2015-10_acisj_seismic performance rc columns seven- and eleven-spiral rebar

579ACI Structural Journal/September-October 2015

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

This research proposes innovative seven- and 11-spiral transverse reinforcement to replace two- and six-spiral reinforcement, respec-tively, to decrease spiral size to address the issue of spiral fabrica-tion in large columns. Moreover, this research proposes using large reinforcing bars or H-shaped steel as longitudinal reinforcement to reduce the potential of reinforcing bar cage failure. The objec-tives of this research were to investigate the seismic performance of seven- and 11-spiral columns and the effect of using large rein-forcing bars and H-shape steel as longitudinal reinforcement. Cyclic tests of columns showed that seven- and 11-spiral columns, even with less amounts of transverse reinforcement, exhibited higher ductility capacities than tied columns. The use of H-shaped steel as longitu-dinal reinforcement increased ductility and energy dissipation of the column. Among ACI 318, Caltrans BDS, and Caltrans SDC methods to estimate probable moment strength, only the Caltrans SDC method produced conservative results for all columns examined.

Keywords: columns; confinement; cyclic; ductility; multi-spiral; seismic; transverse reinforcement.

INTRODUCTIONThe use of two-spiral transverse reinforcement in oblong-

shaped concrete columns (Fig. 1(a)) has been an advanta-geous option compared with conventional tie reinforcement due to inherent superior confinement of spiral reinforcement than tie reinforcement.1-5 Tests conducted by Tanaka and Park1 showed that an oblong two-spiral column had seismic performance similar to that of the rectangular-tied benchmark column, although the transverse reinforcement of the former was only approximately 50% of the latter. Tests carried out in Japan4 showed that oblong two-spiral columns designed with transverse reinforcement 22 to 59% of the rectangular-tied benchmark column had similar seismic performance to the benchmark column. Wu et al.5 found that oblong two-spiral columns with transverse reinforcement 43% of that of oblong-tied columns had similar strength, ductility, and energy dissi-pation to the tied columns. The California Department of Transportation Bridge Design Specifications (Caltrans BDS 2003)6 and Seismic Design Criteria (Caltrans SDC 2010)7 include provisions for the design of two-spiral columns.

Due to superior seismic performance of two-spiral columns, innovative spiral reinforcement schemes have been developed for other cross-sectional shapes. For instance, innovative five-spiral reinforcement8 and six-spiral reinforcement5 have been developed for square columns (Fig. 1(b)) and rectangular columns (Fig. 1(c)), respectively. Cyclic tests indicated that five- and six-spiral columns with less transverse reinforcement performed similarly or better than tied columns. Yin et al.8 pointed out that the cost of confinement design by five-spiral reinforcement for an

11-story apartment project in Taiwan is only 59% of that by conventional tie reinforcement. The use of five-spiral rein-forcement reduces the material cost by 43%. Moreover, it reduces the labor cost for reinforcing bar cage assembling by 33% due to automation in the production of five-spiral reinforcement. This also decreases the construction time.

When columns are large (for example, large bridge columns), the size of the spiral in two-spiral reinforcement and the size of large spiral in six-spiral reinforcement can exceed the capacities of common bending machines, making their fabrication difficult. Innovative seven-spiral reinforce-ment (Fig. 1(d)) and 11-spiral reinforcement (Fig. 1(e)) are proposed in this research to replace two- and six-spiral rein-forcement, respectively, to resolve difficulty. In seven-spiral reinforcement, each spiral is interlocked with at least two other spirals. The interlocking mechanism has been validated by cyclic tests of shear-critical columns.9 Tests also showed that seven-spiral columns had similar or better shear performance with even less amounts of transverse reinforcement than tied columns. Eleven-spiral reinforcement is seven-spiral rein-forcement with four additional small corner spirals to confine corner concrete—the same used in five- and six-spiral rein-forcement. The first objective of this research was to examine the seismic performance of seven- and 11-spiral columns with transverse reinforcement satisfying the shear and confinement requirements of Caltrans codes6,7 and the MOTC 2008 code.10 The second objective of this research was to investigate the effect of using large reinforcing bars or H-shaped steel as longitudinal reinforcement on the seismic performance of seven-spiral columns. The use of such longitudinal reinforce-ment can reduce the potential of reinforcing bar cage collapse during construction of large, tall columns.11

RESEARCH SIGNIFICANCETwo- and six-spiral transverse reinforcement has been

developed in previous studies for oblong and rectangular columns, respectively. However, when columns are large, the size of the spiral in two- and six-spiral reinforcement can exceed the capacities of common bending machines. More-over, the potential of reinforcing bar cage failure increases with increasing column height. This research proposes seven- and 11-spiral reinforcement to replace two- and six-spiral reinforcement, respectively, to address the issue of

Title No. 112-S47

Seismic Performance of Concrete Columns with Innovative Seven- and Eleven-Spiral Reinforcementby Yu-Chen Ou, Si-Huy Ngo, Hwasung Roh, Samuel Y. Yin, Jui-Chen Wang, and Ping-Hsiung Wang

ACI Structural Journal, V. 112, No. 5, September-October 2015.MS No. S-2014-134.R1, doi: 10.14359/51687706, received October 28, 2014, and

reviewed under Institute publication policies. Copyright © 2015, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.

580 ACI Structural Journal/September-October 2015

spiral fabrication in large columns. Moreover, this research proposes the use of large reinforcing bars or H-shaped steel as longitudinal reinforcement to reduce the potential of rein-forcing bar cage failure.

EXPERIMENTAL PROGRAMColumn design

Figure 2 shows the cross-sectional design of all columns. Figure 3 shows the geometry and dimension of all columns. The scale factor of all columns was 1/3. Tables 1 and 2 list the material properties and reinforcement amount design parameters, respectively. Nomenclature of the columns is as follows: D and C denote oblong and rectangular cross sections, respectively; T and M denote tie and multi-spiral transverse reinforcement, respectively; R and H denote the use of deformed bars and H-shaped steel as longitudinal rein-

Fig. 1—(a) Two-spiral reinforcement; (b) five-spiral rein-forcement; (c) six-spiral reinforcement; (d) seven-spiral reinforcement; and (e) 11-spiral reinforcement.

Fig. 2—Cross-sectional design for columns: (a) DTR1; (b) DMR1; (c) DMR2; (d) DMH; (e) CTR1; and (f) CMR1. (Note: 1 mm = 0.0394 in.).


forcement, respectively; and the numbers following R—1 and 2—refer to small and large longitudinal bars, respectively.

Six columns were tested, including four oblong columns and two rectangular columns. The four oblong columns were designed to have similar flexural strength and so did the two rectangular columns. For the oblong columns, one was designed with conventional tie transverse reinforcement (DTR1, Fig. 2(a)) and three were designed with innova-tive seven-spiral reinforcement (DMR1, DMR2, and DMH shown in Fig. 2(b), (c), and (d), respectively). Column DMR1 used the same type of longitudinal reinforcement as column DTR1. The effect of seven-spiral reinforcement could be evaluated by comparing columns DMR1 and DTR1.

Columns DMR2 and DMH used large reinforcing bars and H-shaped steel as longitudinal reinforcement, respec-tively. The effect of such longitudinal reinforcement on column behavior could be evaluated by comparing the two columns with Column DMR1. Note that the yield strength of H-shaped steel was lower than that of longitudinal bars in the other oblong columns (Table 1). Thus, the longitudinal reinforcement ratio in Column DMH was higher than those of the other oblong columns (Table 2). For the two rectan-gular columns, one was designed with conventional tie rein-forcement (CTR1, Fig. 2(e)) and the other with 11-spiral reinforcement (CMR1, Fig. 2(f)). The effect of 11-spiral reinforcement on column behavior could be evaluated by comparing the two rectangular columns.

The required amount of transverse reinforcement in this study was governed by code-required confinement rather than code-required shear strength. Equations (1) and (2), and Eq. (3) and (4) are confinement equations for spiral and tied columns, respectively, in Caltrans BDS.6 Equations (1) and (5), and (3) and (6) are confinement equations for spiral and tied columns, respectively, in the MOTC 2008.10 Equa-tions (1) and (3) are intended to ensure that spalling of cover concrete does not reduce axial load strength of the column.12 Equations (2), (4), (5), and (6) are intended to ensure adequate curvature capacity in yielding regions.6,12 The difference between Eq. (2) and (4) used in Caltrans BDS6 and Eq. (5) and (6) used in MOTC 2008 is that the former considers the effect of axial load while the latter does not. The columns in this research were designed with the amounts of transverse reinforcement satisfying both Caltrans BDS and MOTC 2008. Table 2 lists the amounts of transverse reinforcement required by Caltrans BDS and MOTC 2008 and the provided amounts for all columns. When calculating the code-re-

Fig. 3—Geometry and dimension of all columns. (Note: Dimensions in mm (in.).)

Table 1—Material properties

Column Cross section

Concrete Transverse reinforcement Longitudinal reinforcement

fcʹ, MPa (ksi)

fcaʹ, MPa (ksi)

Size @ spacing mm, (in.)

fy, MPa (ksi)

fya, MPa (ksi)

fua, MPa (ksi)

Quantity size, mm (in.)

fy, MPa (ksi)

fya, MPa (ksi)

fua, MPa (ksi)

DTR1

34.3 (4.97)

48.2 (6.99)

D12@75 ([email protected])

490 (71.1)

581 (84.2)

614 (89.0)

18-D25 (18-No. 8)

412 (59.7)

469 (68.0) 675 (97.9)

DMR1 56.0 (8.12)

270-D8@60 (10.63-D8@ 2.36)

648 (94.0)

673 (97.6)DMR2 47.1

(6.83)

6-D36 (6-No. 11) 484 (70.2) 680 (98.6)

12-D19 (12-No. 6) 469 (68.0) 690 (100)

DMH 45.5 (6.60) 6H-shaped steel 343 (49.7) 379 (55.0) 510 (74.0)

CTR1 47.0 (6.82)

D12@75 ([email protected])

581 (84.2)

614 (89.0)

22-D25 (22-No. 8) 412 (59.7) 469 (68.0) 675 (97.9)

CMR1 45.5 (6.60)

Large: 270D8@60 ([email protected]) 648

(94.0)673

(97.6)Small: 200-D8@60 ([email protected])

Notes: H-shaped steel is 100 x 100 x 6 x 8 mm ( b d t tf w fx x x ); 1 mm = 0.0394 in.


quired amount of transverse reinforcement for seven- and 11-spiral reinforcement, the volumetric ratio of each spiral was designed not less than that required by Eq. (1), (2), and (5). The Ac in Eq. (1) is the area enclosed by the outside edges of the spirals.

The required amount of transverse reinforcement in Table 2 for tied columns included detailing requirements, such as hook anchorage, which was not required in spiral reinforcement. The transverse reinforcement provided exceeded the required amount due to the use of standard reinforcement sizes and detailing requirements (only in tie reinforcement). Design results (Table 2) showed transverse reinforcement of oblong seven-spiral columns was only 49% of the oblong tied column and the rectangular 11-spiral column was 75% of the rectangular tied column. Detailing

requirements contributed to 20% and 16% of the amounts of transverse reinforcement for oblong and rectangular tied columns, respectively. Figure 4 shows reinforcing bar cages of four oblong columns during fabrication.

rsc

yt

g

c

ff

AA

= ′ −

0 45 1. (Caltrans BDS and MOTC) (1)

rsc

yt

e

c g

ff

Pf A

= ′ +′

0 12 0 5 1 25. . . (Caltrans BDS) (2)

A s hff

AAsh t c

c

yt

g

c

=′

−

0 3 1. (Caltrans BDS and MOTC) (3)

Table 2—Amount of reinforcement

Column type Cross section

Volumetric ratio of longitudinal reinforcement

Amount of transverse reinforcement kgf/m (lbf/ft) (volumetric ratio)

Required Provided

MOTC10 Caltrans BDS6 Total Detailing requirement

DTR1 2.05% 68.03 (45.73) (2.31%)

48.52 (32.61) (1.65%)

80.36 (54.01) (2.73%)

16.00 (10.75) (0.54%)

DMR1 DMR2 DMH

2.05% 2.13% 2.95%

39.69(26.68)(1.59%)

39.69 (26.68) (1.59%)

39.05 (26.25) (1.57%)

0.0

CTR1 2.14% 69.03 (46.40) (2.01%)

47.40 (31.86) (1.38%)

73.60 (49.47) (2.14%)

11.35 (7.63) (0.33%)

CMR1 2.14% 40.67 (27.34) (1.30%)

40.67 (27.34) (1.30%)

55.58 (37.36) (1.78%) 0.0

Fig. 4—Reinforcing bar cages for columns: (a) DTR1; (b) DMR1; (c) DMR2; and (d) DMH.


Fig. 5—Test setup: (a) setup illustration; and (b) photograph.

Fig. 6—Lateral force-drift relationships for columns: (a) DTR1; (b) DMR1; (c) DMR2; (d) DMH; (e) CTR1; and (f) CMR1.


A s hff

Pf Ash t c

c

yt

e

c g

=′

+′

0 12 0 5

1 25. .

. (Caltrans BDS) (4)

rsc

yt

ff

= ′0 12. (MOTC) (5)

A s hffsh t cc

yt

=′

0 12. (MOTC) (6)

Test setup and loading protocolAll columns were tested under single-curvature lateral

cyclic loading along the weak direction of their cross section (Fig. 5). Lateral cyclic loading was applied using two hydraulic actuators with displacement control to drift levels of ±0.25%, ±0.375%, ±0.5%, ±0.75%, ±1%, ±1.5%, ±2%, ±3%, ±4%, ±6%, ±8%, and ±10%.13 The drift was defined as lateral displacement at the midheight of the block on the column top divided by the height from the midheight of the block to the column base (2100 mm [82.7 in.]). Each drift level was repeated three times to examine stiffness and strength degradation within a drift level. An axial load ratio of 10% of concrete compressive strength times column gross cross-sectional area was applied to each column by two hydraulic jacks and maintained constant throughout testing. The reaction force to each hydraulic jack was provided by a high-strength rod connected to a hinge anchored on the strong floor. This axial loading system tilted as the column deformed laterally during testing, leading an additional moment at the column base. The effect of this additional moment was removed from the measured lateral force using the following equations (illustrated in Fig. 5(a))

M FL M FL P P LP= + = + × ′ − × ′−D Dcos sinq q (7)

′ = + −F FMLP D (8)

Note that the lateral force presented hereafter is the modi-fied lateral force, ′F .

TEST RESULTS AND DISCUSSIONLateral force-drift responses

Figure 6 shows lateral force-drift plots for all columns. Significant events are indicated in the plots: idealized yield, cover concrete spalling, first fracture of transverse and longi-tudinal reinforcement, and ultimate point. The ultimate point was defined as the point in the envelope of the measured cyclic response corresponding to a 20% decrease in lateral force from the peak load. The lateral force-drift curves were idealized by a bilinear relationship based on the FEMA 35614 idealized force-displacement procedure. The idealized force- displacement response includes two line segments: 1) the first line segment passes through the actual envelope response at approximately 60% of the force at the idealized yield point; and 2) the second segment ends at the ultimate point. The idealized yield point was selected so that areas below actual and idealized curves were similar. Ductility was calculated by dividing ultimate drift by idealized yield drift. Table 3 lists the characteristics of the lateral force-drift relationships. Figure 7 shows the photographs of all columns at the end of testing. The photograph of the short side of Column DTR1 was not taken, and hence is not shown in Fig. 7. Figure 8 shows a close view of the plastic hinge regions of the seven- and 11-spiral columns, revealing damage details of the columns.

All columns showed ductile flexural-dominated behavior (Fig. 6 to 7). The ductility capacity of the columns ranged from 6.10 to 11.09 (Table 3). The two oblong seven-spiral columns with deformed bars as longitudinal reinforcement (DMR1 and DMR2) had similar strength and ductility (Table 3). These two columns had in average 19% higher ductility than the oblong tied column (DTR1), although the transverse reinforcement of the former was only 49% of that of the latter (Table 2). This finding demonstrates superior performance of seven-spiral reinforcement to conventional tie reinforcement. The oblong seven-spiral column with H-shaped steel as longitudinal reinforcement (DMH) had a

Table 3—Characteristics of lateral force-drift relationships

Column Cross section Idealized yield drift, % Peak load, kN (kip) Ultimate drift, % Displacement ductility

DTR1 1.08 764 (171.9) 8.02 7.40

DMR1 0.96 748 (168.3) 8.32 8.71

DMR2 0.94 745 (167.6) 8.34 8.87

DMH 0.85 693 (155.9) 9.43 11.09

CTR1 1.19 941 (211.7) 7.23 6.10

CMR1 1.33 1019 (229.3) 8.70 6.54


significantly greater ductility (on average 26%) than those with deformed bars as longitudinal reinforcement (DMR1 and DMR2) (Table 3). This is attributed to the better buckling resistance of H-shaped steel than deformed bars and the extra confinement effect provided by the flange of H-shaped steel.

The failure of the seven-spiral columns with deformed bars as longitudinal reinforcement (DMR1 and DMR2) was initiated due to strong pushing force from buckling of longi-tudinal reinforcement, which eventually led to fracture of spirals and fracture of longitudinal reinforcement itself. As the diameter of longitudinal bars increased, final buckling

length increased (Fig. 8(a) and (b)), increasing the extent of spiral fracture. The failure of the column with H-shaped steel (DMH) was also initiated by buckling of the H-shaped steel flange beside cover concrete. However, the restraint from both the H-shaped steel web and the spiral was able to localize the buckling of the flange within approximately the vertical spacing of the spiral (Fig. 8(c)). Note that the H-shaped steel satisfies the seismically compact requirement—no spirals fractured. This, together with the extra confinement effect from the flange of the H-shaped steel, means the core concrete was mostly preserved and Column DMH had much

Fig. 7—End of testing for columns: (a) long side of DTR1; (b) short side of CTR1; (c) long side of CTR1; (d) short side of DMR1; (e) long side of DMR1; (f) short side of DMR2; (g) long side of DMR2; (h) short side of DMH; (i) long side of DMH; (j) short side of CMR1; and (k) long side of CMR1.


greater ductility than the columns with deformed bars. The column with H-shaped steel (DMH) failed eventually due to flange fracture. The lower strength of this column (DMH) than the columns with deformed bars is attributed to a lower ratio of tensile strength to yield strength (Table 1). The failure mechanism of the oblong tied column (DTR1) was similar to the oblong seven-spiral columns with deformed bars as longitudinal reinforcement (DMR1 and DMR2).

The rectangular 11-spiral column (CMR1) exhibited a 7% higher ductility than the corresponding tied column (CTR1). The transverse reinforcement of the spiral column was 75% of the tied column. The failure mechanism of the rectangular 11-spiral column (Fig. 8(d)) resembled that of the oblong seven-spiral columns with deformed bars as longitudinal reinforcement (DMR1 and DMR2). The rectangular tied column failed without any fracture of tie reinforcement. However, several hooks popped out at testing end (Fig. 7(b)

and (c)). Thus, the tie reinforcement was not fully mobilized to confine concrete and longitudinal reinforcement.

No signs of separation of spirals were observed in all oblong and rectangular spiral columns because no longi-tudinal cracks were observed on the sides of the columns (Fig. 7(d), (f), (h), and (j)). This finding indicates that spirals were effectively interlocked.

Equivalent viscous dampingTo evaluate the energy dissipation capacity of the columns,

the equivalent viscous damping ratio was calculated for each column by Eq. (9)15 and is shown in Fig. 9.

xπeq

D

eff p

EK

=2 2D

(9)

Among the oblong spiral columns, the column with H-shaped steel (DMH) had the highest energy dissipation,

Fig. 8—Close view of plastic hinge regions for multi-spiral columns: (a) DMR1; (b) DMR2; (c) DMH; and (d) CMR1.

Fig. 9—Comparison of equivalent damping ratios of: (a) oblong columns; and (b) rectangular columns.


followed by Column DMR2 (large longitudinal bars) and then by Column DMR1 (Fig. 9(a)). The H-shaped steel and large longitudinal bars had higher buckling resistance and hence resulted in higher energy dissipation. The better confinement of the H-shaped steel to core concrete further increased energy dissipation. The oblong tied column (DTR1) showed energy dissipation capacity that degraded earlier than the oblong spiral column (DMR1). A similar finding was obtained for rectangular columns (Fig. 9(b)). The spiral reinforcement appeared to provide better restraint to buckling of longitu-dinal reinforcement and better confinement to core concrete than the tie reinforcement and hence better preserved the energy dissipation capacity of the column at high drifts.

Curvature ductility distributionTo evaluate the distribution of section rotations along the

height of the column, curvature ductility distribution was calculated for Columns DMR1, DMR2, DMH, CTR1, and

CMR1 and is shown in Fig. 10. The curvature distribution of the oblong tied column (DTR1) was not calculated due to malfunction of the rotational gauge at the column base. The curvature ductility was defined as the curvature divided by the yield curvature. The curvature was calculated from rotations, which were measured by inclinometers. The yield curvature was defined as the curvature corresponding to the idealized yield point. The two oblong seven-spiral columns with deformed bars as longitudinal reinforcement had similar curvature ductility distributions (Fig. 10(a) and (b)). The column with H-shaped steel had a curvature ductility distribution that concentrated toward the column base. As stated, this is because H-shaped steel had higher buckling resistance and provided more effective confinement to core concrete than deformed bars, hence reducing the extent of core concrete damage. This is also evident from a smaller area of concrete spalling in the H-shaped column (Fig. 7(h) and (i)) than in oblong deformed-bar columns (Fig. 7(d)

Fig. 10—Curvature ductility for columns: (a) DMR1; (b) DMR2; (c) DMH; (d) CTR1; and (e) CMR1.


through (g)). The curvature ductility distribution of the rectangular tied column (Fig. 10(d)) showed more curva-ture spreading toward the column top than the rectangular 11-spiral column (Fig. 10(e)). This again shows the higher capability of the 11-spiral reinforcement to confine concrete and limit the extent of damage than the tie reinforcement.

NOMINAL MOMENT STRENGTH AND MAXIMUM PROBABLE MOMENT STRENGTH FOR

CAPACITY DESIGNNominal moment strength

The ratios of measured moment at the column base, Mmax (average of positive and negative drift loading), to moment corresponding to shear strength and various moment strengths were calculated for each column and are listed in Table 4. The fourth column of Table 4 lists the values of Mmax/MVn_SDC, where MVn_SDC is the moment corresponding to nominal shear strength calculated based on the Caltrans SDC method7 and actual material strengths. The values ranged from 0.22 to 0.32, indicating flexural failure of all columns. The fifth column of Table 4 lists the values of Mmax/Mn. The Mn is nominal moment strength and was calcu-lated based on actual material strengths. The tensile strength of concrete was neglected and the ultimate strain was assumed equal to 0.003. Steel reinforcement was modeled using the elastic perfectly plastic stress-strain relationship. The ratios of Mmax/Mn exceeded 1.0 for all columns. The oblong seven-spiral column DMR1 and the rectangular 11-spiral column CMR1 had 5.1 and 8.8% higher over-strength (Mmax/Mn) than the tied columns DTR1 and CTR1, respectively, likely due to the superior confinement effect of multi-spiral reinforcement, leading to higher overstrength. Seven-spiral column DMR2 had 7.3% lower overstrength than seven-spiral column DMR1. This is likely due to the reduced bond effect associated with the large-diameter bars used in Column DMR2. Seven-spiral column DMH had the lowest overstrength, 17.1% lower than Column DMR1,

likely due to the lower ratio of tensile strength to yield strength of H-shaped steel (Table 1) and lower bond than deformed bars.

Maximum probable moment strengthAs mentioned, the superior confinement characteristics of

multi-spiral columns increased overstrength. Therefore, it is important to examine methods to estimate maximum probable moment strength used for capacity design, such as for foun-dation design and shear design. Three methods were exam-ined in this research: ACI 318-11,12 Caltrans BDS,6 and the Caltrans SDC7 method, which are denoted as Mp_ACI, Mp_BDS, and Mp_SDC, respectively. These methods have very different approaches to calculate maximum probable moment strength.

In the calculation of Mp_ACI, the same assumptions as those for Mn were used except that yield strength of longitudinal reinforcement was assumed to be 1.25 times specified yield strength, and specified concrete compressive strength was used. A comparison of Mmax with Mp_ACI shows that the ACI 318-1112 method was not conservative for all columns (sixth column in Table 4). The ACI 318.1112 method in average underestimated Mmax by 11%. The degree of noncon-servatism was higher in multi-spiral columns (for example, DMR1 and CMR1) than tied columns (DTR1 and CTR1).

The Mp_BDS was defined as 1.3 times nominal moment strength for a well-confined section with an axial load below nominal axial load strength at the balanced strain condition, which is the case for columns examined herein. The nominal moment strength was calculated based on specified material properties. A comparison of Mp_BDS with Mmax shows better results than the ACI 318-1112 method (seventh column in Table 4). The Caltrans BDS method yielded conservative estimate for all tied columns. However, it did not provide a conservative estimate for multi-spiral columns with deformed bars as longitudinal reinforcement, in which the Caltrans BDS method in average underestimated Mmax by 4%. The Caltrans BDS could not fully capture the overstrength

Table 4—Flexural strengths and curvature ductility

ColumnCross

sectionMmax, kN·m

(kip·ft)

M

MVn SDC

max

_

M

Mn

maxM

Mp ACI

max

_

M

Mp BDS

max

_

M

Mp SDC

max

_ mf_u mf_ %4 mf_ %6

DTR1 1604 (1184) 0.22 1.17 1.14 1.00 0.91 19 NA NA

DMR1 1570 (1159) 0.30 1.23 1.23 1.07 0.98 19 27 29

DMR2 1564 (1154) 0.31 1.14 1.15 1.00 0.91 17 29 38

DMH 1456 (1075) 0.29 1.02 1.02 0.89 0.90 21 56 NA

CTR1 1978 (1460) 0.29 1.13 1.09 0.97 0.85 23 13 18

CMR1 2140 (1579) 0.32 1.23 1.17 1.05 0.96 25 18 25

Note: NA is data not available.


effect in multi-spiral columns due to superior confinement of multi-spiral reinforcement. It generated a conservative estimate for the multi-spiral column with H-shaped steel as longitudinal reinforcement. This is attributed to the low overstrength of H-shaped steel, as mentioned.

The calculation of Mp_SDC involved the use of more real-istic material models than the other two methods. Moment- curvature analysis was conducted. In the analysis, reinforce-ment steel was modeled using a stress-strain relationship considering strain-hardening behavior. Actual yield and tensile strengths (Table 1) were used and ultimate tensile strain was reduced, as suggested in the Caltrans SDC method. Concrete was modeled with actual concrete compressive strength (Table 1). Core and cover concrete were modeled using confined and unconfined concrete models,16 respectively. The moment-curvature curve was idealized with a bilinear elastic perfectly plastic response. The moment corresponding to the yield of the bilinear response was defined as plastic moment strength. The Mp_SDC was defined as 1.2 times the plastic moment strength.

A key issue in the Caltrans SDC method was to determine lateral confining pressure by multi-spiral reinforcement in confined concrete modeling. A multi-spiral reinforcement contains regions confined by one spiral and overlapping regions confined by more than one spirals. For regions confined by one spiral, confining pressure, f1, can be calcu-lated from equilibrium (Fig. 11(a)).

2 1 1 1V f dssin a = (10)

V A fsp yh1 1 1 1= sinb (11)

From Fig. 11(a)

sin //

a11 1

22

= =dD

dD

(12)

By substituting Eq. (11) and (12) into Eq. (10), confining pressure by one spiral can be obtained.

fA f

D ssp yh

11 1 1

1

2=

sinb (13)

When one more spiral is added to form an overlapping region, confining pressure f12, due to the combined action of the two spirals can be derived again by force equilibrium (Fig. 11(b)).

2 21 1 2 2 12V V f dssin sina a+ = (14)

Following a similar derivation, f12 can be acquired.

2 21 1 1 1 2 2 2 2 12A f A f f dssp yh sp yhsin sin sin sinb a b a+ = (15)

2 21 1 11

2 2 22

12A f dD

A f dD

f dssp yh sp yhsin sinb b+ = (16)

fA f

D sA f

D ssp yh sp yh

121 1 1

1

2 2 2

2

2 2= +

sin sinb b (17)

The first and second terms on the right side of Eq. (17) are confining pressure only by spiral 1 and that only by spiral 2, respectively. This means confining pressure in the overlap-ping region by two spirals is simply the sum of confining pressure from each of the two spirals separately.

f12 = +f f1 2 (18)

Using a similar procedure, it can be shown that if a region is confined by n spirals; confining pressure in the region is equal to the sum of confining pressure from each of the n spirals separately.

f f f fn n12 1 2... ...= + + + (19)

With the aforementioned models for confining pressure, the stress-strain relationship for any confined region in multi-spiral columns can be determined by the Mander et al.16 model. Concrete modeling for seven-spiral columns consisted of an unconfined concrete model for cover concrete, and a confined concrete model for regions enclosed by one spiral and that for regions where two spirals overlap. For the 11-spiral column, in addition to confined concrete models for regions enclosed by one spiral and by two spirals, concrete modeling also included a confined concrete model for overlapping regions enclosed by three spirals.

The Caltrans SDC method yielded conservative results for all columns (eighth column in Table 4). The exceptionally low Mmax/Mp_SDC value for the rectangular tied column indicates that overstrength of the rectangular tied column was much lower than predicted. This again reveals lower effectiveness of rectan-gular tie reinforcement for confining concrete than spiral rein-forcement. The higher overstrength of the oblong tied column than the rectangular tied column is because the two side regions of the oblong tied column were confined by semicircular ties, which provided better confinement than rectilinear ties.

Fig. 11—Confining pressure due to: (a) one spiral; and (b) two spirals.


Ultimate curvature ductilityThe ultimate curvature ductility µϕ_u for each column was

calculated by the moment-curvature analysis used to deter-mine Mp_SDC as discussed previously and is listed in the ninth column of Table 4. The 10th and 11th columns of Table 4 list the measured curvature ductility at 4% drift (µϕ_4%) and 6% drift (µϕ_6%), respectively, from the column base (Fig. 10). A comparison of µϕ_u with µϕ_6%, or µϕ_4% if µϕ_6% was not avail-able, shows that for the spiral columns, the measured curvature ductility was equal to or larger than the analytical curvature ductility. Note that the measured curvature ductility included the slip of longitudinal reinforcement out of the foundation, which was not considered in the analytical curvature ductility. Conversely, the rectangular tied column (CTR1) showed measured curvature ductility 22% lower than the analytical curvature ductility. This suggests that the analytical curvature ductility was not conservative for the rectangular tied column.

CONCLUSIONSFour oblong and two rectangular concrete columns were

tested under lateral cyclic loading. Innovative seven- and 11-spiral transverse reinforcement schemes were examined and compared with conventional tie reinforcement. The main conclusions are summarized as follows.

1. All columns exhibited ductile flexural-dominated behavior. The oblong seven-spiral columns with deformed bars as longitudinal reinforcement (DMR1 and DMR2) had on average 19% higher ductility than the oblong tied column (DTR1), although the transverse reinforcement of the former was only 49% of the latter. The rectangular 11-spiral column (CMR1) had a 7% higher ductility than the rectangular tied column (CTR1), even though the transverse reinforcement of the former was 75% of that of the latter.

2. The seven-spiral column with H-shaped steel as longitu-dinal reinforcement (DMH) had higher energy dissipation and in average 26% higher ductility than the other seven-spiral columns. This is attributed to the higher buckling resistance of the H-shaped steel than the deformed bars and extra confine-ment effect of the flange of the H-shaped steel on core concrete.

3. When longitudinal deformed bars were the same size, the oblong seven-spiral column (DMR1) and rectangular 11-spiral column (CMR1) had 5.1% and 8.8% higher over-strength than the tied columns (DTR1 and CTR1), respec-tively. The use of large longitudinal deformed bars (DMR2) and H-shaped steel (DMH) reduced overstrength by 7.3% and 17.1%, respectively, as compared with Column DMR1.

4. For maximum probable moment strength for capacity design, the ACI 318 method produced nonconservative results for all columns (in average 11% lower). The Caltrans BDS method provided conservative results for tied columns, but yielded nonconservative results for multi-spiral columns with deformed bars as longitudinal reinforcement (in average 4% lower). The Caltrans SDC method, by using more realistic steel and concrete stress-strain relationships, gave conservative estimates for all columns.

AUTHOR BIOSYu-Chen Ou is a Professor of civil and construction engineering at National Taiwan University of Science and Technology, Taipei, Taiwan. He received his PhD from the University at Buffalo, the State University

of New York, Buffalo, NY. He is the Vice President of the Taiwan Chapter – ACI. His research interests include reinforced concrete structures and earthquake engineering.

Si-Huy Ngo is a Lecturer of civil engineering at Hong Duc University, Thanhhoa, Vietnam, and a PhD Student of civil and construction engi-neering at National Taiwan University of Science and Technology. He received his MS from National Taiwan University of Science and Tech-nology. His research interests include reinforced concrete structures and prefabrication construction technology.

Hwasung Roh is an Assistant Professor in the Department of Civil Engi-neering at Chonbuk National University, Jeonju, South Korea. He received his PhD from the University at Buffalo, the State University of New York, in 2007. His research interests include nonlinear inelastic reinforced concrete frame structural analysis, seismic design and performance evaluation, and bridge deck vibration.

Samuel Y. Yin is the CEO and Chief R&D Officer of Ruentex Group in Taiwan. He is Past President of the Taiwan Concrete Institute and an Adjunct Professor of civil engineering at National Taiwan University. His research interests include integration of construction systems, precise plan-ning of prefabrication construction methods, fast precast construction tech-nology, and innovation for reinforcing bar processing and assembly.

Jui-Chen Wang is an Assistant Vice President at Ruentex Engineering & Construction Co., Ltd. He received his PhD in civil engineering from National Taiwan University. He specializes in prefabrication construction technologies, including bridge piers and building systems.

Ping-Hsiung Wang is an Assistant Technologist at National Center for Research on Earthquake Engineering, Taipei, Taiwan, and a PhD Student of civil engineering at National Taiwan University. He received his MS from National Taiwan University. His research interests include reinforced concrete structures and precast concrete structures

ACKNOWLEDGMENTSThe authors would like to thank CECI Engineering Consultants, Inc.,

Taiwan, and National Center for Research on Earthquake Engineering (NCREE), Taiwan for their financial support. Also, the third author (H. Roh) appreciates a partial financial support from the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2015-R1D1A3A01-020017).

NOTATIONAc = area of core concrete measured to outside edges of trans-

verse reinforcementAg = gross area of cross sectionAsh = total cross-sectional area of tie reinforcement within

sections having dimensions of st and hcAsp1, Asp2 = cross-sectional areas of Spirals 1 and 2, respectivelyD1, D2 = diameters of Spirals 1 and 2, respectivelyd = dimension between two cutting points for free body

diagram as shown in Fig. 11ED = energy dissipation per cycle or area of hysteresis loopF = measured lateral forceFʹ = modified lateral forceFp, Fn = forces at Dp and Dn, respectivelyf1, f2 = confining pressures provided by Spirals 1 and 2, respectivelyf12 = confining pressure in overlapping region of Spirals 1 and 2f12...n = confining pressure in overlapping region of n spiralsfcʹ, fcaʹ = specified and actual compressive concrete strengths, respectivelyfn = confining pressure provided by spiral nfua = actual steel tensile strengthfy, fya = specified and actual steel yield strengths, respectivelyfyh1, fyh2 = yield strengths of Spirals 1 and 2, respectivelyfyt = specified yield strength of transverse reinforcementhc = column core dimension measured to outside edges of trans-

verse reinforcementKeff = effective stiffness and defined as (Fp – Fn)/(Δp – Δn)L, Lʹ = lengths as defined in Fig. 5(a)M = total moment at column baseMmax = measured maximum momentMn = nominal moment strengthMP – D = moment due to effect of P-ΔMp_ACI = maximum probable moment strength based on ACI 318Mp_BDS = maximum probable moment strength based on

Caltrans BDS


Mp_SDC = maximum probable moment strength based on Caltrans SDCMVn_SDC = moment corresponding to nominal shear strength calculated

based on Caltrans SDC methodP = axial loadPe = design axial loads = spiral pitchst = vertical spacing of transverse reinforcementV1, V2 = resisting forces provided by Spirals 1 and 2, respectivelya1, a2 = angles as shown in Fig. 11b1, b2 = angles as shown in Fig. 11D = lateral displacement at midheight of block on column topDʹ = displacement as defined in Fig. 5(a)Dp, Dn = maximum positive and negative displacements of loop,

respectivelymf_4% = measured curvature ductility at 4% drift from column basemf_6% = measured curvature ductility at 6% drift from column basemf_u = analytical curvature ductility at ultimate conditionq = angle as shown in Fig. 5(a)rs = ratio of volume of spiral reinforcement to total volume of

core concrete based on out-to-out of spiralsxeq = equivalent viscous damping ratio

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