Evaluation response reduction factor of RC framed staging ... · Evaluation response reduction...

INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING

Volume 4, No 3, 2014

© Copyright by the authors - Licensee IPA- Under Creative Commons license 3.0

Research article ISSN 0976 – 4399

Received on October, 2013 Published on February 2014 215

Evaluation response reduction factor of RC framed staging elevated water

tank using static pushover analysis Tejash Patel1, Jignesh Amin2, Bhavin Patel3

1- Post Graduate Student, SVIT, VASAD, Gujarat.

2- Associate Professor, Civil engineering department SVIT, VASAD, Gujarat.

3- Senior Associate Engineer , VMS Consultancy, Ahmadabad, Gujarat

[email protected]

doi: 10.6088/ijcser.201304010022

ABSTRACT

The basic principal of earthquake resistance design of structures is that the structure should

not collapse but damage to the structural elements is permitted. Since a structure is allowed to

be damaged in case of severe shaking, the structure should be designed for seismic forces

much less than what is expected under strong shaking, if the structures were to remain

linearly elastic. Response reduction factor is the factor by which the actual base shear force

should be reduced, to obtain the design lateral force. The response reduction factor (R) is

depends on Over strength (Rs), Ductility (Rµ), Redundancy (RR). In the present study efforts

are made to evaluate the response reduction factors of RC framed staging elevated water

tanks having staging height of 12 m but having varying capacities. The effects of seismic

zone and fundamental time period of water tank on the Response reduction factor are also

discussed. Displacement controlled nonlinear pushover analysis is used to evaluated the base

shear capacity and ductility of tanks. It is observed that value of R for elevated water tank is

significantly affected by the seismic zone, time period and capacity of tanks.

Key words: Response reduction factor, seismic design, static nonlinear pushover analysis,

ductility.

1. Introduction

Severe damages were observed in buildings, public utility structures like water tanks and

hospitals during 26th January 2001 Bhuj earthquake. Earthquake can induce large horizontal

and overturning forces in elevated water tanks and are quite vulnerable to damage in

earthquakes due to their basic configuration involving large mass concentrated at top with

relatively slender supporting system. The basic principal of designing structures for strong

ground motion is that the structure should not collapse but damage to the structural elements

is permitted. Since a structure is allowed to be damaged in case of severe shaking, the

structure should be designed for seismic forces much less than what is expected under strong

shaking, if the structures were to remain linearly elastic. Response reduction factor is the

factor by which the actual base shear force should be reduced, to obtain the design lateral

force. Base shear force is the force that would be generated if the structure were to remain

elastic during its response to the design basic earthquake (DBE) shaking. Ozhendekci et al.

(2006) evaluated the seismic response modification factor for eccentrically braced frames.

Conclusion was made that one constant R-value cannot reflect the expected inelastic behavior

of all building which have the same lateral load resisting system. Pore et al. (2006) described

effect of response reduction factor in performance based seismic design of RC building for

India. The author concluded that response reduction factor evaluated in accordance with the

Evaluation response reduction factor of RC framed staging elevated water tank using static pushover

analysis

Tejash Patelet al

International Journal of Civil and Structural Engineering

Volume 4 Issue 3 2014 216

available literature, are much lower than the factor specified by the IS 1893. Bhavin et al.

(2010) formulated response reduction factor RC framed staging of elevated storage reservoir

according to procedure suggested by ATC-19 [1]. The values of response reduction factor of

RC elevated water tank are given in IS 1893 (Part-II) 2002, which is arrived at empirically

based on engineering judgment. The values of response reduction factor of elevated water

tank adopted by difference codes/standards are summaries in Table 1.

Table 1: “R” factor as per international standards for elevated water tank

Codes/standards “R” factor

IBC 2000/ FEMA 368 1.5 to 3.0

ACI 350.3 2.0 to 4.75

IS:1893-2002(Part -2) RCC frame support (draft code) 1.8 (OMRF)

2.5 (SMRF)

One constant R-value for elevated water tank cannot reflect the expected inelastic behavior of

all elevated water tanks located in different seismic zone and having different capacities. In

the present study efforts are made to evaluate the response reduction factor of five existing

RC framed staging elevated water tanks having staging height of 12 m but having varying

capacities. The effects of seismic zone and fundamental time period of water tank on the

Response reduction factor are also discussed. Displacement controlled nonlinear pushover

analysis is used to evaluated the base shear capacity and ductility of tanks.

2. Concept of response reduction factor

The concept of R factor is based on the observations that well detailed seismic framing

systems can sustain large inelastic deformations without collapse and have excess of lateral

strength over design strength. Response reduction (R) factors are essential seismic design

tools, which are typically used to describe the level of inelasticity expected in lateral

structural systems during an earthquake. The response reduction factor (R) is depends on

Over strength (Rs), Ductility (Rµ), Redundancy (RR). According to ATC-19, it is described

as

R = Rs * RR * Rµ.

Figure 1: Conception of response reduction factor


analysis

Tejash Patelet al



Over strength factor (Rs) accounts for the yielding of a structure at load higher than the

design load due to various Partial safety factors, strain hardening, oversized members,

confinement of concrete. Non-structural elements also contribute to the over strength.

Ductility factor (Rµ) is a ratio of ultimate displacement or code specified permissible

displacement to the yield displacement. Higher ductility implies that the structure can

withstand stronger shaking without collapse. Redundancy factor (RR) depends on the number

of vertical framing participate in seismic resistance. Yielding at one location in the structure

does not imply yielding of the structure as a whole. Hence the load distribution, due to

redundancy of the structure, provides additional safety margin. The Over strength factor,

Ductility factor and Redundancy factor can be workout on the basis of generalized pushover

curve shown in figure 1.

3. Description of water tank

In present study five RC elevated water tanks having a capacity of 20m3, 30m3, 50m3, 60m3,

and 70m3 are considered. For all the tanks, the height of staging is 12m and staging comprise

of 4 columns as shown in Figure 2. The brief description of the elevated water tanks are given

in Table.2.

Figure 2: Staging configuration of water tank

Table 2: Description of water tank

Capacity 20m3 30m3 40m3 50m3 70m3

Location Maheshana

(Gujarat)

Ahmadabad

(Gujarat)

Ahmadabad

(Gujarat)

Gandhinagar

(Gujarat)

Kalol

(Gujarat)

Seismic Zone III III III III III

Container

length and

width

3.8 3.8 4.5 5.69 6.0

Height of

container(m) 2.45 2.85 2.75 2.80 2.80

Container

Wall

thickness(m

m)

150 150 150 150 150


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Top slab

container

thickness(m

m)

120 125 125 120 125

Bottom slab

container

thickness(m

m)

200 200 200 200 200

Height of

staging(m) 12 12 12 12 12

Tie beam

levels

Plinth + @

4.0 m c/c

Plinth + @

4.0 m c/c

Plinth + @

4.0 m c/c

Plinth + @

4.0 m c/c

Plinth +

@ 4.0 m

c/c

Column

size(mm) 350x350 350x350 350x350 350x350 400x400

No. of bar

and dia. Of

bar in

column

4-20 # 4-25 # 6-20 # 8-16 # 8 -20#

Plinth

beam(mm) 230x450 230x450 230x450 230x450 230x450

Size of

Braces

beam(mm)

230x450 230x450 230x450 230x450 230x450

Bottom slab

beam(mm) 300x500 300x500 250x600 300x700 300x700

No of

column 4 4 4 4 4

Length of

column(m) 4 4 4 4 4

Soil type Medium Medium Medium Medium Medium

4. Structural modeling and analysis procedure

ETABS v.9.5 software is used to perform the non linear static pushover analysis. The RC

beams and columns are modeled as 3-D frame elements with centerline dimension. Slabs are

modeled as membrane elements and are assumed to behave as rigid diaphragms. Column

foundations are assumed to be fixed. Damping ratio of 5 percent is assumed for all natural

modes. Flexure moment (M3), axial biaxial moment (P-M2-M3) and axial compressive shear

force (V) hinges are assigned at the face of beam, column, and bracing respectively using the

static pushover analysis.

ATC-40 has described the modeling procedure, acceptance criteria and analysis procedures

for nonlinear static pushover analysis. The force-deformation criterion for hinges used in

pushover analysis is shown in figure 3.


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Figure 3: Force-deformation criterion for hinges used in pushover analysis

In figure 3, five points labeled A, B, C, D, and E are used to define the force deflection

behavior of the hinge and three points labeled IO, LS and CP are used to define the

acceptance criteria for the hinge. IO, LS and CP stand for Immediate Occupancy, Life Safety

and Collapse Prevention respectively. The values assigned to each of these points vary

depending on the type of member as well as many other parameters defined in the ATC-40 .

In order to achieve the objective, the following procedure was adopted

1. Developing a three dimensional model of existing RC frame.

2. Application of gravity loads, live loads, water load, etc.

3. Application of static lateral load induced due to earthquake, at CG of container

4. Developing M-θ & V- δ relationship for RC Trestle.

5. Pushing the structure using the load patterns of static lateral loads, to displacements

larger than those associated with target displacement using static pushover analysis

6. Developing pushover curve and estimating the force and deformations in each

element at the level of displacement corresponding to target displacement

7. The element force and deformation demands of last step are then compared with the

element capacities.

Moment-rotation (M- θ) and Axial load-Bending Moment (P-M) relationships for flexural

and compression members have been developed using Kaustub Dasgupta’s (2000) software.

After assigning hinge properties to the structure, the static pushover cases were defined.

Typically, the gravity loads were applied first and then subsequent lateral static pushover load

cases were specified to start from the final conditions of the gravity pushover. In the gravity

case, the structure was loaded with the dead load and 25% of the live load. The application of

gravity loads was force-controlled whereas the application of lateral loads was displacement-

controlled. The first mode response of the structure was assigned as the load pattern for the

lateral push applied to the structure. The procedure involves applying horizontal loads, in a

prescribed pattern, to a model of the structure, incrementally; i.e., “pushing” the structure;

and plotting the total applied shear force and associated lateral displacement at each

increment. The nonlinear static procedure requires prior estimation of target displacement.

The target displacement serves as an estimate of the maximum displacement of the selected

point (node) in the subject structure during the design earthquake.

A

LS IO

B

CP E D

C

Displacement

Fo

rce


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The node associated at CG of container is the target point/node selected for comparison with

target displacement. The maximum limit for the roof displacement is specified as 0.004H,

where H is the height of the structure. The base shear and roof displacements are recorded at

every step, to obtain the pushover curve.

5. Results and discussion

5.1 Pushover curve of 20m3 water tank

For 20m3 water tank the height from the base to CG of container is 14.71m and hence target

displacement is set to 58.84 mm. The 3-D modeling of 20m3 water tank in ETAB is shown in

Fig.4. The displacement is applied step-by-step to the structure in an incremental manner.

The base shear and roof displacement is recorded at every step. Due to plan symmetry of

structure, the pushover analysis is carried out in X direction only. Hence, earthquake loads on

tank in full condition is given in X-direction only. The push over curve for 20m3, 30m3, 40m3,

50m3 and 70m3 water tanks is shown in Fig.5 to 9 for seismic zone-III respectively. From

result it is observed that the first hinge is formed at 8th step. The maximum number of hinges

formed in elastic range only. Hence, it indicates that there is a need of retrofitting for

members. The calculation for evaluation of response reduction factor for 20m3 water tank in

seismic zone-III is shown below.

Figure 4: 3D modeling of 20m3 tank Figure 5: Pushover curve for 20m3

Figure 6: Pushover curve for 30m3 Figure 7: Pushover curve for 40m3


analysis

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Figure 8: Pushover curve for 50m3 Figure 9: Pushover curve for 70m3

5.1.1 Estimation of strength factor

Maximum Base Shear (from pushover curve) Vo= 240 kN

Design Base shear (as per EQ calculation) Vd = 89.7287 kN

Using equation for strength factor, given in ATC – 19 Rs = Vo / Vd = 240 / 89.729

Rs = 2.68

5.1.2 Estimation of ductility factor

Maximum drift capacity ∆m = 58.84 mm (0.004 H)

Yield drift ∆y = 24mm (from pushover curve)

Using equation for displacement ductility ratio, given in ATC-19 [1]

µ = ∆m / ∆y = 58.84 / 24 =2.46

Using equation for ductility factor, derived by Miranda and Bertero

R µ = {(µ - 1 / Φ) + 1}

Φ for medium soil = 1+{1 /(12T -µT)}–{(2 / 5T)*e-2(ln(T) – 0.2)^2}

T = 0.7231seconds (From ETABS model)

Φ = 0.8263

Rµ = 2.82

5.1.3 Estimation of redundancy factor

The value of redundancy factor as suggested in ATC-19 is summaries in Table 3.

Table 3: Redundancy factor (RR) from ATC-19

Lines of vertical seismic framing

Drift redundancy factor

2 0.71

3 0.86

4 1

RR = 0.71


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5.1.4 Estimation of response reduction factor R:

R= RS x Rµ x RR = 2.68 x 2.82 x 0.71

R=5.36 Table 4 shows the value of R-factor and its key component for 20m3 water tank for different

seismic zones.

Table 4: “R” factor of 20m3 Capacity ESR

Zone II III IV V

Time period 0.8932 0.7231 0.5837 0.5049

Ductility ratio (µ) 2.22 2.46 2.57 2.80

Ductility factor (Rµ) 2.63 2.82 2.86 3.12

Redundancy factor (RR) 0.71 0.71 0.71 0.71

Over strength factor (RS) 3.75 2.68 1.783 1.188

Response reduction factor 7.01 5.36 3.62 2.63

Table 5 to 8 shows the time period, ductility factor, and response reduction factor for 30m3,

40m3, 50m3 and 70m3 capacity water tank in different seismic zones. The response reduction

factor and ductility factor is considerably affected by the seismic zone, capacity of container

and fundamental time period of water tanks. The effects of the time period on response

reduction factor and ductility factor of water tanks are shown in Fig. 10 and 11 respectively.

As the time period of the water tank increases, the response reduction factor is also increases.

Fig. 12 and 13 shows the variation of response reduction factor and ductility factor with

seismic zone. Response reduction factor reduces as the seismic zone increases and it

increases as the fundamental time period increases. It is observed that ductility factor (Rµ)

increases as the seismic zone increases, whereas over strength factor (Rs) reduces as the

seismic zone increase. For all considered water tank the values of R-factor reduces as the

seismic zone increases. It is also observed that R-factor varies from 2.63 to 4.0 for tank in full

condition in seismic zone-V.


Zone II III IV V

Time period 0.9104 0.7810 0.6319 0.5602

Ductility ratio (µ) 2 2.20 2.456 2.69



Over strength factor (RS) 4 2.95 2.02 1.71



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Table 6:“R” factor of 40m3 Capacity ESR

Zone II III IV V

Time period 0.9658 0.7638 0.6934 0.5413







Zone II III IV V

Time period 1.2106 0.9305 0.7712 0.6735







Zone II III IV V

Time period 1.1426 0.8909 0.7123 0.6038




Over strength factor(RS) 3.92 3.20 2.54 1.92



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Figure 10: Variation of “R” factor with Time period

Figure 11 Variation of “Rµ” factor with Time period

Figure 12: Variation of “R” factor with Seismic zone


analysis

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Figure 13: Variation of “Rµ” factor with Seismic zone

5.2 Conclusions

In this study the response reduction factor (R) of exiting RC framed elevated water tank

having a 12m height of staging but different capacities are evaluated.

The significant outcomes of works are summarized as follows:

1. The response reduction factor is considerably affected by the seismic zone and

fundamental time period of water tanks. It reduces as the seismic zone increases and

increases as the fundamental time period increases.

2. To ensure the consistent level of damaged, values of response reduction factor should

be based on both fundamental period of the staging and type of soil.

3. The values of response reduction factor for a given RC framing system should vary

between seismic zones. Also the reinforcement detailing requirements should vary

with seismic zone.

4. Estimation of response reduction factor with exact analysis will help in an economical

design.

5. It is observed that response reduction varies from 2.63 to 4 for tank in full condition

in seismic zone V.

6. References

1. ATC -19, (1995), Structural Response Modification Factors ATC-19 Report, Applied

Technology Council Redwood City California.

2. ATC 40, (1996), Seismic Evaluation and Retrofit of Concrete Buildings, Volume

ATC-40 Report, Applied Technology Council.


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3. Bhavin Patel and Dhara shah, (2010), Formulation of Response Reduction Factor for

RCC Framed Staging of Elevated Water Tank, World Congress on Engineering ,

London ,U.K.

4. Chopra A.K., (2001), Dynamics of Structures–Theory and Applications to Earthquake

Engineering, Pearson Education, Singapore, private limited.

5. Dasgupta. P. (2000), Effect of Confinement on Strength and Ductility of Large RC

Hollow Sections”. M.Tech Thesis, I.I.T. – Kanpur.

6. FEMA 273, (1997), NEHRP Guidelines for The Seismic Rehabilitation of Buildings,

Developed by The Building Seismic Safety Council for The Federal Emergency

Management Agency, Report NO. FEMA 273, Washington, D.C.

7. I.S 456 2000, Indian Standard Code of Practice for Plain and Reinforced Concrete,

Bureau of Indian Standards, New Delhi.

8. I.S 1893 2000, Indian Standard Criteria for Earthquake Resistant Design of Structures

Part-1 General Provisions and Buildings, Bureau of Indian Standards, New Delhi.

9. Ozhendekci Devrim, Ozhendekci Nuri and Zafer Ozturk, (2006), The Seismic

Response Modification Factor For Eccentrically Braced Frames, 1st ECEES, Geneva.

10. Park R. and Paulay, T., Reinforced Concrete Structure, John Wiley and Sons, Inc.,605

Third Avenue, New York, 1975.

11. Paulay, T, and Priestley M.J.N, (1992), Seismic Design of Reinforced Concrete and

Masonry Buildings, john Wiley & Sons, Inc., USA.

12. Pore S.M., Bhunia D., Prakash V., Pandey A.D. and Prajapati G.I., (2006),

Evaluation of Response Reduction Factor for RC Building in Performance Based

Seismic Design, 2nd International Congress on Computational Mechanics and

Simulation (ICCMS-06), Organized by Indian Institute of Technology Guwahati and

Indian Association for Computational Mechanics (IndACM), December 8-10,2006,

Indian Institute of Technology Guwahati, GUWAHATI, INDIA.

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