Rationalizing Response Reduction Factor R for better...

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 EngineeringInternational Institute of Information Technology

Hyderabad - 500 032, INDIANovember 2014

Two Day National Conference on

RECENT RESEARCH ADVANCES IN CIVIL RECENT RESEARCH ADVANCES IN CIVIL RECENT RESEARCH ADVANCES IN CIVIL RECENT RESEARCH ADVANCES IN CIVIL ENGINEERINGENGINEERINGENGINEERINGENGINEERING (RRACE (RRACE (RRACE (RRACE –––– 2014)2014)2014)2014)

7 7 7 7 –––– 8 NOVEMBER, 20148 NOVEMBER, 20148 NOVEMBER, 20148 NOVEMBER, 2014

1

Rationalizing Response Reduction Factor (R) for better Performance of

Reinforced Concrete Framed Buildings

Swajit Singh Goud1 and R Pradeep Kumar

2

1PhD Student, Earthquake Engineering Research Centre, IIIT- Hyderabad, Telangana, Indiaa

2Professor 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

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 multi-

bay 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.




2

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.

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.

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

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 15 m

Depth of Foundation 2 m

Live Load (Typical/ Terrace) 2.5, 1.25 kN/m²

Floor Finish 1 kN/m²

Type of Soil II Medium

I: Importance Factor 1.5

Slab Thickness 0.12 m

Wall Thickness (External/Internal) 0.23, 0.1 m

Concrete Grade M25

Steel Grade Fe415

Fig - 2: Building plan (All Dimensions in mm)

4. DESIGN

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


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structure by keeping same or increased member size in both

cases.

Following 8 cases have been considered in the

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: Building 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 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)

Typical reinforcement detailing of ductile and non

reinforced member is shown in Fig. -3.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.

Fig - 3: Typical ductile and non-ductile detail for Zone III

Table 2: Base Shear values on building and frame 4

Design Zone II III

Normal

R Factor 3 3

Building Base Shear (kN) 736 1196

Frame Base Shear (kN) 203 396

Ductile

R Factor 4 4

Building Base Shear (kN) 552 897

Frame Base Shear (kN) 151 297


RECENT RESEARCH ADVANCES IN CIVIL RECENT RESEARCH ADVANCES IN CIVIL RECENT RESEARCH ADVANCES IN CIVIL RECENT RESEARCH ADVANCES IN CIVIL ENGINEERINGENGINEERINGENGINEERINGENGINEERING (RRACE (RRACE (RRACE (RRACE

7 7 7 7 –––– 8 NOVEMBER, 20148 NOVEMBER, 20148 NOVEMBER, 20148 NOVEMBER, 2014 structure by keeping same or increased member size in both

cases have been considered in the present

Building designed for Gravity and Seismic Loads


of Zone II (Intermediate Moment Resisting Frame)

Building designed for Gravity and Seismic

g designed for Gravity and Seismic

Loads of Zone III (Intermediate Moment Resisting Frame)


Building Designed for Gravity and Seismic

Loads of Zone IV (Special Moment Resisting Frame)

Building designed for Gravity and Seismic

: Building Designed for Gravity and Seismic

Loads of Zone V (Special Moment Resisting Frame)

einforcement detailing of ductile and non ductile

Assuumed R and

base shear value of considered building is shown in Table 2.

shown in Table 3.

ductile detail for Zone III

Base Shear values on building and frame 4

IV V

3 3

1861 2888

671 1098

5 5

1117 1733

408 687

Table -3: Dimensions of Beams and Columns

Mo

del

Column

Dim. (mm) Beam Dimension (mm)

Ex. Int. Plinth I

Floor Floor

I, II 325 x

275

325 x

275

250 x

300

250 x

325

250 x

300

III,

VII

450 x

300

450 x

300

250 x

300

250 x

450

250 x

350

V 475 x

325

475 x

325

250 x

350

250 x

450

250 x

450

VI 475 x

325

475 x

325

250 x

350

300 x

450

300 x

450

VII 575 x

350

575 x

350

250 x

400

300 x

500

300 x

500

VII

I

575 x

350

575 x

350

300 x

400

300 x

550

300 x

550

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

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.

linear Static Analysis was performed using SAP2000

Version 14. Non-linear static analysis

knowledge of material property, stress

plastic hinge property, types of hinges, hinge location,

hinge length and moment-curvature relationship.

SAP defines plastic hinge properties as per FEMA

Hinge property defined in the form of force

curve with five points labeled A, B, C, D, and E

SHOWN IN Fig -4.The value of these points obtained from

moment curvature relationship of element depends on the

type of geometry, material property, longitudinal

reinforcement, shear reinforcement and loads subjected to

particular member.

Fig - 4: (a) A-B-C-D-E Curve for Moment vs. Rotation, (b)

Idealized Monotonic Backbone Curve

For the present study a two dimensional model of each

structure middle frame Fig -2 was modeled in SAP to

perform Non-Linear Static analysis. Equivalent Loads from

third dimension were applied on considered f

pushover analysis 100% dead load and 2

(RRACE (RRACE (RRACE (RRACE –––– 2014)2014)2014)2014)

Dimensions of Beams and Columns

Beam Dimension (mm)

II

Floor

III

Floor

IV

Floor Terr.

250 x

300

250 x

300

250 x

300

250 x

300

250 x

350

250 x

350

250 x

300

250 x

300

250 x

450

250 x

425

250 x

350

250 x

300

300 x

450

250 x

425

250 x

350

250 x

300

300 x

500

300 x

500

250 x

350

250 x

350

300 x

550

300 x

500

250 x

350

250

x300

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

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

linear static analysis requires the

knowledge of material property, stress-strain model,

plastic hinge property, types of hinges, hinge location,

curvature relationship.

SAP defines plastic hinge properties as per FEMA-356 [10].

n the form of force–deformation

curve with five points labeled A, B, C, D, and E AS

The value of these points obtained from

moment curvature relationship of element depends on the

type of geometry, material property, longitudinal

ent, shear reinforcement and loads subjected to

E Curve for Moment vs. Rotation, (b)

Idealized Monotonic Backbone Curve

For the present study a two dimensional model of each

was modeled in SAP to

Linear Static analysis. Equivalent Loads from

third dimension were applied on considered frame. For

pushover analysis 100% dead load and 25% of live loads




4

were considered as initial load. Reinforcement in the

members were defined using Auto hinges with hinge type P-

M3 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].

Hinge length given by Park and Paulay Eqs. (2) Was used.

Locations of hinges (Fig -5) were calculated using Eqs. 3-5

[11].

0.5 (2)

(3)

(4)

(5)

Lp = Length of Plastic Hinge

H = Depth of Section

HBeam = Depth of Beam

Hcolumn = Depth of Column

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 (Vy),

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.

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.

Table 4: Pushover Parameters

Model KE (kN/m) Vy (kN) Vmax (kN) ∆max (m)

I 7583 322.3 585 0.24

II 7583 269.3 539 0.29

III 13595 693.3 1008 0.22

IV 13595 606.9 925 0.26

V 19066 875.9 1318 0.18

VI 20115 514.1 1115 0.29

VII 31059 1584.0 1911 0.19

VIII 34198 867.1 1738 0.24

Fig - 6: Pushover Curve for all models

Fig - 7: Interstorey drift profile




5

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

el

Vd

(kN)

Vmax

(kN)

∆y

(m)

∆d

(m) µ R µ Rs R

I 203 585 0.100 0.22 2.23 1.86 2.88 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.

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.

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.

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.

[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.




6

[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).

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