LTR RVW

EVALUATION OF RESPONSE REDUCTION FACTOR USING NONLINEAR STATIC ANALYSIS

LITERATURE REVIEW

Submitted by

L. Venkata Ramana Reddy

MT14STR012

Structural Engineering

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1.1 General

Jain and Navin (1995) evaluated seismic overstrength of multistory reinforced concrete frames by nonlinear pseudostatic analysis on four-bay, three, six, and nine story frames designed for seismic zones I to V as per IS 1893:1984. The member sizes in the exterior and the interior frames were kept the same in a given zone which led to the same lateral stiffness and hence the exterior and the interior frames were designed for the same lateral force. Pseudostatic nonlinear analysis was done for interior and exterior frames in all the five seismic zones. The frames were subjected to monotonically increasing lateral load profile, which is similar to that for the first mode of elastic vibration. The maximum base shear coefficient (Cy), at roof displacement equal to 2.5% of the building height divided by the unfactored design base shear coefficient (Cw) was taken as overstrength of the structure. Final conclusions of this study are

1. The dependence of overstrength is most significant on seismic zone. Overstrength in zone I can be as much as five times that in zone V. The average overstrength of these frames in zones V and zone I are 2.84 and 12.7 respectively.

2. The overstrength increases as the number of stories decreases and overstrength of the three-story frame is higher than the nine-story frame by 36% in zone V and 49% in zone I.

3. Interior frames have 17% (zone V) to 47% (zone I) higher overstrength as compared to the exterior frames of the same building. This is because interior frames have higher steel due to higher design gravity loads than exterior frames.

4. Finally it is showed that the overstrength being much higher for low seismic zones, for low-rise buildings, and for higher design live load.

Figure 1.1 Force displacement curve for zone I Figure 1.2 Force displacement curve for zone v

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Figure 1.3 Force displacement curve Figure 1.4 Over-strength for Internal Frames

Andrew Whittaker et al (1999) presented a draft formulation that represents the response modification factor as the product of factors related to reserve strength, ductility, and redundancy. Pertinent data from various analytical and experimental studies on reserve strength and ductility are also presented. Using the experimental data, the Berkeley (1980) researchers described R as the product of three factors that accounted for reserve strength (Rs), ductility (Rµ) and added viscous damping (Rξ). After much research of Freeman (1990), Uang (1991) and ATC (1995a and b), a new formulation for R is recommended in which R is expressed as the product of three factors reserve strength (Rs), ductility (Rµ) and redundancy factor (RR). The over strength results from partial safety factors, load factors, member over size, effect of non-structural elements, strain hardening etc. The redundancy factor is introduced to account for the number and distribution of active plastic hinges. Due to different number of plastic hinges, structures characterized by the same shear resistance have different reliability. The ductility factor is a measure of the global nonlinear response of a framing system and not the components of that system. Relations between the ductility factor and the displacement ductility were developed by assuming that a multistory building can be modeled as a single-degree-of-freedom (SDOF) system.

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Figure 1.5 Base shear vs Roof displacement

Figure 1.6 Ductility Factors (ATC 1995a) Figure 1.7 MDOF Modification Factors

The following Krawinkler and Nassar equation was developed assuming damping equal to 5% of critical.

Where α is the post-yield stiffness as percentage of the initial stiffness of the system and the parameters of a and b are given in above table.

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Table 1.1 Draft Redundancy Factors

Lines of vertical seismic framing Draft redundancy factor2 0.713 0.864 1.00

The conclusions of this study are

1. Evaluations of studies by others clearly show that the reserve strength of code-compliant b

uildings varies widely as a function of building type, building height, and seismic zone. Values for strength factors must address these variations, and the influence of higher-mode effects must be studied further.

2. The relations between the ductility factor and the global displacement ductility are well established for bilinear SDOF systems but should be extended to multiple-degree-of-freedom systems using a modification factor similar to that proposed by Krawinkler and Nassar.

3. A draft redundancy factor whose values vary as a function of the number of lines of strength- and stiffness-compatible vertical seismic framing is proposed. Four lines of such framing in each principal direction of a building are proposed as the benchmark value. The values assigned to the factor in this paper are preliminary and mutable.

Samar et al (1997) performed a seismic nonlinear time-history analysis on four, six, and eight storey reinforced concrete buildings to evaluate the seismic ductility reduction and overstrength factors. For comparison purpose they kept the same floor plan for all three buildings and also the member sizes in all three buildings were kept the same in order to have the same lateral stiffness which is based on gross moment of inertia.

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From the obtained results they drawn the following conclusions.

1. The dependency of overstrength is most significant on seismic zone and then on number of stories. The overstrength of buildings in lower seismic zones is significantly higher than the overstrength of buildings in higher seismic zones. This is primarily due to the prominence of gravity loads in the design for low seismic zones.

2. The variation in overstrength with the number of storeys is more significant in lower seismic zones as compared to higher seismic zones. This is also due to a greater prominence of gravity loads in design of low-rise buildings in lower seismic zones.

3. The ductility demand ratios, as well as the ductility reduction factors, decrease as the number of stories increases. It observed that the seismic zoning has a slight effect on the ductility reduction factor (R) for all studied buildings.

4. Finally it concluded that, overstrength factor is more for low seismic zones and low-rise buildings. The dependency of overstrength is most significant on seismic zone and then on number of zones.

Apurba mondal et al (2013) focused on estimation of actual values of R factor for realistic RC moment frame buildings designed and detailed following the Indian standards and comparing these values with the value suggested in the design code. They used pushover analysis in determining R factor for regular RC framed building structures, by considering different acceptable performance limit states.

Figure 1.12 Base shear v/s Roof displacement

The values of R obtained for four realistic designs at two performance levels by considering the

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following effects.

1. Sensitivity of R to the fundamental period. Time period is calculated based on an eigen solution of the structural model used in DRAIN-2DX and based standard formula given in IS 1893 code, and R values are compared for both time periods.

2. Effects of not adhering to the strong-column-weak-beam criterion on R value.3. P–D effects.4. Effects of the lateral load distribution pattern used in nonlinear static analysis.

a) As per IS 1893-2002, the lateral load distribution is given by

Qi=V d

W i hi2

∑i=1

n

W ihi2

b) As per ASCE7

Qi=V d

W i hik

∑i=1

n

W ihik

c) As per EC8 or ATC-40

Qi=V d

W i∅ 1 i

∑i=1

n

W i∅ 1 i

Performance level1 refers to limits based on both inter storey drift ratio and member rotation capacity given by ATC-40.

Table 1.3 Deformation limits for different performance levels as per ATC-40

Performance level

Immediateoccupancy

Damagecontrol

Lifesafety

Structuralstability

Maximum interstorey driftratio

0.01 0.01–0.02 0.02 0.33Vi/Pi

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Performance level2 refers to limits based on member rotation limits based on section dimensions and actual reinforcements.

Table 1.4 Plastic rotation limits for RC beams controlled by flexure, as per ATC-40

Immediateoccupancy

Lifesafety

Structuralstability

ρ−ρ ,

ρbd

Transverse reinforcement

V

bw b d √ f c, Plastic rotation limit

≤0 C ≤3 0.005 0.020 0.025

≤0 C ≤6 0.005 0.010 0.020

Immediateoccupancy

Lifesafety

Structuralstability

P

Ag f c,

Transverse reinforcement

V

bw bd √ f c, Plastic rotation limit

≤0.1 C ≤3 0.005 0.010 0.020≤0.1 C ≥6 0.005 0.010 0.015≥0.4 C ≤3 0.000 0.005 0.015≥0.4 C ≥6 0.000 0.005 0.010

By considering above effects in the non linear analysis they arrived at following conclusions.

1) Based on Performance Limit 1, the Indian standard over-estimates the R factor, which leads to the potentially dangerous underestimation of the design base shear.

2) Based on Performance Limit 2, the IS 1893 recommendation is on the conservative side. It should however be noted that this limit does not include any structure level behaviour such as inter storey drift.

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3) The strong-column-weak-beam criterion in design does not make any major difference in terms of R.

4) R (for PL1) comes to be close to the IS 1893 recommended value If P–D effects are not considered. So, R= 5.0 may be safe for a design where P–D effects are actually negligible at the ultimate state.

5) The IS 1893 and the ASCE7 lateral load distributions give R almost in the same range. However, a load distribution based on the fundamental mode shape estimates R in a range of higher values.

M. Ferraioli et al reviewed the existing methods for determining the behaviour factor of multi-storey moment-resisting steel frames. The effects of storeys, spans and regularity in elevation of frames on the behaviour factor were considered.

The conclusions of this study are

1. The Redundancy factor (Rρ) is almost constant for all multi-bay multi-story frames considered in this study with very similar redundancy and plastic redistribution capacity. The mean value of the redundancy factor is Rρ=1.64 for both regular and irregular moment resisting frames which is greater than the value Rρ=1.3 recommended by EC8 for multi-bay multi-story frames.

2. The overstrength factor (RΩ) is little sensitive to the lateral load pattern (uniformly distributed and triangular) used during pushover analysis. But it is greatly influenced by the number of stories of structure. In particular, the higher values are obtained for low-rise buildings that have greater reserve of strength because the ratio of gravity loads to seismic loads is very high.

3. Results showed that the overstrength reduction factor recommended by EC8 and Italian Code for multi-bay multi-story frames is conservative. But the behaviour factor proposed by these codes may be not conservative. In case of high-rise steel frames, the

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compression failure of a first-story column limits the ultimate displacement capacity of the structure because the high axial force reduces the plastic moment capacity of the first-story columns.

4. On the basis of these results, a local ductility criterion based on a limit of the axial force ratio is proposed to control the ductility of columns and so ensure that the recommended behaviour factor is conservative.

Vishva K. Shastri et al (2015) considered a RC framed staging elevated water tank to evaluate the response reduction factor with and without considering the effects of flexibility of soil. Three different types of soil conditions representatives of hard soil, medium soil and soft soil has considered in their study. He observed that flexibility of supporting soil has considerable effect on response reduction factor, time period and overall performance of water tank indicating that idealization of fixity at base may be seriously erroneous in soft soils. A conservative structural design method neglects the soil flexibility and its effects on super structural response. To neglect the effects of soil flexibility is practical for light structures in comparatively stiff soil to soft soil such as low rise buildings and simple rigid retaining walls. The effect of soil flexibility becomes noticeable for heavy structures like power plants, high-rise buildings and elevated water tanks resting on relatively soft soil. The maximum limit for the roof displacement is specified as 0.004H, where H is the height of the CG of container from the base of the structure.

Figure 1.22 Understanding of Response Reduction Factor

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The soil flexibility can be modeled as by providing translation, rocking and torsional elastic springs constant instead of rigidity of supports so as by providing soil properties in the model (FEMA 356).

Table 1.7 Elastic constants for Rigid Footing Spring Constraint

Figure 1.23 Pushover Curve (Rigid base) Figure 1.24 Pushover Curve (Elastic base-hard soil)

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Figure 1.25 Elastic base with medium soil Figure 1.26 Elastic base with soft soil

From the obtained results the following conclusions are drawn.

1) The response reduction factor decreases while time period increases from fixed base to soft base. So it can be observed that avoidance of effect of soil flexibility might lead to mistaken and inappropriate results of flexibly supported RC frame structures.

2) The effect of the soil-flexibility in case of soft soil reduces values of R factor about 30% for the considered tank as compared to rigid base condition.

3) The value of base shear is reduced up to 20% in case of soft soil to fixed base condition due to flexibility of soil. Here from the results we can observe that effect of soil flexibility is almost negligible in case of hard soil.

1.2 Summary

From the review of literature, it was found that three factors (Rs, Rµ and RR) affect the actual value of response reduction factor (R) and therefore they must be taken into consideration while determining the appropriate response reduction factor to be used during the seismic design process and also found that the response reduction factor is affected following factors.

Building type, building height and seismic zone Soil type (flexibility of soil) Ductility class (Ordinary moment resisting frame, Special moment resisting frame) Lateral Earthquake load distributions Type of Design (Limit state design and Working stress design) Capacity of tank (in case of liquid retaining tanks)

In all above literatures, the Performance level at which the ultimate stress (Vu) should take is not clearly mentioned. The performance level should be based on both member rotation capacities

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and inter-storey drift whichever occurs first. And also no allowance is made in the Response reduction factor formulation for the effects of plan and vertical irregularity which should be considered.

1.3 Objective of the study

The main objective of the study is to find Response Reduction Factor (R) of Reinforce concrete buildings and comparison of these values with IS code values. The objects in detail are as fallows

i) Finding of R factor for regular building frames with single story, multistorey-single bay, multistorey-multi bay frames.

ii) Study of effect of seismic zone and ductility class (OMRF and SMRF)iii) Study of effect of irregularity iv) Study of effect of soil flexibility on R factor.

1.4 References

[1] Miranda,E. and Bertero, V. V. (1994), ‘Evaluation of strength reduction factors for earthquakeresistant design’, Earthquake Spectra, 10(2), pp. 357-379.

[2] Sudhir K. Jain and Rahul Navin (1995), ‘seismic overstrength in reinforced concrete frames’, J.Struct. Eng. 1995.121:580-585.

[3] Whittaker,A., Hart,G. and Rojahn,C. (1999), ‘Seismic Response Modification Factors’, Journal of Structural Engineering, 438-444.

[4] Gholamreza Abdollahzadeh and Amirhosein Maleki Kambakhsh (2012), ‘Height Effect on Response Modification Factor of Open Chevron Eccentrically Braced Frames’, Iranica Journal of Energy & Environment 3 (1): 72-77, 2012.

[5] Mondal, A., Ghosh, S. and Reddy, G. (2013), ‘Performance-based evaluation of the response reduction factor for ductile RC frames’, Engineering Structures 56(2013), 1808-1819.

[6] Tande,S. and Ambekar,R.V. (2013), ‘An investigation of seismic response reduction factor for earthquake resistant design’, International Journal of Latest Trends in Engineering and Technology, Vol.2, Issue 4 July 2013.

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[7] Vishva K. Shastri and Jignesh A Amin. (2015), ‘Effects of soil condition on response reduction factor of elevated rc water tank’, International Journal of Advance Engineering and Research Development Volume 2,Issue 6, June -2015.

[8] R. Ghateh, M.R. Kianoush and W. Pogorzelski (2015) ‘Seismic response factors of reinforced conc

rete pedestal in elevated water tanks’, Engineering Structures 87 (2015) 32–46.

[9] ATC (1996), ATC - 40 : Seismic Evaluation and Retrofit of concrete buildings , Vol. 1 , Applied Technology Council , Redwood City , USA.

[10] FEMA, Prestandard and Commentary for the Seismic Rehabilitation of Building, FEMA-356, Federal Emergency Management Agency, Washington, D.C, 2000.

[11] ATC 19 (1995), Seismic Response Modifi cation Factors, Applied Technical Council, California Seismic Safety Commission, Redwood City, California.

[12] CEN Eurocode 8. Design Provisions for earthquake resistance of structures (European Prestandard ENV 1998). Brussels (Belgium): Comité Européen de Normalisation; 2004.

EN 1998-1:2004

The seismic design procedure in Euro code is a single level design procedure that reduces elastic spectral demands to the strength design level through the use of behavior factor q. This behaviour factor varies as a function of ductility, building strength, structural system and stiffness regularity. The behaviour factor q shall be derived as follows

q= qo kw ≥ 1.5

Where qo is the basic value of the behaviour factor

kw is the factor reflecting the prevailing failure mode in structural systems with walls

Table: qo values for buildings that are regular in elevation

STRUCTURAL TYPE DCM DCH

Frame system, dual system, coupled wall system

3.0αu/α1 4.5αu/α1

Uncoupled wall system 3.0 4.0αu/α1

Torsionally flexible system 2 3

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Inverted pendulum system 1.5 2

For buildings which are not regular in elevation, the value of qo should be reduced by 20%.

αu: seismic action at development of global mechanism

α1: seismic action at 1st flexural yielding anywhere

The factors αu and α1 may be obtained from a nonlinear static (pushover) global analysis.

When the multiplication factor αu/α1 has not been evaluated through an explicit calculation, for buildings which are regular in plan the following approximate values of αu/α1 may be used.

Frame or frame-equivalent dual systems αu/α1

One-storey buildings 1.1Multistorey, one-bay frames 1.2Multistorey, multi-bay frames or frame-equivalent dual structures

1.3

Wall- or wall-equivalent dual systems αu/α1

wall systems with only two uncoupled walls per horizontal direction

1

other uncoupled wall systems 1.1wall-equivalent dual, or coupled wall systems 1.2

For buildings irregular in plan, default value = average of default value of buildings regular in plan and 1.0 .

Values of αu/α1 higher than those given in above tables may be used, provided that they are confirmed through a nonlinear static (pushover) global analysis.

The maximum value of αu/α1 that may be used in the design is equal to 1.5, even when the analysis results in higher values.

If a special and formal Quality System Plan is applied to the design, procurement and construction in addition to normal quality control schemes, increased values of qo may be allowed. The increased values are not allowed to exceed the values given in Table 5.1 by more than 20%.

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IS 1893 (Part 1) 2002

The seismic design procedure in India is a single level design procedure that reduces elastic spectral demands to the allowable strength design level through the use of response modification factor (R). IS 1893 gives a value of R values for ordinary and special RC moment resisting frames (OMRF and SMRF). The SMRF needs to follow the ductile detailing requirements of IS13920. IS 1893 does not explicitly segregate the components of R in terms of ductility and overstrength. Also, it does not specify any reduction in the response reduction factor on account of any irregularity (vertical or plan-irregularity) in the framing system.

Values of R for RC framed structures, as per IS 1893

Structural system R

Ordinary moment resisting frame (OMRF) 3

Special moment resisting frame (SMRF) 5

BSLJ 2004

The seismic design of Japanese buildings is a two-phase design for earthquakes. The first phase design is for medium earthquake motions, and this is basically working stress design. The unreduced seismic forces are evaluated by following eq

Qi=C i∑i=1

n

W i

C i=ZRt A iC0

Qi= seismic shear force at i-th W i = seismic weight of i-th story n = number of storiesC i = shear coefficient at i-th storyZ = seismic zone factorRt = vibration characteristics factorAi = vertical distribution factor C0 = standard shear coefficient (=0.2 for moderate earthquake)

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The second phase design is intended to give protection to buildings in case of severe ground shaking. It requires the checking of several aspects of the building. These include story drift, vertical stiffness distribution, horizontal eccentricity and ultimate lateral load carrying capacity. The ultimate lateral load carrying capacity is calculated by any method, including incremental nonlinear analysis. It is required that the ultimate lateral load carrying capacity in each story thus found must exceed the required shear force Qun given below

Qun=D s Fes Qud

Qud= standard seismic shear in a story calculated from the same equation 1 with Co=1(severe

earthquake)

Ds = structural characteristics factor which takes into account inelastic deformations and energy dissipation.

Fes = F s Fe

Fes= a shape factor is intended to take into account their regularity of the structure expressed in terms of rigidity factor and eccentricity determined as follows

F s = basic shape factor determined as a function of the rigidity factor R s

F s =1.0 when R s≥ 0.6

F s=2.0−R s

0.6 when R s<¿0.6

F e= basic shape factor determined as a function of eccentricity factor Re

F e =1.0 when Re≤ 0.15

F e=1 + .5

0.15 (Re - 0.15) when .15 < Re <0.3

F e = 1.5 when Re ≥ 0.3

Structural TypeFraming Members Rigid frames or very

ductile shear wallwith βW≤ 0.3

Very ductile orductile shear wall

with βW≤ 0.7

Very ductile or ductileshear wall withβW≤ 0.7,or less ductile shear wall

Most ductile .30 .35 .40

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Very ductile .35 .40 .45Ductile .40 .45 .50Others .45 .50 .55

βW= ratio of load carried by shear walls to total story shear.

ASCE7-2010

The seismic design procedure in America is a single level design procedure that reduces elastic spectral demands to the strength design level through the use of response modification factor (R). This response modification factor varies as a function of ductility, building strength, structural system and this R values given along with over strength factor and deflection amplification factors. The seismic base shear V, in a given direction shall be determined in accordance with the following equation

V=C sW

C s= the seismic response coefficientW = the effective seismic weight

C s=S DS

RI

SDS = the design spectral response acceleration parameter R = the response modification factor I = the occupancy importance factor

Table R, Ω0∧Cd factors of RCC Frames

Seismic Force-Resisting System

ResponseModificationCoefficient

R

OverstrengthFactorΩ0

DeflectionAmplification

Factor Cd

Special reinforced concrete moment

Frames 8 3 5½

Intermediate reinforced concrete

moment frames5 3 4½

Ordinary reinforced concrete moment 3 3 2½

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Frames

The R reduces forces to a strength level, not an allowable stress level.For structures having a horizontal structural irregularity and vertical structural irregularity, the design forces shall be increased 25 percent for the elements of the seismic force-resisting system.

Basic Combinations for Strength Design

(1.2 + 0.2SDS)D + ρQE + L + 0.2S

(0.9 – 0.2SDS)D + ρQE + 1.6H

The value of this factor is either 1.0 or 1.3. This factor has an effect of reducing the R factor for less redundant structures, thereby increasing the seismic demand.

Basic Combinations for Strength Design with overstrength Factor

(1.2 + 0.2SDS)D + ΩoQE + L + 0.2S

(0.9 – 0.2SDS)D + ΩoQE + 1.6H

Some elements of properly detailed structures are not capable of safely resisting ground-shaking demands through inelastic behavior. To ensure safety, these elements must be designed with sufficient strength to remain elastic.

NZS4203-1992

According to the New Zeeland design norm, the seismic acceleration coefficient Cb from the seismic force relation is determined by taking into consideration the fundamental oscillation period (T1), the structural ductility factor (μ), and the soil type. The seismic force is computed using the following relation

V= CW t

C= Cb (T,1)RZLs for serviceability limit state

C= Cb (T, μ)RZLu for ultimate limit state

C=lateral force coefficient W t= total seismic weight of a structureR = risk factorZ= zone factor

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Cb = base seismic acceleration coefficient (see in fig.)

Fig. Basic seismic aceeleration coefficiient

Table Structural Ductility Factor of RCC Frames

Seismic Force-Resisting System Structural Ductility Factor (μ)

Elastically responding structures 1.25

Structures with limited ductility1. Frames2. Walls3. Cantilevered face loaded walls

332

Ductile structures1. Moment resisting frames2. Walls

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5

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