Bending Ductility of Rectangular High Strength Concrete Columns

Engineering Structures 29 (2007) 1783–1790 www.elsevier.com/locate/engstruct

Bending ductility of rectangular high strength concrete columns Jonathan M. Woods a , Panos D. Kiousis b,∗ , Mohammad R. Ehsani a , Hamid Saadatmanesh a , Wolfgang Fritz a a The University of Arizona, Department of Civil Engineering and Engineering Mechanics, Tucson, AZ 85721, United States b Colorado School of Mines, Division of Engineering, Golden, CO 80401, United States

Received 7 March 2005; received in revised form 27 December 2005; accepted 25 September 2006 Available online 13 November 2006

Abstract A study was conducted on eight high strength concrete columns ( f c0 = 69 MPa) with dimensions 203 × 203 × 2030 mm. The intent of the study was to isolate the effects of the spacing and volumetric content of the transverse reinforcement on the bending ductility of high strength concrete columns. To this end, four of the columns were reinforced with ties of constant spacing (76 mm) but different diameter (3.2, 4.8, 6.4, and 8.0 mm), while the other four columns were reinforced with ties of different spacing but constant volumetric content (1.1%). Clear trends in the effects of the volumetric content and spacing of the transverse reinforcement were observed within a range of values outside of which the effects were minimal. c 2006 Elsevier Ltd. All rights reserved.

Keywords: High strength concrete; Ductility; Tie spacing; Volumetric content

1. Introduction Use of high strength concrete (HSC) typically results in smaller column cross-sections and longer unsupported spans. In addition, the lower permeability that is typically associated with HSC results in higher durability and resistance to chemical agents. In recent years, the compressive strength of concrete that can be achieved reliably in the field has exceeded 90 MPa. However, HSC is used with caution due to its lower ductility in compression than normal strength concrete (NSC). As a result, current confinement requirements [1], which have been based mostly on NSC experience and testing, may not be applicable to HSC columns. This caution is illustrated by the common practice of some US State Departments of Transportation that place upper limits on the compressive strength of concrete in highway construction projects. For example, the Colorado Department of Transportation places an upper limit for castin-place concrete of f c0 = 40 MPa, and for precast concrete of f c0 = 60 MPa. The potential benefits from the use of HSC have triggered significant interest among researchers, a ∗ Corresponding author. Tel.: +1 303 384 2205; fax: +1 303 273 3602.

E-mail address: [email protected] (P.D. Kiousis). c 2006 Elsevier Ltd. All rights reserved. 0141-0296/$ - see front matter doi:10.1016/j.engstruct.2006.09.024

fact that is evident from the continuously growing number of related published research activities [2–10]. This paper is part of a broader study undertaken by the senior authors and their students [2,3,11] aiming to a better qualitative and a more accurate quantitative identification of the response of HSC columns to combined axial and cyclic bending loads. In earlier studies [2,3] the authors examined the effects of confinement on the axial ductility of HSC cylindrical specimens and the bending ductility of HSC columns. In this study, the effects of confinement on the bending ductility of columns are examined in relation to the volumetric content and spacing of transverse reinforcement. 2. Test method 2.1. Specimens Eight prismatic column specimens, designed with crosssectional/axial load combinations ensuring failure after yielding of the tensile reinforcement (below balance), were built and tested. All specimens were cast from one batch of concrete with a 28-day compressive strength f c0 = 69 MPa (Fig. 1) and dimensions 203 × 203 × 2030 mm. The slump at the time of arrival was 190 mm. This rather high slump was

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J.M. Woods et al. / Engineering Structures 29 (2007) 1783–1790

Notation HSC Ag Atie dt L tie st Vg Vties δp δu δy µp µy ρt

High strength concrete Gross cross-sectional area of the column Cross-sectional area of the tie Tie diameter Length of the tie Tie spacing Gross volume of the concrete column Volume of the ties over the length of the column L Transverse deflection of the column at the peak load Transverse deflection of the column at incipient failure Transverse deflection of the column at first yield of the reinforcement Ductility based on peak deflection Ductility based on yield deflection Volumetric content of the transverse reinforcement

designed to allow easier flow through the tightly spaced steel reinforcement cages. A more detailed description of the specimens is presented elsewhere [11]. All columns were reinforced with eight #13 grade 60 longitudinal bars (nominal f y = 414 MPa, tested f y = 402 MPa), which were placed symmetrically so that there were three bars on each column face. Transverse reinforcement, also grade 60 (nominal f y = 414 MPa, tested f y = 280 MPa), was provided with ties that were placed in pairs of rectangular and diamond configuration (Fig. 2). The clear concrete cover for the ties was 13 mm. The features of all specimens are summarized in Table 1. The calculated combination of axial load and bending moment for balanced failure was Pb = 1165 kN, Mb = 90 kN m. The columns were divided into two groups. The first group, labeled “S”, consisted of columns with constant tie spacing st = 76 mm and varying volumetric content of transverse reinforcement ρt . The second group, labeled “V”, consisted of columns with constant volumetric content of transverse reinforcement ρt = 0.011 but varying tie diameter dt and spacing st . Each column is identified by its group letter (S or V), the tie diameter and the tie spacing in mm. For example, column S4.8-76 describes a specimen that belongs to the group of constant tie spacing with tie diameter of 4.8 mm and tie spacing 76 mm. The volumetric content of the transverse reinforcement is defined as ρt =

Vties Vg

(1)

where Vties = n · L tie · Atie is the volume of the transverse reinforcement, n is the number of sets of rectangular and diamond ties over the column length L, L tie is the total length of one set of rectangular and diamond ties (less hooked ends), Atie is the cross-sectional area of the tie, Vg = A g L is the

Fig. 1. Concrete stress–strain relation.

Fig. 2. Sketch of cross-sectional characteristics of a typical column.

gross volume of the concrete column, and A g is the gross crosssectional area of the column. 2.2. Test set-up The test set-up and the locations of measuring devices (points A through E) are shown schematically in Fig. 3. The available facilities did not allow the application of cyclic horizontal load on vertical columns. Thus, the specimens were placed in the horizontal position, subjected to an axial compression using a 900 kN jack in a self-contained system (Fig. 3), and then loaded cyclically in four-point bending. The self-contained system for the application of the axial load consists of one jack, one flat end plate, two stiffened end plates, and two steel rods of diameter 51 mm placed on each side along the length of the column. The transverse load was applied by a 490 kN actuator through a four-point loading system. The applied point loads were 580 mm apart, while the supports were 1830 mm apart. This configuration created a length of 580 mm of constant bending and zero shear between the two points of load application. Deflections were measured at the supports, the points of load application and at the center of the columns using LVDTs and string potentiometers. The points of deflection measurement are shown as points A through E in Fig. 3. Two measurements of

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J.M. Woods et al. / Engineering Structures 29 (2007) 1783–1790 Table 1 Specimen design details Specimen

f c0 (MPa)

Axial reinforcement

P/P0

Tie diameter (mm)

Tie spacing (mm) (in)

Volumetric content (%)

S3.2-76 S4.8-76 S6.4-76 S8.0-76 V5.5-66 V6.4-86 V8.0-135 V9.5-133

69 69 69 69 69 69 69 69

8 bars 13 mm 8 bars 13 mm 8 bars 13 mm 8 bars 13 mm 8 bars 13 mm 8 bars 13 mm 8 bars 13 mm 8 bars 13 mm

0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16

3.2 4.8 6.4 8.0 5.5 6.4 8.0 9.5

76 76 76 76 66 86 135 193

0.3 0.67 1.2 1.87 1.09 1.1 1.08 1.14

P0 = 0.85 f c0 (A g − As ) + As f y = 2.78 MN.

Fig. 3. Schematic of column loading.

deflection (front and back of the column) were taken at the central point D and were averaged. Strain gauges were also placed at the central reinforcing bars at the top and bottom of the specimens at mid-span, in order to identify the initial yield and to measure the curvature of the mid-span cross-section as a function of the applied load. Unfortunately, most gauges failed earlier than expected and could not be used for their intended purposes. 2.3. Testing procedure The columns were mounted on the loading system as shown in Fig. 3, and loaded axially to 445 kN. This axial load was convenient because it allowed the use of additional data from an earlier study [3]. The column was subsequently loaded transversely in four-point bending while maintaining the axial load constant. During the application of the transverse load, the deformation controlled axial compression of the specimen tended to change. Thus, a continuous adjustment of the pressure in the jack was necessary to maintain the axial load constant. Failure was declared when the specimen could not sustain the axial compression of 445 kN. The rate of transverse loading was 1/3 mm s−1 . The pattern of cyclic transverse loads was applied as follows: Two displacement cycles with amplitudes

Fig. 4. Schematic of transverse loading history.

of ±2 mm were applied. These cycles were followed by two cycles with ±4 mm amplitude. Additional pairs of cycles were applied with amplitudes that increased by ±4 mm until the column could no longer sustain its axial compression of 445 kN. The loading pattern is illustrated in Fig. 4. Due to slight variations in the controller and the differences in stiffness of the supports under tension and compression, the actual deformation pattern in each specimen did not adhere exactly to the defined loading specification. However, the variations were small, and reasonable loading consistency was maintained for all experiments. The response of column specimen V9.5133 could not be reported due to a malfunction of the data acquisition system that failed to record the test data.

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Fig. 5. Transverse load–deflection diagram for column specimen S3.2-76 − ρt = 0.003.


3. Results and discussion 3.1. Crack propagation and failure mode Crack propagation was monitored throughout the loading process. Despite their differences in measured ductility, all column specimens exhibited similar patterns of crack development and ultimately failed in a similar way. Cracks developed first at the bottom of the specimen at a deflection of 2 mm and corresponding load of approximately 70 kN. Shear and flexural cracks became quite noticeable at approximately 10 mm of deflections and load in the order of 160 kN. Due to the cyclic nature of loading with curvature reversals, the cracks maintained a relative symmetry about the horizontal centroidal axis. The increase in compressive stresses in the column section, caused by the combined action of bending stresses and axial loading, initiated a process of concrete crushing. The longitudinal steel bars yielded in tension at a transverse loading of approximately 184 kN. The peak load was approximately 200 kN and corresponded to deflections in the neighbourhood of 13 mm. At that point, the concrete shell in compression spalled. The post-peak ability to carry load varied from specimen to specimen based on the volumetric content ρt and spacing st of the transverse reinforcement. However, the modes of failure in all specimens remained similar. In general, the tendency to develop more shear cracks decreased in the post-peak region of deformations. On the other hand, the flexural cracks increased in length and became wider. Core crushing followed the spalling on both sides. During the latter stages of loading, buckling deformations of the longitudinal bars became more pronounced and failure followed either due to bar buckling, or due to tie breaking, which in turn resulted in instantaneous bar buckling. All columns tested here exhibited “high stress, low cycle” fatigue of their longitudinal reinforcement. This relates to steel rupture caused by fatigue due to a small number of cycles of loading at high stress levels [12]. 3.2. Load–deflection diagrams The deflection response of a column under cyclic transverse load provides a means to determine the hysteretic energy


dissipation, which is commonly used to evaluate the anticipated seismic performance of reinforced concrete structures. The load–deflection response of a transversely loaded column can be evaluated by the deflection ductility index µ. Two definitions of the ductility index were considered here: (1) µ y = δu /δ y , and (2) µ p = δu /δ p , where δu is the ultimate transverse deflection of the column, δ y is the transverse deflection of the column at first yield of the axial reinforcement, and δ p is the transverse deflection of the column at peak transverse load. The ultimate deflection is defined as the one corresponding to incipient loss of axial load capacity. The values of ductility index are greatly influenced by the accuracy of the denominator, which is commonly a small number. The peak-load deflection δ p was determined experimentally for all columns, whereas experimental determination of δ y was possible only for two columns due to sensor failures as is discussed later. As a result, in most cases δ y was calculated theoretically. Both ductility indices µ p and µ y are discussed here. However, in the analysis presented later, µ p , which is known with greater accuracy, is favoured, even though it is unconventional. The load–deflection responses of the columns with constant tie spacing (designated by the letter “S”) are presented in Figs. 5–8. No pinching tendencies in the hysteresis loops were observed. For these columns, increase in tie diameter dt (and thus in the transverse reinforcement content ρt ) results consistently in increased deflection at failure (the point at which the axial load capacity is lost) and improved ability to dissipate post-peak energy.

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Fig. 11. Transverse load–deflection diagram for column specimen V 8.0-135 − ρt = 0.011.

Theoretical load–deflection relations for all columns, assuming monotonic load increase, are also presented in Figs. 5 through 11. To calculate the theoretical deflections, the axial compression stress–strain model of Mander et al. [13] was used for the confined concrete, and the Kent and Park [14] model was used for the unconfined concrete, up to an assumed crushing strain of 0.003 (Fig. 12(a)). Theoretical moment–curvature relations are developed for each column (for example, Fig. 12(b)) based on these models and the crosssection geometry. At any point of the column x, the transverse deflection is δ(x), and the corresponding moment is Fig. 9. Transverse load–deflection diagram for column specimen V5.5-66 − ρt = 0.011.

M(x) = P · x + N δ(x) ≤ P · a + N δ(x).

(2)

The second moment term, N · δ(x) is negligible in prepeak deformations, but becomes significant in the post-peak response. From the moment at any point x the curvature κ(x) can be calculated based on the moment–curvature relations. Finally, the deflection at the center of the beam is calculated as (Fig. 12(c)) δcenter = t A/C =

L 2

Z

κ(x)x dx.

(3)

0

Fig. 10. Transverse load–deflection diagram for column specimen V6.4-86 − ρt = 0.011.

The load–deflection responses of the columns with constant volumetric ratio (specimens are designated by the letter “V”) are presented in Figs. 9–11. All specimens were designed to have transverse reinforcement volume content ρt = 0.011 which was achieved by using different combinations of tie diameters and spacings. The intent of this series of experiments is to examine the effects of tie spacing for constant transverse reinforcement content. No pinching tendencies in the hysteresis loops were observed in these column specimens either. For these columns, decrease of tie spacing results in larger deformation to failure and increased ability to dissipate postpeak energy.

Note that Eq. (3) is nonlinear in δ and thus the calculation of δcenter is iterative. The moment–curvature relations for each cross-section are omitted for economy of space. Note that the stress–strain models for confined [13] and unconfined [14] concrete do not capture cyclic degradation, and are more representative of lower strength concretes. As a result, the theoretical load–deflection relations derived here tend to overestimate the post-peak response of all columns. The specimens were instrumented with strain gauges with the intent of identifying the initial yield. Unfortunately, only the sensors in columns S8.0-76 and V5.5-66 produced reliable yield load information. For the remaining columns, the yield load was calculated theoretically by ignoring the tensile strength of concrete and p assuming its compressive response to be elastic (E = 4700 f c0 ). The yield load was evaluated at 184 kN, at a maximum compressive strain of 0.0016, which is compatible with the assumption of elastic concrete response. This value is reasonably close to those found experimentally in columns S8.0-76 and V5.5-66, which were 186 kN and 180 kN respectively.

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Table 2 Testing results Specimen

Vol. content of transverse steel (%)

Yield load (kN)

Peak load (kN)

Ductility index using peak deflection

Ductility index using yield deflection

S3.2-76 S4.8-76 S6.4-76 S8.0-76

0.3 0.67 1.2 1.87

184 184 184 186

209 199 198 193

1.84 2.49 3.09 3.12

2.61 3.64 4.07 4.2

V5.5-66 V6.4-86 V8.0-135

1.09 1.1 1.08

180.2 184 184

200 200 189

3 3.03 2.31

4.45 4.54 2.64

The summary of the results of the experimental study is presented in Table 2. The influence of transverse reinforcement content ρt on the ductility indices, µ p and µ y , for constant tie spacing is demonstrated in Fig. 13. It becomes clear that increase of ρt up to the value of 1.25%, while maintaining constant tie spacing st = 76 mm, tends to produce higher ductility. It is pointed out here that increasing values of ρt are achieved by using larger diameter ties at the same spacing. This results in larger confinement of the core. It also results in a higher buckling resistance due to a stiffer supporting mechanism of the longitudinal reinforcing bars, which, as a result, carry their load with a smaller eccentricity, es , and reduced rotation (Fig. 14). The observations in Fig. 13 are discussed further in the section of “Analysis of Results” which follows. The influence of the tie spacing, st , on the ductility indices, µ p and µ y , when the transverse reinforcement content ρt remains constant is demonstrated in Fig. 15. The observed trend is that increased tie spacing st (over 85 mm) results in reduced ductility µ p of the specimen if the confining reinforcement content ρt remains unchanged. This can be explained as follows: Larger spacing results in lower buckling capacity of the axial reinforcement, which in turn results in loss of ductility. In addition, larger tie spacing results in a sparse discrete confinement with wide unconfined regions along the column length and loss of ductility. Further related discussion is presented in the section “Analysis of Results” that follows. 4. Analysis of results It is interesting to note from Fig. 13 that, as ρt approaches zero, the ductility index µ p tends to the value of one, which implies a very brittle response for complete lack of confinement. In such cases, crushing of the cover coincides with failure, and thus the ductility index, µ p , becomes 1. Of course, index µ y has a higher magnitude given that the first yield does not coincide with column failure even in the complete absence of confinement. It is also interesting to note from Fig. 13 that the ductility index diagram becomes flat for large values of ρt . This is also expected for two reasons: (1) For large enough values of ρt the lateral support of the longitudinal reinforcement becomes very stiff, and buckling of the longitudinal reinforcement depends only on the tie spacing. (2) Given that column failure below the balanced point is driven by bending with a large part of the cross-section being in tension, increase in strength and ductility of the compressed

part of the cross-section makes only a limited contribution to the column ductility. These observations are general and are not limited to the 76 mm tie spacing that is presented in Fig. 13. To help visualize tendencies of behaviour, Fig. 13 is recreated with the addition of all data produced in this study and two additional columns from Keller [3]. The new plot is presented in Fig. 16, where every point represents a physical experiment. The results from Keller [3] correspond to columns of identical geometry and reinforcement, very similar concrete strength, and the same loading conditions, including axial compression, to the specimens tested here. The points symbolized by an open triangle and connected by the solid curve are the original data presented in Fig. 13 with tie spacing of 76 mm. The other points represent different spacings as shown in Fig. 16. Each point belongs to a curve of equal tie spacing st . We do not have enough information to define these curves reliably since only one experimental data point is available per curve. Nevertheless, a relation similar to that of Fig. 13 can be hypothesized given the tendency of ductility index µ p to flatten off for large values of ρt and approach 1 for ρt = 0. Thus, qualitative relations of ductility index and steel content for various values of constant tie spacing are generated, based on the expected trends described earlier, and are presented in Fig. 16 (dashed curves). The intent of these relations is to aid the visualization of the expected ductility in terms of st and ρt , and to provide guidance for future experimental studies to populate such relations with real data. Such quantitative relations can provide the basis for future design guidelines to achieve a required level of ductility. A similar analysis is performed on the data of Fig. 15. We notice here that the ductility index diagram becomes flat for very small tie values of st , when ρt is maintained at a constant value. This tendency is explained based on the fact that at small tie spacing values, the axial reinforcement buckles at very large loads which tend to crush the concrete in compression. Thus, further decrease in tie spacing does not have a significant effect. A flat diagram of the ductility index for large values of tie spacing st is also expected. In this case, large values of tie spacing result in large unsupported lengths of the longitudinal reinforcing bars. As a result, the effectiveness of the ties to either prevent buckling of the longitudinal reinforcement or increase the confinement of concrete becomes minimal. For the qualitative needs of the present analysis, it is assumed that the ductility index tapers off to its lowest value (µ p = 1) for transverse reinforcement spacing which is


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Fig. 13. Dependence of ductility index on transverse reinforcement content.

Fig. 14. Buckling dependence of the longitudinal bars on the stiffness of the ties.

Fig. 15. Dependence of ductility index on transverse reinforcement spacing. Fig. 12. Basis for theoretical calculation of transverse deflections of columns.

approximately equal to the side dimension of the column, which often corresponds to a large slenderness of the axial reinforcement and early buckling. Lack of confinement results in a complete loss of strength once cover spalling occurs, and thus a value of µ p = 1. This observation is also supported by an earlier study by Keller [3] where a column of identical geometry, concrete strength, and loading sequence, including

axial load, using ρt = 0.12% and st = 203 mm had a ductility index value µ p = 1.0. To demonstrate the effects of the interaction of tie spacing st , transverse reinforcement content ρt , and ductility index µ p , Fig. 15 was reproduced by adding all experimental data that were produced in this study as shown in Fig. 17. The points that are symbolized by the open triangles and connected by the solid curve are the points shown in Fig. 15 and they correspond to a constant transverse reinforcement

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Fig. 16. Dependence of ductility index on transverse reinforcement content. Data and hypothesis.

designed to demonstrate the effects of transverse steel content while maintaining constant tie spacing. The remaining four column specimens were designed to demonstrate the effects of tie spacing while maintaining constant transverse reinforcement content. It was found that there is a rational and qualitatively predictable interrelation between the ductility index and the transverse reinforcement spacing and content. This relation appears to be “banded”, indicating that for a given tie spacing there is a range of values of transverse reinforcement content that can influence column ductility in a positive manner. Similarly, for a given transverse reinforcement content, there is a range of tie spacing values that can have a positive effect on the column ductility. It is anticipated that future experimental studies will provide sufficient quantitative information to relate transverse steel content and spacing to the ductility of columns, which in turn will result in safer and more economical designs with high strength concrete. Acknowledgment NSF support of this research through project MSS - 9504186 is gratefully acknowledged. References

Fig. 17. Dependence of ductility index on transverse reinforcement spacing. Data and hypothesis.

content of 1.1%. Each of the remaining points belongs to a constant ρt curve. As in the case of Fig. 16, the information is not sufficient for defining these curves reliably since only one experimental point is available per curve. However, using the analysis presented earlier, it is hypothesized that each curve converges to ductility index µ p = 1 when the tie spacing tends to the value of the column side dimension (= 203 mm in this study). Similarly, each curve tends to a maximum value as the tie spacing decreases. Thus, qualitative relations of st and µ p as a function of ρt are generated and presented (dashed curves) in Fig. 17. Again, the intent of these relations is to provide visualization of the interrelation of st , ρt and µ p and also to provide guidance for future experimental studies to populate such relations with real data which can then provide the basis for design guidelines to achieve a required level of ductility. 5. Summary and conclusion A study was conducted in which eight HSC columns were tested in bending under constant axial compression. The goal of the study was to develop a better understanding of the effects of the spacing and content of the transverse reinforcement on the bending ductility of columns. Four of these columns were

[1] ACI Committee 318. Building code requirements for structural concrete (ACI-318-05) and commentary (ACE 318R-05). Farmington Hills (MI): American Concrete Institute; 2005. [2] Mei H, Saadatmanesh H, Kiousis PD, Ehsani MR. Confinement effects on high strength concrete. ACI Structural Journal 2001;98(4):548–53. [3] Keller M. Comparison of high strength concrete columns: ACI, 1.5% with fibers, and 3% lateral reinforcement. MS thesis. Department of Civil Engineering and Engineering Mechanics, The University of Arizona; 1998. [4] Shin S, Ghosh SK, Moreno J. Flexural ductility of ultra-high-strength concrete members. ACI Structural Journal 1989;86(4):394–400. [5] Sheikh SA, Shah DV, Khoury SS. Confinement of high-strength concrete columns. ACI Structural Journal 1994;91(1):100–11. [6] Paultre P, L´egeron F, Mongeau D. Influence of concrete strength and transverse reinforcement yield strength on behaviour of high-strength concrete columns. ACI Structural Journal 2001;98(4):490–501. [7] Foster SJ, Attard MM. Experimental tests on eccentrically loaded highstrength concrete columns. ACI Structural Journal 1997;94(3):295–303. [8] Xiao Y, Yun HW. Experimental studies on full-scale high-strength concrete columns. ACI Structural Journal 2002;99(2):199–207. [9] Ho JCM, Pam HJ. Inelastic design of low-axially loaded highstrength reinforced concrete columns. Engineering Structures 2003;25(8): 1083–96. [10] Hwang SK, Yun HD. Effects of transverse reinforcement on flexural behaviour of high-strength concrete columns. Engineering Structures 2004;26(1):1–12. [11] Woods JM. Relationship of tie spacing and diameter to the ductility of high strength concrete columns under cyclic lateral loads. MS thesis. Department of Civil Engineering and Engineering Mechanics, The University of Arizona; 1999. [12] El-Bahy A, Kunnath SK, Stone WC, Taylor AW. Cumulative seismic damage of circular bridge columns: Benchmark and low-cycle fatigue tests. ACI Structural Journal 1999;96(4):633–43. [13] Mander MJ, Priestley N, Park R. Theoretical stress–strain model for confined concrete. ASCE Journal of Structural Engineering 1988;114(8): 1804–26. [14] Kent DC, Park R. Flexural members with confined concrete. ASCE Journal of the Structural Division 1971;97(7):1969–90.

Bending Ductility of Rectangular High Strength Concrete Columns

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