3U12 + 2U6 2U8
48.2 48.2 48.2 35.5 35.5 48.2 48.2
– 140 80 5.5 9.1 140 80 5.5 9.1 140 80 5.5 9.1 140 80 5.5 9.1 140 80 5.5 9.1 140 80 5.5 9.1
Detailed types of cross sections were shown in Fig. 1.
160
160
(a) Type A
(b) Type B
105
sive strength of 50 MPa. To prevent premature shear failure, all the specimens were provided with 8-mm-diameter steel stirrups spaced at 120 mm over the entire length of the beam. To facilitate the installation of the transverse reinforcement, two GFRP bars with a diameter of 6 mm were used in compression zone as hangers for the stirrups in specimens B1–B6. Detailed investigation purposes of each specimen will be further presented hereafter along with the discussion on the associated test results.
300 140
300 140
55
80
55
250
250 140
80
55
a
Beam no.
160
160
(c) Type C
(d) Type D
Fig. 1. Typical cross-sections of beam specimens (units:mm).
In this paper, a composite beam consisting of FRP bars, steel and concrete is proposed and studied. It takes advantages of both ductile steel shapes and corrosion-resistant FRP-reinforced concrete. The encased steel shapes are adopted to improve the ductility and energy-dissipating capacity of conventional FRP-RC members. As recommended by the Chinese standard for steel reinforced concrete composite structures [12], the thickness of concrete cover for encased steel shapes should be not less than 100 mm. Therefore, the surrounding concrete in turn can provide sufficient protection to the steel shapes, impeding or delaying their corrosion. Meanwhile the concrete can inhibit the potential local buckling of the steel shapes. In this study, an experimental research on seven beam specimens was carried out to achieve the following objectives: (1) to investigate the flexural behavior of the proposed composite beams in terms of failure modes, strength, stiffness, ductility and energy absorption capacity; (2) to evaluate the role of some parameters including concrete compressive strength, amounts of GFRP reinforcement as well as ratio and configuration of encased structural steel shapes; and (3) to validate an analytical model developed to predict the load carrying capacity of the composite beams. 2. Experimental program 2.1. Beam specimens The test matrix for the experimental program is given in Table 1 and the typical cross-sections of beam specimens are shown in Fig. 1. A total of seven beam specimens with a total length of 2400 mm were constructed and tested in flexure. The main test parameters were concrete compressive strength, amounts of GFRP reinforcement as well as ratio and configuration of encased structural steel shapes. Specimen B1 was tested for comparison purpose and reinforced with GFRP bars only while specimens B2 to B7 were FRP-RCS beams reinforced with both GFRP bars and encased structural steel shapes. The clear concrete cover for longitudinal GFRP bars was 20 mm and all the embedded hot-rolled structural steel shapes had an identical cross-section of 140 mm depth (ds) by 80 mm flange breadth (bf), web and flange thicknesses of 5.5 mm (tw) and 9.1 mm (tf), respectively. Since specimens B2 to B5 had a rectangular cross-section of 160 mm 250 mm (breadth width) while the cross sections of specimens B6 and B7 was 160 mm 300 mm, the ratio of encased steel area to gross cross-sectional area is 0.054 for specimens B2 to B5 while the corresponding ratio for specimens B6 and B7 is 0.045. In addition, both specimens B4 and B5 were constructed from the concrete with a target 28-day cubic compressive strength of 35 MPa while the others had a target concrete compres-
2.2. Materials The GFRP bars used in this study were manufactured by the pultrusion technique and the surface was eventually treated to enhance the bond characteristics. They were made of continuous longitudinal glass (E-type) fiber strands bond with together with thermosetting polyster resin and the percent of glass fibers as provided by manufacturer was 70% by weight. The mechanical properties of each type of GFRP bars were obtained from standard tests of three tensile coupons according to ASTM [4]. The tensile rupture stress ffu were 680 and 750 MPa, respectively for U12 (12 mm nominal diameter) GFRP bars and U8 (8 mm nominal diameter) GFRP bars with an elastic modulus, Ef, 38 GPa. Tensile coupon tests were also conducted on steel components followed the standard GB/T 228-2002 [9] and the resulting yield stress fy, ultimate stress fu as well as corresponding Young’s modulus Es were 273 MPa, 385 MPa and 199 GPa, respectively. The concrete cubic compressive strength fcu was obtained by testing three 150 mm concrete cubes for each batch according to the standard GB/T 50081 [8]. The average concrete compressive strength at the time of beam testing was 48.2 MPa for specimens B1, B2, B3, B6 and B7 while the corresponding value for specimens B4 and B5 was 35.5 MPa. In general, the cylinder strength fc can be calculated as 0.8 times the cubic strength fcu. 2.3. Test method As shown in Fig. 2, all specimens were simply supported and subjected to fourpoint bending. Each of the specimens had a clear span of 2000 mm and shear spans of 750 mm; therefore, bending was constant in the central zone with a length of 500 mm. The static load was applied by a hydraulic jack to the specimens through a steel spreader beam. The load was monotonically applied in two stages. The first stage was load-controlled, in which the load was applied step by step at a rate of 5 kN per step for FRP-RCS beams until 75% of expected strength of the specimens, whereas the loading rate for FRP-RC beams was 2 kN per step for their low load carrying capacity. The second stage was carried out in displacement-controlled mode and the loading increment was 1 mm per step. At the end of each increment, all the data were collected and cracks were sketched. The specimen was considered to have failed when its load carrying capacity dropped to 80% of its maximum measured load or it developed a major physical deterioration. In order to measure deflections of the beam specimens, the displacements at beam mid-span, loading points and supports were monitored by transducers. The schematic arrangement of the transducers was included in Fig. 2. Electrical resistance strain gauges were also affixed on at strategic locations of GFRP bars and surfaces of encased steel shapes before concrete casting.
3. Test results and discussion A summary of test results is presented in Table 2. The average crack spacing at low loading stage, ultimate loads, displacement ductility, energy absorption capacity and failure modes of all beam specimens are included in the table. The displacement ductility factor (l) in this study is defined as the ratio of mid-span displacement at ultimate stage (Du) and that at yield stage (Dy), where the former is obtained at 0.8Pp after reaching the peak load Pp, while the latter is obtained by linearly interpolating the displacement at 0.75Pp to the level of Pp [16]. The ultimate and yield deflections
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in Figs. 3 and 4. Throughout the loading, no apparent signs of bond failure between GFRP bars and concrete were observed in all the specimens. For all FRP-RCS beam specimens, failure was initiated by yielding of encased steel shapes followed by crushing of concrete. However, the concrete crushing did not result in complete loss of load carrying capacity mainly due to the beneficial residual strength of encased steel shapes. The load carrying capacity even partially recovered in some specimens with further incremental deflection. Sounds indicating the fracture of fibers of tensile GFRP bars became audible for the large deflection, and eventually rupture of the GFRP bars triggered the final failure of specimens. The failure of FRP-RCS beams was gradual and ductile and the corresponding photos at failure conditions are shown in Fig. 5. Furthermore, the mid-span deflections of FRP-RCS beam specimens at failure conditions ranged between 28.98 mm and 42.82 mm, corresponding to a deflection-to-clear span ratio of 1/69 and 1/47, respectively. The ultimate deformability of the specimens was related to the amount of the GFRP bars. This is attributed to the final failure modes resulted by fracture of FRP reinforcement. However, for FRP-RC beam specimen B1 with identical arrangement and ratio of GFRP reinforcement to that of specimen B2, its failure arose from the sudden rupture of the GFRP bars and no compression failure of concrete occurred. The corresponding final failure was included in Fig. 5. The different failure modes between the FRP-RCS and FRP-RC beam specimens indicated that using encased steel shapes changed the failure mode from a non-ductile manner to a ductile one. In addition, the final rupture of GFRP bars in all specimens again confirmed that force transfer was sufficient to develop the full tensile capacity of the GFRP bars. The failure modes of all beam specimens are shown in Fig. 5.
Hydraulic actuator Steel spreader beam
250(B1~B5) 300(B6~B7)
Beam specimen
Rigid Support LVDT 200 200
750
500 2000
750
200 200
Fig. 2. Schematic of experimental setup and instrumentation (units:mm).
at beam mid-span are also listed in Table 2. Note that although FRP reinforced beams behaved essentially in an elastic brittle fashion after cracking up to failure, the ductility factor was still calculated as the method described above for comparison purpose. Furthermore, energy absorption was also calculated to estimate the energy-dissipating capacity of all specimens before their final failure and it was determined as the area under the load–deflection curve. The effect of the test parameters on the flexural behavior such as the load carrying capacity, the stiffness and the ductility are discussed in the following sections. 3.1. General observations and failure modes Typical cracking patterns of FRP-RC and FRP-RCS beam specimens at different loading stages are depicted in Figs. 3 and 4, respectively. At low loading level, all specimens exhibited a similar cracking behavior. The cracks induced by pure bending appeared firstly in the flexural span at approximately 15% of their measured peak loading. As the load increased, additional flexural cracks were formed within both the mid-span and shear span regions and the cracks in flexural zone propagated quickly toward the vicinity of about 3/5 depth of the beams. The average crack spacing at the low loading stage was given in Table 2 and the cracking patterns were plotted in Figs. 3a and 4a, respectively. It can be found that the specimens experienced flexural cracking below 30% of their peak loads and the encased structural steel shapes had no significant effect on the crack spacing, but specimen B7 with an encased structural steel shape shifted to tension zone had relatively larger crack spacing. At moderate and high loading stages, flexural cracks in all specimens became considerably wider and inclined cracks in the vicinity of tensile bars occurred gradually and propagated to join the flexural cracks. With further loading, the cracks in shear spans became progressively more inclined and extended towards the loading points gradually for the increased shear force, as shown
3.2. Load–deflection behavior 3.2.1. Effect of using structural steel shapes The effect of the encasement of steel shapes on load–deflection behavior was investigated by tests of specimens B1 and B2. These two specimens were constructed from the concrete in the same batch and reinforced with three 12 mm-diameter longitudinal GFRP bars, respectively. As shown in Fig. 6, the load–deflection curve was essentially linear up to the failure for specimen B1, and bilinear for specimen B2. The two specimens exhibited similar load–deflection behavior up to flexural cracking regardless of the presence of an encased steel shape in specimen B2. This is because that the behavior of uncracked beams is determined by the gross moment of inertia of the concrete cross section. Upon cracking, since the flexural stiffness of specimens was mainly dependent on the amount of reinforcement, specimen B1 experienced distinct degradation of flexural stiffness whereas the stiffness of specimen
Table 2 Summary of test results. Specimen no. a
Average crack spacing (mm) Loading capacity Mexp (kN m) Dy (mm) Du (mm)
l Energy absorption (kN mm) Analytical moment Man (kN m) Man/Mexp Failure modesb a b
B1
B2
B3
B4
B5
B6
B7
102.8 36.7 30.5 36.3 1.19 2144 – – FF
101.0 59.8 15.1 42.8 2.83 5346 60.9 1.02 CC
101.6 54.5 13.8 34.0 2.47 3835 54.7 1.01 CC
102.0 44.5 12.2 29.0 2.37 2667 48.3 1.09 CC
102.0 59.3 14.8 47.7 3.22 6068 56.7 0.96 CC
102.8 77.6 13.3 36.1 2.71 6077 74.6 0.96 CC
176.0 68.2 12.2 35.8 2.93 5303 70.7 1.04 CC
Average crack spacing at low load stage. FF = fracture of FRP reinforcement; CC = crushing of compression concrete.
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(a) Maximum applied load P=28.7 kN (29.3%Pp)
(a) Maximum applied load P=49.0 kN (30.7%Pp)
(b) Maximum applied load P=57.0 kN (58.2%Pp)
(b) Maximum applied load P=98.0 kN (61.4%Pp)
(c) Maximum applied load P=87.1 kN (89.0%Pp)
(c) Maximum applied load P=143.8 kN (90.2%Pp)
Fig. 3. Cracking patterns of specimen B1 at different loading stages.
B2 reduced slightly. It can be observed from Fig. 6 that the postcracking stiffness of specimen B2 was apparently higher than that of specimen B1, indicating the significant enhancing effect of using encased steel shapes on stiffness. As the load increased, yielding of encased steel shape led to substantially inelastic deformation of specimen B2 while specimen B1 showed no yielding until reaching its ultimate load carrying capacity for the previously mentioned elastic brittle nature of FRP material. As seen from Fig. 6, the measured peak load of specimen B2 was 63% greater than that of specimen B1 due to the contribution of the encased steel shape. Furthermore, at a mid-span deflection of 11.1 mm corresponding to the serviceability deflection limitation of l/180 recommended by [2], the measured loads at specimens B1 and B2 were 44.2 kN and 118.8 kN, respectively, that is to say, the measured load of specimen B2 was 2.69 times that of specimen B1, indicating the obvious improvement of load carrying capacity by using encased steel shapes. Referring to Table 2, it is evident that the displacement ductility and energy absorption of FRP-RC beams were improved by using encased steel shapes. The ductility and the energy absorption of specimen B2 were 2.38 and 2.49 times that of specimen B1, respectively. In addition, specimen B2 gained an ultimate deformability 18% higher than that of specimen B1.
3.2.2. Effect of concrete compressive strength The impact of the concrete compressive strength on flexural behavior can be evaluated by comparing the capacity of specimens B2 and B5 reinforced with identical amount of longitudinal GFRP bars. With reference to Fig. 6, specimen B2 constructed from higher strength concrete gained the flexural strength comparable to that of specimen B5, indicating that use of higher strength concrete has little effect on improving the load carrying capacity of FRPRCS beams. This may be attributed to the slight reduction of the ultimate strain of concrete with the increase of strength. The crushing of compression concrete occurred in specimen B2 ahead of specimen B5. Therefore, specimen B5 experienced a larger deflection before reaching its peak load, resulting in the up-shifting of neutral axis and further increase of tensile stress of FRP reinforcement. Moreover, comparison of the load–deflection curves of specimens B2 and B5 can also find that the crushing of higher strength concrete led to a relatively sharper drop of the load carrying capacity after peak load. This can be explained by two factors. First, higher strength concrete exhibits a more brittle stress–strain
Fig. 4. Cracking patterns of specimen B2 at different loading stages.
behavior. Second, higher strength concrete results in a lower depth of compression zone, and thus the aforementioned initial crushing of concrete cover triggered the substantial loss of the compressive concrete of specimen B2. Table 2 also shows that the increase of concrete compressive strength led to a reduction of the ductility and the energy absorption capacity of specimens. 3.2.3. Effect of amount of GFRP reinforcement The influence of the amount of longitudinal GFRP bars was examined by comparing test results of specimens of Group No.1, (specimens B2 and B3), and Group No.2, (specimens B4 and B5), respectively. As expected, since specimen B2 had higher reinforcement ratio, it achieved higher load carrying capacity and more favorable deformability than that of specimen B3. The flexural strength of specimen B2 was 59.8 kN m, that is, approximately 9.8% greater than that of specimen B3. Furthermore, with increasing ratio of GFRP reinforcement from 6.3% (B3) to 9.4% (B2), the increases in the ultimate deflection, the energy absorption capacity and the displacement ductility as shown in Table 2 were 26%, 39.4% and 14.6%, respectively. Similar remarks can be made by comparing test results of specimens of Group No.2. 3.2.4. Effect of ratio and configuration of encased steel shapes Tests of specimens B6 and B7 were also conducted to evaluate the effect of the ratio and configuration of encased structural steel shapes. Test results indicate that both the two specimens exhibited similar load–deflection behavior to that of specimen B2. As mentioned previously, both specimens B6 and B7 had a larger crosssection than that of specimen B2, and thus they exhibited higher stiffness and flexural strength. However, the ultimate deflection was slightly reduced for higher strain demand on FRP reinforcement. Specimen B7 with an eccentrically encased steel shape demonstrated an apparent inelastic behavior after experiencing a mid-span deflection of 7.0 mm; meanwhile the crushing of concrete was slightly delayed to a mid-span deflection of 25.98 mm. However, horizontal cracks along the interface of top steel flange and concrete, referring to as shear splitting failure, were observed in the shear spans of specimen B7 at high loading stage. Hence, further study on FRP-RCS beams with similar configuration of encased steel shapes to specimen B7 should be carried out to better understand the flexural behavior.
X. Li et al. / Construction and Building Materials 28 (2012) 255–262
259
(a) Specimen B1
(b) Specimen B2
(c) Specimen B3
(d) Specimen B4
(e) Specimen B5
(f) Specimen B6
(g) Specimen B7 Fig. 5. Failure modes of beam specimens.
4. Analytical investigation on flexural strength of GFRP-RCS beams As described previously, FRP reinforcement possesses some particular properties such as linear strain–stress behavior up to fail-
ure, and thus the design of the proposed FRP-RCS beams correspondingly differs from that of conventional concrete encased steel beams. For simplicity, the following assumptions were introduced in calculation of the flexural strength of FRP-RCS beams: (1) plane sections remain plane and thus strain varies linearly through
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240
Total Applied Load (kN)
B6
dcb 1 1 ¼ ¼ 1 þ ey =e0c 1 þ ba ds
ð2Þ
np ¼
dcp 1þk ¼ 1 þ efb =e0c ds
ð3Þ
200
B7
160
B2
B3
120
B5
B4 B1
80 40 0
0
10
20
30
40
50
Mid-span Deflection (mm) Fig. 6. Load–deflection curves of beam specimens.
the cross section; (2) the tensile strength of concrete is neglected; (3) the equivalent rectangular stress block in compression zone is a valid substitution for a nonlinear stress distribution at ultimate and the concrete strain e0c at compression failure is 0.003; (4) the stress–strain behavior of steel and FRP reinforcement is assumed to be perfect elasto-plastic and linearly elastic, respectively; and (5) no buckling of encased steel shapes occurs for the good confinement of the surrounding concrete and perfect bond exists between steel and FRP reinforcement and concrete. Fig. 7 illustrates the assumed basic analytical conditions of internal strain, stress, and resultant force for a cracked section at ultimate condition. According to ACI-440-1R [1], the balanced failure is the condition where crushing of compression concrete and rupture of tension FRP bars occur simultaneously. However, this condition is defined as the perfect failure in this study for the good utilization of strength of both concrete and FRP bars, whereas the balanced failure of FRP-RCS beams represents the simultaneous yielding of steel fiber at centerline of tension flange and compression failure of concrete. This is because the yielding of steel before failure is very important to FRP-RCS beams and it shall result in a ductile failure manner. A factor n to determine the failure mode of FRP-RCS beams is defined as follows,
n¼
nb ¼
dc ds
ð1Þ
where dc is the neutral axis depth and ds is the distance from centerline of tension flange to extreme compression fiber, as shown in Fig. 7. According to Eq. (1) and strain distribution shown in Fig. 7, the factor n for the balanced failure nb and the perfect failure np can be calculated as,
where dcb, dcp is the neutral axis depth at the balanced failure and the perfect failure condition, respectively; ey = fy/Es is the yield strain of steel; efb is the ultimate strain of FRP reinforcement; kds is the distance from centroid of longitudinal tension GFRP reinforcement to centerline of tension flange. According to Eqs. (1)–(3), five types of possible flexural failures (FRP fracture failure; perfect failure; steel yielding-concrete crushing failure; balanced failure and over-reinforced failure) of an FRPRCS beam can be expected depending on the value of factor n, as shown in Fig. 7b. For an FRP-RCS beam with a ratio of encased steel area to gross cross-sectional area not less than 0.02 that is recommended by the Chinese code [12] for conventional concrete encased steel members, its failure generally starts by steel yielding followed by concrete crushing and lastly by FRP rupture and thus the factor n usually varies between np and nb. Like conventional concrete encased steel beams, according to the location of neutral axis and stress distribution of encased steel shapes at failure condition, three types of cross sections can be further distinguished in calculation of the load carrying capacity of FRP-RCS beams with a factor n varying between np and nb. 4.1. Type-I cross section For an FRP-RCS beam with type-I cross sections, the bottom flange of its encased steel shape shall have yielded under tension and meanwhile the top flange shall have yielded under compression at failure condition. The corresponding strain and stress distribution are shown in Fig. 7. To meet the above assumption, the factor n should satisfy the following condition which is determined by strain compatibility. 0
k 6 n 6 nb 1 ba
ð4Þ
From the axial equilibrium condition, the following equation can be obtained. 0:85b1 fc0 bds n þ fy A0f Afb Ef e0c
1þkn 0 Af f y þ fy ds tw ð2n k 1Þ ¼ 0 n
where b1 is the factor relating depth of equivalent rectangular compressive stress block to neutral axis depth, which can be taken according to the [2]; b is the breadth of cross section; A0f and Af
Perfect failure Balanced failure
(a) Cross section
(b) Strain distribution
ð5Þ
(c) Strain distribution for concrete failure
Fig. 7. Analytical model for type-I section at ultimate.
(d) Resultant forces
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are the areas of top and bottom steel flanges, respectively; Afb is the total area of longitudinal tension GFRP reinforcement; k0 ds is the distance from centerline of top flange to extreme compression fiber. From Eqs. (4) and (5), the factor n can be determined and then the expression for the nominal moment strength MnI of FRP-RCS beams with type-I cross sections can be computed by taking the moment of tensile and compressive stress resultants of bars, encased steel shapes and concrete about centerline of the bottom flange of the encased steel shapes.
ð1 þ k nÞ 2 kds M nI ¼ 0:85b1 fc0 bds nð1 0:5b1 nÞ þ Afb Ef e0c n " 2 # k b2 n2 2 þ A0f fy k1 ds þ tw ds fy 1 ð1 nÞ2 a 2 3
The encased steel shape in an FRP-RCS beam with type-III cross sections shall have yielded completely under tension at failure condition and the corresponding strain and stress distribution are shown in Fig. 9. The nominal moment strength MnIII of can be calculated based on the following equations.
0:85b1 fc0 bds n fy As Afb Ef e0c
1þkn ¼0 n
ð10Þ
0
ð6Þ
Note that the resultant force of GFRP bars in compression was neglected herein since GFRP bars with low elastic modulus and compressive strain generally do not significantly add to the moment capacity unless they are disproportionately large in area. 4.2. Type-II cross section For an FRP-RCS beam with type-II cross sections, the bottom flange of its encased steel shape shall have yielded under tension while the top flange may be under tension or compression but it has not yielded yet at failure condition. The corresponding strain and stress distribution are shown in Fig. 8. Similarly, the nominal moment strength MnII of FRP-RCS beams with type-II cross sections can be determined as follows, 0
nk 1þkn Af f y Afb Ef e0c n ba n ( ) 0 ½ð1 þ ba Þn k 2 fy ds t w k1 ¼0 2nba
0:85b1 fc0 bds n þ fy A0f
ð7Þ 0
4.3. Type-III cross section
np 6 n 6
k 1 þ ba
ð11Þ
2
MnIII ¼ 0:85b1 fc0 bds nð1 0:5b1 nÞ þ Afb Ef e0c 2 2
A0f fy k1 ds 0:5t w k1 ds fy
ð1 þ k nÞ kds n ð12Þ
where As is the total areas of steel shape. In the aforementioned equations, there is only one unknown n. If the factor n is determined, the ultimate moment can be obtained easily. Hence, the analytical procedure is performed by assuming a cross-sectional type firstly, and then the corresponding value n can be estimated according to Eqs. (5), (7), (10). Note that the factor n should satisfy the corresponding condition shown in Eqs. (4), (8), (11). If not another type of cross section shall be assumed. Based on the above procedure, the nominal moment strength of the tested FRP-RCS beams was computed and it was found that all the specimens had the type-II cross sections. The analytical results coupled with the comparison between the experimental and analytical results were shown in Table 2. It indicates that the proposed analytical models can predict the flexural strength of FRP-RCS beams well. The mean and standard deviation values of Man/Mexp were 1.01 and 0.05, respectively.
0
k k
ð8Þ 5. Summary and conclusion
0:5b1 nÞ þ 0
Afb Ef 0c
e
(
ð1 þ k nÞ kds n 0 2
nk k1 ½ð1 þ ba Þn k 2 2 þ 0:5t w ds fy k1 þ nba ba n ) 0 ½ð1 þ ba Þn k 3 3ba n þ A0f fy k1 ds
(a) Cross section
ð9Þ
A new type of GFRP-RCS composite member is developed to improve the ductility and stiffness of GFRP-RC beams. The flexural behavior of the proposed composite beams was studied by testing of seven simply supported beam specimens and an analytical method was proposed to predict the nominal flexural strength of FRP-RCS beams. Based on the results of this investigation, the following conclusions can be drawn:
(b) Strain distribution for concrete failure
(c) Resultant forces
Fig. 8. Analytical model for type-II section at ultimate.
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(a) Cross section
(b) Strain distribution for concrete failure
(c) Resultant forces
Fig. 9. Analytical model for type-III section at ultimate.
(i) The use of encased steel shapes can provide a significant improvement in load carrying capacity, stiffness, ductility and energy absorption capacity of the conventional FRP-RC beams. (ii) Due mainly to the beneficial residual strength of encased steel shapes following concrete crushing, the proposed FRP-RCS beams exhibited desirable ductility and energy-dissipation capability. (iii) The experimental results indicate that concrete compressive strength has insignificant effect on the load carrying capacity of FRP-RCS beams. Moreover, higher strength concrete results in a relatively sharper drop of the load carrying capacity after concrete crushing. (iv) The increase of longitudinal GFRP reinforcement ratio leads to the increase of the load carrying capacity, the deflection capacity and the ductility of FRP-RCS beams. (v) Conventional beam theory is still valid to develop an analytical model for predicting flexural strength of FRP-RCS beams and the analytical results show a reasonable agreement with the experimental values.
Acknowledgments The authors would like to express their sincere appreciation for the partial financial support from the National Natural Science Foundation of China (Contract Number: 51008300) and the Jiangsu Provincial Science and Technology Department (Contract Number: BK2010185). The experimental work described in this paper was conducted at the Jiangsu Key Laboratory of Environmental impact and Structural Safety in Civil Engineering in the China University of Mining and Technology. Helps during the testing from staffs and students at the Laboratory are greatly acknowledged. References [1] ACI 440 1R-06. Guide for the design and construction of concrete reinforced with FRP bars. Michigan (USA): American Concrete Institute (ACI), Committee 440; 2006.
[2] ACI Committee 318. Building code requirements for structural concrete (ACI 318-08) and commentary (318R-08). Farmington Hills, MI: American Concrete Institute; 2008. [3] Ashour AF. Flexural and shear capacity of concrete beams reinforced with GFRP bars. Constr Build Mater 2006;20(10):1005–15. [4] ASTM D3916. Standard test method for tensile properties of pultruded glassfiber-reinforced plastic rod. ASTM International; 2008. [5] Benmokrane B, Chaallal O, Masmoudi R. Flexural response of concrete beams reinforced with FRP reinforcing bars. ACI Struct J 1996;91(1–2):47–55. [6] El-Tawil S, Deierlein GG. Strength and ductility of concrete encased composite columns. J Struct Eng 1999;125(9):1009–19. [7] Etman EE. Innovative hybrid reinforcement for flexural members. J Compos Constr 2011;15(2):2–8. [8] GB/T 50081. Standard for test method of mechanical properties on ordinary concrete. Beijing (China): China Architecture and Industry Press; 2002 [in Chinese]. [9] GB/T 228. Metallic materials-tensile testing at ambient temperature. Beijing (China): Standards Press of China; 2002 [in Chinese]. [10] Harris HG, Somboonsong W, Ko FK. New ductile hybrid FRP reinforcing bar for concrete structures. J Compos Constr 1998;2(1):28–37. [11] ISIS Canada. Reinforcing concrete structures with fiber reinforced polymers, Design Manual No. 3, ISIS Canada, Winnipeg. Manitoba, Canada; 2007. [12] JGJ 138-2001. Technical specification for steel reinforced concrete composite structures. Beijing (China): China Architecture and Industry Press; 2001 [in Chinese]. [13] Lau D, Pam HJ. Experimental study of hybrid FRP reinforced concrete beams. Eng Struct 2010;32(12):3857–65. [14] Mufti AA, Newhook JP, Tadros G. Deformability versus ductility in concrete beams with FRP reinforcement. In: EI-Badry, editor. 2nd International conference of advanced composite material in bridges and structure, Canadian society for civil engineering, Montreal, Canada; 1996, p. 189–99. [15] Nanni A, Henneke MJ, Okamoto T. Behavior of concrete beams with hybrid reinforcement. Constr Build Mater 1994;8(2):89–95. [16] Park R. Evaluation of ductility of structures and structural sub-assemblages from laboratory testing. Bull New Zealand Soc Earthquake Eng 1989;22(3):155–66. [17] Toutanji HA, Saafi M. Flexural behavior of concrete beams reinforced with glass fiber-reinforced polymer (GFRP) bars. ACI Struct J 2000;97(5):712–9. [18] Weng CC, Yen SI, Jiang MH. Experimental study on shear splitting failure of full-scale composite concrete encased steel beams. J Struct Eng 2002;128(9):1186–94. [19] Vijay PV, GangaRao HV. Bending behavior and deformability of glass fiberreinforced polymer reinforced concrete members. ACI Struct J 2001;98(6):834–42.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Flexural behavior of GFRP-reinforced concrete encased steel composite beams Xian Li ⇑, Henglin Lv, Shuchun Zhou State Key Laboratory for Geomechanics & Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221006, China
a r t i c l e
i n f o
Article history: Received 10 May 2011 Received in revised form 16 August 2011 Accepted 16 August 2011 Available online 13 October 2011 Keywords: Flexural strength FRP reinforcement Concrete encased steel beams Ductility Corrosion
a b s t r a c t To improve the ductility and meanwhile ensure satisfactory corrosion-resistant performance, a new type of FRP-reinforced concrete encased steel (FRP-RCS) composite beams comprised of ductile structural steel shapes in combination with corrosion-resistant FRP-reinforced concrete was proposed and studied. An experimental investigation on flexural behavior of the proposed FRP-RCS beams was conducted by testing a total of seven simply supported beam specimens subjected to four-point bending loads. The test specimens included one FRP-reinforced concrete (FRP-RC) beam reinforced with GFRP bars only and six FRP-RCS beams reinforced with both GFRP bars and encased structural steel shapes. The main parameters considered in this study were concrete compressive strength, amounts of GFRP reinforcement as well as ratio and configuration of encased structural steel shapes. The test results indicate that using encased steel shapes can provide a significant enhancement in load carrying capacity, stiffness, ductility and energy absorption capacity of tested beams. The tested FRP-RC beam suffered a brittle failure caused by the sudden fracture of tensile GFRP bars whereas the proposed FRP-RCS beams behaved in a ductile manner mainly due to the beneficial residual strength of encased steel shapes following concrete crushing. In addition, an analytical method was suggested to predict the load carrying capacity of the proposed FRP-RCS beams. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Corrosion of steel reinforcement has become a major concern for reinforced concrete structures in aggressive and corrosive environments, reducing service life of the structures and resulting in a substantial increase of maintenance and repair costs. Fiber reinforced polymers (FRP) bars have gradually gained the acceptance as an attractive substitute of steel reinforcement in the last decades thanks to their well-known advantageous properties such as high strength, light weight and corrosion resistance. Extensive studies [3,5,17,19] on FRP-reinforced concrete (FRP-RC) members were conducted to evaluate their flexural and shear performance. As a result, some guidelines [1,11] were developed to aid the design and construction of FRP-RC members. However, these studies also implied that FRP-RC members exhibited limited ductility under bending since FRPs possess some mechanical properties quite different from those of conventional steel bars, including elastic brittle stress–strain relationship. To compensate the lack of ductility, the design of FRP-RC members was suggested by Mufti and co-workers [14,19] to be based on the concept of deformability, rather than the usual concept of ductility used in steel-reinforced concrete members. The margin of ⇑ Corresponding author. Tel./fax: +86 516 83590601. E-mail address: [email protected] (X. Li). 0950-0618/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2011.08.058
safety against failure was also suggested to be higher than that used in steel-reinforced concrete design. Therefore, upcoming collapse of the members can be observed by some warning in forms of extensive cracking and ample deflection. This design concept was adopted by ACI-440-1R [1]; however, it can not be applied to cases such as seismic application where the internal force redistribution is very important. Alternative techniques using FRP hybrid rods or combinations of FRP rods with different material characteristics in an effort to develop an inelastic behavior are being realized to be favorable. Since the reinforcing fibers such as glass, aramid, carbon fibers and steel core have different stiffness and ultimate strains, hybrid FRP bar consisting of more than one reinforcing material behaves in an elastic-pseudo ductile manner. Results of some experimental studies [7,10,15] indicated that the use of the hybrid FRP bars can increase the flexural capacity and ductility of FRP-RC members. However, such efforts have thus far resulted in limited practical developments. Research conducted by Lau and Pam [13] demonstrated that the ductility of FRP-RC beams could be improved by adding a certain amount of conventional steel reinforcement since yielding of the steel bars resulted in significant inelastic deformation. Meanwhile, several investigations [6,18] on concrete encased steel members verified their desirable ductility and energy-dissipating capacity for seismic application. However, to date, no research information can be found related to the flexural behavior of FRP-RC members with encased structural steel shapes.
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Table 1 Cross sectional details of tested beams. Sectional typea
Cross section B D (mm)
Top bars
Bottom bars
fcu (MPa)
Steel shape ds bf tw tf (mm)
B1 B2 B3 B4 B5 B6 B7
A B B B B C D
160 250 160 250 160 250 160 250 160 250 160 300 160 300
2U6 2U6 2U6 2U6 2U6 2U6 2U12 + U8
3U12 3U12 2U12 2U8 3U12 3U12 + 2U6 2U8
48.2 48.2 48.2 35.5 35.5 48.2 48.2
– 140 80 5.5 9.1 140 80 5.5 9.1 140 80 5.5 9.1 140 80 5.5 9.1 140 80 5.5 9.1 140 80 5.5 9.1
Detailed types of cross sections were shown in Fig. 1.
160
160
(a) Type A
(b) Type B
105
sive strength of 50 MPa. To prevent premature shear failure, all the specimens were provided with 8-mm-diameter steel stirrups spaced at 120 mm over the entire length of the beam. To facilitate the installation of the transverse reinforcement, two GFRP bars with a diameter of 6 mm were used in compression zone as hangers for the stirrups in specimens B1–B6. Detailed investigation purposes of each specimen will be further presented hereafter along with the discussion on the associated test results.
300 140
300 140
55
80
55
250
250 140
80
55
a
Beam no.
160
160
(c) Type C
(d) Type D
Fig. 1. Typical cross-sections of beam specimens (units:mm).
In this paper, a composite beam consisting of FRP bars, steel and concrete is proposed and studied. It takes advantages of both ductile steel shapes and corrosion-resistant FRP-reinforced concrete. The encased steel shapes are adopted to improve the ductility and energy-dissipating capacity of conventional FRP-RC members. As recommended by the Chinese standard for steel reinforced concrete composite structures [12], the thickness of concrete cover for encased steel shapes should be not less than 100 mm. Therefore, the surrounding concrete in turn can provide sufficient protection to the steel shapes, impeding or delaying their corrosion. Meanwhile the concrete can inhibit the potential local buckling of the steel shapes. In this study, an experimental research on seven beam specimens was carried out to achieve the following objectives: (1) to investigate the flexural behavior of the proposed composite beams in terms of failure modes, strength, stiffness, ductility and energy absorption capacity; (2) to evaluate the role of some parameters including concrete compressive strength, amounts of GFRP reinforcement as well as ratio and configuration of encased structural steel shapes; and (3) to validate an analytical model developed to predict the load carrying capacity of the composite beams. 2. Experimental program 2.1. Beam specimens The test matrix for the experimental program is given in Table 1 and the typical cross-sections of beam specimens are shown in Fig. 1. A total of seven beam specimens with a total length of 2400 mm were constructed and tested in flexure. The main test parameters were concrete compressive strength, amounts of GFRP reinforcement as well as ratio and configuration of encased structural steel shapes. Specimen B1 was tested for comparison purpose and reinforced with GFRP bars only while specimens B2 to B7 were FRP-RCS beams reinforced with both GFRP bars and encased structural steel shapes. The clear concrete cover for longitudinal GFRP bars was 20 mm and all the embedded hot-rolled structural steel shapes had an identical cross-section of 140 mm depth (ds) by 80 mm flange breadth (bf), web and flange thicknesses of 5.5 mm (tw) and 9.1 mm (tf), respectively. Since specimens B2 to B5 had a rectangular cross-section of 160 mm 250 mm (breadth width) while the cross sections of specimens B6 and B7 was 160 mm 300 mm, the ratio of encased steel area to gross cross-sectional area is 0.054 for specimens B2 to B5 while the corresponding ratio for specimens B6 and B7 is 0.045. In addition, both specimens B4 and B5 were constructed from the concrete with a target 28-day cubic compressive strength of 35 MPa while the others had a target concrete compres-
2.2. Materials The GFRP bars used in this study were manufactured by the pultrusion technique and the surface was eventually treated to enhance the bond characteristics. They were made of continuous longitudinal glass (E-type) fiber strands bond with together with thermosetting polyster resin and the percent of glass fibers as provided by manufacturer was 70% by weight. The mechanical properties of each type of GFRP bars were obtained from standard tests of three tensile coupons according to ASTM [4]. The tensile rupture stress ffu were 680 and 750 MPa, respectively for U12 (12 mm nominal diameter) GFRP bars and U8 (8 mm nominal diameter) GFRP bars with an elastic modulus, Ef, 38 GPa. Tensile coupon tests were also conducted on steel components followed the standard GB/T 228-2002 [9] and the resulting yield stress fy, ultimate stress fu as well as corresponding Young’s modulus Es were 273 MPa, 385 MPa and 199 GPa, respectively. The concrete cubic compressive strength fcu was obtained by testing three 150 mm concrete cubes for each batch according to the standard GB/T 50081 [8]. The average concrete compressive strength at the time of beam testing was 48.2 MPa for specimens B1, B2, B3, B6 and B7 while the corresponding value for specimens B4 and B5 was 35.5 MPa. In general, the cylinder strength fc can be calculated as 0.8 times the cubic strength fcu. 2.3. Test method As shown in Fig. 2, all specimens were simply supported and subjected to fourpoint bending. Each of the specimens had a clear span of 2000 mm and shear spans of 750 mm; therefore, bending was constant in the central zone with a length of 500 mm. The static load was applied by a hydraulic jack to the specimens through a steel spreader beam. The load was monotonically applied in two stages. The first stage was load-controlled, in which the load was applied step by step at a rate of 5 kN per step for FRP-RCS beams until 75% of expected strength of the specimens, whereas the loading rate for FRP-RC beams was 2 kN per step for their low load carrying capacity. The second stage was carried out in displacement-controlled mode and the loading increment was 1 mm per step. At the end of each increment, all the data were collected and cracks were sketched. The specimen was considered to have failed when its load carrying capacity dropped to 80% of its maximum measured load or it developed a major physical deterioration. In order to measure deflections of the beam specimens, the displacements at beam mid-span, loading points and supports were monitored by transducers. The schematic arrangement of the transducers was included in Fig. 2. Electrical resistance strain gauges were also affixed on at strategic locations of GFRP bars and surfaces of encased steel shapes before concrete casting.
3. Test results and discussion A summary of test results is presented in Table 2. The average crack spacing at low loading stage, ultimate loads, displacement ductility, energy absorption capacity and failure modes of all beam specimens are included in the table. The displacement ductility factor (l) in this study is defined as the ratio of mid-span displacement at ultimate stage (Du) and that at yield stage (Dy), where the former is obtained at 0.8Pp after reaching the peak load Pp, while the latter is obtained by linearly interpolating the displacement at 0.75Pp to the level of Pp [16]. The ultimate and yield deflections
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in Figs. 3 and 4. Throughout the loading, no apparent signs of bond failure between GFRP bars and concrete were observed in all the specimens. For all FRP-RCS beam specimens, failure was initiated by yielding of encased steel shapes followed by crushing of concrete. However, the concrete crushing did not result in complete loss of load carrying capacity mainly due to the beneficial residual strength of encased steel shapes. The load carrying capacity even partially recovered in some specimens with further incremental deflection. Sounds indicating the fracture of fibers of tensile GFRP bars became audible for the large deflection, and eventually rupture of the GFRP bars triggered the final failure of specimens. The failure of FRP-RCS beams was gradual and ductile and the corresponding photos at failure conditions are shown in Fig. 5. Furthermore, the mid-span deflections of FRP-RCS beam specimens at failure conditions ranged between 28.98 mm and 42.82 mm, corresponding to a deflection-to-clear span ratio of 1/69 and 1/47, respectively. The ultimate deformability of the specimens was related to the amount of the GFRP bars. This is attributed to the final failure modes resulted by fracture of FRP reinforcement. However, for FRP-RC beam specimen B1 with identical arrangement and ratio of GFRP reinforcement to that of specimen B2, its failure arose from the sudden rupture of the GFRP bars and no compression failure of concrete occurred. The corresponding final failure was included in Fig. 5. The different failure modes between the FRP-RCS and FRP-RC beam specimens indicated that using encased steel shapes changed the failure mode from a non-ductile manner to a ductile one. In addition, the final rupture of GFRP bars in all specimens again confirmed that force transfer was sufficient to develop the full tensile capacity of the GFRP bars. The failure modes of all beam specimens are shown in Fig. 5.
Hydraulic actuator Steel spreader beam
250(B1~B5) 300(B6~B7)
Beam specimen
Rigid Support LVDT 200 200
750
500 2000
750
200 200
Fig. 2. Schematic of experimental setup and instrumentation (units:mm).
at beam mid-span are also listed in Table 2. Note that although FRP reinforced beams behaved essentially in an elastic brittle fashion after cracking up to failure, the ductility factor was still calculated as the method described above for comparison purpose. Furthermore, energy absorption was also calculated to estimate the energy-dissipating capacity of all specimens before their final failure and it was determined as the area under the load–deflection curve. The effect of the test parameters on the flexural behavior such as the load carrying capacity, the stiffness and the ductility are discussed in the following sections. 3.1. General observations and failure modes Typical cracking patterns of FRP-RC and FRP-RCS beam specimens at different loading stages are depicted in Figs. 3 and 4, respectively. At low loading level, all specimens exhibited a similar cracking behavior. The cracks induced by pure bending appeared firstly in the flexural span at approximately 15% of their measured peak loading. As the load increased, additional flexural cracks were formed within both the mid-span and shear span regions and the cracks in flexural zone propagated quickly toward the vicinity of about 3/5 depth of the beams. The average crack spacing at the low loading stage was given in Table 2 and the cracking patterns were plotted in Figs. 3a and 4a, respectively. It can be found that the specimens experienced flexural cracking below 30% of their peak loads and the encased structural steel shapes had no significant effect on the crack spacing, but specimen B7 with an encased structural steel shape shifted to tension zone had relatively larger crack spacing. At moderate and high loading stages, flexural cracks in all specimens became considerably wider and inclined cracks in the vicinity of tensile bars occurred gradually and propagated to join the flexural cracks. With further loading, the cracks in shear spans became progressively more inclined and extended towards the loading points gradually for the increased shear force, as shown
3.2. Load–deflection behavior 3.2.1. Effect of using structural steel shapes The effect of the encasement of steel shapes on load–deflection behavior was investigated by tests of specimens B1 and B2. These two specimens were constructed from the concrete in the same batch and reinforced with three 12 mm-diameter longitudinal GFRP bars, respectively. As shown in Fig. 6, the load–deflection curve was essentially linear up to the failure for specimen B1, and bilinear for specimen B2. The two specimens exhibited similar load–deflection behavior up to flexural cracking regardless of the presence of an encased steel shape in specimen B2. This is because that the behavior of uncracked beams is determined by the gross moment of inertia of the concrete cross section. Upon cracking, since the flexural stiffness of specimens was mainly dependent on the amount of reinforcement, specimen B1 experienced distinct degradation of flexural stiffness whereas the stiffness of specimen
Table 2 Summary of test results. Specimen no. a
Average crack spacing (mm) Loading capacity Mexp (kN m) Dy (mm) Du (mm)
l Energy absorption (kN mm) Analytical moment Man (kN m) Man/Mexp Failure modesb a b
B1
B2
B3
B4
B5
B6
B7
102.8 36.7 30.5 36.3 1.19 2144 – – FF
101.0 59.8 15.1 42.8 2.83 5346 60.9 1.02 CC
101.6 54.5 13.8 34.0 2.47 3835 54.7 1.01 CC
102.0 44.5 12.2 29.0 2.37 2667 48.3 1.09 CC
102.0 59.3 14.8 47.7 3.22 6068 56.7 0.96 CC
102.8 77.6 13.3 36.1 2.71 6077 74.6 0.96 CC
176.0 68.2 12.2 35.8 2.93 5303 70.7 1.04 CC
Average crack spacing at low load stage. FF = fracture of FRP reinforcement; CC = crushing of compression concrete.
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(a) Maximum applied load P=28.7 kN (29.3%Pp)
(a) Maximum applied load P=49.0 kN (30.7%Pp)
(b) Maximum applied load P=57.0 kN (58.2%Pp)
(b) Maximum applied load P=98.0 kN (61.4%Pp)
(c) Maximum applied load P=87.1 kN (89.0%Pp)
(c) Maximum applied load P=143.8 kN (90.2%Pp)
Fig. 3. Cracking patterns of specimen B1 at different loading stages.
B2 reduced slightly. It can be observed from Fig. 6 that the postcracking stiffness of specimen B2 was apparently higher than that of specimen B1, indicating the significant enhancing effect of using encased steel shapes on stiffness. As the load increased, yielding of encased steel shape led to substantially inelastic deformation of specimen B2 while specimen B1 showed no yielding until reaching its ultimate load carrying capacity for the previously mentioned elastic brittle nature of FRP material. As seen from Fig. 6, the measured peak load of specimen B2 was 63% greater than that of specimen B1 due to the contribution of the encased steel shape. Furthermore, at a mid-span deflection of 11.1 mm corresponding to the serviceability deflection limitation of l/180 recommended by [2], the measured loads at specimens B1 and B2 were 44.2 kN and 118.8 kN, respectively, that is to say, the measured load of specimen B2 was 2.69 times that of specimen B1, indicating the obvious improvement of load carrying capacity by using encased steel shapes. Referring to Table 2, it is evident that the displacement ductility and energy absorption of FRP-RC beams were improved by using encased steel shapes. The ductility and the energy absorption of specimen B2 were 2.38 and 2.49 times that of specimen B1, respectively. In addition, specimen B2 gained an ultimate deformability 18% higher than that of specimen B1.
3.2.2. Effect of concrete compressive strength The impact of the concrete compressive strength on flexural behavior can be evaluated by comparing the capacity of specimens B2 and B5 reinforced with identical amount of longitudinal GFRP bars. With reference to Fig. 6, specimen B2 constructed from higher strength concrete gained the flexural strength comparable to that of specimen B5, indicating that use of higher strength concrete has little effect on improving the load carrying capacity of FRPRCS beams. This may be attributed to the slight reduction of the ultimate strain of concrete with the increase of strength. The crushing of compression concrete occurred in specimen B2 ahead of specimen B5. Therefore, specimen B5 experienced a larger deflection before reaching its peak load, resulting in the up-shifting of neutral axis and further increase of tensile stress of FRP reinforcement. Moreover, comparison of the load–deflection curves of specimens B2 and B5 can also find that the crushing of higher strength concrete led to a relatively sharper drop of the load carrying capacity after peak load. This can be explained by two factors. First, higher strength concrete exhibits a more brittle stress–strain
Fig. 4. Cracking patterns of specimen B2 at different loading stages.
behavior. Second, higher strength concrete results in a lower depth of compression zone, and thus the aforementioned initial crushing of concrete cover triggered the substantial loss of the compressive concrete of specimen B2. Table 2 also shows that the increase of concrete compressive strength led to a reduction of the ductility and the energy absorption capacity of specimens. 3.2.3. Effect of amount of GFRP reinforcement The influence of the amount of longitudinal GFRP bars was examined by comparing test results of specimens of Group No.1, (specimens B2 and B3), and Group No.2, (specimens B4 and B5), respectively. As expected, since specimen B2 had higher reinforcement ratio, it achieved higher load carrying capacity and more favorable deformability than that of specimen B3. The flexural strength of specimen B2 was 59.8 kN m, that is, approximately 9.8% greater than that of specimen B3. Furthermore, with increasing ratio of GFRP reinforcement from 6.3% (B3) to 9.4% (B2), the increases in the ultimate deflection, the energy absorption capacity and the displacement ductility as shown in Table 2 were 26%, 39.4% and 14.6%, respectively. Similar remarks can be made by comparing test results of specimens of Group No.2. 3.2.4. Effect of ratio and configuration of encased steel shapes Tests of specimens B6 and B7 were also conducted to evaluate the effect of the ratio and configuration of encased structural steel shapes. Test results indicate that both the two specimens exhibited similar load–deflection behavior to that of specimen B2. As mentioned previously, both specimens B6 and B7 had a larger crosssection than that of specimen B2, and thus they exhibited higher stiffness and flexural strength. However, the ultimate deflection was slightly reduced for higher strain demand on FRP reinforcement. Specimen B7 with an eccentrically encased steel shape demonstrated an apparent inelastic behavior after experiencing a mid-span deflection of 7.0 mm; meanwhile the crushing of concrete was slightly delayed to a mid-span deflection of 25.98 mm. However, horizontal cracks along the interface of top steel flange and concrete, referring to as shear splitting failure, were observed in the shear spans of specimen B7 at high loading stage. Hence, further study on FRP-RCS beams with similar configuration of encased steel shapes to specimen B7 should be carried out to better understand the flexural behavior.
X. Li et al. / Construction and Building Materials 28 (2012) 255–262
259
(a) Specimen B1
(b) Specimen B2
(c) Specimen B3
(d) Specimen B4
(e) Specimen B5
(f) Specimen B6
(g) Specimen B7 Fig. 5. Failure modes of beam specimens.
4. Analytical investigation on flexural strength of GFRP-RCS beams As described previously, FRP reinforcement possesses some particular properties such as linear strain–stress behavior up to fail-
ure, and thus the design of the proposed FRP-RCS beams correspondingly differs from that of conventional concrete encased steel beams. For simplicity, the following assumptions were introduced in calculation of the flexural strength of FRP-RCS beams: (1) plane sections remain plane and thus strain varies linearly through
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240
Total Applied Load (kN)
B6
dcb 1 1 ¼ ¼ 1 þ ey =e0c 1 þ ba ds
ð2Þ
np ¼
dcp 1þk ¼ 1 þ efb =e0c ds
ð3Þ
200
B7
160
B2
B3
120
B5
B4 B1
80 40 0
0
10
20
30
40
50
Mid-span Deflection (mm) Fig. 6. Load–deflection curves of beam specimens.
the cross section; (2) the tensile strength of concrete is neglected; (3) the equivalent rectangular stress block in compression zone is a valid substitution for a nonlinear stress distribution at ultimate and the concrete strain e0c at compression failure is 0.003; (4) the stress–strain behavior of steel and FRP reinforcement is assumed to be perfect elasto-plastic and linearly elastic, respectively; and (5) no buckling of encased steel shapes occurs for the good confinement of the surrounding concrete and perfect bond exists between steel and FRP reinforcement and concrete. Fig. 7 illustrates the assumed basic analytical conditions of internal strain, stress, and resultant force for a cracked section at ultimate condition. According to ACI-440-1R [1], the balanced failure is the condition where crushing of compression concrete and rupture of tension FRP bars occur simultaneously. However, this condition is defined as the perfect failure in this study for the good utilization of strength of both concrete and FRP bars, whereas the balanced failure of FRP-RCS beams represents the simultaneous yielding of steel fiber at centerline of tension flange and compression failure of concrete. This is because the yielding of steel before failure is very important to FRP-RCS beams and it shall result in a ductile failure manner. A factor n to determine the failure mode of FRP-RCS beams is defined as follows,
n¼
nb ¼
dc ds
ð1Þ
where dc is the neutral axis depth and ds is the distance from centerline of tension flange to extreme compression fiber, as shown in Fig. 7. According to Eq. (1) and strain distribution shown in Fig. 7, the factor n for the balanced failure nb and the perfect failure np can be calculated as,
where dcb, dcp is the neutral axis depth at the balanced failure and the perfect failure condition, respectively; ey = fy/Es is the yield strain of steel; efb is the ultimate strain of FRP reinforcement; kds is the distance from centroid of longitudinal tension GFRP reinforcement to centerline of tension flange. According to Eqs. (1)–(3), five types of possible flexural failures (FRP fracture failure; perfect failure; steel yielding-concrete crushing failure; balanced failure and over-reinforced failure) of an FRPRCS beam can be expected depending on the value of factor n, as shown in Fig. 7b. For an FRP-RCS beam with a ratio of encased steel area to gross cross-sectional area not less than 0.02 that is recommended by the Chinese code [12] for conventional concrete encased steel members, its failure generally starts by steel yielding followed by concrete crushing and lastly by FRP rupture and thus the factor n usually varies between np and nb. Like conventional concrete encased steel beams, according to the location of neutral axis and stress distribution of encased steel shapes at failure condition, three types of cross sections can be further distinguished in calculation of the load carrying capacity of FRP-RCS beams with a factor n varying between np and nb. 4.1. Type-I cross section For an FRP-RCS beam with type-I cross sections, the bottom flange of its encased steel shape shall have yielded under tension and meanwhile the top flange shall have yielded under compression at failure condition. The corresponding strain and stress distribution are shown in Fig. 7. To meet the above assumption, the factor n should satisfy the following condition which is determined by strain compatibility. 0
k 6 n 6 nb 1 ba
ð4Þ
From the axial equilibrium condition, the following equation can be obtained. 0:85b1 fc0 bds n þ fy A0f Afb Ef e0c
1þkn 0 Af f y þ fy ds tw ð2n k 1Þ ¼ 0 n
where b1 is the factor relating depth of equivalent rectangular compressive stress block to neutral axis depth, which can be taken according to the [2]; b is the breadth of cross section; A0f and Af
Perfect failure Balanced failure
(a) Cross section
(b) Strain distribution
ð5Þ
(c) Strain distribution for concrete failure
Fig. 7. Analytical model for type-I section at ultimate.
(d) Resultant forces
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are the areas of top and bottom steel flanges, respectively; Afb is the total area of longitudinal tension GFRP reinforcement; k0 ds is the distance from centerline of top flange to extreme compression fiber. From Eqs. (4) and (5), the factor n can be determined and then the expression for the nominal moment strength MnI of FRP-RCS beams with type-I cross sections can be computed by taking the moment of tensile and compressive stress resultants of bars, encased steel shapes and concrete about centerline of the bottom flange of the encased steel shapes.
ð1 þ k nÞ 2 kds M nI ¼ 0:85b1 fc0 bds nð1 0:5b1 nÞ þ Afb Ef e0c n " 2 # k b2 n2 2 þ A0f fy k1 ds þ tw ds fy 1 ð1 nÞ2 a 2 3
The encased steel shape in an FRP-RCS beam with type-III cross sections shall have yielded completely under tension at failure condition and the corresponding strain and stress distribution are shown in Fig. 9. The nominal moment strength MnIII of can be calculated based on the following equations.
0:85b1 fc0 bds n fy As Afb Ef e0c
1þkn ¼0 n
ð10Þ
0
ð6Þ
Note that the resultant force of GFRP bars in compression was neglected herein since GFRP bars with low elastic modulus and compressive strain generally do not significantly add to the moment capacity unless they are disproportionately large in area. 4.2. Type-II cross section For an FRP-RCS beam with type-II cross sections, the bottom flange of its encased steel shape shall have yielded under tension while the top flange may be under tension or compression but it has not yielded yet at failure condition. The corresponding strain and stress distribution are shown in Fig. 8. Similarly, the nominal moment strength MnII of FRP-RCS beams with type-II cross sections can be determined as follows, 0
nk 1þkn Af f y Afb Ef e0c n ba n ( ) 0 ½ð1 þ ba Þn k 2 fy ds t w k1 ¼0 2nba
0:85b1 fc0 bds n þ fy A0f
ð7Þ 0
4.3. Type-III cross section
np 6 n 6
k 1 þ ba
ð11Þ
2
MnIII ¼ 0:85b1 fc0 bds nð1 0:5b1 nÞ þ Afb Ef e0c 2 2
A0f fy k1 ds 0:5t w k1 ds fy
ð1 þ k nÞ kds n ð12Þ
where As is the total areas of steel shape. In the aforementioned equations, there is only one unknown n. If the factor n is determined, the ultimate moment can be obtained easily. Hence, the analytical procedure is performed by assuming a cross-sectional type firstly, and then the corresponding value n can be estimated according to Eqs. (5), (7), (10). Note that the factor n should satisfy the corresponding condition shown in Eqs. (4), (8), (11). If not another type of cross section shall be assumed. Based on the above procedure, the nominal moment strength of the tested FRP-RCS beams was computed and it was found that all the specimens had the type-II cross sections. The analytical results coupled with the comparison between the experimental and analytical results were shown in Table 2. It indicates that the proposed analytical models can predict the flexural strength of FRP-RCS beams well. The mean and standard deviation values of Man/Mexp were 1.01 and 0.05, respectively.
0
k k
ð8Þ 5. Summary and conclusion
0:5b1 nÞ þ 0
Afb Ef 0c
e
(
ð1 þ k nÞ kds n 0 2
nk k1 ½ð1 þ ba Þn k 2 2 þ 0:5t w ds fy k1 þ nba ba n ) 0 ½ð1 þ ba Þn k 3 3ba n þ A0f fy k1 ds
(a) Cross section
ð9Þ
A new type of GFRP-RCS composite member is developed to improve the ductility and stiffness of GFRP-RC beams. The flexural behavior of the proposed composite beams was studied by testing of seven simply supported beam specimens and an analytical method was proposed to predict the nominal flexural strength of FRP-RCS beams. Based on the results of this investigation, the following conclusions can be drawn:
(b) Strain distribution for concrete failure
(c) Resultant forces
Fig. 8. Analytical model for type-II section at ultimate.
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(a) Cross section
(b) Strain distribution for concrete failure
(c) Resultant forces
Fig. 9. Analytical model for type-III section at ultimate.
(i) The use of encased steel shapes can provide a significant improvement in load carrying capacity, stiffness, ductility and energy absorption capacity of the conventional FRP-RC beams. (ii) Due mainly to the beneficial residual strength of encased steel shapes following concrete crushing, the proposed FRP-RCS beams exhibited desirable ductility and energy-dissipation capability. (iii) The experimental results indicate that concrete compressive strength has insignificant effect on the load carrying capacity of FRP-RCS beams. Moreover, higher strength concrete results in a relatively sharper drop of the load carrying capacity after concrete crushing. (iv) The increase of longitudinal GFRP reinforcement ratio leads to the increase of the load carrying capacity, the deflection capacity and the ductility of FRP-RCS beams. (v) Conventional beam theory is still valid to develop an analytical model for predicting flexural strength of FRP-RCS beams and the analytical results show a reasonable agreement with the experimental values.
Acknowledgments The authors would like to express their sincere appreciation for the partial financial support from the National Natural Science Foundation of China (Contract Number: 51008300) and the Jiangsu Provincial Science and Technology Department (Contract Number: BK2010185). The experimental work described in this paper was conducted at the Jiangsu Key Laboratory of Environmental impact and Structural Safety in Civil Engineering in the China University of Mining and Technology. Helps during the testing from staffs and students at the Laboratory are greatly acknowledged. References [1] ACI 440 1R-06. Guide for the design and construction of concrete reinforced with FRP bars. Michigan (USA): American Concrete Institute (ACI), Committee 440; 2006.
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