Abstract
This paper presents a comparison between the seismic design provisions of the U.S. ASCE 7, the Colombian NSR-10, and the Ecuadorian NEC-2015 for the design of low-rise reinforced-concrete (RC) frames. The code provisions are compared, illustrating the main differences in the requirements for ductility, strength, and analysis for low-rise RC frames. A four-story building is designed according to each design code, and its performance is evaluated according to ASCE 41-13 using pushover and incremental dynamic analysis. In terms of code language, differences are observed in the strong column-weak beam requirement, the allowable drift limit, and the R and C d factors used by the codes. The results show that the NEC-2015 design is controlled by the strong column-weak beam requirement, while drift limit and strength are the controlling factors in the NSR-10 and ASCE 7 designs. The seismic performance evaluation shows adequate behavior of the three buildings, with columns in the NEC-2015 building showing a slightly better behavior.
Introduction
Reinforced concrete moment-resisting frames are a widely used structural system in buildings across the world, especially in developing countries. According to reports from the World Housing Encyclopedia, they account for 60% of the building stock in Colombia (WHE 2017a) and 80% in Mexico (WHE 2017b). These frames are designed following the requirements of local design codes, which are the result of theoretical research, experimental testing and the experience acquired from observations of past earthquakes. Current seismic provisions of design codes vary between countries; however, they keep a common set of fundamental principles.
Presently, most seismic design provisions for RC moment-resisting frames from Latin American countries are influenced by ASCE 7 (2013) and ACI 318 (2011). For instance, most design provisions for RC in the Colombian NSR-10 (2010) are based on ACI 318, with a similar trend observed in the Chilean NCh433 (2012) and in the Ecuadorian NEC-2015 (2015).
Despite a notable influence from ASCE 7 and ACI 318, the Colombian NSR-10 and Ecuadorian NEC-2015 include a small group of changes in seismic design provisions, which may have significant effects on the seismic behavior of buildings. Identifying these effects is important for earthquake risk mitigation from a technical and practical perspective. Technically, code committee members will have valuable information about the effects of specific seismic provisions on seismic performance. Additionally, practitioners will benefit from knowing which design practices translate into better seismic performance. For this purpose, this paper compares the seismic design provisions for low-rise frames of U.S., Colombian, and Ecuadorian design codes. A conceptual comparison is performed in terms of each code's requirements for ductility, strength, and analysis, focusing on aspects with high relevance for engineering practice, such as the strong column- weak beam (SCWB) capacity design criterion, the seismic reduction factor (R), and the displacement amplification factor (C d ). Additionally, a four-story residential building is designed according to the three design codes and the results are examined, looking at the differences in member dimensioning and column capacity. The seismic performance of these buildings is investigated by means of pushover analyses of their typical planar frames, which are used to obtain the inputs to evaluate performance according to ASCE 41-13 (2013). Building performance is further examined using incremental dynamic analyses, and behavior is compared at the life safety and collapse prevention levels.
Comparison of Seismic Design Provisions for Reinforced-Concrete Frames
Given the extensive similarities between the aforementioned design codes, a selection of design provisions for residential buildings in a high seismic zone is provided in Table 1. This selection is based on parameters that are of high importance for practitioners and includes provisions for analysis and design of RC moment-resisting frames. Highlighted in bold in this table are provisions whose changes have a high potential to exert a notable influence on building design. A comparison of these provisions is presented here, in terms of design forces, ductility, and interstory drift (ISD).
Comparison of seismic design provisions
The Colombian and Ecuadorian codes have developed their design spectra using uniform risk criteria; these spectra are similar to ASCE 7 spectra. However, these spectra are prescribed at the design level instead of at the level of maximum considered earthquake (MCE). For the calculation of seismic design forces, the three codes use the same method to calculate the lateral force profile using a potential rule; however, the seismic reduction coefficient is smaller in the Colombian NSR-10 (R = 7) compared to NEC-2015 and ASCE 7 (R = 8). In practice, this means that for the same given spectral design acceleration (S a ), the design base shear will be higher using this code. In addition, if modal spectral analysis is used, this code has a higher minimum base shear requirement than the Ecuadorian and U.S. codes. Despite their high level of similarity, NEC-2015 does not require orthogonality effects; therefore, it could be expected that this code will have the smallest seismic design forces among the three design codes.
Ductility requirements are handled in a similar fashion by the three codes, mostly through the detailing of ductile elements, joint confinement, and the like. The only major differences are observed in the NEC-2015, where the SCWB criteria are handled following the deterministic approach suggested by Paulay and Priestly (1992), where the seismic moments in the columns are magnified using an overstrength factor (Ω0) and a dynamic amplification factor (ω f ), as shown in Table 1. The first considers the flexural overstrength of the beams framing into the column, and the second considers the changes in moment patterns due to higher mode effects. Compared with U.S. code, great design differences may result when the flexural strength of the beams are dominated by gravity loads, especially for low-rise buildings, where the overstrength factor could be as high as 4 for the usual collapse mechanism (flexural hinging at beam ends and in the base of the columns). Paulay and Priestley (1992) recommended changing the collapse mechanism for this type of structure, but this requires restricting the ductility demands (i.e., reducing the R factor) and NEC-2015 does not have provisions for doing so.
The ISD requirements show the biggest number of differences between the three design codes. To start, each code has its own way to define the displacement amplification factor C d . In ASCE 7, this value is defined as a variable that depends on the seismic force-resisting system and not on R, as opposed to NEC-2015, where it is defined as C d = 0.75R to account for the effects of a building's capacity to dissipate energy. The Colombian NSR-10 does not prescribe C d ; instead, it states that the ISD must be checked for unreduced seismic forces, which for practical comparison purposes means that C d = R and that buildings follow the rule of equal displacements. The most significant difference in this area comes from the NSR-10, where a value of 1% of the story height is imposed as a limit to the ISD, regardless of the importance of the building. However, this limit is meant to be checked using gross sections, and it must be increased to 1.43% if cracked sections are used. These values are significantly smaller than the 2% prescribed in ASCE 7 and NEC 2015, suggesting that designs fulfilling the NSR-10 ISD are expected to have bigger cross sections to meet this requirement.
Although they are few in number, important differences exist in the seismic provisions of ASCE 7, NEC-2015, and NSR-10. The most notable differences are the SCWB requirement in NEC-2015 and the limit imposed on the ISD in NSR-10.
Building Design
A four-story RC moment-resisting frame building is considered in this article, where all frames are part of the seismic-resisting system. The total building height is 12 m, with a clear interstory height of 2.55 m and approximate periods (T a ; see Table 1) of 0.43, 0.52, and 0.45 s for ASCE 7, NEC-2015, and NSR-10. This building is designed following the customary design practices of each code, using the equivalent lateral force procedure for an unreduced base shear coefficient, C = 1.0, representative of high-seismicity zones such as California, Pasto, Colombia, and Manabí, Ecuador). The design response spectra for these zones are shown in Figure 1.
Design response spectrum comparison for the three design codes.
A three-dimensional (3-D) model of the building was created in ETABS 2015 (Habibullah 1997). Sections are modeled using concrete with f c = 28 MPa and reinforcing steel with F y = 420 MPa. Exterior partition walls are modeled as distributed loads over their respective beams, assuming a weight of 2.5 kN/m2, which results in 6.34 kN/m for a free interstory height of 2.55 m. The building's self-weight is set to be calculated by the program. Superimposed uniform dead and live loads of 3 and 2 kN/m2 are considered, representing the typical usage of a residential building. A roof live load of 0.5 kN/m2 is applied in the topmost floor. The total dead load for the building is 8.1 kN/m2. Following common building practices in Ecuador and Colombia, the building is assumed to have a one-way ribbed slab that does not contribute to seismic resistance, although it works as a rigid diaphragm. This slab was modeled using a membrane element in ETABS which distributes loads but does not contribute to the stiffness of either the gravity system or the seismic system.
The building plan views are shown in Figures 2 and 3. The building's first three floors are identical, while the fourth has an L-shaped re-entrant corner. In order to make a proper comparison between design codes, the locations of structural elements (i.e., beams and columns) are the same for the three designs. Ribs are considered in the Y-direction of the building in all floors.
Typical structural plan views for first, second, and third floors (mm): (a) NEC-2015 and ASCE 7-10; (b) NSR-10.
Structural plan view for fourth floor (mm): (a) NEC-2015 and ASCE 7; (b) NSR-10.
The building is analyzed following the equivalent lateral force procedure of each code. Because of the building's irregularity, the seismic reduction factor according to NSR-10 and NEC-2015 has to be decreased from its basic value by a factor of 0.9, resulting in R = 6.3 and R = 7.2, respectively. The design base shears are V S ,ASCE = 0.125 W, V S ,NEC = 0.139 W, V S ,NSR = 0.159 W.
Column design for the three codes shows two typical columns sections that are representatives of Column Groups A and B (Figure 3), whose steel reinforcement is shown in Figure 4. Interaction diagrams of the Group A columns are plotted in Figure 5. Column dimensions and steel reinforcement were detailed in accordance with the design requirements of each code. Columns dimensions in Group A are 40 × 65 cm for NEC-2015 and ASCE 7 and 45 × 65 cm for NSR-10. In terms of reinforcement, the steel reinforcement ratio (ρ) for the NEC-2015 columns is significantly higher (ρ = 2.38%) than that for the NSR-10 columns (ρ = 1.25%) and the ASCE 7 columns (ρ = 1.25%). This difference occurs because column design in NEC-2015 is controlled by the SCWB requirement, unlike NSR-10 and ASCE 7, whose designs are respectively controlled by drift requirements and flexural-compression demand. Because of having a higher ρ, NEC-2015 columns have larger moment capacities than their ASCE 7 and NSR-10 counterparts (Figure 5).
Design results for columns (mm): (a) Group A; (b) Group B.
Nominal and design capacity interaction diagrams, with demand results for Group A columns: (a) ASCE 7 Column X; (b) ASCE 7 Column Y; (c) NEC-2015 Column X; (d) NEC-2015 Column Y; (e) NSR-10 Column X; (f) NSR-10 Column Y.
The dimensions of the Group B columns (Figure 4) in NEC-2015 and ASCE 7 are controlled by the same requirement as for the Group A columns, which results in 45 × 45-cm columns with respective steel reinforcement ratios of ρ = 2.29% and ρ = 1.19%. On the other hand, the NSR-10 design is controlled by the drift requirement, which results in 40 × 60-cm columns with ρ = 1.0%, which is assigned to fulfill the minimum requirement of this code. This column has a larger moment capacity in the Y-direction than the NEC-2015 and ASCE 7 columns, although it is larger than the NEC-2015 column by a slight margin due to the high reinforcement ratio of these columns. In contrast to its strength in the Y-direction, the NSR-10 column has the smallest moment capacity in the X-direction.
Stirrup detailing in columns is the same for the three designs (Figure 4), as the NSR-10 and NEC-2015 codes have adopted the SMF detailing requirements of ASCE 7/ACI 318.
Beams designs following ASCE 7 and NEC-2015 produced the same results, both in terms of dimensions and steel reinforcement. This is the result of having similar base shear coefficients; also, any difference is offset by the fact that NEC-2015 does not consider directionality effects. On the other hand, beam dimensions in NSR-10 differ from those in ASCE 7 and NEC-2015 in that, for both building directions, they are 40 × 45 cm as opposed 35 × 45 cm in the X-direction and 30 × 35 cm in the Y-direction (Figures 2 and 3) in NEC-2015 and ASCE 7, respectively. Despite having larger dimensions, NSR-10 beams demand almost the same steel reinforcement as NEC-2015 and ASCE 7 beams; thus, they are provided with the same reinforcing bar configuration (Figure 6).
Beam structural detailing for each design code (mm).
Period calculations resulted in the NSR-10 building having T1 = 0.44 s, T2 = 0.435 s, and T3 = 0.387 s, and the ASCE 7/NEC-2015 buildings having T1 = 0.622 s, T2 = 0.493 s, and T3 = 0.485 s.
Due to differences in drift calculation methodologies, to compare the elastic performance of the three seismic designs, their elastic drifts are calculated following the NSR-10 criteria (i.e., gross sections and C d = R) for the lateral load pattern prescribed in this code. The results for the X-direction (Figure 7a) show that ASCE 7 and NEC-2015 have a maximum drift of 1.4% at the third floor, while the 1% limit of the NSR-10 is attained at the second floor. The drift in the Y-direction shows that the NSR-10 building has significantly smaller drift because of its higher stiffness in this direction (Figure 7b). The ASCE 7/NEC-2015 buildings exhibit the same behavior, with a maximum drift of 2.35% at the second and third floor and 1.1% at the first. These results are as expected because the latter buildings have significantly smaller column and beam sections in that direction. For both directions, ASCE 7 and NEC-2015 have the same values because column and beam dimensions are the same for these designs.
Drift results using elastic spectrum and gross sections: (a) X-direction; (b) Y-direction.
Seismic Performance Analysis
For a comprehensive view of structural behavior, OpenSees (Mazzoni et al. 2006) was used to perform a 2-D pushover analysis for the typical X and Y frames of the buildings, which correspond to the B- and 1-axes in Figure 3. Beams and columns are modeled with concentrated plasticity models, using the modified Ibarra-Medina-Krawinkler (2005) deterioration model with peak oriented hysteresis. The parameters of this model are calculated according to Haselton et al. (2008) based on the structural details of columns and beams. Joint shear is considered using the pinching4 model from Opensees, with the input parameters calculated based on typical code-conforming details following the recommendations of Kim et al. (2009). The column, beam, and joint parameters for structural elements in the B frames of the three buildings are summarized in Table 2. The foundation is modeled as rigid, and gravity loads are calculated based on the expected loads and using the combination 1.05 D + 0.25 L. P-delta effects are included, with gravity loads calculated based on the tributary area of the beams. Rayleigh damping is applied to the structure, with 3% damping in the first and third modes. The 3% value is selected as the midpoint in the range recommended by Deierlein et al. (2010) for reinforced concrete frames.
Modeling parameters for beams (kN, m, rad)
Note: Beams: maximum reinforced section; columns: A type; joints: midspan first floor.
Pushover Analysis
Displacement control is used in the pushover analysis, with a load pattern based on the first mode of vibration. The pushover results for the B and 1 frames are presented in Figure 8, along with the points of first yielding in a beam, first yielding in base columns, target displacement, first ultimate moment in a beam, and first ultimate moment in base columns.
Pushover analysis results: (a) X-direction; (b) Y-direction.
The pushover results for the B frame (Figure 8a) show that the behavior in the elastic range ends at a displacement of 48 mm for the three buildings, corresponding to approximately 0.4% of the building height. The behavior in the nonlinear range shows the differences between the design codes. Because of the higher reinforcement ratios in columns in the X-direction, the NEC-2015 building can withstand a higher maximum base shear before starting to deteriorate. Among the three buildings, the ASCE 7 building has the smaller maximum base shear value, but has hardening and postpeak slopes similar to those of its counterparts, indicating similar deformation capacities.
The results for Frame 1 show that NEC-2015 and ASCE 7 have the same behavior in the elastic range but NEC-2015 has higher capacity in the inelastic range because of its higher column-reinforcing ratios. On the other hand, because of beams and columns with higher values of inertia, the NSR-10 building has a steeper elastic slope than its ASCE 7 and NEC-2015 counterparts. Additionally, the NEC-2015 building reaches a higher base shear at the end of the hardening branch, although at a lower roof displacement than in the ASCE 7 and NEC-2015 buildings. Postpeak behavior exhibits higher deterioration in the NSR-10 building because of the lower column reinforcement ratio of 1%, as opposed to 2.29% in the NEC-2015 building. This led to both buildings having similar strength for a 690-mm roof deformation (5.75% roof drift). The ASCE 7 building has the smallest strength among the buildings.
The buildings’ drift profiles during the pushover analysis are examined at 1%, 3%, and 5% of roof drift (Figure 9). The results for Frame B (Figure 9a) show that the three buildings have similar drift profiles along the building height. The only difference is that the drift in the ASCE 7 building is slightly larger than its counterparts at the first story but is slightly smaller at the top story.
Drift profiles in height for 1%, 3%, and 5% of roof drift: (a) X-direction; (b) Y-direction.
The profiles for Frame 1 show that the ASCE 7 and NSR-10 buildings have similar drift profiles despite their differences in building overstrength. The NEC building has a smaller drift profile at the first story and a slightly larger drift profile at the top story. These differences were accentuated at 1% of roof drift and became smaller at 3% and 5% of roof drift.
The behavior of the frames is further evaluated based on ASCE 41-13 (2013) performance criteria at the life safety level. The target displacement calculated for each frame is shown in Table 3, together with the parameters used for its calculation. The results show that ASCE 7 has the highest target displacement of the three buildings, followed by NEC-2015 and then NSR-10. The maximum rotations for each element type at the target displacement are reported in Table 4, together with the life safety limit required by ASCE 41-13. Column rotations are reported at the base level because the upper-floor columns did not exhibit nonlinear behavior.
Target displacement (mm)
Element maximum rotation at the target displacement level (rad)
This analysis shows that buildings designed according to the three design codes fulfill the life safety limit for columns and joints; however, their beams exceed the allowed deformation level. All rotations in the three buildings are lower than the collapse prevention limit of 0.05 rad. In terms of column performance, similar results are observed for Frame B of the three buildings. In contrast, columns in Frame 1 of the NEC-15 building have 87% of the average rotation of the ASCE 7 and NEC-2015 buildings, suggesting better seismic behavior. Comparison of the NSR-10 and ASCE 7 results indicates that, for this case, higher values of R and C d do not exert an influence on the expected behavior of the building.
Incremental Dynamic Analysis
The seismic performance of the three buildings is further investigated by means of incremental dynamic analyses carried in OpenSees using the Newmark integration method. The far-field suite of FEMA P-695 (2009) is used, with the seismic records scaled to 0.25, 0.5, 0.75, 1.0, 1.5, and 2.0 times the maximum considered earthquake, which is used as the intensity measure (IM) in this analysis. The seismic performance of the buildings is examined at the life safety and the collapse prevention levels defined by ASCE 41. For this purpose, story displacements and interstory drift were recorded for each seismic record applied to Frames B and 1, which are representative of the building's X- and Y-directions. A 1% interstory drift limit was considered for life safety according to ASCE-41 requirements for buildings with heavy partitions. The collapse prevention level was set based on Table 10-8 of ASCE-41, which recommends a 6% interstory drift. The results for each building at each performance level were fitted to a lognormal distribution following the procedure recommended by Baker (2014). The results for the X- and Y-directions are shown in Figures 10 and 11.
Incremental dynamic analyses of the B frames (X-direction): (a) life safety; (b) collapse prevention.
Incremental dynamic analyses of the 1 frames (Y-direction): (a) life safety; (b) collapse prevention.
The life safety results in the X-direction (Figure 10) show that the ASCE 7, NSR-10, and NEC-2015 designs have almost identical performance. This was expected since the three buildings have columns with the same dimensions and, although they have steel reinforcement ratios, these do not exert a big influence at this performance level.
In terms of collapse prevention, the three designed buildings have an approximate 20% probability of exceedance at the MCE level. The performance comparison shows that the ASCE 7 building has a smaller probability of exceedance than its NSR-10 and NEC-2015 counterparts for IM values up to 1.0 times the MCE. When this value is exceeded, the probability of exceedance of the ASCE 7 building is higher than those of the NSR-10 and the NEC-2015 buildings.
The results for the 1 frames (Figure 11) indicate that the Y-direction is the weaker for these buildings, as expected based on the pushover results. The results for life safety show that the NSR-10 building performs better than its counterparts, also as expected, due to the better behavior shown by this building in the elastic range and up to 1% drift (120 mm) in the pushover results. Despite having different steel reinforcement ratios, the NEC-2015 and ASCE 7 buildings have similar performance at this level, suggesting that member dimensioning controls building behavior at this demand level.
Regarding collapse prevention, the three buildings performed similarly, all showing a high value (50%) of collapse probability at the MCE level. At first sight, the similarities between the three buildings at this level may seem to be at odds with the pushover results (Figure 8b), but the deterioration slope shown above 600 mm in this figure is similar for the three buildings. This suggests that neither the larger cross sections of NSR-10 nor the SCWB ratios above 2.0 of NEC-2015 exert an important influence in performance at the level of collapse prevention.
Conclusions
The results discussed in this paper allow several conclusions to be drawn in terms of the code requirements for low-rise RC frames and the resulting designs and their seismic performance.
ASCE 7, NSR-10, and NEC-2015 are little different in their design provisions for RC frames. The main differences lie in their requirements for drift limits and SCWB ratios. ASCE 7 and NEC-2015 share the same interstory drift limit requirement (2%), which is more relaxed than the 1% limit imposed by NSR-10. NEC-2015's SCWB ratio, based on the criteria proposed by Pauley and Priestly (1992), is in most cases significantly higher than 6/5 ratio imposed by ASCE 7 and NSR-10.
Although few, the differences among the three codes have a notable influence on building design and seismic performance, here studied using a four-story building whose seismic performance was evaluated using ASCE 41-13 and incremental dynamic analyses.
The ASCE 7 building design is controlled by the strength requirements for structural members. It has the smallest overstrength among the three designs in the X- and Y-directions. Moreover, as evaluated according to ASCE 41-13, its ductility and the performance of its joints and columns are satisfactory at the life safety level and are similar to those of the NSR-10 and NEC-2015 designs. However, the beams in all three designs fail to fulfill the life safety requirement. The results of the incremental dynamic analyses show that the performance of the ASCE 7 building and its counterparts is similar at the collapse prevention level. Nonetheless, the probability of exceedance of this limit is approximately 50% for the three buildings when the intensity measure is equal to the maximum considered earthquake.
The Colombian NSR-10 requires that drift be checked using gross sections and unreduced seismic forces; also, it must not exceed 1%, which is half the limit allowed by ASCE 7 and NEC-2015. This requirement controls the dimensions of the structural members in NSR-10 design, which requires columns and beams with larger cross sections than those called for in ASCE 7 and NEC-2015. Consequently, the NSR-10 building has the strongest elastic performance and slightly better behavior at the life safety level. However, because of their larger size, NSR-10 columns have reinforcement ratios that are close to the minimum, which leads to a higher rate of deterioration in the nonlinear range. As a result, NSR-10 building performance is similar to ASCE-10 and NEC-2015 performance at the collapse prevention level, as evidenced by the results of the incremental dynamic analyses.
Given that NEC-2015 has a stricter SCWB requirement, the building designed using this code has columns with larger reinforcement ratios than those of the ASCE 7 and NSR-10 buildings. Thus they exhibit higher moment capacity and slightly better behavior according to the pushover analysis. However, the incremental dynamic analyses show that NEC-2015 performance at the collapse prevention level is similar to that of its ASCE 7 and NSR-10 counterparts.
All things considered, the comparisons provided here demonstrate that a few variations in code requirements lead to differences in the structural design and performance of low-rise RC frame buildings. In terms of seismic performance, it has been shown that the NSR-10 1%drift limit offers a slight benefit at the life safety level. It has also been shown that neither this requirement nor the NEC-2015's stricter SCWB requirement improves performance at the collapse prevention level.
In future work, a similar investigation for midrise and high-rise RC frame buildings will be carried out.
Notation
The following notation is used in this paper:
dead load. live load. redundancy. horizontal seismic load. maximum value of the elastic design spectrum. building height. building length perpendicular to the seismic force application direction. accidental torsion. maximum story displacement, assuming there is no increase in accidental torsion. average displacement between external points assuming there is no increase in accidental torsion. interstory drift. design load in and above a given story level. seismic design force acting between the story level and above. height below the story level. design base shear. base shear for equivalent lateral force procedure. gross inertia. reinforcement ratio.
Footnotes
Acknowledgments
The third author wishes to acknowledge the Chilean Government and CONICYT for granting his Ph.D. scholarship in the framework of the program Doctorado Nacional Para Extranjeros.