Rationalizing Response Reduction Factor R for better Performance
of Reinforced Concrete Framed Buildings
by
Swajit Singh Goud, Pradeep Kumar Ramancharla
in
Two Day National Conference on RECENT RESEARCH ADVANCES IN CIVIL ENGINEERING (RRACE –
2014)
(RRACE)
Report No: IIIT/TR/2014/-1
Centre for Earthquake Engineering
International Institute of Information Technology
Hyderabad - 500 032, INDIA
November 2014
Two Day National Conference on
RECENT RESEARCH ADVANCES IN CIVIL ENGINEERING (RRACE – 2014)
7 – 8 NOVEMBER, 2014
Rationalizing Response Reduction Factor (R) for better Performance of
Reinforced Concrete Framed Buildings
Swajit Singh Goud1 and R Pradeep Kumar2
1
2
PhD Student, Earthquake Engineering Research Centre, IIIT- Hyderabad, Telangana, Indiaa
Professor and Head, Earthquake Engineering Research Centre, IIIT- Hyderabad, Telangana, India
Abstract
Seismic resistant design philosophy incorporates the non linear response of the structure by using appropriate Response
reduction factor (R). The value of R is directly related to the ductility level provided in the structure. Greater the assumed value of
R, grater will be the ductility in the structure. The non linear response of structure will be more than the linear response because
of material non linearity, factor of safety in load combinations, structural redundancy and ductility. Use of higher values of R is
encouraged because of significant reduction in base shear leading to more economic structure. Value of R for reinforced concrete
structure depends on the type of framing system. Proposed IS 1893 draft classifies framing into three categories i.e. 1) Ordinary
Moment Resisting Frame (OMRF), 2) Intermediate Moment Resisting Frame (IMRF), and 3) Special Moment Resisting Frame
(SMRF). In the paper, study is done to compute the value of R, component wise of a G+4 storey building designed for all seismic
zones, considering ductile and non ductile design provisions and the same is compared with the assumed R to check the safety of
the structures. R provided is computed from the obtained pushover curves.
Key Words: Ductile design, Response reduction factor and Pushover analysis.
--------------------------------------------------------------------***---------------------------------------------------------------------1. INTRODUCTION
Seismic design of structures is based on elastic force. The
nonlinear response of structure is not incorporated in design
philosophy but its effect is incorporated by using
appropriate response reduction factor (R). The concept of
response reduction factor is to de-amplify the seismic force
and incorporate nonlinearity with the help of over strength,
redundancy and ductility. Ductile detailing is done in
structure to increase the ductility and to reduce the amount
of damage compared to non-ductile detailed structure. High
ductile designed frame will attract more damage compared
to structure designed for lower ductility, due to large yield
excursion [1]. The design seismic forces are reduced
drastically by using higher values of R and incorporating
higher ductility.
Response reduction factor (R) is defined differently in
different countries for different types of structural systems.
In Indian seismic code, IS1893:2002 [2], value of R for
reinforced concrete structure is specified based on, ordinary
moment resisting frame (OMRF) and special moment
resisting frame (SMRF), and in the latest proposed draft [3]
one additional R value incorporated for reinforced concrete
structure based on Intermediate moment resisting frame
(IMRF). The value of R varies from 3-5 in IS code as per
type of resisting frame, but the existing literature does not
provide information on what basis R values are considered.
In the present study, response reduction factor is computed
for G+4 storey building designed for all seismic zones
considering ductile and non ductile detailing and compared
1
with the assumed values of R provided in seismic code. The
computation of R is done component wise to understand the
effect of each parameter i.e., stiffness, over strength and
ductility. Computation of R is done from pushover curve
which is based on available literature.
2. RESPONSE REDUCTION FACTOR
IS code defines R as Response Reduction factor, ASCE [4]
defines as Response modification coefficient and EC [5]
defines as Behaviour factor. IS-1893 provides R factor for
reinforced concrete structures with three ductility classes;
OMRF, IMRF and SMRF with R value as 3, 4 and 5,
respectively. EC8 provides behavior factor for regular RC
structures with two ductility classes: Medium ductility
(DCM) and High ductility (DCH). Behavior factor includes
over strength factor with a value of 1.3 for multistory multibay frame. Euro code also mentions a reduction in behavior
factor for irregular buildings. ASCE07 provides appropriate
response modification coefficient (R), system over strength
factor (Ωo) and the deflection amplification factor (Cd),
these factors shall be used in determining the base shear,
element design forces and design story drift, respectively.
Response reduction factor consists of majorly four
parameters; strength, redundancy, ductility and damping.
(1)
Where RS, RR, Rµ, Rξ and Rs represents overstrength,
redundancy, ductility and damping factors, respectively.
Two Day National Conference on
RECENT RESEARCH ADVANCES IN CIVIL ENGINEERING (RRACE – 2014)
7 – 8 NOVEMBER, 2014
2.1 Overstrength Factor (RS)
Over-strength factor (RS) defined as the ratio of maximum
base shear to the design base shear (Vd). It is a measure of
over-strength that a structure has beyond the design elastic
force. The value of RS depends on the factor of safety
considered in the materials and load combinations. The
value of over-strength factor varies in the range of 2-3 as
reported in many experimental studies [6].
2.2 Redundancy Factor (RR)
Redundancy factor (RR) is defined as ratio of maximum base
shear (Vm) to yield base shear (Vy). Structure having more
number of vertical members comes in category of redundant
structural system. ASCE 07 suggest redundancy factor RR as
1 conservatively.
trade are 150 and 250 mm, respectively. Mid Landing of
staircase is resting on beam connected to the column.
Table -1: Basic assumptions and structural details
Dimension in X Direction
16.5
m
Dimension in Y Direction
17.6
m
Storey Height
Depth of Foundation
Live Load (Typical/ Terrace)
Floor Finish
Type of Soil
I: Importance Factor
Slab Thickness
2.3 Ductility Factor (Rµ)
In the last decade extensive work has been done to
determine the ductility factor by Newmark and Hall, Nassar
and Newmark, Vidic et al. and Krawinkler and Nassr. In the
present study, a relationship developed by Pristley is used.
As the non linear response of RC structure do not have well
defined yield point, several methods had been proposed to
determine the yield displacement [7].The method shown in
Fig.1 is used in present study.
Fig -1: Determination of Yield displacement and ultimate
displacement.
Wall Thickness (External/Internal)
Concrete Grade
Steel Grade
15
m
2
m
2.5, 1.25
kN/m²
1
kN/m²
II Medium
1.5
0.12
m
0.23, 0.1
m
M25
Fe415
Fig - 2: Building plan (All Dimensions in mm)
4. DESIGN
2.4 Damping Factor (Rε)
Damping factor Rξ is applicable for the structures installed
with additional energy dissipating devices, the damping
factor is assumed to be 1 for buildings without such devices.
3. BUILDING DETAILS
For the current study a 5 story building is considered. Fig.-2
shows center line diagram, beam location, column
orientation. Building consists of four 2BHK flats on each
floor. Building does not have any horizontal or vertical
irregularities, cantilever projections or heavy overhangs. It is
also symmetric about X and Y axes to avoid torsion. All the
walls are supported on beams and every beam intersection is
supported by a column. Dog legged type staircase is
considered with flight and landing width is 1.25 m, riser and
2
All considered models are designed as per IS design codes.
Models I, III, V and VII were designed as per IS 456-2000
(Normal Detailing) [8], and models II, IV, VI and VIII were
designed as per IS 456-2000 and IS 13920-Proposed Draft
(Ductile Detailing) [9].
Increase in R factor lead to significant decrease in base
shear, which ultimately lead to significant amount of
decrease in member dimensions and reinforcement.
Pushover curve of two buildings designed for ductile and
normal detail having different member sizes, shown that
ductility of structure was increased, but initial stiffness and
strength was decreased in ductile detailed building, which
will lead to high amount of damage in ductile detailed
building. Thus, initial stiffness and strength of ductile
detailed building is kept equal to non ductile detailed
Two Day National Conference on
RECENT RESEARCH ADVANCES IN CIVIL ENGINEERING (RRACE – 2014)
7 – 8 NOVEMBER, 2014
structure by keeping same or increased member size in both
cases.
Following 8 cases have been considered in the present
study:
Model I: Building designed for Gravity and Seismic Loads
of Zone II
Model II: Building designed for Gravity and Seismic Loads
of Zone II (Intermediate Moment Resisting Frame)
Model III: Building designed for Gravity and Seismic
Loads of Zone III
Model IV: Buildingg designed for Gravity and Seismic
Loads of Zone III (Intermediate Moment Resisting Frame)
Model V: Building designed for Gravity and Seismic Loads
of Zone IV
Model VI: Building Designed for Gravity and Seismic
Loads of Zone IV (Special Moment Resisting Frame)
Fr
Model VII: Building designed for Gravity and Seismic
Loads of Zone V
Model VIII:: Building Designed for Gravity and Seismic
Loads of Zone V (Special Moment Resisting Frame)
einforcement detailing of ductile and non ductile
Typical reinforcement
reinforced member is shown in Fig. -3.Assuumed
Assuumed R and
base shear value of considered building is shown in Table 2.
Design member sizes of all models are shown in Table 3.
Table -3: Dimensions of Beams and Columns
Column
Beam Dimension (mm)
Mo Dim. (mm)
del
I
II
III
IV
Ex. Int. Plinth
Floor Floor Floor Floor
325 x 325 x 250 x 250 x 250 x 250 x 250 x
I, II
275 275 300 325 300 300 300
III, 450 x 450 x 250 x 250 x 250 x 250 x 250 x
VII 300 300 300 450 350 350 300
475 x 475 x 250 x 250 x 250 x 250 x 250 x
V
325 325 350 450 450 425 350
475 x 475 x 250 x 300 x 300 x 250 x 250 x
VI
325 325 350 450 450 425 350
575 x 575 x 250 x 300 x 300 x 300 x 250 x
VII
350 350 400 500 500 500 350
VII 575 x 575 x 300 x 300 x 300 x 300 x 250 x
I
350 350 400 550 550 500 350
Terr.
250 x
300
250 x
300
250 x
300
250 x
300
250 x
350
250
x300
5. PUSHOVER ANALYSIS
Pushover analysis is Non Linear Static Analysis done to
determine the capacity of structure. With the help of
pushover curve non linear behavior of structure subjected to
lateral loads can be observed. Literature shows that assumed
lateral load pattern applied for the structure to perform
pushover analysis affects the capacity of the structure. Non-
linear Static Analysis was performed using SAP2000
Version 14. Non-linear
linear static analysis requires the
knowledge of material property, stress
stress-strain model,
plastic hinge property, types of hinges, hinge location,
hinge length and moment-curvature
curvature relationship.
SAP defines plastic hinge properties as per FEMA
FEMA-356 [10].
Hinge property defined inn the form of force
force–deformation
curve with five points labeled A, B, C, D, and E AS
SHOWN IN Fig -4.The
The value of these points obtained from
moment curvature relationship of element depends on the
type of geometry, material property, longitudinal
reinforcement,
ent, shear reinforcement and loads subjected to
particular member.
Fig - 3: Typical ductile and non-ductile
ductile detail for Zone III
Table 2: Base Shear values on building and frame 4
Design Zone
II III IV
V
R Factor
3
3
3
3
Normal Building Base Shear (kN) 736 1196 1861 2888
Frame Base Shear (kN)
203 396 671 1098
R Factor
4
4
5
5
Fig - 4: (a) A-B-C-D-E
E Curve for Moment vs. Rotation, (b)
Idealized Monotonic Backbone Curve
Ductile Building Base Shear (kN) 552 897 1117 1733
Frame Base Shear (kN)
3
151 297
408
687
For the present study a two dimensional model of each
structure middle frame Fig -2 was modeled in SAP to
perform Non-Linear
Linear Static analysis. Equivalent Loads from
third dimension were applied on considered fframe. For
pushover analysis 100% dead load and 225% of live loads
Two Day National Conference on
RECENT RESEARCH ADVANCES IN CIVIL ENGINEERING (RRACE – 2014)
7 – 8 NOVEMBER, 2014
were considered as initial load. Reinforcement in the
members were defined using Auto hinges with hinge type PM3 and M3 hinges were assigned to columns and beams,
respectively. Shear hinge is assigned to beam and columns
of brittle type, the calculation of shear calamity can be
referred from [11].
Less number of hinges was formed in Model V and VII,
which means capacity of the structure was not fully utilized.
More number of hinges were formed in ductile detailed
building, which means capacity of the structure was utilized
more efficiently.
Hinge length given by Park and Paulay Eqs. (2) Was used.
Locations of hinges (Fig -5) were calculated using Eqs. 3-5
[11].
Table 4: Pushover Parameters
Model KE (kN/m) Vy (kN)
I
7583
322.3
II
7583
269.3
III
13595
693.3
IV
13595
606.9
V
19066
875.9
VI
20115
514.1
VII
31059
1584.0
VIII
34198
867.1
0.5 (3)
(2)
(4)
(5)
Lp = Length of Plastic Hinge
H = Depth of Section
HBeam = Depth of Beam
Hcolumn = Depth of Column
Vmax (kN)
585
539
1008
925
1318
1115
1911
1738
Fig - 5: Hinge location at column and beam
Mander model for confined concrete and Park model for
steel stress–strain were considered. The points B and C on
Fig -4 are related to yield and ultimate curvatures values.
Fig -6 shows the obtained pushover curves for all models
are shown in. Fig -6 shows that model I and II and mode III
to IV has same stiffness because of same member
dimensions. Whereas models V and VI and model VII and
VIII has different stiffness because ductile detailed members
of zone IV and V had larger member dimensions. The
strength of ductile detailed member is less than non ductile
detailed members because of reduction in longitudinal
reinforcement. The increase in ductility in ductile detailed
structure is because of increase in shear reinforcement
comparatively. Table 3 shows the pushover parameters in
terms of elastic stiffness (KE), Yield base shear (V y),
maximum base shear (Vmax) and maximum displacement
(∆max).
Hinge Mechanism in some models formed properly, where
as in some structures hinges were not formed in many
members, proper hinge mechanism will increase the
capacity of structure and it can be achieved by altering
reinforcement and member dimensions, which leads to
performance based design in place of Limit state design.
4
Fig - 6: Pushover Curve for all models
Fig - 7: Interstorey drift profile
∆max (m)
0.24
0.29
0.22
0.26
0.18
0.29
0.19
0.24
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Ductility factors for ductile detailed structure were higher
than that of non ductile detailed structure. The ductility
factors for both cases were nearly same irrespective to the
severity in the higher seismic zones. The overstrength factor
ranges from 3.57 to 1.74, the higher value of overstrength
factor is because of limitation of minimum member
dimensions in the structure irrespective to the design forces.
7. CONCLUSIONS
Design of members by changing member dimensions, due to
increase in R factor leads to significant decrease in
performance of structure. Thus member dimensions should
be kept same as obtained in non ductile detailing.
Response reduction factor provided in IS 1893 should be
provided with the corresponding ductility and overstrength
factor as provides in other seismic code for checking the
safety of structure based on performance based design.
Fig - 8: Displacement profile
Fig.-7 and 8 shows maximum interstorey drift and
displacement profile of the structures, respectively, obtained
from pushover analysis. The drift and displacement profile
varies depending upon the relative stiffness and ductility of
members between two floors.
6. RESPONSE REDUCTION FACTOR
CALCULATION
The value of response reduction factor, R depends on the
performance limit considered for the structure. The
performance limit corresponding to R is not provided in IS
1893.Performance limits are defined in differently in PBSD
guidelines, like ATC-40 [12] and FEMA-356 .There is
slight variation in definitions of performance limits of these
codes.
Table 5: Response reduction factor computation
Mod Vd
Vmax
∆y
∆d
µ Rµ
Rs
el (kN) (kN) (m) (m)
I
203
585 0.100 0.22 2.23 1.86 2.88
First the non ductile design is done followed by ductile
design to fix the member sizes (stiffness), by providing
overstrength factor member dimensions for ductile design
can be fixed directly.
REFERENCES
[1] Lu, Y., Hao, H., & Carydis, P. G. (2001). “Seismic
performance of RC frames designed for three different
ductility levels” Engineering Structures, 23, 537-547.
R
5.4
II
151
539
0.092 0.23 2.47 1.99
3.57
7.1
III
396
1008
0.098 0.21 2.19 1.84
2.55
4.7
IV
297
925
0.089 0.26 2.90 2.19
3.12
6.8
V
671
1318
0.089 0.22 2.42 1.96
1.97
3.8
VI
408
1115
0.072 0.23 3.25 2.34
2.73
6.4
VII
1098
1911
0.081 0.18 2.19 1.84
1.74
3.2
VIII
687
1738
0.068 0.20 2.95 2.21
2.53
5.6
The performance limit can be considered at global level
(Interstorey drift) and elemental level (Plastic rotation). The
performance limit for obtaining R is mainly used to
determine ductility. In the present study the performance
limit is considered as the point corresponds to 2%
interstorey drift or 15% strength drop from maximum base
shear, whichever is less.
5
Based on the assumed performance limits the IS-1893
recommendation of R is on conservative side. It is more
safe for Zone II and III, whereas for zone IV and V the
computed R is close to the assumed one (Table 5).
Performance limit corresponding to the R should be
provided in IS-1893 as ductility factor is dependent on the
performance limit which ultimately changes the calculated
R.
[2] Indian Standard Criteria for Earthquake Resistant Design
of Structures Part I: General Provisions and Buildings, IS
1893:2002. New Delhi: Bureau of Indian Standards.
[3] Jain, S. K., & Murty, C. R. Proposed Draft Provisions
and Commentary on Indian Seismic Code IS 1893 (Part-1).
IIITK-GSDMA Project of Builiding Codes.
[4] ASCE 7-05, Minimum design loads for buildings and
other structures. Reston (USA): American Society of Civil
Engineers.
[5] CEN Eurocode 8, Design provisions for earthquake
resistance of structures (European Prestandard ENV 1998).
Brussels (Belgium).
[6] Charney, F. A., & Bertero, V. V. (1982). “An evaluation
of the design and analytical seismic response of a seven
storey reinforced concrete frame wall structure” Berkeley:
Earthquake Engineering Research Institute.
Two Day National Conference on
RECENT RESEARCH ADVANCES IN CIVIL ENGINEERING (RRACE – 2014)
7 – 8 NOVEMBER, 2014
[7] Park, R. (1989). “Evaluation of ductility of structuresand
strucutral assemblages from laboratory testing.” Bulletin of
thr New Zealand National Society for Earthquake
Engineering , 22 (3), 155-166.
[8] Indian Standard Code of Practice for Plain and
Reinforced Concrete,IS 456: 2000. New Delhi: Bureau of
Indian Standards.
[9] Jain, S. K., & Murty, C. R. Proposed Draft Provisions
and Commentary on Ductile Detailing of RC Structures
Subjected to Seismic Forces. IIITK-GSDMA Project of
Builiding Codes.
[10] Prestandard and Commentary for Seismic
Rehabilitation of Buildings, FEMA 356-2000. Washington
D.C: Federal Emergency Management Agency (FEMA).
[11] Mehmet, I., & Hayri, B. O. (2006). “Effects of plastic
hinge properties in nonlinear analysis of reinforced concrete
buildings.” Engineering Structures , 28, pp. 1494-1502.
[12] Seismic Evaluation and Retrofit of Concrete Buildings,
ATC 40-1996. California: Applied Technology Council
(ATC).
6