Structural Performance of Self-Consolidating Concrete Used in Confined Concrete Columns
This paper compares the mechanical performance of highly confined columns cast with normal concrete (NC) vibrated into place to ensure proper filling and consolidation equivalent to that of identical columns cast with self-consolidating concrete (SCC). The tested columns had nominal concrete compressive strengths of 40 to 80 MPa. Two confining stirrup configurations representing different degrees of confinement were used. The confining stirrups had nominal steel yield strengths of 400 to 800 MPa. A total of 16 columns were tested in this experimental investigation: 11 were cast either with NC or SCC in reinforced sections; five accompanying columns were cast without reinforcement. Three of the unreinforced columns were tested in uniaxial compression to determine the overall concrete compressive strength of the large-scale columns, while two others were cored to determine the distribution of the in-place compressive strength and modulus of elasticity along the column height. The test results on reinforced columns showed that SCC yielded greater ductility, although it developed slightly lower ultimate compressive strength than NC. The study also confirmed that an increase in the stirrup yield strength can generate a high degree of confinement in well-confined concrete columns provided that stirrup spacing is kept small. The coring of unreinforced concrete columns demonstrated that the distribution of in-place properties over the column height is more homogeneous in the case of SCC than NC, which was also found to be generally adequate.
Keywords: confined concrete; ductility; rheology; strength; vibrated concrete.
Casting concrete in heavily reinforced sections, such as those in columns and beams in moment-resisting frames in seismic areas and in some repair sections, makes the placement of concrete quite difficult. Providing proper consolidation can require internal or external vibration that can be critical in sections with high-density reinforcement. Ensuring thorough consolidation of critical structures with durability and safety concerns is essential and can often depend on the competence of the vibration crew to ensure adequate consolidation. Using standard vibration techniques with conventional concrete that is not fluid enough may lead to some surface and structural defects resulting from lack of proper bond development between the concrete and the reinforcement as well as the entrapment of air voids in the concrete. Flowable concrete is normally used to reduce labor cost and shorten construction time. Such concrete can have slump consistency close to 200 mm to facilitate placement and consolidation. Special attention should be given to vibration consolidation of the plastic concrete, however, to avoid segregation and bleeding, which may further impair structural performance and surface quality.
One way to reduce the intensive labor demand for vibration of highly congested sections is to use self-consolidating concrete (SCC). Such concrete can spread readily into place and fill the formwork without any mechanical consolidation and with minimum risk of separation of the material constituents. Such concrete is proportioned to exhibit a low yield value and a moderate viscosity to maintain high deformability and filling capacity of the formwork with minimum segregation and flow blockage.
SCC has been used in a variety of projects in North America, including precast/prestressed applications, repair of concrete infrastructure and, to some extent, construction of reinforced concrete structures. For such concrete to have wider acceptance for casting complex and congested structural elements, particularly in seismic areas, more information regarding in-place properties of the hardened concrete should be made available. For seismic construction requiring heavy reinforcement, specifying engineers considering using this new category of high-performance concrete must have adequate knowledge of the structural performance of elements cast with SCC.
Extensive research has been carried out at the University of Sherbrooke since the early 1990s to develop formulation expertise required to produce SCC with 28-day compressive strengths of 30 to 80 MPa with engineering properties comparable or superior to existing technology. The work has focused particularly on SCC suitable for filling highly congested and restricted sections, including repair applications as well as precast/prestressed applications. The research involved testing the effect of SCC stability on the homogeneity of in-place properties, including mechanical properties, bond strength with embedded reinforcement and prestressing strands, microstructure characteristics, and durability. The determination of the structural performance of highly congested columns cast with SCC with nominal concrete strengths of 40 to 80 MPa was also part of the investigation and included the comparison of the structural response (load versus deflection, ultimate strength, and ductility) of highly congested columns cast with SCC to that of similar specimens cast with conventionally vibrated normal concrete (NC) of equal strength. Part of those data was reported by Paultre et al. (1996) regarding the structural behavior of congested columns cast with SCC with compressive strengths in the 60 and 80 MPa ranges, as well as control columns cast with adequately consolidated NC of similar strength. The results indicated that high-strength SCC can provide ductility equivalent to that of high-strength NC but with lower ultimate confined concrete strength.
The main objective of the study reported herein was to compare the structural performance of highly confined concrete columns cast with NC and SCC. The effects of concrete compressive strength (40 to 80 MPa), confining stirrup configuration, and stirrup yield strength (400 and 800 MPa) were also evaluated. The distribution of compressive strength and elastic modulus along the height of plain unreinforced columns was also determined for specimens cast with either NC or SCC.
The construction of heavily reinforced concrete members, such as columns and beams in moment-resisting frames in seismic areas, makes the placement of concrete quite difficult. SCC can be used to facilitate the construction of elements without mitigating structural performance and durability. Most studies on SCC reported in the literature deal with mixture proportioning and characterization of fresh and hardened concrete properties with limited information on structural performance. One of the barriers to the widespread acceptance of SCC is the lack of information regarding structural properties of sections cast with SCC. This paper presents for the first time-to the best of the authors’ knowledge-results on the mechanical behavior of normaland high-strength self-consolidated confined concrete columns under concentric axial loading. The results should be of interest to engineers considering the use of such concrete in various structural applications.
The approach in this research on the development of high-performance SCC for casting highly congested columns involved using high paste volume (and low aggregate volume) to promote high deformability and reduce the risk of blockage and segregation during concrete placement. The water-cementitious material ratio (w/cm) was selected as a function of the targeted compressive strength. The cohesiveness and stability of the plastic concrete were enhanced by incorporating a moderate concentration of viscosity-enhancing admixture (VEA), also known as viscosity-modifying admixture, to retain some of the free water in suspension, hence increasing the plastic viscosity of the mixture.
SCC can be distinguished from conventional concrete not only by its high fluidity, but also by its composition. The most important distinctions are:
* Use of a high content of powder materials (
* Use of large quantities of high-range water-reducing admixture; and
* Use of a VEA in some cases when the water content is not low enough to promote sufficient viscosity of the paste.
Khayat, Manai, and Trudel (1997) proposed a mixture design for high-performance SCC suitable for casting highly congested structural elements. Such concrete was proportioned with 0.41 w/cm, 186 L/m^sup 3^ of ternary binder, 300 L/m^sup 3^ of coarse aggregate (maximum size of 10 mm), and a 0.60 sand-paste ratio, by volume. These values were used in this study for characterizing the SCC.
A Type 10 Canadian portland cement (CSA3-A5-M98, similar to standard specification for portland cement ASTM C 150-99 Type I cement) was used. Powder materials incorporated in SCC were silica fume, limestone powder, and blast-furnace slag. The admixtures included a naphthalene high-range water-reducing admixture, a set retarder, and welan gum VEA. Table 1 presents the concrete mixture proportions used for the concrete of the column specimens tested in this study. Table 2 shows the properties of hardened concrete based on standard cylinders prepared when casting each column specimen. These mechanical properties for plain concrete are: compressive strength f’^sub c^ ; modulus of elasticity E^sub c^; peak axial strain ε^sub co^; and axial strain when axial stress reduces to 0.5f’^sub c^ (ε^sub c50u^).
EXPERIMENTAL PROCEDURE AND INSTRUMENTATION
This research was completed in two steps. The first step involved the study of the rheological properties of the SCC, while the second part consisted of validating the use of SCC for structural applications. To perform the second step, concrete columns were made with SCC and NC.
Workability of self-consolidating concrete
The workability of fresh SCC was characterized by using a number of testing methods described as follows. These tests provided the means for comparing different mixtures and predicting the response of fresh concrete for mixture optimization.
Slump-flow test-Conventional concrete has a relatively high yield value; however, under vibration, the yield value is artificially lowered, leading to the spread and compaction of concrete. SCC has a low yield value (or high deformability), making vibration unnecessary. The consistency of SCC is evaluated with the slump-flow test, which consists of determining the mean spread of the concrete at the base of the slump test after the end of spreading. Such a value can be related to the yield stress of the concrete, and the rate of spread with time can be related to the plastic viscosity (Khayat, Assaad, and Daczko 2004). The slump-flow test is used to assess filling ability or the unrestricted deformability of SCC.
Filling-capacity test-This so-called caisson filling capacity test (Yurugi et al. 1993) evaluates the ability of concrete to flow through a series of parallel bars with constant spacing without segregation or blockage, as shown in Fig. 1. SCC with relatively low dynamic segregation resistance or high viscosity and relatively low filling ability will have limited flow through this highly restricted section. SCC with a filling capacity greater than 80% can be expected to fill congested formwork.
Funnel test-A trap is opened in a funnel filled with concrete (Fig. 2), and the time required to empty the funnel is measured. This test is based on a model proposed by Ozawa, Sakata, and Okamura (1995) except that the outlet opening of 65 × 75 mm was modified to 75 × 75 mm. This test is used to evaluate the flowing ability of the SCC, and can assess the dynamic stability of the concrete. A long flowout duration can be due to segregation (aggregates stacking at the opening) or excessive concrete viscosity.
The structural research involved axial compression testing of square 235 × 235 × 1400 mm column specimens for which the typical geometry and stirrup configurations are shown in Fig. 3. Their structural performances are compared with seven other test specimens previously tested by Cusson and Paultre (1994) and Paultre et al. (1996), where the concrete mixture proportions for these columns can be found as well.
The principal variables of the investigated column specimens are: (a) type of concrete (SCC or NC); (b) nominal concrete compressive strength (40, 50, 60, or 80 MPa); (c) type of stirrup configuration (Type B or D, as illustrated in Fig. 3); and (d) nominal steel yield strength of stirrups (400 or 800 MPa).
The experimental program of this study included the construction of nine steel-reinforced columns made with SCC (f’^sub c^ = 40 to 80 MPa) and two others made with NC (f’^sub c^ = 40 MPa). These columns, together with those previously tested by Cusson and Paultre (1994) and Paultre et al. (1996), form a complete group of 18 confined concrete columns, enabling the full comparison of the test variables listed previously. In addition, three 50 to 60 MPa unreinforced concrete columns were cast to determine the column compressive strength under concentric loading. Two other columns were prepared to evaluate the vertical distribution of in-place compressive strength and modulus of elasticity by testing core samples taken from the bottom, middle, and top sections of these column specimens. In general, the distribution of in-place mechanical properties along the height of unreinforced columns was more homogeneous in SCC columns than NC columns. More details on the testing of the unreinforced concrete columns can be found in Khayat, Paultre, and Tremblay (2001).
Each column specimen is identified with a label consisting of a number followed by a series of letters, as presented in Table 3. The number corresponds to the nominal concrete compressive strength series (7 corresponds to the 80 MPa series, 8 corresponds to 60 MPa series, and 10 corresponds to the 40 to 50 MPa series). The letters B and D indicate the transverse reinforcement configuration type (as illustrated in Fig. 3); the letter X identifies an unreinforced column; SCC indicates that the concrete is self-consolidating (if not mentioned, vibrated NC was used); and the letter O indicates the use of stirrups made of ordinary steel (if not mentioned, high-strength steel stirrups were used).
The details of the steel reinforcement used for the column specimens tested are presented in Table 3 along with the concrete compressive strengths and elastic moduli based on 150 x 300 mm cylinders. All column specimens have the same percentage of longitudinal reinforcement (ρ^sub g^ = 3.6%), the number of longitudinal bars n^sub b^ of 8 for Tie Configuration B and 12 for Tie Configuration D, and diameter d^sub b^ varying from 11.3 to 19.5 mm. The transverse reinforcement volumetric ratio and diameter were ρ^sub h^ = 4.9% and d^sub h^ = 9.5 mm for Tie Configuration B, respectively, and ρ^sub h^ = 4.8% and dh = 7.9 mm for Tie Configuration D, respectively. A tie spacing of 50 mm on centers was used in all columns. The transverse reinforcement ratio varied from 90 to 360% of the requirement recommended by ACI 318 Code (2002) for seismic construction. The steel properties were obtained from tensile loading tests performed on at least three samples from each lot of reinforcing bars. The yield strength of the longitudinal reinforcement f^sub y^ varied from 414 to 495 MPa, and that of the transverse reinforcement f^sub yh^ ranged from 410 to 440 MPa for ordinary steel (hot-rolled) and 680 to 891 MPa for high-strength steel (cold-formed).
During casting of the concrete columns, NC was thoroughly vibrated in the forms, while SCC was only placed into forms from the top without any mechanical vibration. Filling the forms took less than a minute for each column made with SCC and an average of 15 min for each NC column. Fresh concrete was sampled with standard 150 × 300 mm cylinders to determine the concrete compressive strength. Additionally, testing of standard 100 x 200 mm cylinders under controlled deformation rates was conducted to obtain other key concrete properties listed in Table 2 and the complete stressstain curve of the unconfined concrete. Cylinder strengths were determined within a day of testing the corresponding columns.
The axial deformation of column specimens were measured using four linear variable differential transformers (LVDTs) installed at each corner of the column, in the central part, over a length of 800 mm. Two layers of stirrups at midheight were instrumented with strain gauges to record the strain in the ties. Each column was capped with thin sulfur layers to achieve flat, smooth, and parallel surfaces for uniform compression loading. To ensure that the failure would occur in the instrumented region of the tested specimens, the tapered ends of each test column were further confined with bolted boxes made from 13 mm-thick steel plates. The test specimens were loaded on a rigid hydraulic press with load-controlled capabilities, having a maximum compressive load capacity of 6700 kN. An average loading rate of 1 kN/s was maintained during the test, which lasted between 45 and 90 min for each column. During testing, a data acquisition system recorded the load and longitudinal deformations of the column specimens at regular intervals, as well as the lateral deformation of the instrumented ties. The testing was terminated when the loading system reached its maximum displacement or when the column specimen was unable to sustain additional loading.
Workability of self-consolidating concrete
In general, all four SCC mixtures with compressive strengths of 40 to 80 MPa had adequate filling capacity test values (82 to 96%), which were greater than the targeted value of 80%. Higher strength concretes displayed higher V-funnel flow times. For instance, the 80 MPa SCC had a particularly high flow time, which is indicative of high viscosity.
The experimental results are presented in Table 4 and illustrated in Fig. 4 to 11. They also include the test results from seven additional columns tested by Cusson and Paultre (1994) and Paultre et al. (1996) to allow full comparison between column specimens. Figure 4 and 5 show the axial load/axial strain relationship for all columns tested, as recorded during testing. Figure 6 to 11 show the results expressed in terms of load applied on the concrete Pc normalized with respect to the axial capacity of the unconfined concrete cross section before spalling (P^sub oc^ = 0.85f’^sub c^A^sub c^) or the axial capacity of the confined concrete core section after spalling (P^sub occ^ = 0.85f’^sub c^A^sub cc^). The axial load applied on the concrete was determined for each column specimen by subtracting the load sustained by the longitudinal bars from the total load recorded during testing. The computation of the axial load sustained by the longitudinal bars was based on their total cross-sectional area Ast, on the steel stress-strain curves obtained from tensile loading tests, and the assumption of strain compatibility between steel and concrete. These curves were constructed using the techniques presented in Cusson and Paultre (1994).
In Table 4, several parameters were calculated from the resulting load-displacement curves obtained during the column axial load tests. Measured strength parameters P^sub max^, P^sub c1^, and P^sub c2^ are the maximum axial load carried by the column, the axial load carried by the concrete prior to cover spalling (first peak load), and the maximum axial load carried by confined concrete (second peak load), respectively. The theoretical strength parameters P^sub o^, P^sub oc^, and P^sub occ^ are the axial capacities of the column cross section, of the concrete cross section before spalling A^sub c^, and of the concrete cross section after spalling A^sub cc^, respectively. The ductility parameters (ε^sub co^, ε^sub c1^, ε^sub c2^, and ε^sub c50c^) are the axial strain in plain concrete corresponding to f ‘^sub c^ , the axial strain in the column concrete at the first peak load, the axial strain in the column concrete at the second peak load, and the axial strain in confined concrete when the load reduces to 0.5P^sub c2^, respectively.
ANALYSIS OF RESULTS
Homogeneity of strength and elastic modulus along column height
The coring campaign carried out on the unreinforced columns 10X-2 and 10XSCC-2 allowed the measurement of in-place mechanical properties of both types of concrete along column height. The 50 MPa NC showed a linear decrease in compressive strength and elastic modulus over the column height, with greater values obtained at the bottom (f’^sub c^ = 53 MPa and E^sub c^ = 37 GPa) than at the top (f’^sub c^ = 46 MPa and E^sub c^ = 36 GPa). On the other hand, the 50 MPa SCC column evidenced a uniform distribution of in-place properties, with f’^sub c^ = 45 to 47 MPa and E^sub c^ = 29 GPa. Such heterogeneity in the vertical distribution of compressive strength for NC may be attributed to the phenomenon of water migration upwards under the own weight of concrete, leading to consolidation at the bottom and a local increase in water content near the top of the column. More results on this part of the study are presented in Khayat, Paultre, and Tremblay (2001).
Effect of type of concrete on column strength and ductility
Strength-The majority of column specimens listed in Table 4 carried a maximum axial load P^sub max^ higher than the corresponding theoretical capacity P^sub o^. The highest ratios of P^sub max^/P^sub o^ were found in the 40 MPa series with values close to 1.5, regardless of concrete type. As nominal concrete strength increased, however, columns made with SCC started to show lower ratios than corresponding columns made with NC. For instance, in the 80 MPa series, P^sub max^/P^sub o^ values of 1.17 and 1.00 were found for NC and SCC, respectively. Similar observations can be made when other strength ratios (P^sub c1^/P^sub oc^ and P^sub c2^/P^sub occ^) are considered.
Ductility-Although the use of SCC, as opposed to NC, did not result in higher peak loads, it resulted in improved ductility, especially for the 40 MPa SCC columns. The ratio of the strain at the peak stress of confined concrete to the strain at the peak stress of corresponding unconfined concrete ε^sub c2^/ε^sub co^, which is an indicator of ductility, varied from 5.71 to 13.73 for NC columns with high-yield strength ties and from 6.36 to 14.15 for SCC columns with high-yield strength ties. The highest increase in ductility from the use of SCC over NC was observed in columns with lower nominal concrete strength.
Effect of tie yield strength on column strength and ductility
Strength-All columns made with high-yield-strength ties (800 MPa) had maximum axial load P^sub max^ greater than the corresponding theoretical capacity (P^sub o^ = 0.85f’^sub c^A^sub c^ + f^sub y^A^sub st^). Higher P^sub max^/P^sub o^ values were found for columns made with high-yield-strength ties when compared with columns made with normal-strength ties (400 MPa), regardless of concrete type. The relative increase in strength obtained by the use of high-yield-strength ties, however, decreased as the nominal concrete strength increased. This indicates that confinement is less effective when nominal concrete strength increases. For instance, in the 40 MPa series, an increase of P^sub max^/P^sub o^ from 1.18 to 1.50 was found when high-yield-strength ties were used instead of normal-strength ties, while P^sub max^/P^sub o^ increased from 1.02 to 1.17 in the 60 MPa series. Similar observations can be made when other strength ratios (P^sub c1^/P^sub oc^ and P^sub c2^/P^sub occ^) are considered.
Most columns made with normal-strength ties reached a maximum load on concrete prior to spalling P^sub c1^ close to their corresponding theoretical concrete capacity P^sub oc^. Values of P^sub c1^/P^sub oc^ varied from 0.85 to 1.03 for the 60 and 80 MPa series and from 1.10 to 1.13 for the 40 MPa series. Ratios lower than 1.00 are due to premature spalling of the concrete cover, which is frequently observed in high-strength concrete columns (Cusson and Paultre 1994). Unreinforced 50 MPa columns displayed similar ratios that varied from 0.96 to 1.07. This indicates that the columns made with normalstrength ties tested in this study can be considered as columns with low or negligible confinement in terms of strength increase.
Ductility-Columns made with normal-strength ties exhibited the smallest level of confinement. Values of ε^sub c2^/ε^sub co^ varied from 1.47 in the 80 MPa series to 5.77 in the 40 MPa series. These values are rather small when compared with those measured on columns made with high-yield-strength ties, which varied from 5.71 in the 80 MPa series to 14.15 in the 60 MPa series. Columns made with normal-strength ties cannot provide high levels of ductility, because once the low-yield strength of the steel is reached, additional lateral expansion of the concrete core cannot be further restrained, resulting in rapid tie failure, sudden loss of confinement, and buckling of the longitudinal bars. Specimens 7DSCCO and 7BSCCO, illustrated in Fig. 12, displayed such brittle behavior with the typical failure plane occurring at approximately 35 to 40 degrees from the vertical axis. An earlier study (Cusson and Paultre 1994) found that failure by crushing of concrete or with a failure plane of 45 degrees was an indication of the achievement of optimal confinement in the column. In general, it can be concluded that high-yieldstrength ties provided the columns with superior confinement and, as a result, the columns displayed smooth, progressive failure by concrete crushing. This behavior was more distinct for SCC in the 40 MPa series.
Effect of tie configuration on column strength and ductility
Strength-The strength parameters in Table 4 revealed that columns made with Tie Configuration B performed just as well as columns made with Tie Configuration D, irrespective of concrete strength (40 to 80 MPa), concrete type (SCC versus NC), and tie yield strength (400 to 800 MPa). For instance, when the nine columns made with Tie Configuration B are compared with the nine columns made with Tie Configuration D, the average P^sub c1^/P^sub oc^ value increased by 1%, and the average P^sub c2^/P^sub occ^ value increased by 2% when configuration D is used over configuration B. It is interesting to note that the smaller clear spacing of Tie Configuration D (three individual ties per set and 12 longitudinal bars) did not result in earlier spalling of the concrete cover when compared with Tie Configuration B (two individual ties per set and eight longitudinal bars).
Ductility-Similarly, the ductility parameters indicated that columns of Tie Configuration B performed just as well as columns of Tie Configuration D, irrespective of concrete strength, concrete type, and tie yield strength. For instance, the average ε^sub c1^/ε^sub co^ value increased by 5%, and the average εc50c/εco value increased by 3% when Tie Configuration D is used over Tie Configuration B. Although the ductilities provided by Tie Configurations B and D are similar, Cusson and Paultre (1994) demonstrated that these two tie configurations were far superior in providing ductility to a tie configuration using only one square tie per set with four longitudinal corner bars (of similar ρ^sub h^, ρ^sub g^, and s).
It is therefore suggested that Tie Configuration B, with a center-to-center spacing of 50 mm, should be given preference in the design of highly-confined concrete columns because it can provide excellent strength and ductility. Moreover, the construction of columns with such tie configuration is less labor intensive than columns with Tie Configuration D for the same volume of steel reinforcement.
It is believed that the lower ultimate strengths and higher ductilities measured for SCC columns compared with NC columns are probably due to a lower SCC modulus of elasticity. SCC contains a smaller volume of coarse aggregate than NC, resulting in lower elastic modulus and larger transverse expansion under compressive load. As a matter of fact, this tendency was demonstrated by comparing the less ductile high-strength NC columns in the 80 MPa series to the more ductile normal-strength SCC in the 40 MPa series. It was found that the difference in ductility between NC and SCC columns decreased as nominal concrete strength increased, probably due to the higher strength and stiffness of the paste itself.
It is therefore suggested that ductility can be achieved, not only by using closely-spaced ties of high-yield strength, but also by using a concrete such as SCC with a high paste content (or low aggregate content). This could also be due to the fact that SCC can develop better bond to the reinforcement, and hence improve ductility, than NC subjected to an extended duration of mechanical consolidation. More research is needed to confirm this statement.
The mechanical performance of highly confined columns cast with NC vibrated into place was compared with that of identical columns cast with SCC. The following conclusions were obtained:
* The use of SCC significantly reduced the time of casting highly congested column sections. The optimized mixtures allowed adequate placement of concrete into heavily reinforced columns and achieved high levels of filling capacity, regardless of tie configuration and design strength;
* Distribution of in-place properties along the column height was found to be more homogeneous for SCC columns than NC columns;
* Columns made with SCC offered slightly lower axial load-carrying capacities but were more ductile than equally confined columns made with NC. The lower modulus of elasticity of SCC, resulting in larger lateral expansion under a given compressive load, may be responsible for this difference between NC and SCC;
* Columns made with high-yield-strength ties provided significantly better confinement than similar columns made with normal-strength ties, regardless of concrete type. Although columns made with normal-strength ties displayed some ductility, they did not offer axial capacities higher than the expected theoretical values;
* Confinement was more effective in normal-strength concrete than in high-strength concrete, as the highest ductility (promoted by the use of either SCC concrete or high-yield-strength ties) was obtained in columns with lower nominal concrete strength; and
* Tie Configuration B (with s = 50 mm) should be given preference in the design of highly confined concrete columns because it can provide excellent strength and ductility (like Tie Configuration D), and the construction of columns with Tie Configuration B is less labor intensive than with Tie Configuration D for the same volume of steel reinforcement.
The financial assistance provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) and by the Fonds de recherche sur la Nature et les technologies du Québec (NATEQ) is gratefully acknowledged.
1 MPa = 145 psi
1 mm = 0.0394 in.
1 kN = 0.2248 kip
A^sub c^ = cross-sectional area of concrete
A^sub cc^ = cross-sectional area of concrete core bounded by centerline of outer tie
A^sub g^ = gross cross-sectional area of column
A^sub st^ = cross sectional area of longitudinal steel reinforcement
d^sub b^ = longitudinal steel bar diameter
d^sub h^ = transverse steel bar diameter
E^sub c^ = modulus of elasticity of plain concrete
f^sub c^ = stress in concrete
f^sub cc^ = maximum stress in confined concrete
f’^sub c^ = compressive strength of plain concrete measured on 150 × 300 mm cylinders
f^sub y^ = yield strength of longitudinal reinforcement steel
f^sub yh^ = yield strength of transverse reinforcement steel
n^sub b^ = number of longitudinal steel bars in column cross section
P = axial load carried by column
P^sub c^ = axial load carried by concrete
P^sub c1^ = axial load carried by concrete at onset of cover spalling
P^sub c2^ = maximum axial load carried by confined concrete
P^sub max^ = maximum axial load carried by column
P^sub o^ = axial capacity of column cross section
P^sub oc^ = axial capacity of concrete cross section
P^sub occ^ = axial capacity of concrete core bounded by centerline of outer tie
s = center-to-center spacing between sets of ties
ε^sub c^ = axial strain in concrete
ε^sub c1^ = axial strain in column concrete corresponding to P^sub c1^
ε^sub c2^ = axial strain in column concrete corresponding to P^sub c2^
ε^sub c50c^ = axial strain in confined concrete when stress reduces to 0.5f^sub cc^
ε^sub c50u^ = axial strain in unconfined concrete when stress reduces to 0.5f’^sub c^
ε^sub co^ = axial strain in plain concrete corresponding to f’^sub c^
ρ^sub g^ = volumetric ratio of longitudinal reinforcement in column cross section
ρ^sub h^ = volumetric ratio of transverse reinforcement in concrete core
ACI Committee 318, 2002, “Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary (318R-02),” American Concrete Institute, Farmington Hills, Mich., 443 pp.
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Patrick Paultre, FACI, is a Canada Research Chair in Seismic Engineering at the University of Sherbrooke, Sherbrooke, Quebec, Canada. He is a member of Joint ACI-ASCE Committees 352, Joint and Connections in Monolithic Concrete Structures, and 441, Reinforced Concrete Columns.
Kamal H. Khayat, FACI, is Professor of Civil Engineering at the University of Sherbrooke. He is a member of ACI Committees 234, Silica Fume in Concrete; 236, Material Science of Concrete; and 552, Geotechnical Cement Grouting. He is Secretary of ACI Committee 237, Self-Consolidating Concrete. His research interests include rheology, self-consolidating concrete, and repair.
ACI member Daniel Cusson is a research officer at the National Research Council, Ottawa, Ontario, Canada. He is a member of ACI Committee 363, High-Strength Concrete. His research interests include early-age behavior of high-performance concrete structures and in-place performance and durability of rehabilitated concrete bridges.
ACI member Stephan Tremblay is a structural engineer with Georgia Transmission Corp., Tucker, Ga. He received his MSc from the University of Sherbrooke. His research interests include the study of self-consolidating concrete and its structural use in highly reinforced members.
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