III. MATERIAL Y MÉTODO
4. FÁRMACOS QUE PUEDEN PRODUCIR IU [75]
The columns were tested horizontally; therefore, certain geometric adjustments are needed to convert the measured test data according to the cantilever column model shown in the schematic drawing of the specimen in Fig. 11. The tip displacement Δ is the tangential deviation of the contraflex- ural Point B, calculated as
D =dLa b+a (1)
where δL is the deflection at the point of application of lateral
load PL.
The lateral force Vʹ at the right hinge B can be determined from the applied force PL as
′ = +
V P a
a b
L (2)
As discussed by Liu and Sheikh,8 the shear force V at the base of the cantilever column differs from the applied lateral force Vʹ at Point B. As a result, the base shear force V can be determined from the components of the axial load P and lateral force Vʹ, as shown in Eq. (3)
V = Vʹcosθ – Psinθ (3)
where the inclination θ of the stub-column interface is
q = + D
a b (4)
Moment at the most damaged section is found by summing the moments caused by both the lateral and axial load. The following expression is used to calculate the moment in the most damaged section
M = V (L – Dmd) + PΔ (5)
where L = H + c = 1841 mm (72.5 in.) is the shear span of the column; and Dmd is the distance from the column-stub
interface to the most damaged section.
As mentioned earlier, 10M bars were precast in the testing region of the columns to measure core deformations after cover spalling and to obtain curvature. However, as a result of high deformation of the column and considerable concrete crushing in the damaged region, the measured curvature values from these rods were not found to be accurate at large displacements. Thus the curvature results reported here were obtained using strains from the strain gauges installed on the longitudinal bars. In cases where the strain gauges on the outer bars in the most damaged region stopped functioning before the failure of columns, curvature was obtained from the strain gauges located on the inner bars to extend the moment curvature (M-Φ) behavior. This extension is shown in dotted line in Fig. 12, while the horizontal dashed lines in each graph in Fig. 12 represent the nominal moment capacity of the column section (Mn). To evaluate the value
of Mn by sectional analysis, the stress-strain relationship of
unconfined concrete was used with the ultimate strain of 0.0035. Meanwhile, linearly elastic stress-strain relation- ship was assumed for longitudinal GFRP reinforcement with ultimate tensile and compressive strengths provided in Tables 2 and 3, respectively. In addition to the M-Φ response of the most damaged section, the shear-versus-tip deflection relationship (V-Δ) is also provided for each column. The dashed lines on the V-Δ curves represent the nominal shear capacity Vn with a decreasing slope caused by secondary
effects. Vn is calculated using the following expression
V M P
L
n = n y
− D
(6)
where P is the applied axial load; Δy is the yield displace-
ment; and L is the shear span. Although GFRP-reinforced columns do not undergo yielding, the procedure used by Liu and Sheikh8 for steel-reinforced columns was also used in this study to define a hypothetical yield displacement Δy
to evaluate the displacement ductility factor. Displacement Δy is determined corresponding to the nominal lateral load
capacity Vn along a straight line joining the origin and a
point of 65% Vn on the ascending branch of the lateral shear-
versus-tip deflection curve, which is determined for a specific axial load applied on the column.
Table 5—Ductility parameters
Spec- imen μΦ μΔ δ, % NΔ80 W80 NΔ W Vmax, kN (kip) Mmax, kN.m (kip.ft) P28-C- 12-50 >10.0 6.8 7.3 84 210 159 456 70.0 (15.7) 224 (165) P28-C- 12-160 >9.0 3.2 3.0 17 22 99 160 71.1 (16.0) 152 (112) P28-C- 16-160 >5.3 2.8 2.6 11 10 86 134 59.4 (13.4) 123 (91) P28-B- 12-50 >15.6 9.2 9.0 94 260 178 671 78.2 (17.6) 227 (167) P42-C- 12-50 >11.8 5.8 4.4 30 65 142 395 74.9 (16.8) 219 (161) P42-C- 12-160 >7.5 3.7 3.0 16 28 50 93 58.8 (13.2) 162 (119) P42-B- 12-160 >9.5 2.3 1.9 7 9 70 96 63.1 (14.2) 160 (118) P42-B- 16-160 >10.7 4.0 3.3 18 34 119 239 70.0 (15.7) 187 (137) P42-B- 16-275 >8.8 2.5 2.1 7 8 56 60 69.8 (15.7) 154 (113)
Ductility parameters
Several ductility parameters have been used to explain the behavior of reinforced concrete sections in the literature.7 Curvature and displacement ductility factors (μΦ, μΔ), drift ratio (δ), cumulative displacement ductility ratio (NΔ80), and work damage indicator (W80) are used in this study to quan- tify the deformability of the specimens.6 Figure 13 provides a graphical representation of how the displacement-related ductility parameters are calculated while parameters based on curvature can be defined in a similar manner. The results on ductility parameters are summarized in Table 5. The curvature at the most damaged section is obtained from the strain gauges on the longitudinal bars. Because the strain gauges stopped functioning before the failure of columns, the ultimate curvature ductility factors will be higher in most cases than the values reported here.
Fig. 10—Plastic hinge regions at end of testing.
Fig. 12—Moment-curvature and shear-deflection responses of columns. (Note: 1 mm = 0.039 in.; 1 kN = 0.225 kip; 1 kNm = 0.738 kip.ft; 1 rad/km = 305×10–6 rad/ft.)
The values of NΔ80 and W80 are respectively the cumula- tive displacement ductility ratio and the work damage indi- cator over a number of cycles until the shear capacity of the column drops to 80% of the peak load. As shown in Fig. 12, the column loses its stiffness (shown by Ki in Fig. 13) as
the test progresses and becomes negative for most columns during the last few cycles of testing. Due to the presence of the axial load on a highly deformed column during the last cycles, the shear force has to switch direction to main- tain equilibrium. To avoid adding negative energies to the work damage indicator, only cycles with a positive Ki are
included in the calculation of NΔ and W. Although this does not capture the full response of the column, the results show a similar trend to the reliable values of NΔ80 and W80.
Effect of axial load level
Two levels of column axial load (0.27Po and 0.42Po) were
used in this study. In steel-reinforced columns, it has been found that increasing the axial load would result in faster deterioration of the core concrete and initiation of longitu- dinal bar buckling.7 Similar behavior was observed for the GFRP-reinforced concrete columns tested here. The plastic hinge length (most damaged zone) shown in Table 1 is greater for columns with higher axial load indicating wider spread of the damaged zone. The effect of axial load on column ductility is more visible on well-confined specimens. For example, Columns P28-C-12-50 sustained an axial load of 0.28Po and achieved a displacement ductility factor μΔ of
6.8 while the similar Column P40-C-12-50 carrying an axial load of 0.42Po showed μΔ of 5.8. The same observation can
also be found by comparing the test results of other columns shown in Table 5 and Fig. 12.
An increase of axial load from 0.28Po to 0.42Po did not
significantly affect the flexural strength of GFRP-reinforced columns. For example, the measured flexural strengths of columns P28-C-12-50 and P42-C-12-50 were almost iden- tical. This experimental observation confirms the similarity between nominal moment capacities of specimens under
different axial loads evaluated using sectional analysis. Similar results were also reported by Choo et al.5
Effect of GFRP bar type
In general, there was not a significant difference between the performances of the columns reinforced with two different types of GFRP bars. The maximum moment capacity at the most damaged section, as shown in Table 1, is slightly higher for columns reinforced with GFRP Type B. This can be attributed to the fact that both longitudinal bars and spirals of Type B have considerably larger actual areas compared with the nominal areas than those of GFRP Type C. The length of the damaged region is very similar for columns in pairs such as P28-C-12-50 and P28-B-12-50 or P42-C-12-160 and P42-B-12-160, in which the only difference was the type of GFRP bar. The latter pair of columns showed a similar deflected shape at all stages and failure for both columns occurred at almost the same lateral displacement.
Effect of spiral pitch and reinforcement ratio
Research on steel-reinforced columns has shown that increasing the transverse reinforcement ratio and decreasing Fig. 14—Hysteresis response of steel-confined versus GFRP-reinforced column. (Note: 1 mm = 0.039 in.; 1 kN = 0.225 kip.)
the spiral/tie pitch delay column failure by confining the concrete core prevents premature buckling of the longi- tudinal bars.7,8 Consequently, columns with lower spiral spacing have higher strength and ductility.
Similar conclusions can be made for GFRP-reinforced columns using the results obtained in this experimental study. The moment capacity of the column considerably increased as the spiral spacing reduced from 160 to 50 mm (6.2 to 2 in.). The maximum shear capacity is approximately similar for all columns. This is expected because the maximum shear occurs in the first few cycles and is not affected by the spiral configuration. Table 5 shows that the absorbed energy is significantly higher for columns with smaller spiral spacing and the resulting higher transverse reinforcement. Closer spiral spacing resulted in better confinement of the concrete core and delayed the buckling of the longitudinal bars. For instance, the lateral drift ratio for column P28-C-12-50 is more than twice that of column P28-C-12-160. Reducing the spiral spacing from 160 to 50 mm (6.2 to 2 in.) resulted in a 50% increase in the moment capacity of the column.
The transverse reinforcement ratio can be adjusted by changing the size of the spiral as well. However, the effect on column response is not as noticeable as adjusting the spiral spacing. The effect of changing the spiral size can be observed by comparing columns P42-B-12-160 and P42-B-16-160. Increasing the spiral size from 12 to 16 mm (0.47 to 0.63 in.) resulted in a 13% increase in the moment capacity of the column and doubled the dissipated energy.
Comparison of GFRP-reinforced and steel- reinforced columns
GFRP-reinforced concrete columns generally show a softer ascending branch of shear-versus-deflection behavior than steel-reinforced concrete columns due to the lower modulus of elasticity of GFRP. The difference in stiffness is significant even though reinforcement represents only a small portion of the column’s properties. A comparison of the shear-versus-lateral tip deflection relationships of two columns is shown in Fig. 14. Column P27-NF-2 had 9.5 mm (No. 3) steel spiral with 100 mm (4 in.) pitch which resulted in ρsh = 0.9%. The longitudinal steel reinforcement ratio
for this column was 3.01%. Both these values were similar to those of column P28-C-12-160, as were the column dimensions and testing conditions. The concrete strength for column P-27-NF-2 was 40 MPa while this value for column P28-C-12-160 was 35 MPa (5080 psi). The hyster- etic response shows that the steel-reinforced column absorbs more energy in each lateral deflection loop as a result of the yielding and Bauschinger effect of the longitudinal steel reinforcement. It should be noted that a lack of yield plateau in GFRP bars results in a much lower residual deflec- tion when the load is removed. The stiffness of the steel- reinforced column is higher than that of the GFRP-reinforced column and the higher shear capacity of column P27-NF-2 is due to the higher modulus of elasticity of the steel reinforce- ment. The capacity gap could simply be decreased by using a larger amount of the GFRP reinforcement to balance its low stiffness which may reduce deformability of the column.
Both columns showed stable post-peak descending branches and high ductility. However, it can be seen that the GFRP-reinforced column has a longer post-peak descending branch before final failure than the steel-reinforced column. This is mainly due to the fact that the steel bars have very low tangent modulus after yielding and therefore are more susceptible to buckling under compression than GFRP bars which maintain their modulus of elasticity throughout the entire duration of loading.
GFRP reinforcement does not experience yielding and results in a nearly linear elastic moment-versus-curvature relationship of columns with no post-peak decline, as shown in Fig. 12, unlike the steel-reinforced columns in which the steel yields and the moment curvature response displays a descending branch. The GFRP transverse reinforcement despite being softer than steel at small strains, continue to provide increasing confinement until the column failure.
Strain effectiveness of GFRP spirals
The maximum strain in the GFRP spiral, εsp,80%, was
recorded for each column at the stage when shear capacity dropped to 80% of the peak shear and also just before failure. The results are summarized in Table 6. As expected, in columns with high axial load, a greater hoop strain is observed. The average value of εsp,80% for all nine columns
is 0.00546, which is close to the recommended Canadian code12 design value of 0.006. Maximum recorded spiral strains before column failure indicate that GFRP spirals were able to provide increasing confinement to the core while the
Table 6—Average spiral strain in most damaged region Specimen Maximum spiral strain at 80% peak εfh80%, µε Maximum spiral strain εfh, µε Ultimate spiral strain εufh, µε εfh/εufh P28-C- 12-50 4145 4145 24,900 0.167 P28-C- 12-160 3612 4031 24,900 0.162 P28-C- 16-160 4450 5605 19,900 0.282 P28-B- 12-50 9306 9779 21,100 0.463 P42-C- 12-50 2276 6440 24,900 0.259 P42-C- 12-160 7835 11,882 24,900 0.477 P42-B- 12-160 5010 7581 21,100 0.359 P42-B- 16-160 6597 13,054 21,300 0.613 P42-B- 16-275 5902 9723 21,300 0.456 Average “B” 6704 10,034 21,200 0.473 Average “C” 4464 6421 23,900 0.269
maximum strain is significantly less than the rupture strain. The average maximum spiral strain for the nine columns is about four times the steel yield strain before failure. The ratio between the maximum spiral strain and ultimate GFRP strain—spiral efficiency—is also listed for all the columns in Table 6. The increase in the moment capacity of the columns, especially those reinforced with a 16 mm (0.63 in.) spiral, over the last few cycles indicates the effec- tive confinement provided by the GFRP spiral. This strength gain over the last cycles can clearly be seen in the moment- versus-curvature response of columns P28-C-16-160, P42-B-16-160, and even P42-B-16-275.
Comparison with code requirements for confinement
The transverse GFRP spirals in specimens P28-C-12-50 and P28-B-12-50 were designed for a targeted lateral drift ratio of 4% according to CAN/CSA-S806-12,12 while spec- imen P42-C-12-50 was designed to achieve 2.5% drift ratio, and the rest of specimens had only substandard trans- verse reinforcement in terms of confinement spiral spacing required by this design code.
Both columns P28-C-12-50 and P28-B-12-50 outper- formed the design expectations, with measured drift ratios of 7.3 and 9.0%, respectively. Column P42-C-12-50 also achieved a lateral drift ratio of 4.4%, which exceeded the designed target of 2.5%. In fact, only columns P42-B-16-275 and P42-B-12-160 had a lateral drift ratio lower than 2.5%. The widely spaced spirals in P42-B-16-275 led to the prema- ture buckling of longitudinal reinforcement and limited deformability. Specimen P42-B-12-160 showed a lateral drift ratio of only 1.9% due to the presence of honeycomb regions in the testing region. The experimental results indicated that, if designed according to CSA-S806-12,12 GFRP-reinforced columns can achieve much higher lateral drift capacity than design expectations.
SUMMARY AND CONCLUSIONS
To understand the behavior of concrete columns reinforced longitudinally with GFRP bars and transversely with GFRP spirals, nine large-scale specimens were tested under lateral displacement excursions and constant axial load. Exper- imental results in the form of moment-versus-curvature and shear-versus-tip deflection hysteretic responses and various ductility parameters are presented. The following conclusions can be drawn from this study:
1. The crushing strength of GFRP bars in compression is approximately half of their ultimate tensile strength, and the modulus of elasticity in compression for a GFRP bar was found to be similar to that under tension.
2. Columns reinforced with GFRP bars and spirals showed a stable response, and the type of GFRP material used did not cause a significant change in the behavior of the columns.
3. Columns P28-B-12-50 and P28-C-12-50 were designed for a lateral drift ratio of 4% and they achieved a lateral drift ratio in excess of 7%. Column P42-C-12-50 achieved a lateral drift ratio of 4.4%, which was 1.9% higher than the design value.
4. Columns that were subjected to a higher axial load sustained more damage and displayed lower levels of ductility and deformability. The amount and detailing of
transverse reinforcement is more critical for high axially loaded columns.
5. GFRP bars, due to their larger stiffness at larger strains, performed in a more stable manner than steel bars.
6. The transverse steel reinforcement provides effective confinement to the core at early stages; however, as the steel starts to yield, the confinement is less effective, allowing the concrete core to expand. GFRP spirals, on the other hand, provide an increasing level of confinement with increased deformation which delays crushing of the core concrete.
AUTHOR BIOS
Arjang Tavassoli is a Project Associate at Parsons Brinckerhoff Halsall
Inc. in Toronto, ON, Canada. He received his BASc and MASc in civil engi- neering from the University of Toronto, Toronto, ON, Canada, in 2011 and 2013, respectively.
James Liu is a Structural Engineer with Brown and Company Engi-
neering Ltd. in Toronto, ON, Canada. He received his BS in civil engi- neering from Tongji University, Shanghai, China, and his PhD from the University of Toronto. His research interests include analysis and retrofit of concrete structures.
Shamim Sheikh, FACI, is a Professor of civil engineering at the Univer-
sity of Toronto. He is Chair of ACI Subcommittee 441-E, Columns with Multi-Spiral Reinforcement. He is a former Chair and member of Joint ACI-ASCE Committee 441, Reinforced Concrete Columns, and a member of ACI Committee 374, Performance-Based Seismic Design of Concrete Buildings. In 1999, he received the ACI Chester Paul Seiss Award for Excellence in Structural Research. His research interests include earth- quake resistance and design of concrete structures, confinement of concrete, use of fiber-reinforced polymer for sustainable concrete structures.
REFERENCES
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3. De Luca, A.; Matta, F.; and Nanni, A., “Behavior of Full-Scale Glass Fiber-Reinforced PolymerReinforced Concrete Columns under Axial Load,” ACI Structural Journal, V. 107, No. 4, July-Aug. 2010, pp. 589-596.
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6. Sharbatdar, M. K., and Saatcioglu, M., “Seismic Design of FRP Rein- forced Concrete Structures,” Asian Journal of Applied Sciences, V. 2, No. 3, 2009, pp. 211-222. doi: 10.3923/ajaps.2009.211.222
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DISCUSSION
Discussion 111-S22/From the March-April 2014 ACI Structural Journal, p. 257
Bond Strength of Spliced Fiber-Reinforced Polymer Reinforcement. Paper by Ali Cihan Pay, Erdem Canbay,
and Robert J. Frosch
Discussion by José R. Martí-Vargas
Professor, ICITECH, Institute of Concrete Science and Technology, Universitat Politècnica de València, València, Spain
The discussed paper presents an interesting experi- mental study on the bond behavior of unconfined tension lap-spliced reinforcement. Steel-reinforced concrete beams and reinforced beams with fiber-reinforced polymer (FRP) bars—glass FRP and carbon FRP—were tested to provide additional experimental data for a better understanding of the bond strength between FRP and concrete.
Variables such as splice length, surface condition, modulus