Inelastic Seismic Demands For Reinforced Concrete Frames In Dubai M. H. AlHamaydeh American University of Sharjah, Assistant Professor, Sharjah, UAE J. A. Abdalla American University of Sharjah, Professor, Sharjah, UAE S. H. Abdalla, A. H. Al-Rahmani, A. A. Mostafa and M. T. Albahttiti American University of Sharjah, Graduate/Undergraduate Students ABSTRACT: The presented study correlates the linear to the nonlinear seismic responses for typical buildings in Dubai. Two Reinforced Concrete (RC) framed buildings with four and eight storys were considered representing typical construction in Dubai. The buildings were designed according to the provisions of the 2009 International Building Code (IBC'09) design criteria. Based on recent seismological studies of UAE, the mapped spectral accelerations necessitated a Seismic Design Category (SDC) D. The buildings were modeled and designed using ETABS based on the design response spectrum procedure described in the IBC’09. An ensemble of Near-Field moderate and Far-Field strong ground motion records was used, reflecting the seismological setup of Dubai. The linear and nonlinear dynamic responses to the earthquake records were computed using ETABS and IDARC respectively. Upon proper design and detailing of the buildings exhibited desirable behavior when subjected to the earthquake motions. Keywords: Reinforced Concrete, Inelastic Seismic Response, Non-Linear Earthquake, Moment Resisting Frame 1. INTRODUCTION The inelastic dynamic analysis is a powerful tool for evaluating the structural responses during a given earthquake. Unfortunately, this type of analysis is both complex and expensive. The linear elastic analysis on the other hand, is fairly simple and inexpensive, but lacks the necessary accuracy. To combine the benefits of both methods, one needs to accurately relate the two procedures. The relation should enable realistic prediction of inelastic structural behavior through elastic procedures. This relation can be readily translated into modification factors for different response parameters. Such correction factors will be referred to as "bias factors" throughout this paper. A bias factor is numerically evaluated as the ratio of one nonlinear parameter to the corresponding linear parameter. e.g; the deformation bias factor is equal to the inelastic deformation divided by the elastic deformation. This paper attempts to correlate the linear to the nonlinear seismic responses with acceptable reliability. Two reinforced concrete framed buildings with four and eight floors are considered. The subject buildings are representative of typical construction in Dubai, despite the fact that they are hypothetical. The two buildings were designed and detailed according to the provisions of the 2009 International Building Code (IBC’09). 2. BUILDINGS DESCRIPTION & DESIGN The two buildings considered in this study consist of 4- and 8-stories as shown in figures 1 and 2. The lateral load resisting systems for the buildings is a perimeter Special Moment-Resisting Frame (SMRF). The gravity load resisting system consists of non-moment-resisting frames with 8in. (20cm) thick two-way solid slabs connecting them.

The buildings have a square plan with four 19’-8” (6m) bays in each direction as shown in figure 3. Typical floor-to-floor heights are 10’-6” (3.2m). All structural members and reinforcements were proportioned using the available materials in Dubai; the concrete had a specified compressive strength of fc

’ = 4.6 ksi (32MPa) and the steel rebars had a yield stress fy = 67 ksi (460MPa).

   

Figure 1. 3D view of the two buildings

Figure 2. Elevation view of the two buildings

 

Figure 3. Plan view of a typical floor in the buildings Being office buildings, the Occupancy Category is II and the Importance Factor, I = 1 according to the IBC’09 code. In addition to the dead loads, the RC solid slabs were designed to sustain a uniform live load of 50 psf (2.4kPa) on typical floors and 20 psf (0.95kPa) on the roof. A 40 psf (1.9kPa) equipment load was considered at the penthouse. The buildings were designed using the Response Spectrum requirements in the IBC’09. Both design and detailing followed standard engineering practice. A stiff soil profile was assumed for the sake of the seismic design of the buildings (Site Class: D). Mapped acceleration parameters were adopted from a recent seismic hazard study of Dubai (Sigbjornsson, 2006); Ss = 0.71g and S1 = 0.59g. Site coefficients were taken as per the IBC’09 to be Fa = 1.233 and Fv = 1.5. The design spectral acceleration parameters SDS and SD1 were calculated to be 0.59g and 0.58g, respectively. Consequently, the buildings are assigned a Seismic Design Category (SDC) of D. In accordance to the IBC’09 provisions, the buildings’ periods used for the story-to-story drift calculations were that specified by Method "B", Tb, while the periods used for the strength design were

limited to the upper limit of 1.4 times the period determined by Method "A", Ta. Beams and columns were sized to limit the building drift to 2.5% of the story height for the 4-story building while the drift was limited to 2% of the 8-story building. The designed member sizes and reinforcements are summarized in Tables 1 and 2 for the two buildings. Table 1. Member sizes and reinforcements for the 4-story building

Perimeter Gravity

Stor

y

Beams Columns Beams Columns Size Reinforcement Size Reinforcement Size Reinforcement Size Reinforcement

B (i

n)

H (i

n)

Long

.

Tran

sv.

B (i

n)

H (i

n)

Long

.

Tran

sv.

B (i

n)

H (i

n)

Long

.

Tran

sv.

B (i

n)

H (i

n)

Long

.

Tran

sv.

4 12 22 4 # 6 3#3@ 4” 13 24 4 # 6 3#4@ 3” 8 14 2 #5 2#3@ 5" 10 10 3 # 6 2#3@ 6" 3 12 22 4 # 6 3#3@ 4” 13 24 4 # 6 3#4@ 3” 8 14 2 #5 2#3@ 5" 10 10 3 # 6 2#3@ 6" 2 12 22 4 # 6 3#3@ 4” 13 24 4 # 6 3#4@ 3” 8 14 2 #5 2#3@ 5" 10 10 3 # 6 2#3@ 6" 1 12 22 4 # 6 3#3@ 4” 13 24 4 # 6 3#4@ 3” 8 14 2 #5 2#3@ 5" 10 10 3 # 6 2#3@ 6"

Table 2. Member sizes and reinforcements for the 8-story building

Perimeter Gravity

Stor

y

Beams Columns Beams Columns Size Reinforc. Size Reinforc. Size Reinforc. Size Reinforc.

B (i

n)

H (i

n)

Long

.

Tran

sv.

B (i

n)

H (i

n)

Long

.

Tran

sv.

B (i

n)

H (i

n)

Long

.

Tran

sv.

B (i

n)

H (i

n)

Long

.

Tran

sv.

8 13 26 4 #7 3#3@ 5” 14 20 5 # 9 4#4@ 3” 8 14 2 # 5 2#3@ 3" 11 11 3 # 6 2#3@ 10"7 13 26 4 #7 3#3@ 5” 14 20 5 # 9 4#4@ 3” 8 14 2 # 5 2#3@ 3" 11 11 3 # 6 2#3@ 10"6 13 26 4 #7 3#3@ 5” 14 20 5 # 9 4#4@ 3” 8 14 2 # 5 2#3@ 3" 11 11 3 # 6 2#3@ 10"5 13 26 4 #7 3#3@ 5” 14 20 5 # 9 4#4@ 3” 8 14 2 # 5 2#3@ 3" 11 11 3 # 6 2#3@ 10"4 13 26 5 #7 3#3@ 5” 15 28 5 # 11 4#4@ 3” 8 14 2 # 5 2#3@ 3" 14 14 3 # 7 2#3@ 12"3 13 26 5 #7 3#3@ 5” 15 28 5 # 11 4#4@ 3” 8 14 2 # 5 2#3@ 3" 14 14 3 # 7 2#3@12"2 13 26 5 #7 3#3@ 5” 15 28 5 # 11 4#4@ 3” 8 14 2 # 5 2#3@ 3" 14 14 3 # 7 2#3@12"1 13 26 5 #7 3#3@ 5” 15 28 5 # 11 4#4@ 3” 8 14 2 # 5 2#3@ 3" 14 14 3 # 7 2#3@12"

For analysis purposes, modified section properties were used to account for cracking. For columns, 70% of the gross moment of inertia was used. Since beams usually crack twice as much as columns, 35% of the gross moment of inertia was used. Effective mass factors for the buildings are all above the 90% value required by the IBC’09 in both principal directions. It should be noted here, that although the buildings themselves are hypothetical, the performed design was realistic and measures up to the current state-of-the-practice in structural engineering offices. 3. MODELING ASSUMPTIONS Since both buildings are symmetrical about each of the principal axes there would be no effect of torsion contained in the calculated dynamic response. The assemblage of column and beam elements of the RC framing is interconnected by two-way horizontal floor diaphragm slabs that are assumed to be rigid in their own plane. Second order P-Delta effects are included in the nonlinear analyses as well as the hysteretic strength deterioration and the stiffness degradation. In the linear analyses, an overall damping ratio of 5% of the critical was used for all modes of vibration. Nonlinear analyses, on the other hand, incorporated Rayleigh damping. Proportionality coefficients were chosen to give 5% of the critical damping in the first two elastic modes of vibration. Different damping ratios are associated with higher modes of vibration.

All columns were assumed to be fixed at the base. Each analysis considered combinations of gravity loads and lateral loads which were time-history inertia forces developed from the time-history base acceleration records. The linear analytical models for the buildings were three-dimensional, developed for use with the ETABS computer program (Habibuilah, 2010) based on centerline dimensions. Nonlinear analytical models were developed for the IDARC-2D program (Reinhorn, 2009), which is highly specialized but limited to two-dimensions. In the IDARC models, plastic hinge beam and column elements were used for modeling both structural elements. The inelastic behavior is represented by three-component elements with concentrated plastic hinges and rigid zones at the ends to simulate the increase in stiffness at joints. Beam and column elements were modeled considering flexural and shear deformations, but only column elements consider axial deformations. The axial deformation component is modeled using a linear-elastic spring, while flexural and shear components are modeled using the three-parameter Park hysteretic models. The three-parameter Park hysteretic model incorporates stiffness degradation, strength deterioration, and a trilinear monotonic envelope among other things. 4. GROUND MOTION A suites of synthetic ground motion time-histories consistent with a uniform hazard spectrum for Dubai were developed by others (Sigbjornsson, 2006). The uniform hazard spectrum combined scenarios of moderate close earthquakes and large distant ones for the UAE region. In this study, the same group of 20 records having a 10% probability of exceedance in 50 years was used. All the motions are for stiff soil sites and are scaled to match the target response spectra defined in the mentioned study. 5. RESULTS AND DISCUSSION 5.1. Story Displacement The nonlinear response was found to be noticeably different from the linear elastic response in general. Noticeable differences were also found between the two nonlinear responses of the two buildings. All story displacements have been normalized by the spectral displacement at the fundamental period of vibration according to the IBC’09 design response spectra, Sd(T1). The nonlinear displacements are found to be generally less than the linear displacements resulting in bias factors that are less than unity. This is evident in figures 4 and 5 below which is in agreement with the conclusion reached by Newmark (Veletsos, 1965) that the elastic and inelastic displacements are approximately equal for buildings with relatively long periods.

Figure 4. 4-story building linear and nonlinear story displacement

Figure 5. 8-story building linear and nonlinear story displacement

5.2. Story Drift Angle By definition, the story drift angle is directly influenced by the lateral displacements and thus exhibits similar behavior. Consequently, the above discussion of the displacement results can be extended to the drift angles. The story drift angles were considerably lower than the code limits indicating that minimal damage due to this level of ground shaking is expected.

Figure 6. 4-story building linear and nonlinear story drift angle

Figure 7. 8-story building linear and nonlinear story drift angle

5.3. Story Shear All the reported story shears have been normalized by the weight of the building. It has been found that the story shears are overestimated in the linear elastic analysis, compared to the nonlinear models. This is obvious in the median bias factors of 0.25 and 0.20 for the 4-story and the 8-story buildings

respectively.

Figure 8. 4-story building linear and nonlinear story shear

This behavior is believed to be caused by the yielding or "softening" hysteretic rules used in the nonlinear analysis. This behavior is adopted by building codes to reduce design seismic forces and thus yield lighter and more ductile building designs.

Figure 9. 8-story building linear and nonlinear story shear

5.4. Story Ductility Demand: The ability of a particular story level to deform beyond its yield limit is referred to as the story ductility. In this research, Modal Pushover Analyses (MPA) or pseudo-static analyses were carried out using the IDARC program. Once the story yield deflection capacities were determined, the maximum deformations obtained from the time-history analyses were compared to them. The displacement ductility demand (μ) for a given earthquake record is calculated according to the following equation:

y

m

ΔΔ

=μ (5.1)

Where (Δm) is the maximum displacement caused by an earthquake time-history and (Δy) is the yield deformation. Both evaluated quantities are for each story level.

Figure 10. 4-story building linear and nonlinear story ductility demand

With the denominator constant, the ductility demands are functions of the response to the excitation time-histories. It is noticed that the nonlinear story ductility demands are showing more uniformity along the building height compared to the linear demands for both buildings.

Figure 11. 8-story building linear and nonlinear story ductility demand

5.5. Bias Factors: Tables 3 and 4 summarize the median bias factors for the 4-story and 8-story buildings respectively. Statistical information about the spread of data or variation is given as well as the 16th and 84th percentiles. The values could be used to predict the nonlinear responses of similar building sizes designed by IBC’09 in Dubai with a reasonably high level of confidence. Table 3. 4-story bias factor of building response

Story Disp. / Spectral Disp. Story Drift Angle

Story Median 16th Percentile

84th Percentile λ ζ Median 16th

Percentile 84th

Percentile λ ζ

4 0.893 0.717 1.112 -0.113 0.219 1.008 0.789 1.288 0.008 0.2453 0.851 0.676 1.072 -0.161 0.231 0.755 0.609 0.935 -0.281 0.2152 0.884 0.700 1.117 -0.123 0.234 0.697 0.553 0.879 -0.361 0.2311 1.165 0.918 1.478 0.153 0.238 1.071 0.844 1.359 0.069 0.238 Story Shear / Bldg. Weight Story Ductility Demand

Story Median 16th Percentile

84th Percentile λ ζ Median 16th

Percentile 84th

Percentile λ ζ

4 0.320 0.260 0.394 -1.138 0.208 1.059 0.769 1.459 0.057 0.3203 0.262 0.213 0.323 -1.338 0.207 0.791 0.594 1.054 -0.234 0.2862 0.248 0.200 0.308 -1.393 0.215 0.726 0.560 0.940 -0.321 0.2591 0.279 0.220 0.353 -1.278 0.237 1.117 0.833 1.500 0.111 0.294

Table 4. 8-story bias factor of building response Story Disp. / Spectral Disp. Story Drift Angle

Story Median 16th Percentile

84th Percentile λ ζ Median 16th

Percentile 84th

Percentile λ ζ

8 0.458 0.329 0.636 -0.781 0.329 0.796 0.669 0.949 -0.228 0.1757 0.480 0.340 0.678 -0.734 0.345 0.692 0.578 0.829 -0.368 0.1806 0.477 0.349 0.653 -0.740 0.313 0.670 0.544 0.824 -0.401 0.2075 0.477 0.356 0.639 -0.741 0.293 0.637 0.536 0.757 -0.451 0.1734 0.498 0.366 0.679 -0.696 0.310 0.777 0.645 0.935 -0.253 0.1853 0.476 0.355 0.638 -0.742 0.293 0.783 0.649 0.945 -0.245 0.1882 0.484 0.363 0.647 -0.725 0.289 0.848 0.700 1.028 -0.165 0.1921 0.614 0.454 0.830 -0.488 0.302 1.358 1.096 1.682 0.306 0.214 Story Shear / Bldg. Weight Story Ductility Demand

Story Median 16th Percentile

84th Percentile λ ζ Median 16th

Percentile84th

Percentile λ ζ

8 0.180 0.147 0.221 -1.714 0.204 0.796 0.669 0.949 -0.228 0.1757 0.196 0.153 0.250 -1.632 0.247 0.692 0.578 0.829 -0.368 0.1806 0.228 0.179 0.290 -1.478 0.240 0.670 0.544 0.824 -0.401 0.2075 0.226 0.174 0.293 -1.488 0.262 0.637 0.536 0.757 -0.451 0.1734 0.228 0.176 0.296 -1.477 0.261 0.777 0.645 0.935 -0.253 0.1853 0.237 0.171 0.328 -1.439 0.325 0.783 0.649 0.945 -0.245 0.1882 0.208 0.160 0.271 -1.569 0.262 0.848 0.700 1.028 -0.165 0.1921 0.195 0.157 0.244 -1.633 0.221 1.358 1.096 1.682 0.306 0.214

6. SUMMARY AND CONCLUSIONS Short buildings design is mainly governed by strength rather than drift requirements. On the other hand, mid-rise buildings are usually designed for drift rather than strength requirements. This reduces the ductility demands by increasing the amount of over-strength. This is clear from the 4-story building ductility demands being greater than the 8-story demands. The buildings exhibited desirable behavior when subjected to the earthquake motions. AKCNOWLEDGEMENT Acknowledgement is due to the American University of Sharjah (AUS) for funding this project under grant (FRG09-25). REFERENCES ICC, 2009. International Building Code, 2009 edition, International Code Council, Falls Church, Virginia. Habibuilah, A. (2010). ETABS, Integrated Finite Element Analysis and Design of Structures, User's Manual.

Computers & Structures Inc., Berkeley, California. Reinhorn, A., Roh, H., Sivaselvan, M., Kunnath, S.K., Valles, R.E., Madan, A., Li, C., Lobo, R. and Park, Y.

(2009). IDARC 2D Version 7.0: A Program for the Inelastic Damage Analysis of Buildings. Technical Report MCEER-09-0006, Multidisciplinary Center for Earthquake Engineering Research, State University of New York at Buffalo.

Sigbjornsson, R., and ElNashai, A. S. (2006). Hazzard Assessment of Dubai, United Arab Emirates, for Close and Distant Earthquakes. Journal of Earthquake Engineering 10:5,749-773.

Veletsos, A., Newmark, N., Chelapati, C., "Deformation Spectra for Elastic and Elasto-Plastic Systems Subjected to Ground Shock and Earthquake Motions, Proceedings, Third World Conference on earthquake Engineering, New Zealand, 1965.