an evaluation on overstrength factors of reinforced ... · 1 and bülent akbaş 2 1 research...

4th International Conference on Earthquake Engineering and Seismology

October 11-13, 2017 – ANADOLU UNIVERSITY – Eskisehir/Turkey

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An Evaluation on Overstrength Factors of Reinforced Concrete Buildings

Oğuzhan Çetindemir1

and Bülent Akbaş2

1Research Assistant, Civil Eng. Department, Antalya Bilim University, Antalya, Turkey and

PhD Student, Civil Eng. Department, Gebze Technical University, Kocaeli, Turkey 2 Professor, Civil Eng. Department, Gebze Technical University, Kocaeli, Turkey

Email: [email protected]

ABSTRACT:

On August 17, 1999, the moment magnitude (Mw) 7.4 Kocaeli earthquake which was considered to be one of

the most catastrophic events to have ravaged a highly industrialized province since the 1923 Tokyo earthquake,

struck the Marmara Region of northwestern Turkey. Subsequently, on November 12, 1999 the Mw 7.2 Düzce

earthquake hit the same region. Most of the collapsed and damaged structures were typically four-to-eight-

story reinforced concrete buildings (RCBs). Due to the calamitous consequences of these earthquakes, Turkish

Earthquake Code-2007 (TEC-07) and lastly Turkish Earthquake Code-2016 (TEC-16) draft version were

accepted. One of the essential change in TEC-16 is earthquake load reduction factor, Rₐ and one of its

parameters, overstrength factor (Ω) which depends on different factors and the most important of them is

ductility (µ) that is also one of the most crucial keys to design earthquake resistant RCBs. This study mainly

focuses on investigating of Ω values for three different stories (3, 6 and 9) of RCBs. Nonlinear dynamic time

history analyses were performed according to TEC-16 by generating 3D finite element models (FEMs) under

a set of strong ground motions. Using the output of the analyses, Ω values were calculated for each of 3D

FEMs. Finally, the results obtained from the analyses were compared to TEC-16 Ω values and discussed at the

end of the analyses.

KEYWORDS: Overstrength Factor, Nonlinear Dynamic Time History Analyses, Ductility, Reinforced

Concrete Buildings, Strong Ground Motions, Turkish Earthquake Code 2016-Draft Version

1. INTRODUCTION

During major earthquakes in recent years, many reinforced concrete buildings (RCBs) suffered from local

failures and total collapse in Turkey. Therefore, in the last two decades, earthquake codes have undergone

radical changes. In 2016, Turkish Earthquake Code-2016 (TEC-16) draft version was offered. One of the most

important changes in TEC-16 is earthquake load reduction factor, Rₐ and its mentioned parameter overstrength

factor (Ω). Different Ω values are given for every type of building structural systems according to structural

system behavior factors, R and allowed total building height classes, (BHC) in TEC-2016 draft version [1].

Moreover, in TEC-16, some formulas are given in order to calculate Ω. Although all of these given values and

equations below help to calculate Ω values and in reality, those given values for Ω may not be the same for

each building types. Because of different parameters that can also affect ductility, µ Eq. (1) like buildings

material and section properties and etc., every individual building must have its own unique Ω value.

𝜇∆ = ∆𝑚𝑎𝑥/∆𝑦 (1)

𝑅 = 𝑅𝜇 ∗ Ω = 𝑉𝑒/𝑉𝑑 (2)

𝑅𝜇 = 𝑉𝑒/𝑉𝑦, Ω = 𝑉𝑦/𝑉𝑑 (3)

mailto:[email protected]



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𝑅𝜇 ≈ 𝜇∆ (4)

𝑅𝑎 = Ω + (R/I − Ω) (T/𝑇𝐵), 𝑇 ≤ 𝑇𝐵 (5)

𝑅𝑎 = 𝑅/𝐼, 𝑇 > 𝑇𝐵 (6)

𝑅𝜇 is a strength reduction factor, structures with periods bigger than 0.5 sec 𝑅𝜇 can be considered as equal to

structural ductility (𝜇∆) in Eq. (4) and earthquake load reduction factor, Rₐ is shown in Eq. (5) and Eq. (6).

𝑉𝑒 is the maximum seismic demand for elastic response, 𝑉𝑦 is the base shear corresponding to the maximum

inelastic displacement also known as actual strength, 𝑉𝑑 is the design base shear Eq. (3). The relationships

between the force reduction factor (R), structural overstrength (Ω), and the ductility reduction factor (𝑅𝜇) are

shown Fig.1. [7].

Past experience and observation of building behavior following earthquakes has shown that a structure can be

economically designed for a fraction of the estimated elastic seismic design forces, while maintaining the basic

life safety performance objective. This design philosophy implies that structural inelastic behavior (and

damage is expected. This reduction in design seismic force is effected through the use of force reduction factor,

R. The intent of the R factor is to simplify the structural design process such that only linearly elastic static

analysis is needed for most building design.

While some deformation-controlled members, detailed to provide ductility, are expected to deform

inelastically, force-controlled members that are designed to remain elastic would experience a significantly

higher seismic force level than that predicted based on actual design seismic forces. To account for this effect,

the code uses a seismic force amplification factor, Ω, such that the realistic seismic force in these force-

controlled members can be conveniently calculated from the elastic design seismic forces. To control drift or

to check deformation capacity in some deformation-controlled members, a similar approach is also adopted.

Figure 1. The relationships between the force reduction factor, R, structural overstrength, Ω,

and the ductility reduction factor, 𝑅𝜇 [7].

The typical response envelope relating force to deformation is shown in Figure 1 and can be established from

either testing or a pushover analysis. The structure first responds elastically, which is then followed by an

inelastic response as the lateral forces are increased. A series of plastic hinges form throughout the structure,

leading to a yielding mechanism at the strength level 𝑉𝑦.



3

The design method follows a simplified procedure. Based on the fundamental linear elastic period of the

structure, a base shear, 𝑉𝑒 is then reduced by a factor, R, to establish a design seismic force level 𝑉𝑑 beyond

which elastic analysis is not valid. To estimate internal forces that develop in force-controlled members for

capacity design, the corresponding forces at the design seismic force level, 𝑉𝑑 are then amplified by a system

overstrength factor, Ω.

The 3D pushover analysis and nonlinear dynamic time history analysis (NDTHA) are performed in order to

calculate 𝑉𝑦 and 𝑉𝑑. There are various studies in the literature that regarding to calculating not only Ω, but also

𝑅𝑎 and other parameters related to ductility, µ [6, 7, 8, 11]. These studies are mainly focused on nonlinear

static analysis and nonlinear dynamic time history analysis. The time history analysis is the most reliable

analysis method among all the nonlinear analysis methodologies.

However, its easy application comparing to time history analysis, nonlinear static analysis is still being carried

out by many researchers. In this study, pushover capacity curve (Base Shear-Top Displacement) is plotted by

carrying out nonlinear static analysis (NSA) on 3-, 6-, and 9-stories RCBs. In addition to NSA, maximum

displacements and base shear capacities are plotted by using NDTHA.

2. ANALYTICAL STUDY

2.1. Details of 3-,6-, and 9-Story Reinforced Concrete Buildings and Scaled Ground Motions

In this study, three buildings with 3-, 6-, and 9-stories in which seismic loads are fully resisted by reinforced

concrete moment frames, are designed based on TEC-16 and Turkish Building Code (TBC-500) [2]

requirements and 3D finite element models (FEMs) for each building are modelled by using Sap2000 V18 [3].

The concrete used in the structural system has a compressive strength of 25 MPa and a steel yield strength of

420 MPa. The system is designed with 4 spans in the X-direction and 3 spans in the Y-direction. The span

lengths are 5 m and 4 m for X and Y direction respectively. The typical story height is 3 m for each model and

the columns are assumed to be fixed to the ground. Floor plan and elevation of 3-, 6-, and 9-stories RCBs are

shown in Fig. 2.

Figure 2. Floor plan and elevation of 3-, 6-, and 9-stories of RCBs



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Fundamental periods of vibration for the 3-, 6-, and 9-stories of RCBs are found after a modal analysis and

shown in Table 1.

Table 1. Fundamental periods of vibration for the 3- 6-, and 9-stories

The nonlinear dynamic analysis of three RCBs 3D models was carried out using 11 strong ground motions

listed in Table 2 after they were all scaled to the design spectrum corresponding to earthquake ground motion

level with probability of exceeding 10% in 50 years with return period of 475 years which is also defined as

standard design earthquake ground motion in TEC-2016 [1].

Table 2. Selected strong ground motions for nonlinear dynamic analysis

Number Event Year Scale

Factor Station Mag Mechanism Rjb(km) Rrup(km) Vs30(m/s)

Lowest

useable

freq

(Hz)

1 Duzce,

Turkey 1999 3.2129

Lamont

1060 7.14 strike slip 25.78 25.88 782 0.075

2 Duzce,

Turkey 1999 1.7618 Mudurnu 7.14 strike slip 34.3 34.3 535.24 0.1

3 Hector,

Mine 1999 0.7151 Hector 7.13 strike slip 10.35 11.66 726 0.0375

4 Kobe,

Japan 1995 3.8127 Chihaya 6.9 strike slip 49.91 49.91 609 0.1

5 Kobe,

Japan 1995 4.489 OKA 6.9 strike slip 86.93 86.94 609 0.0625

6 Kobe,

Japan 1995 2.8911 TOT 6.9 strike slip 119.64 119.64 609 0.0625

7 Kocaeli,

Turkey 1999 0.7599 Izmit 7.51 strike slip 3.62 7.21 811 0.125

8 Kocaeli,

Turkey 1999 0.7693 Gebze 7.51 strike slip 7.57 10.92 792 0.1

9 Kocaeli,

Turkey 1999 1.1425 Arcelik 7.51 strike slip 10.56 13.49 523 0.0875

10

Helena,

Montana-

01

1935 2.7602 Carroll

College 6 strike slip 2.07 2.86 593.35 0.1625

11 Imperial

Valley-06 1979 0.9314

Cerro

Prieto 6.53 strike slip 15.19 15.19 471.53 0.1125

All buildings were designed for a local soil class ZB in downtown Bostancı, İstanbul where 𝑆𝑠 and 𝑆1 are found

1.007g and 0.274g respectively [5]. By using target spectrum, scale factors for every selected strong ground

motions are found [4] and plotted over the design spectra (target spectrum) Fig. 3.

Story Period (T, sec)

3-Story 0.24071

6-Story 0.50226

9-Story 0.75198



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Figure 3. Horizontal Elastic Design Spectra (Target Spectra) and Scaled Response Spectra for Selected

Strong Ground Motions according to TEC-16 Draft Version

2.2. Analyses Results

In all analyses, the geometric and material nonlinearities are considered. First, the 3D pushover analysis is

carried out for three different models in X and Y directions. The pushover capacity curves are shown below

for 3-,6-, and 9-stories RCBs respectively in Fig. 4. Secondly, NDTHA is carried out and base shear

capacities are calculated for each direction.

Figure 4. Pushover Capacity Curves for 3-, 6-, 9-Story RCBs

The overstrength, which is specified as member or structural capacity, is usually defined using Ω, which can

be defined as the ratio of maximum base shear in actual behavior to first significant yield in structure. By using

Eq. (3) overstrength factors for each FEM are calculated and shown in Table 3 and the differences between

the base shears obtained using NSA and NDTHA are also shown.

Several studies have been carried out in the past pointed out the considerable differences between these

approaches yielding different results [8, 10, 14]. One of the main reasons is being due to the fact that NSA

cannot take into account the effects of energy content, duration and the frequency content of a strong ground

motion. In addition, it’s well known that as the building height increases, the results between two approaches

differs significantly because of the importance of higher-mode effect. Furthermore, the cyclic loading effect

may be the reason for different top displacement values between NSA and NDTHA methods shown in Fig. 4.

0.00

2.00

0.00000 0.20000 0.40000 0.60000 0.80000 1.00000 1.20000 1.40000 1.60000 1.80000 2.00000

Spec

tral

Acc

eler

atio

n (

G),

Sae

T, PerIod (Sec)

Horizontal Elastic Design Spectra (Target Spectra) and Scaled Response Spectra for Strong Ground Motions according to TEC-2016 Draft Version

Earthquake Ground Motion Level-2 TargetSpectrum (EQL-2) for Soil Class (ZB)RSN1148_KOCAELI_ARE000.AT2

RSN1161_KOCAELI_GBZ000.AT2

RSN1165_KOCAELI_IZT180.AT2

RSN164_IMPVALL.H_H-CPE147.AT2

RSN1112_KOBE_OKA000.AT2

RSN1117_KOBE_TOT000.AT2

RSN1102_KOBE_CHY000.AT2

RSN1619_DUZCE_MDR000.AT2

RSN1613_DUZCE_1060-N.AT2

RSN-1 HELENA, MONTANA

0

2000

4000

6000

8000

10000

12000

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

Bas

e Sh

ear,

KN

Top Displacement, m

Pushover Capacity Curves for RCBs

Pushover Curve-Xdirection (3-Storey)Pushover Curve-Ydirection (3-Storey)Pushover Curve-Xdirection (6-Storey)Pushover Curve-Ydirection (6-Storey)



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and Fig. 6. [14]. The building with less displacement in the NDTHA method is subjected to more earthquake

effects than the NSA method [10].

Table 3. Overstrength factors

Analysis Type Parameters 3- Story 6- Story 9- Story

Pushover Analysis

Global Direction X Y X Y X Y

Design base shear,

Vd (kN) 1279.5 1223 2240 2088 3990 3909

Base shear capacity,

Vy (kN) 3215 3137.5 5272.2 5009 9565 9450

Overstrength factor,

Ω = Vy/Vd 2.51 2.56 2.35 2.4 2.4 2.42

Nonlinear Dynamic

Analysis

Design base shear,

Vd (kN) 1905 1235 1890 1984 3054 2.452

Base shear capacity,

Vy (kN) 5850 3778 5686 5987 9524 7237

Overstrength factor,

Ω = Vy/Vd 3.07 3.05 2.94 3.02 3.11 2.95

According to nonlinear dynamic time history analysis results, maximum base shear capacities and maximum

top displacements for all 3D models in the direction of X and Y are given below in Fig. 5 and Fig. 6.

Figure 5a. Maximum Base Shear in the direction of X and Y for 3-story RCB

Figure 5b. Maximum Base Shear in the direction of X and Y for 6-story RCB

Figure 5c. Maximum Base Shear in the direction of X and Y for 9-story RCB

-10000

0

10000

0 10 20 30

Bas

e S

hea

r, K

N

Time, sec

Maximum Base Shear in X direction

(RSN1112_KOBE_OKA000)

-10000

0

10000

0 10 20 30

Bas

e S

hea

r, K

N

Time, sec

Maximum Base Shear in Y direction


-10000

0

10000

0 10 20 30

Bas

e S

hea

r, K

N

Time, sec

Maximum Base Shear in X direction (RSN1161_KOCAEL_GBZ000)

-10000

0

10000

0 10 20 30

Bas

e S

hea

r, K

N

Time, sec


(RSN1161_KOCAEL_GBZ270)

-20000

0

20000

0 10 20 30

Bas

e S

hea

r, K

N

Time, sec

Maximum Base Shear in X direction

(RSN1117_KOBE_TOT000)

-10000

0

10000

0 10 20 30

Bas

e S

hea

r, K

N

Time, sec





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Figure 6a. Maximum Top Displacements in the direction of X and Y for 3-story RCB

Figure 6b. Maximum Top Displacements in the direction of X and Y for 6-story RCB

Figure 6c. Maximum Top Displacements in the direction of X and Y for 9-story RCB

3. CONCLUSIONS

Many reinforced concrete buildings (RCBs) in Turkey suffered from major failure during recent earthquakes

and that lead to significant changes in Turkish Earthquake Codes. Many seismic codes permit a reduction in

design loads, taking advantage of the fact that the structures possess significant reserve strength (that is Ω) and

capacity to dissipate energy (ductility, µ) [13].

-15

-10

-5

0

5

10

15

20

0 10 20 30

To

p D

isp

lace

men

t, c

m

Time, sec

Top Displacement in X direction


Joint 40-X direction (3-storey) -30

-20

-10

0

10

20

30

0 10 20 30

To

p D

isp

lace

men

t, c

m

Time, sec

Top Displacement in Y direction


Joint 84-Y direction (3-storey)

-25

-20

-15

-10

-5

0

5

10

15

0 10 20 30

To

p D

isp

lace

men

t, c

m

Time, sec

Top Displacement in X direction (RSN1161_KOCAEL_GBZ000)

Joint 15-X direction (6-Storey)-80

-60

-40

-20

0

20

40

60

0 10 20 30

To

p D

isp

lace

men

t, c

m

Time, sec

Top Displacement in Y direction (RSN1161_KOCAEL_GBZ270)

Joint 128-Y direction (6-Storey)

-100

-50

0

50

100

0 10 20 30

To

p D

isp

lace

men

t, c

m

Time, sec

Top Displacement in X direction


Joint 155-X direction (9-Storey)-60

-40

-20

0

20

40

60

80

0 10 20 30

To

p D

isp

lace

men

t, c

m

Time, sec

Top Displacement in Y direction


Joint 188-Y direction (9-Storey)



8

In this study, overstrength factors, Ω and its parameters 𝑉𝑦 and 𝑉𝑑 for RCBs are calculated by carrying out

nonlinear static analysis (Pushover analysis) and nonlinear dynamic time history analysis (NDTHA). The main

outcomes of this study and ideas for future studies can be summarized as follows:

(1) Overstrength factor (Ω) in TEC-16 draft code, is given 3 for the buildings which can resist seismic loads

by reinforced concrete moment frames. The results by carrying out pushover analysis which are presented in

Table 3 show that Ω values for 3- and 9-story RCBs are found to be about 2.5. The overstrength factor

decreases when the ductility of the frame decreases and for that reason, 6-story RCB, Ω value was found to be

smaller than 2.5 in both X and Y directions which is lower than the other FEMs.

(2) Nonlinear dynamic time history analysis results demonstrate that Ω values are compatible with the given

values in TEC-16.

(3) For a future study, according to TEC-16, different types of earthquake ground motion levels (DD-1, DD-

2, DD-3, DD-4) and local soil classes (ZA, ZB, ZC, ZD, ZE and ZF) can be used to generate different target

spectrums and then carry out nonlinear dynamic analysis by using earthquake records that are scaled according

to their individual target spectrums. Moreover, this study can be expanded by analyzing different types of

structural systems.

REFERENCES

[1] Turkish Earthquake Code (Draft Version), 2016.

[2] Turkish Building Code, TBC-500, 2000.

[3] CSI (2016). SAP2000: Static and Dynamic Finite Element Analysis of Structures V-18, Computers and

Structures, Inc., Berkeley, California.

[4] Pacific Earthquake Engineering Research (PEER) Center. (2006). PEER Strong Motion Database,

http://peer.berkeley.edu/smcat/.

[5] Turkey Earthquake Hazard Map and Interactive Web Application, https://testtdth.afad.gov.tr/.

[6] Arslan, M. Hakan, and I. Hakkı Erkan. "An Investigation on Overstrength Factor (Ω) of Reinforced

Concrete Buildings in Turkish Earthquake Draft Code (TEC-2016)", World Academy of Science, Engineering

and Technology, International Journal of Civil, Environmental, Structural, Construction and Architectural

Engineering 10.12 (2016): 1421-1425.

[7] Elnashai, A. S., and A. M. Mwafy. "Overstrength and force reduction factors of multistory reinforced‐

concrete buildings", The Structural Design of Tall and Special Buildings 11.5 (2002): 329-351.

[8] Mwafy, A. M., and A. S. Elnashai. "Static pushover versus dynamic collapse analysis of RC

buildings", Engineering structures 23.5 (2001): 407-424.

[9] Salem, Y. S., and K. Sham. "Nonlinear Time-History Analysis of Modular Structures Isolated by Sliding

Plates under Seismic Loads", 15th World Conference on Earthquake Engineering. Lisbon.

[10] Uygun, Gökay, and Zekai Celep. "Betonarme Bir Binanın Deprem Güvenliğinin Deprem Yönetmeliği

2007’deki Doğrusal ve Doğrusal Olmayan Yöntemlerle Karşılaştırmalı İncelenmesi”, Altıncı Ulusal Deprem

Mühendisliği Konferansı, 16-20 Ekim 2007, İstanbul.

[11] Alam, M. Shahria, M. Moni, and S. Tesfamariam. "Seismic overstrength and ductility of concrete

buildings reinforced with superelastic shape memory alloy rebar", Engineering Structures 34 (2012): 8-20.

[12] A Brief Guide to Seismic Design Factors, SEAOC Seismology Committee, 2008.

[13] R. M. Mahmoud and R. Akbari, Seismic behaviour factor, R, for steel Xbraced and knee-braced RC

buildings, Engineering Structures, Elsevier, 25 1505–1513, 2003.

[14] Çağlar, Naci, et al. "TDY2007’ye Göre Tasarlanmış Betonarme Bir Yapının Doğrusal Elastik Olmayan

Analiz Yöntemleri ile İncelenmesi." ISITES2014 Karabük (2014).

http://peer.berkeley.edu/smcat/



https://testtdth.afad.gov.tr/

an evaluation on overstrength factors of reinforced ... · 1 and bülent akbaş 2 1 research...

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