MCEER/NCEER Bulletin Articles: Research
Confinement of Rectangular Bridge Columns for Moderate Seismic Areas
by Nadim I. Wehbe, M. Saiid Saiidi and David H. Sanders
This article presents research conducted under the NCEER Highway Project to develop detailing guidelines for reinforced concrete bridge columns located in areas of differing seismicity. Comments and questions should be directed to Nadim Wehbe, University of Nevada, Reno, at (702) 7846072; email: wehbe@unr.edu.
A welldesigned reinforced concrete bridge should be able to withstand the effects of a strong earthquake with little or no damage. In so doing, the superstructure will ideally be undamaged while the columns should be able to provide relatively large displacements without shear or flexural failures, or significant strength degradation. It has been shown that high ductilities can be achieved in reinforced concrete members if sufficient transverse confinement steel is provided in the member. Large amounts of transverse steel are therefore justified for columns with high ductility demands; however, the amount of confinement for columns not likely to undergo large deformations is uncertain. The objective of the study presented in this article was therefore to develop a method for the design of confinement steel as a function of the ductility demand.
Current design codes (AASHTO 1992; ACI 1995; Caltrans 1983; ATC32 1996) incorporate provisions for the design of transverse confinement reinforcing steel in columns subjected to earthquake loading. The design guidelines for the confinement steel in the potential plastic hinge region have been developed primarily for the most severe earthquake effects. In some cases, these provisions require a high amount of confining reinforcement which leads to constructability problems due to congestion of steel and to higher load demand on the adjoining members. The research presented in this article examines the ductility capacity of rectangular reinforced concrete bridge columns. A simple design equation relating the amount of confinement steel to attainable displacement ductility is presented.
Experimental Study
Four model bridge column specimens (referred to as A1, A2, B1 and B2) were designed, constructed, and tested in the course of this study. The objective of the tests was to determine the ductility capacity of rectangular columns with a moderate amount of confining steel. Two parameters were varied:
 transverse steel reinforcement amount
 column axial load
Each specimen was tested under a constant axial load while subjected to lateral load reversals in the strong direction of the column.
All four column specimens had the same cross section dimensions and height, and were reinforced with identical longitudinal steel. Details of the column specimens are shown in figure 1. Note that footing reinforcement is not shown. Each test column was 380 millimeters (15 in.) wide by 610 mm (24 in.) deep and was reinforced with 18f19 mm (#6) bars, resulting in a longitudinal reinforcement ratio,r_{l} , of 2.2%. The specified concrete compressive strength and steel yield stress were 27.6 MPa (4,000 psi) and 414 MPa (60,000 psi), respectively. The column height was 2,050 mm (6.7 ft.).
Figure 1: Column Details for the Test SpecimensBased on AASHTO (1992) requirements for transverse steel in the plastic hinge region for columns subjected to severe earthquakes, the minimum transverse steel ratio, A_{sh}/(sh) , for the test specimens is 0.008. To prevent premature buckling of longitudinal bars, an upper limit on hoop spacing, s, was set at six times the longitudinal bar diameter (6d_{b}) resulting in a limit of 114 mm (4.5 in.). Each tie set in the potential plastic hinge zone consisted of 1f6 mm (#2) perimeter hoop, 2f6 mm (#2) cross ties in the long direction, and 2f10 mm (#3) cross ties in the short direction. The perimeter tie had a 135° hook whereas the cross tie had a 135° hook on one end and a 90° hook on the other. In all cases, the hook extension was equivalent to ten times the bar diameter. The concrete cover was 28 mm (1 1/8 in.). For specimens A1 and A2, the tie set spacing was set at 110 mm (4.25 in.) corresponding to a transverse reinforcement ratio in the long direction of 0.0037 or 46% of the minimum confinement steel required by AASHTO. For specimens B1 and B2, the spacing of the tie sets was reduced to 83 mm (3.25 in.), resulting in a transverse reinforcement ratio in the long direction of 0.0048 or 60% of the minimum AASHTO requirement. In the short direction, the lateral steel reinforcement ratios were 0.0035 for specimens A1 and A2, and 0.0046 for specimens B1 and B2. These ratios correspond to 44% and 58% of the minimum requirement by AASHTO. The tie set arrangement and spacing were maintained the same along the column height. However, only f10 mm (#3) bars were used outside the potential plastic hinge region (figure 1). All specimens were designed such that the lateral steel was controlled by confinement requirements and not shear.
The experimental procedure was nearly identical for all four specimens. The desired axial load was first applied, then the specimen was subjected to unidirectional lateral loading in the strong direction of the column. Specimens A1, A2, B1 and B2 were subjected to initial axial loads of 615 kN (138 Kips), 1505 kN (338 Kips), 601 kN (135 Kips) and 1514 kN (340 Kips), respectively. Based on the measured concrete compressive strengths, these loads correspond to axial load ratios, P/(F'_{c}A_{g}), of 0.1, 0.24, 0.09 and 0.23. Experimental results are summarized in table 1.
Table 1: Measured and Calculated Response
Specimen
Measured
d_{y} mm (in.)
d_{u} mm(in.)
md
Drift Ratio %
A1
23 (0.92)
121 (4.76)
5.3
5.2
A2
19 (0.75)
100 (3.93)
5.2
4.3
B1
24 (0.94)
161 (6.32)
6.7
6.9
B2
20 (0.79)
123 (4.83)
6.1
5.3
Specimen
Calculated
d_{y} mm (in.)
d_{u} mm(in.)
md
Drift Ratio % A1
21 (0.84)
141 (5.54)
6.6
6.0
A2
19 (0.73)
90 (3.56)
4.9
3.9
B1
22 (0.85)
173 (6.80)
8.0
7.4
B2
19 (0.73)
112 (4.40)
6.0
4.8
Analytical Study
For a reinforced concrete column subjected to a lateral load, it is well established that the total lateral deflection can be attributed to deformations due to flexure, bond slip, and shear (Takeda et al., 1970). When footing rotation is prevented, the total lateral deflection, d_{t} , may be expressed as:
(1)
where:
D_{f} = deflection due to flexure
D_{s} = deflection due to reinforcement bond slip
D_{sh} = deflection due to shear
The flexural deflection was found as the static moment of the area under the column theoretical curvature diagram taken about the column upper end. The theoretical momentcurvature diagrams were obtained assuming trilinear and parabolic stressstrain relationships for steel and concrete, respectively. The unconfined concrete (cover concrete) constitutive relationship was idealized using the Kent and Park (1971) model. The cover concrete was assumed to have spalled to a depth where the concrete fiber reached a strain of 0.004. The confined concrete stressstrain was represented by the Mander et al., (1988) model as modified by Paulay and Priestley (1992) for the ultimate strain of confined concrete. Up to a displacement ductility of 2, the calculated flexural deflections were based on the assumption that the critical cross section occurred at the bottom of the column (top of footing). This assumption agreed with the observed crushing of the cover concrete during the tests which initiated at the columnfooting interface. At higher drifts, however, the confinement provided by the footing shifted the critical section upward. Based on observed column behavior, it was assumed that the ultimate curvature is attained at two tie spacings above the footing.
Figure 2: Bond Slip of Developed BarsLateral deflections due to bond slip (defined as the extension of tensile bars along the embedded length in the footing) were calculated assuming that the bond slip rotation occurs about the neutral axis of the column cross section at the base. The neutral axis location and the strain and stress in the tensile steel at a given lateral load were determined from momentcurvature analysis of the section. The longitudinal bar extension due to slippage, at the top of the footing was calculated at the outermost tensile steel layer in the column by integrating the strain profile along the embedded bar length inside the footing (figure 2). Thus, the bond slip rotation, was found as divided by the distance of the neutral axis to the center of the outermost tensile steel layer. The corresponding lateral deflection at the top of the column was obtained as where L is the column shear span. In finding the strain profile along the embedded bar length, uniform bond stress was assumed along a length required to develop a force equal to the bar tensile force at the bottom of the column. For mm (#11) or smaller deformed bars, the basic bond strength, u, of tension bars was assumed to be (ACI, 1963)
(2)
Shear deflections were calculated using the shear stiffness expression derived by Park and Paulay (1975). For assumed 45E diagonal cracks, the shear stiffness may be expressed as
(3)
where:
1/K_{n, 45} = shear deflection for unit length due to unit shear
E_{s} = elastic modulus of shear reinforcement
b_{w} = section width perpendicular to applied shear
d = effective section depth parallel to applied shear
n = (modular ratio)
E_{c} = elastic modulus of concrete
r_{v} = (shear reinforcement ratio)
A_{v} = area of shear reinforcement
s = spacing of shear reinforcement sets along the member longitudinal axisThe calculated displacements, displacement ductilities, and drift ratios are shown in table 1. The calculated and measured lateral loaddeflection envelopes for the test specimens are also presented in figure 3. Comparison of the analytical and experimental results reveals that the predicted and the measured values are in very good agreement. The calculated drift ratios deviated from the measured ones by 14% and 7% for specimens A1 and B1, respectively, and by 9% for specimens A2 and B2. The predicted ductilities were also reasonably close to the experimental ductilities. The ratios of the calculated to the measured displacement ductilities were 1.22, 0.94, 1.19, and 0.98 for specimens A1, A2, B1, and B2, respectively.
Figure 3: Measured and Calculated Lateral Loaddeflection EnvelopesDuctilityBased Confinement Steel
With the current move toward performancebased design, it is desirable to develop a method to design confinement steel as a function of a target ductility level.For areas of high seismicity, ATC32 (1996) recommends the following equation to determine the amount of confinement steel
(4)
where:
s_{t} = spacing of transverse reinforcement along the axis of the member
h_{c} = crosssectional dimension of column core measured centertocenter of confining reinforcement
A_{g} = gross area of section
P = axial load
f'_{ce} = expected concrete strength
f_{yh} = expected yield stress of transverse reinforcement
r_{l} = longitudinal reinforcement ratioEquation 4 appears to be a comprehensive and rational approach to evaluate the confinement steel required for columns in high seismic risk regions. In addition to the axial load index and the ratio of concrete strength to the lateral steel yield stress, equation 4 incorporates the longitudinal steel ratio as a parameter in determining the confinement steel amount. Therefore, the ATC32 equation was adopted in this study as a bench mark for designing confinement steel for different ductility levels. However, it was felt that at reduced confinement levels, the variation in material strength might have a more pronounced effect on the ductility than the case when high confinement is provided. Therefore, it is suggested that equation 4 be modified as follows:
(5)
where F_{m} is a factor that depends on the target displacement ductility, f_{c,n} = 27.6 MPa (4 ksi) and f_{s,n} = 414 MPa (60 ksi). The values of f_{c,n} and f_{s,n} represent material strengths of concrete and steel, respectively, frequently specified for bridge columns. According to equation 5, increasing the longitudinal steel strength (and thus, flexural capacity) would result in a higher lateral steel area. Other researchers (Saatcioglu, 1991) have reported that the displacement ductility of columns is inversely proportional to the ratio of the applied shear to the square root of concrete strength. The effect of concrete strength on ductility is implied in equation 5 when one multiplies the righthandside of the equation by the square root of f_{c,n}/f'_{ce}.
When F_{m} = 1, equation 5 yields the minimum lateral steel amount required for high seismic regions (high ductility). In order to evaluate F_{m} at different ductility levels, columns similar to the test specimens were analyzed using transverse steel ratios different from those provided in the actual specimens. The analysis was conducted according to the procedure presented earlier and the calculated displacement ductility was compared to the ratio of the lateral steel considered in the analysis [(A_{s})]_{provided} to the lateral steel calculated from equation 5 for F_{m}=1[(A_{s}) _{Fm=1}]. Results of the analysis, including those for the test specimens, are presented in table 2. Table 2 shows that reasonably accurate results may be obtained when the displacement ductility factor is expressed as F_{m}=0.1m_{d}.
Thus, equation 5 can be written as
(6)
Thus, when m_{D}, equation 6 would result in the minimum transverse steel required in areas of high seismic risk. For columns with moderate ductility demand, a value of m_{D}<10 may be used to obtain the amount of confinement steel.
Table 2: Confinement Effect on Calculated Displacement Ductility
m_{D}The validity of equation 6 was verified against experimental results obtained from studies conducted by others on reinforced concrete columns (Wehbe et al., 1997). Figure 4 presents a comparison between equation 6 and other methods, where the lines represent the required transverse steel ratio for an example column similar to the test specimens. In figure 4, equation 6 is plotted for different displacement ductility levels. It can be seen that according to the proposed equation (equation 6), the effect of the axial load on the required transverse steel amount increases as the target displacement ductility increases. For an axial load index ranging between 0 and 0.4, the following observations can be made. When the target displacement ductility is 2, the transverse steel amount according to equation 6 is nearly identical to that required by the ACI nonseismic provision. At a moderate target displacement ductility of 4, the transverse steel amount according to equation 6 is considerably less than the amount required by other seismic provisions. For a target displacement ductility of 8, equation 6 results in a transverse steel amount that is approximately equal to that required by Caltrans. Since the concrete compressive strength and the steel yield stress for the example column were 27.6 MPa (4 ksi) and 414 MPa (60 ksi), respectively, equation 6 reduces to the ATC32 equation when the target displacement ductility is 10.
Figure 4: Comparison of Proposed Equation for Confinement Steel with Existing MethodsConclusions
The proposed equation (equation 6), which is based on the ATC32 approach for minimum transverse steel in highly seismic regions, appears to provide an adequate method to calculate the required transverse steel for rectangular bridge columns with moderate confinement. The applicability of equation 6 should be limited to columns with steel detailing that comply with current seismic practice.References
American Association of State Highway and Transportation Officials (AASHTO), 1992, "Standard Specifications for Highway Bridges," Fifteenth Edition, Washington, D.C.American Concrete Institute (ACI), Committee 318, 1995, "Building Code Requirements for Reinforced Concrete and Commentary," American Concrete Institute, Detroit, Michigan.
American Concrete Institute (ACI), Committee 318, 1963, "Building Code Requirements for Reinforced Concrete, " American Concrete Institute, Detroit, Michigan.
ATC32, 1996, "Improved Seismic Design Criteria for California Bridges: Provisional Recommendations," Applied Technology Council, Redwood City, California.
California Department of Transportation, 1983, "Bridge Design Specifications, 1983 AASHTO with Interims and Revisions by Caltrans," Sacramento, California.
Kent, D. C. and Park R., 1971, "Flexural Members with Confined Concrete," Journal of the Structural Division, ASCE, Vol. 97, No. ST7, July, pp. 19691990.
Mander, J. B., Priestley M. J. N. and Park R., 1988, "Theoretical StressStrain Model for Confined Concrete Columns," Journal of Structural Engineering, ASCE, Vol. 114, No. 8, August, pp. 18041826.
Paulay, T. and Priestley, M. J. N., 1992, "Seismic Design of Reinforced Concrete and Masonry Buildings," John Wiley & Sons, Inc., New York.
Park, R. and Paulay, T., 1975, Reinforced Concrete Structures, Wiley Interscience.
Saatcioglu, M., 1991, "Deformability of Reinforced Concrete Columns," American Concrete Institute, SP 127, pp. 421452.
Takeda, T., Sozen, M. A. and Nielsen N. N., 1970, "Reinforced Concrete Response to Simulated Earthquakes," Journal of the Structural Division, ASCE, Vol. 96, No. ST12, December, pp. 25572573.
Wehbe, N. I., Saiidi, M. S. and Sanders, D. H., 1997, "Effects of Confinement and Flares on the Seismic Performance of Reinforced Concrete Bridge Columns," Center for Civil Engineering Earthquake Research, University of Nevada, Reno, Report No. CCEER972, October.
MCEER Bulletin, Spring 1998, Vol. 12, No. 1
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