Drift capacity of high-strength concrete columns with mixed-grade longitudinal reinforcements

Abstract

A unique reinforced concrete column design method which aims to improve the ductile behavior of reinforced concrete columns by utilizing various steel grades for longitudinal reinforcements is evaluated in this article. Six large-scale reinforced concrete columns were tested, with the columns subjected to axial load and cyclic forces under reversed bending. The parameters varied in the test program including the axial loading level and the ratio and strength of longitudinal steel reinforcement. It was found from the test results that utilizing longitudinal high-strength steel reinforcement by the ratio of 30%, 50%, and 100% of the total longitudinal reinforcement in a column section will increase the lateral loading drift capacity by 18%, 26%, and 55% on average, respectively. Parametric studies via nonlinear finite-element approach were performed to study the influence of various design parameters on the ultimate drift capacity of reinforced concrete columns. The correlation between the ultimate drift capacity and the confinement level, the axial loading level, and the ratio and grade of longitudinal high-strength reinforcing bars was investigated. Design charts for various ultimate drift levels in terms of other design parameters were developed.

Keywords

drift-based design finite-element analysis high-strength steel reinforcement high-strength concrete columns reinforced concrete seismic performance

Introduction

In the contemporary seismic design of reinforced concrete (RC) frame buildings, the beam sidesway mechanism has formed the basis of the commonly used ductile design approach. In this mechanism, the most crucial design issue is the flexural yielding of the RC columns. To achieve a proper design, all the loading scenarios such as the dynamic effects of higher mode vibrations and bidirectional earthquake loading circumstances should be considered. As a result, columns are required to have uneconomically large cross-sections even if high-strength concrete (HSC) is used. This issue is considerably more severe in high-rise buildings or in frames with long span beams. In order to overcome this problem, a designer can come up with two solutions. The first method is to establish an appropriate mechanism other than beam sidesway. A favorable mechanism could be the one in which column hinges are observed in all stories but no soft story is developed. In this case, columns are required to have adequate flexural stiffness even after yielding of longitudinal reinforcements so that the lateral stiffness of the stories would not degrade excessively during seismic excitations. Conventional design methods like confinement of core concrete will not guarantee such an ideal flexural behavior of RC columns since the ductility demand may be excessive due to plastic rotation of the column. In the second method, columns can be designed to be as strong as required by using high-strength material such as high-strength steel (HSS) reinforcement coupling with HSC. In this method, the anchorage problem of HSS reinforcement and the concern about the adequate drift capacity of RC columns should be considered prudently. Currently, the seismic provisions of ACI Committee 318 (2014) limit the yield strength of steel reinforcements to 698 and 420 MPa for the transverse and longitudinal reinforcing bars, respectively. However, recent advances in production capabilities have resulted in the steel reinforcement with yield strengths of greater than 550 MPa. Sokoli and Ghannoum (2016) tested three full-scale columns reinforced with varying steel grades of 420, 550, and 690 MPa under cyclic lateral loading and high axial compression loading. In order to introduce higher steel grades in design codes, further research is required on the seismic behavior of RC frames and members constructed using HSS reinforcements. In this article, the experimental study of columns with mixed-grade longitudinal reinforcement is reported followed by the test results, observations, and applications. To further investigate the effectiveness of the proposed method and to quantify the drift capacity of columns, the analytical study using finite-element modeling is presented. Parametric study is conducted and design charts relating the column design parameters to its drift capacity are provided. The column design method is assessed in this study based on test results and numerical modeling.

Research significance

The objective of this study is to investigate the effectiveness of an RC column design method which uses longitudinal reinforcement with various steel grades as well as HSS transverse reinforcements (Watanabe et al., 1990). It is known that increasing the longitudinal reinforcement ratio will lead to more brittle failure mode of the columns. However, shear capacity of the specimens was higher than the flexural capacity, and test observations showed that the behavior of columns is controlled by flexure. Flexural and shear behavior of columns are studied and the effect of incorporating HSS reinforcement on behavior of columns is investigated. The main concern is to study the flexural as well as drift capacity of columns designed with the proposed method in this article. The result will be useful for designers who want to reduce the column sizes by using mixed-grade reinforcing bars. Through an experimental program and a series of analytical modeling, new drift-based design recommendations and charts are proposed. These provisions can be used as a design tool for HSC columns reinforced with HSS longitudinal and transverse reinforcements.

Experimental investigation

Six half-scale cantilever RC columns were constructed and tested. Specimens represent columns in the lower story of a 20- to 25-story-frame building. Each test unit has a square cross-section of 400 mm × 400 mm as shown in Figure 1. Shear span length for all the specimens is 1000 mm, and the ratio of the column height to depth is 2.5. Fixed end condition was provided using a block of dimensions 900 mm × 1200mm × 950 mm at the bottom of the columns which simulates a stiff foundation beam. The longitudinal reinforcement was from 20 mm diameter deformed bar with yield strength of 430 MPa shown as HD20 and 22 mm diameter deformed bar with yield strength of 930 MPa shown as UHD22. In Units 1 and 4, 16-HD20 was used for longitudinal reinforcement, while 12-HD20 and 4-UHD22 were used in Units 2 and 5. In Units 3 and 6, 8-HD20 and 8-UHD22 were used as longitudinal steel reinforcement. Two overlapping square spiral hoops with 80 mm spacing were used in column specimens as transverse reinforcement. These square spiral hoops were from 9.2 mm diameter deformed bars with the yield strength of 1275 MPa shown as U9.2. The axial load level of columns was $0.3 f'_{c} A_{g}$ for Units 1–3 and $0.6 f'_{c} A_{g}$ for Units 4–6. The design concrete compressive strength was 60 MPa for all the specimens. The summary of all specimens is presented in Table 1, and the mechanical properties of reinforcements are shown in Table 2.

Table 1.

Summary of the column test units.

Unit	$\frac{P}{{f'}_{c} A_{g}}$	$f'_{c}, MPa (ksi)$	Longitudinal reinforcement				Transverse reinforcement
			Number of bars		$ρ'_{t} (%)$	$ρ_{t} (%)$	Spacing, mm(in)	$ρ_{s} (%)$
			HD20	UHD22	$ρ'_{t} (%)$	$ρ_{t} (%)$	Spacing, mm(in)	$ρ_{s} (%)$
1	0.3	60 (8.7)	16	0	0	3.14	80 (3.15)	1.56
2			12	4	29.1	3.32
3			8	8	55.2	3.51
4	0.6		16	0	0	3.14
5			12	4	29.1	3.32
6			8	8	55.2	3.51

Table 2.

Mechanical properties of steel reinforcement.

Type	Nominal area, $m m^{2} (i n^{2})$	Yield strength, $MPa (ksi)$	Ultimate strength, $MPa (ksi)$	Young’s modules, $MPa (ksi)$	Fracture strain (%)
HD20	314 (0.5)	442 (64.1)	590 (85.6)	200,000 (29,007)	29.2
UHD22	387.1 (0.6)	1033 (149.8)	1165 (169)	198,700 (28,819)	12
U9.2	64 (0.1)	1368 (198.4)	1462 (212)	201,200 (29,182)	8

Figure 1.

Testing program details: (a) specimens’ dimensions, (b) loading setup, (c) sections of column units, and (d) loading pattern.

Loading arrangement

The axial loading of $0.3 f'_{c} A_{g}$ or $0.6 f'_{c} A_{g}$ was applied vertically on top of the columns and remained constant during the test for all the specimens. A reversed cyclic loading was applied to the tip of columns using a 2000-kN hydraulic jack with 200 mm maximum travel in both directions in the horizontal direction. The loading history was controlled by the story drift ratio (DR) as shown in Figure 1(a). Test specimens were subjected to one cycle of loading with displacement equivalent to story DR of 0.5% followed by two cycles to each of 1.0%, 2.0%, 3.0%, 4.0%, and so on.

General observations

The overall lateral load-horizontal displacement behavior of Units 1–6 is shown in Figure 2. Hysteresis loops demonstrate stable behavior and good energy dissipation until the end of the test for all the specimens even for Units 4–6 with high axial load level of $0.6 f'_{c} A_{g}$ . It is observed that the lateral load-carrying capacity increased when horizontal displacement is going from 1% to 3% for Units 2 and 3 and from 1% to 2% for Units 5 and 6. Units 1 and 4 did not show any increase in lateral load-carrying capacity when the horizontal displacement increased beyond a DR of 1.0%. Moreover, it is observed that the increase in horizontal load-carrying capacity from DR = 1.0%–3.0% in Units 3 and 6 is larger than that in Units 2 and 5, respectively. In addition, the maximum displacement which Unit 6 can undergo without degradation in lateral load-carrying capacity is larger than that of Unit 4. It can be concluded that the ultimate drift capacity and the increase in horizontal loading capacity in HSC columns could be controlled by the means of mixed-grade longitudinal steel reinforcements even in the case of high axial loading levels.

Figure 2.

Comparison of hysteretic behavior between the experimental and FE results.

Cracking pattern

Crack propagation pattern for Units 1–6 is shown in Figure 3. Flexural cracks formed at a displacement value of about 0.5% of story drift in all the units. Shear cracks developed over the total height of the specimens at about 1.0% of the story drift for the Units with axial load level of $0.3 f'_{c} A_{g}$ , while such cracks were observed to spread at 2% of story drift in specimens with a high axial load level of $0.6 f'_{c} A_{g}$ . Slight crushing of cover concrete was detected at 0.5% of story drift in Units 4–6 and at 1.0% of story drift in Units 1–3, while splitting cracks along both the ordinary-strength and HSS reinforcement occurred at 1.0% of story drift in all the units. It was noted that bond splitting cracks in Units 4–6 with higher axial load level were more serious, especially along the HSS reinforcing bars than the units with the axial loading level of $0.3 f'_{c} A_{g}$ . Spalling of cover concrete was observed in a DR of 2.0% in Units 1–3 and in a DR of 1.0% in Units 4–6. The first sign of buckling of longitudinal reinforcing bars was noticed at a DR of 4.0%–5.0% in Units 1–3 and at DR = 3.0% in the units with high axial loading level. However, this buckling was not severe until the end of the test.

Figure 3.

Crack propagation in test units: (a) Unit 1, (b) Unit 2, (c) Unit 3, (d) Unit 4, (e) Unit 5, and (f) Unit 6

Plastic hinge region

The plastic hinge length of the specimens was calculated based on the curvature distribution measured during the tests. It was observed that plastic hinge rotation was concentrated in the region within 215 mm from the top face of the bottom block for Units 1–3 with axial loading level of $0.3 f'_{c} A_{g}$ . On the other hand, it was observed that the plastic hinge rotation in Units 4–6 spread over the region within 415 mm from the top face of the bottom block. Furthermore, the plastic hinge region in Unit 6 spreads over almost the full height of the column. In general, it was observed that in the units with the same level of axial loading, the curvature distribution profiles of the columns are similar in spite of the different arrangement of mixed-grade longitudinal reinforcement. It can be said that the plastic hinge region becomes larger as the axial load increases. For Units 1–3 with axial load of $0.3 f'_{c} A_{g}$ , the plastic hinge lengths were quite similar. For Units 4–6 with axial load of $0.6 f'_{c} A_{g}$ , the plastic hinge lengths in Units 5 and 6 incorporating HSS bars were longer than that for Unit 4 with normal-strength steel reinforcement.

Strain of longitudinal reinforcement

It was observed that the large strains in normal-strength steel reinforcements in units 1–3 tend to be distributed more widely from the early stage of loading than those in HSS reinforcing bars. This tendency is more significant in Units 4–6 with the high axial loading level. In addition, it can be seen that large strains in normal-strength reinforcing bars were distributed over the height corresponding to the full column depth from the top face of the bottom block while the large strains in the HSS bars were restricted within a narrow region of column, due to the greater elastic range of the material.

Figure 4 shows the strain distribution along the longitudinal bars in Unit 2. The trend of strain variation along the longitudinal bar in specimens with the same axial loading level was similar. In Units 1–3, the maximum strains for normal-strength steel reached around the yield strain, while those for HSS bars were always below the yield strain. In Units 4–6, yielding of both normal and HSS bars was not observed within the bottom base block during the test.

Figure 4.

Strain profiles of longitudinal bars in Unit 2.

Strain of transverse reinforcement

Strain distributions in square spirals along the height of each column were measured by electrical resistance strain gauges at the maximum column displacement in each loading cycle. Strain readings mainly indicate lateral expansion of the core concrete due to internal micro cracking of concrete until serious buckling of longitudinal reinforcement occurs. The amount of transverse reinforcement in Units 1–3, which had an axial loading of $0.3 f'_{c} A_{g}$ , was in excess of the requirement of NZS3101 (2006) by around 50%. In Units 1–3, the strain readings show relatively small values compared with the yielding strain value. Strain readings in Units 4–6 indicate that the deterioration of core concrete is more serious in the region between peripheral spirals and the inside spirals rather than in the region within the inside spirals. This deterioration of core concrete resulted in the buckling of corner longitudinal bars in any direction, whereas the center bars could buckle only in the direction parallel to the loading direction due to being in effectively confined core concrete. In Units 4–6, it was concluded that the diagonal spirals inside the concrete core were more effective than the peripheral square spirals for both confinement of core concrete and shear resistance. In all the test units, it was observed that the spiral strain values increase due to further internal micro cracking of concrete under cyclic loading even if the horizontal load does not increase. In general, it is concluded that the spacing, volumetric ratio, and the yield strength of transverse reinforcement needs to be carefully determined in order to prevent premature buckling of longitudinal reinforcement and shear failure, and also to confine the core concrete effectively.

Bond slip of longitudinal reinforcement

Splitting cracks were observed from about 2% of the story drift in Units 1–3 and from about 1% of story drift in Units 4–6. The splitting cracks spread more widely along the height of column when the axial load was high and when HSS bars were used. Significant deterioration is not observed in hysteresis response of the specimens, and it is concluded that the bond slip of the longitudinal bars is not critical. The reason could be the higher grade of concrete used in the specimens which improved the bond behavior.

Application of test results

It was observed that the flexural behavior of HSC columns under severe earthquake loading can be significantly improved by using arrangements of longitudinal bars with various steel grades. In addition, the use of mixed-grade longitudinal reinforcement makes it possible to closely control the displacement at which maximum moment of a column section is reached by changing the ratios of steel strengths and sectional areas between the high- and normal-strength longitudinal bars. However, when this design method is used, the spacing, volume, and yield strength of transverse reinforcement need to be carefully determined in order to avoid premature buckling of the HSS longitudinal rebars. In general, it is concluded that the limitation of yield strength of transverse reinforcement in ACI Committee 318 (2014) should be relaxed. From the test results, it was found that in the case of axial load level of $0.6 f'_{c} A_{g}$ , the stresses in transverse reinforcement reached the minimum value of 800 MPa before incipient buckling of longitudinal reinforcement was observed.

Analytical investigation

This section presents the three-dimensional (3D) nonlinear finite-element analysis (NLFEA) carried out on the specimens using computer program DIANA 9.4.4 (2012). Finite element (FE) modeling procedures and assumptions were presented in previous research (Alaee and Li, 2017; Kulkarni and Li, 2008; Li and Kulkarni, 2010). Assumptions for modeling of concrete were based on previous recommendations (Okamura and Maekawa, 1991; Rilem, 1985). A constitutive model for concrete including the cracking behavior, the behavior in tension, shear behavior, compression hardening and softening, and the lateral confinement influence was used in the FE analysis as shown in Figure 5(a). The cohesion c, used in concrete modeling, is estimated according to the following equation

c = f_{c} (ε_{uniaxial}^{p}) \frac{1 - \sin φ}{2 \cos φ}

(1)

where $f_{c} (ε_{uniaxial}^{p})$ is the hardening or softening parameter as a function of the plastic strain in the direction of uniaxial compression stress. Tensile strength of concrete $f_{t}$ was calculated according to the CEB-FIP model code (1990) as

f_{t} = 0.30 {(f_{c})}^{\frac{2}{3}}

(2)

The softening function is based on the concrete tensile fracture energy and the crack bandwidth. In this research, a linear tension softening curve is chosen to represent the post-peak tension behavior of concrete. The behavior of concrete in compression is a pressure-dependent relationship in which the higher isotropic stress will result in higher strength and ductility of the concrete. In the presence of the lateral confinement, the compressive stress–strain relationship should be modified in order to take into account the effect of the increased isotropic stress. In this research, a parabolic curve is selected to represent the compressive behavior of concrete.

Figure 5.

(a) Behavior of concrete in tension and compression, (b) Stress-strain relationship for the steel reinforcement, and (c) Bond-slip law by CEB-FIP Code 1990.

The longitudinal reinforcing bars are assumed to act as separate truss elements and the forces are assumed to be developed along the longitudinal axis of the truss members. The Von Mises yield criterion with isotropic strain hardening was used to characterize the constitutive behavior of the reinforcement. The constitutive behavior of the reinforcement is shown in Figure 5(b). For the bond-slip modeling, line-solid connection elements in DIANA 9.4.4 (2012) library were used to connect the reinforcement truss elements to the mother concrete elements.

The local bond stress-slip model presented by CEB-FIP Model (1993) is calibrated based on an empirical model by Eligehausen et al. (1982) as shown in Figure 5(c). Based on Eligehausen et al. (1982), the maximum bond stress is taken as 2.64 times the square root of the concrete compressive strength, while the residual stress is defined as 0.9 times the square root of the concrete compressive strength. The slip levels are also determined based on the tests conducted by Eligehausen et al. (1982). The slip values at the maximum stress level are nominated as $S_{1}$ and $S_{2}$ , and they are defined as $S_{1} = 1 mm$ and $S_{2} = 3 mm$ in this study. The residual stress is assumed to develop at a slip value of 10.5 mm.

Verification of finite-element analysis results

FE analysis results were compared to those obtained from the experiment for the verification purpose. Figure 2 illustrates the comparison between the hysteresis response of test specimens through the experimental observation and the FE numerical prediction. It is observed that the maximum lateral loading capacity obtained from the analytical approach is equivalent to the values of the experimental ultimate loads in all the specimens. There was agreement with regards to the overall global behavior between the experimental and analytical results.

Parametric studies

After verifying the numerical modeling against the available experimental results, an extensive parametric investigation is performed to further investigate the seismic behavior of HSC columns reinforced with HSS reinforcements. The following sections present the application of FE modeling technique to study the influence of critical design parameters, such as the axial loading level, shear span ratio, and various grades of the concrete and steel reinforcement.

Influence of column axial loadings

The influence of the level of column axial loading was investigated using a finite-element approach. The same horizontal loading history as those applied to test units in the experimental program was applied to the columns tip of the numerical models. Figure 6 shows the lateral loading capacity versus horizontal displacements for different levels of applied axial loading on RC column models with different detailing and characteristics. The applied column axial loading varied from $0.1 f'_{c} A_{g}$ to $0.6 f'_{c} A_{g}$ as compared with zero axial load cases. As observed, when the column axial load is increased from $0.3 f'_{c} A_{g}$ to $0.6 f'_{c} A_{g}$ in models with concrete grade of 60 MPa and mixed-grade longitudinal reinforcement, lateral loading capacities are increased around 5%. In models with higher concrete grade of 80 MPa, the same increase in the axial loading level will cause the lateral loading capacity to rise around 15%, which shows the remarkable effect of column axial loading on the lateral loading capacity in models with higher concrete grades. Columns with axial loading of $0.6 f'_{c} A_{g}$ showed a higher lateral loading capacity of about 40% and 60% for concrete grades of 60 and 80 MPa as compared with the cases of zero axial loading.

Figure 6.

Influence of the axial load level on RC columns by FE analysis.

Investigating the behavior of RC columns with various ratios of longitudinal HSS reinforcing bars indicated that the effect of altering the axial loading is identical for HSS ratios of $ρ'_{t} = 30 %, 50 %, and 100 %$ .

The preceding discussions clearly show that incorporating the axial loading levels of up to $0.6 f'_{c} A_{g}$ on test specimens will cause an enhancement in strength of the specimens irrelevant of other parameters such as reinforcement detailing and material properties.

Influence of shear span ratio

The behavior of slender columns, which is the topic of study in this article, is predominantly controlled by flexural response and the truss mechanism remains the most portion of the shear capacity. For an axial compression load of less than $0.1 f'_{c} A_{g}$ , shear transfer within the compression zone, dowel action, and aggregate interlock are likely to degrade when flexural and inclined shear cracks open in alternate directions during reversed cyclic loading. For axial compression loading greater than $0.1 f'_{c} A_{g}$ , the shear transfer in the compression zone of the column section is improved due to the deepening of the neutral axis depth and enhances the shear transferred by aggregate interlock by suppressing the opening of cracks. In this section, the performance of RC columns with various shear span ratios is studied based on FE analysis results. Figure 7 shows the lateral loading capacity versus horizontal displacements for RC columns with different shear span ratios ranging from 2.5 to 5.0. The shear span ratio of 2.5 is near the lower end of $L / h$ value used in the practice. A complete set of analyses was also performed for the shear span ratios of 3.5 and 5.0, which represent the higher end of the range used in practice. It is clearly shown that columns with larger shear span ratios display smaller moment capacity and higher displacement ductility. Parametric studies indicated that decreasing the shear span ratio of a column from 5.0 to 2.5 will increase the maximum lateral loading capacity between 60% and 85%. It was also observed that the mentioned increase in the capacity is larger in models with higher axial load levels. The influence of shear span ratio is observed to be more crucial in sections with minimum ratios of HSS reinforcing bars. In addition, FE analyses show that the influence of shear span ratio becomes less critical as the yield strength of the longitudinal bars is going higher. However, altering the concrete strength did not have any significant influence on the effect of the column shear span ratios.

Figure 7.

Influence of shear span ratio on RC columns by FE analysis.

Influence of mixed-grade longitudinal reinforcement ratio

In this study, the emphasis was put on improving the flexural behavior of columns by arranging different detailing of longitudinal reinforcement with various steel grades. Hence, the performance of the columns is studied in terms of moment and drift capacities. The basic concept in this design method is to observe the longitudinal reinforcements yielding initiating from normal-strength steel bars followed by HSS bars, in the case of increasing displacement demand on the structural member. As a result, flexural strength of the column is expected to increase after yielding of the lowest grade longitudinal reinforcement and the trend will continue until the yielding of HSS bars. In order to quantify the influence of various mixed-grade reinforcement detailing, FE parametric studies were performed, and lateral loading capacity versus horizontal displacements is presented in Figure 8. It is observed that in HSC columns with HSS reinforcements, in a section with the HSS bar ratio of 30%, the lateral loading capacities are between 12% and 24% higher than that in a section without HSS bars. This value is between 17% to 36% and 43% to 66% for a section with HSS ratio of 50% and 100%, respectively. It is observed that the influence of altering the ratio of HSS is reduced in the cases with higher axial loading levels. In addition, the effect of varying longitudinal steel reinforcement is more significant if the grade of steel is higher. Furthermore, the column drift capacity, which is defined as the ultimate displacement capacity divided by the column height, is related to the grade and ratio of HSS reinforcing bars in the section. Further study on drift capacity of RC columns will be presented in this article.

Figure 8.

Influence of various mixed-grade longitudinal reinforcement ratios on RC columns by FE analysis.

Drift capacity estimation

The correlation between the lateral drift capacity and concrete confinement in normal-strength columns has been studied in previous research (Brachmann et al., 2004; Saatcioglu and Razvi, 2012). However, the confinement requirement in ACI Committee 318 (2014) is not based on lateral drift demand, and the design equations have been developed based on axial deformability. Hence, drift demand has not been introduced as a design parameter in confinement criteria requirement.

Several studies have proposed drift-based design equations for RC columns. However, the effect of utilizing HSS reinforcements and the ratio of HSS to normal-strength steel reinforcement has not been incorporated into design equations. Proposed equations in previous studies (Brachmann et al., 2004; Saatcioglu and Razvi, 2012) for normal-strength RC columns are presented as follows

D_{ult} = 0.071 ρ_{c} \frac{f_{yh}}{{f'}_{c} (\frac{A_{g}}{A_{c}} - 1)} (\sqrt{k_{2}} \frac{P_{0}}{P})

(3)

D_{ult} = 0.427 ρ_{s} \frac{f_{yh}}{{f'}_{c}} (1 - 1.368 \frac{P}{{f'}_{c} A_{g}})

(4)

where $D_{ult}$ is the ultimate drift capacity, $k_{2}$ is the confinement efficiency parameter, $P_{0}$ is the nominal concentric compressive capacity of the column, and $P$ is the axial compressive force on the column.

Drift capacity of HSC columns in this study is proposed in terms of the ratio and grade of HSS longitudinal reinforcements, concrete compressive strength, confinement level, and the axial loading level. The approach is based on the calculation of drift capacities for HSC columns with different levels of confinement and axial loading. The computation of column drift capacities was performed using Diana 9.4.4 (2012). Degradation in lateral load-displacement response is caused by the loss of moment capacity in the plastic hinge region as well as the $P - Δ$ effect. Per common practice in literature, the lateral displacement capacity of a column can be defined as a displacement value at which the lateral loading capacity of the column is equal to 80% of the maximum lateral load-carrying capacity (Bayrak and Sheikh, 1997; Brachmann et al., 2004; Legeron and Paultre, 2000; Li and Park, 2004; Saatcioglu and Razvi, 2012).

Confining transverse reinforcement

Previous studies (Pham and Li, 2014; Razvi and Saatcioglu, 1999) showed that different amounts of confinement reinforcement and material properties will not influence the drift capacity and lateral loading capacity as long as the value of $ρ_{s} f_{yh} / f'_{c}$ in an RC column remains constant. The influence of various grades of transverse steel reinforcement in RC columns was studied in this article using the FE approach. Figure 9 summarizes the parametric study results illustrating the calculated drift capacity versus axial loading levels. It is observed that increasing the yield strength of column transverse reinforcement from $f_{yh} = 475 - 1275 MPa$ will increase the drift capacity between 3% and 9% in the case of zero axial loading. However, as the axial loading is going higher than $0.6 f'_{c} A_{g}$ , the influence of column transverse reinforcement deteriorates gradually. In the case of column axial loading of $0.6 f'_{c} A_{g}$ , increasing the yield strength of column transverse reinforcement from $f_{yh} = 475 - 1275 MPa$ will increase the drift capacity by less than 2%. In addition, it is observed that in columns with higher ratios of longitudinal HSS reinforcing bars $(ρ_{Hs})$ , the influence of utilizing higher grade transverse reinforcement is more significant up to the optimum ratio of $ρ'_{t} = 55 %$ . In columns with $ρ'_{t} = 30 %$ , utilizing transverse reinforcement with the yield strength of $f_{yh} = 1275 MPa$ will increase the drift capacity up to 8% compared to utilizing normal-strength transverse reinforcement. This increase in drift capacity is around 10% and 6% in RC columns with $ρ'_{t} = 55 %$ and $ρ'_{t} = 100 %$ , respectively. It is concluded that the most beneficial effect of utilizing HSS transverse reinforcement is obtained when the optimum ratio of $ρ'_{t} = 55 %$ is used.

Figure 9.

Summary of parametric study for drift capacity.

Figure 9 shows the ultimate drift capacities versus volumetric confinement levels for the studied columns with different HSS reinforcement ratios. The value of $ρ_{s} f_{yh} / f'_{c}$ could be specified as a design parameter and linear trends have been shown for different axial loading levels. The general trend of lines indicates that the ultimate drift capacity will increase when a higher confinement level is provided. However, in a certain level of confinement, columns with lower axial loading levels of 0 and $0.1 f'_{c} A_{g}$ are observed to exhibit higher drift capacities. As the level of axial loading is increased, the slope of the drift capacity trend line is decreased. In order to propose an expression to relate the ultimate drift capacity of columns to the defined confinement level, analysis cases with zero axial loads are considered. A basic equation that expresses the RC columns drift capacity to the confinement level is presented as

D_{P = 0} = 0.4 ρ_{s} \frac{f_{yh}}{{f'}_{c}}

(5)

where $D_{P = 0}$ is the ultimate drift capacity of a column with zero axial load, $ρ_{s}$ is the volumetric ratio of transverse reinforcement, $f_{yh}$ is the yield strength of transverse reinforcement, and $f'_{c}$ is the concrete compressive strength.

Axial loading level

As shown in Figure 10, the presence of axial loading has a detrimental effect on drift capacity of columns and the drift capacity decreases as the axial loading level increases from 0 to 0.6. In columns with Grade 60 concrete, drift capacity decreases between 48% and 62% when the axial load level is increased from 0 to 0.6. The decrease in drift capacity is between 42% to 60% and 39% to 58% in RC columns with Grade 80 and Grade 100 concrete, respectively. It was concluded that the effect of axial loading level on deterioration of column drift capacity is more significant in lower concrete grades.

Figure 10.

Ultimate drift capacity versus axial load level.

In order to find a comprehensive expression of ultimate drift capacity, Equation (5) is modified for different axial loading levels. Assuming that any increase in the column axial loading will reduce the ultimate drift capacity linearly, a reduction factor should be applied to Equation (5). As a solution to find the reduction factor, drift values for the cases with axial loading are divided into the drift value of the similar models with zero axial loads. This parameter is specified as the normalized drift value. Drift values in the case of zero axial loads are obtained using Equation (5). Performing a regression analysis on drift capacity values for different axial loading levels ranging from $0.1 f'_{c} A_{g}$ to $0.6 f'_{c} A_{g}$ , the following expression can be presented for the ultimate drift capacity

Reduction factor = 1.5 (1 - 0.9 \frac{P}{{f'}_{c} A_{g}})

(6)

Combining equations (5) and (6), the following expression can be obtained to relate the drift capacity of columns to confinement ratio and axial load level factors

D_{ult} = 0.6 ρ_{s} \frac{f_{yh}}{{f'}_{c}} (1 - 0.9 \frac{P}{{f'}_{c} A_{g}})

(7)

Yield strength of reinforcements

The effect of the yield strength of longitudinal reinforcing bars on drift capacity of RC columns is investigated in this section. FE models with various grades of longitudinal bars were analyzed and the result is illustrated in Figure 10. To find the relation between the drift capacity and the yield strength and ratio of longitudinal HSS bars, FE parametric studies were performed for steel grades of 700, 800, and 950 MPa.

Increasing the yield strength of longitudinal bars from 700 to 950 MPa will result in a 10% decrease in drift capacity of columns. It was noted that the grade of longitudinal steel reinforcement was more influential in the case of moderate axial loading between $0.2 f'_{c} A_{g}$ and $0.4 f'_{c} A_{g}$ . In extreme values of axial loading of 0 and $0.6 f'_{c} A_{g}$ , altering the grade of longitudinal steel reinforcement has a minor effect on drift capacity of columns. In addition, it is observed that the influence of utilizing longitudinal HSS bars is more significant in RC columns with higher concrete grades.

The general trend shows that increasing the ratio of longitudinal HSS bars from $ρ'_{t} = 30 %$ to $ρ'_{t} = 55 %$ will increase the drift capacity between 4% and 17%. However, any further increase of $ρ'_{t}$ from 55% to 100% will decrease the drift capacity by 3%–10%. It is concluded that among all the possible combinations of mixed-grade longitudinal reinforcements in RC column sections, columns with longitudinal HSS bar ratio of $ρ'_{t} = 55 %$ show higher drift capacities.

Considering the ratio and strength of longitudinal reinforcements in the conducted parametric study, Equation (7) would be rearranged as follow

D_{ult} = 0.6 ρ_{s} \frac{f_{yh}}{{f'}_{c}} (1 - 0.9 \frac{P}{{f'}_{c} A_{g}}) (\frac{ρ_{t} f_{y}}{{ρ'}_{t} f_{yHs}})

(8)

where $ρ_{t}$ is the total reinforcement ratio in the column section, $f_{y}$ is the yield strength of ordinary steel in the section, $ρ'_{t}$ is the ratio of longitudinal HSS reinforcements area divided by the total longitudinal reinforcement area in column section, and $f_{yHs}$ is the yield strength of the HSS reinforcement.

Drift-based design charts

For application, it is a common practice to consider the cases that present more conservative drift expressions. Hence, the analysis results of the columns with shear span ratio of 2.5, which produce lower drift capacities, are considered in proposing the design formulation. Allowable story drifts for most of concrete frames are determined to be around 2%–2.5% according to current building codes (IBC, 2006; Uniform Building Code, 1997). While the proposed equation can be used for different DRs, the allowable ultimate DR could be specified to be 4% for HSC frames in high-seismic regions. Substituting this allowable DR in Equation (8) and solving for the HSS reinforcement ratio, a design equation can be developed as follows

\frac{{ρ'}_{t} f_{yHs}}{ρ_{t} f_{y}} = 14.1 ρ_{s} \frac{f_{yh}}{{f'}_{c}} (1 - 0.9 \frac{P}{{f'}_{c} A_{g}})

(9)

Similar design equations were proposed for higher ultimate DRs as well. Design equations are plotted to qualify the effect of different design parameters on the ultimate drift capacity of columns. Figure 11 shows the interaction between $ρ_{s} (f_{yh} / f'_{c})$ and $ρ'_{t} f_{yHs} / ρ_{t} f_{y}$ for certain ultimate DRs. The graphs were plotted for different axial loading levels and it was observed that the line gradient for higher axial load levels is smaller. In order to summarize the proposed design expressions, several design charts were developed in this study. Figure 12 shows design charts for certain ultimate drift values ranging from 4% to 7%. Axial loading levels vary from 0 to $0.6 f'_{c} A_{g}$ in the vertical axis and the minimum value of $ρ_{s} (f_{yh} / f'_{c})$ defined by ACI Committee 318 (2014) is shown in charts as a vertical line. An example is presented here in order to illustrate the design procedure using the proposed design charts. Assume that an RC column which is under an axial load of $0.35 f'_{c} A_{g}$ is required to be designed in a way that it could undergo a drift capacity value of $D_{ult} = 5 %$ . Assume that known parameters of transverse reinforcement ratio $(ρ_{s})$ , transverse reinforcement yield strength $(f_{yh})$ , and concrete compressive strength $(f'_{c})$ will lead to the design value of $ρ_{s} (f_{yh} / f'_{c}) = 0.2$ . Specifying the level of axial loading $(P / f'_{c} A_{g})$ and the confinement ratio ( $ρ_{s} (f_{yh} / f'_{c})$ ) in the design graph of Figure 11 for the case of $D_{ult} = 5 %$ , the intersection point will drop on the curve of $(ρ'_{t} f_{yHs} / ρ_{t} f_{y}) = 1.5$ . As a result, the ratio of longitudinal HSS reinforcement in the column section $(ρ'_{t})$ and its yield strength $(f_{yHs})$ can easily be found.

Figure 11.

Interaction between longitudinal reinforcement yield strength and the confinement level.

Figure 12.

Design chart for various drift ratios.

Conclusion

A study was carried out to investigate the seismic performance of HSC columns with HSS reinforcement. To evaluate the design method of such structural members, the structural performance of six column specimens was investigated. Comprehensive finite-element study and analytical investigations were conducted to present a drift-based design formulation. The following conclusions are drawn based on test results and theoretical considerations:

Utilizing HSS reinforcement by the ratio of 30%, 50%, and 100% in an RC column section can increase the lateral loading capacity by 18%, 26%, and 55% on average, respectively.

Maximum lateral loading capacity increases between 60% and 85%, when the column shear span ratio is decreased from 5.0 to 2.5. In addition, drift capacities were consistently higher for columns with higher shear span-depth ratios $L / h$ . Drift-based design formulation was developed for columns with shear span ratio of 2.5, which produces lower estimates of the drift capacity.

Drift capacity of columns decreases as the axial loading value increases from 0 to $0.6 f'_{c} A_{g}$ . However, the effect of axial loading level on drift capacity deterioration is more significant in columns with lower concrete grades.

The influence of the yield strength of longitudinal steel reinforcement on drift capacity of RC columns is less significant as compared to the influence of other design parameters. However, it was noted that the grade of longitudinal steel bars was more influential in the case of moderate axial loading of $0.2 f'_{c} A_{g}$ to $0.4 f'_{c} A_{g}$ . In addition, it was observed that the effect of utilizing longitudinal HSS reinforcement is more significant in RC columns with higher concrete grades.

Among all the possible combinations of mixed-grade longitudinal reinforcement in RC column sections, the columns with HSS reinforcing bar ratio of $ρ'_{t} = 55 %$ show higher drift capacities. This value can be suggested as an optimum design parameter in drift-based design of RC columns utilizing HSS reinforcing bars.

The influence of various grades of transverse steel reinforcement in RC columns was studied. It was observed that increasing the yield strength of column transverse reinforcement from $f_{yh} = 475 MPa$ to $f_{yh} = 1275 MPa$ will increase the drift capacity between 3% and 9% in the case of zero axial load level. However, as the axial loading level increases to $0.6 f'_{c} A_{g}$ , the influence of column transverse reinforcements deteriorates gradually.

In columns with higher ratios of longitudinal HSS bars $(ρ'_{t})$ , the influence of utilizing higher grade of transverse reinforcement is more significant up to the optimum ratio of $ρ'_{t} = 55 %$ .

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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