Seismic Retrofitting of Structures by Steel Bracings - Science Direct

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ScienceDirect Procedia Engineering 144 (2016) 1364 – 1372

12th International Conference on Vibration Problems, ICOVP 2015

Seismic Retrofitting of Structures by Steel Bracings G Navyaa , Pankaj Agarwalb* a Department of Earthquake Engineering, Indian Institute of Technology , Roorkee, 247667, India. Professor, Department of Earthquake Engineering, Indan Institute of Technology, Roorkee, 247667, India.

b

Abstract

Seismic retrofitting is the modification of existing structures so as to improve the system behaviour or its components repair/strengthening up to the performance it is expected. Detailed seismic evaluation and assessing the vulnerability of the structure are the key ingredients in order to arrive at an appropriate retrofitting scheme. This study proclaims a complete process of retrofitting on a building designed with two different philosophies i.e., as per IS 456: 2000 and IS 1893 (Part 1): 2002 and retrofitted with steel bracing. The fragility analysis was also carried out to indicate the probability of damage under different states which reduces considerably after retrofitting of building. © Published by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license ©2016 2016The TheAuthors. Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICOVP Peer-review under responsibility of the organizing committee of ICOVP 2015 2015. Keywords: Seismic Evaluation; Non Linear Static Analysis; Vulnerability Assessment; Fragility Curves; Techniques of Retrofitting

1. Introduction Recently occurred earthquakes have delineated the vulnerability issues faced by the existing buildings due to the changes in the ground motions lately or which may have been constructed based on earlier codes. In order to protect from the risk triggered by seismic disaster to the life and property, the performance of the structures must be improved and thus seismic retrofitting plays its role. Retrofitting also proves to be a better option catering to the economic considerations and immediate shelter problems rather than replacement of seismic deficient buildings. Two alternative approaches are conceptually adopted and implemented in practice for seismic retrofitting: the first approach focuses on upgrading the structure to resist earthquake induced forces (i.e. modifying the capacity) and is called conventional

* Pankaj Agarwal. Tel.: +91-01332-285317 E-mail address: [email protected]

1877-7058 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICOVP 2015

doi:10.1016/j.proeng.2016.05.166

G. Navya and Pankaj Agarwal / Procedia Engineering 144 (2016) 1364 – 1372

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method of retrofitting. The second approach focuses on reduction of earthquake induced forces (i.e. modifying the demand) or unconventional approach. This present study focuses on complete procedure of seismic vulnerability assessment and retrofitting of G+6 RC frame building designed by two design philosophies i.e. IS 456:2000 and the other with IS 1893:2002 (Part 1): 2002 along with a ductile detailing as per IS 13920:1993.Conventional retrofitting technique i.e. steel bracings is used to improve the elastic and post-yield behavior of the building for resisting the future seismic demand. The re-evaluation is carried out and verified that the seismic retrofitting is a viable method for up gradation of the structural capacity to a seismic deficient building. 2. Seismic Evaluation and Vulnerability Assessment of the Building

Capacity Curve from the Push over Analysis

Highly Damped Response Spectra

Performance Point based on the demand and capacity of Building

Generation of the Fragility Curves (Cummulative Damage )

Finding the Discrete Damage Probability from DPM

Fig.1: Plan and Elevation of the G+6 storied building

Fig. 2: Flow chart of vulnerability Assessment

A G+6 reinforced concrete moment resting frame building located in Zone IV as per IS: 1893 (Part 1): 2002 with a medium type of soil conditions is consider under this study. The total height of the building is 22m with ground and storey height of 4m and 3m respectively. The grade of concrete and reinforcement used in building is M20 and Fy 415D. The size of the beams and columns are assumed to be 300x450 mm and 500x500 mm respectively. Figure 1 shows the typical plan and elevation of the building, analyzed and designed in SAP-2000. The complete flowchart for the seismic vulnerability assessment is given in Figure 2. The nonlinear static pushover analysis of the building is carried out by user-defend plastic hinge parameters. The moment curvatures diagram of beam and column are determined on the basis of Navier's three compatibility equations i.e. Bernoulli's strain compatibility, material constitutive law and the equilibrium equations i-v. Figure 3 shows the typical moment-curvature relations of beams under unconfined and confined condition at the 4th floor.

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i.

Compatibility of tension steel:

ߝ௖௨ ܽ ൌ ߚଵ ൈ ݀ ߝ௖௨ ൅ ߝ௬

(1)

ii.

Compatibility of Compression steel: ߝ௦′ ܿ െ ݀′ ൌ ߝ௨ ܿ

(2) iii.

Constitutive Law of Compression Steel:

Here ߝ௦′ ൐ ߝ௬

iv.

Thus݂௦′ ൌ ݂௬ ൌ ͶͳͷܰȀ݉݉ଶ

(3)

Constitutive Law of Tension Steel: ߝ௦ ൑ ߝ௬ and thus, ݂௦ ൌ ‫ܧ‬௦ ߝ௦

(4)

v.

Equilibrium Equation: ܰ௡ ൌ ͲǤͺͷ݂௖′ܾܽ െ ‫ܣ‬௦ ݂௦ ൅ ‫ܣ‬′௦ ݂௦′ and ܽ ‫ܯ‬௨ ൌ ͲǤͺͷ݂௖′ ܾܽ ቀ݀ െ ቁ ൅ ‫ܣ‬′௦ ݂௦′ ൫݀ െ ݀′ ൯ ʹ

(5) Where, d is the depth of the neutral axis ߝ௦ is the stain at the tension steel ߝ௬ is the stain at the yield condition ߝ௖௨ is the strain of the concrete in the ultimate condition ߚଵ is Whitney’s block parameter ݂௦ᇱ is the stress at the compression steel ݂௬ is the stress at the tension steel The M-phi curves are further converted in moment rotation relationship as given by equation 6, 7 ݀௕ ݂௬ ‫ܮ‬௩ ൅ ܽ ௩ ܼ ‫ܪ‬ ߆௬ ൌ ɸ௬ ൬ ൰ ൅ ͲǤͲͲͳ͵ͷ ൬ͳ ൅ ͳǤͷ ൰ ൅ ͲǤͳ͵ɸ௬ ቆ ቇ ‫ܮ‬௩ ͵ ඥ݂௖ ͲǤͷ݈௣௟ ߆௨ ൌ ߆௬ ൅ ቀɸ௨ െ ɸ௬ ቁ ݈௣௟ ቆͳ െ ቇ ݈௦

(6)

(7) ȣ୷ ൌ Yield rotation ᢥ୷ ൌ Yield curvature ୴ ൌ ͳ ൌ Shear cracking expected to precede flexural cracking at the end ൌ Ͳ ൌ d-d' for beams, columns T sections

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=0.8 b for rectangular section with walls ൌ Total section height ୠ ൌ Mean diameter of longitudinal bars in the affected section ୷ ൌ Yield strength of the longitudinal reinforcement steel ୡ ൌ Concrete compressive strength ୷ ɂ୷ ൌ ൌ ୱ

2

80,82,83,85,86,88,89,91 81,84,87,90 92,94,95,97,98,100,101,103 93,96,99,102

1000

Curvature,ɸ*e-08

0 6.96

117

90 93 96

(b)

Moment,m(knm)

Moment,m *E+08

(a)

92 95 98

Curvature,φ

0

676

91 94 97

2.4713E-05

2.44387E-05

Fig.3: Moment Curvature curves for (a) unconfined beams (b) confined beams

In beams, M3 hinge and in column P-M2-M3 type hinge is used. The obtained pushover curve in the form of base shear v/s roof displacement is converted into the Acceleration Displacement Response Spectra (ADRS) as per ATC 40 [3] and shown in Figure 4. Spectral acceleration,

‫ݏ‬௔ ൌ

௏್ൗ ௐ ఈభ

(8) and Spectral Displacement, ܵௗ ൌ

οೝ೚೚೑ ఈభ ‫כ‬ᢥೝ೚೚೑

(9) Where, ߙଵ = Modal participation factor ൌ

ೈ೔ ᢥ೔ǡభ σ೙ ೔సభ

೒ ೈ೔ ᢥమ ೈ೔ ೔ǡభ ೙ ቀ ቁ σ೔సభ ೒ ೒

Vb = Base shear of the building W = Total Weight of the building Δroof = Drift at the roof ɸroof = Modal shape at the roof α1 = Modal participation factor (b)

1500

3000 Base Shear(KN)

base shear (KN)

(a)

1000 500 0 0

50 Displacement (Cm)

100

2000 1000 0 0

20 Displacement(Cm) 40 60

Fig.4: Push Over Curve in ADRS format for (a) IS 456 : 2000 (b) IS 1893(Part 1) : 2002

80


Force

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fmax fy

Es

Ep

uy

ux

Deformation

Fig.5: Approximation of the effective damping

The seismic demand as per Zone IV in the form of elastic response spectra of IS 1893 (Part 1): 2002 is converted in highly damped spectra by applying the spectra reduction factor. Figure 5 shows the approximation of the effective damping required for the reduction factors calculation as in Eq. (10) and (11). Spectral Reduction Factor for Acceleration, ܴܵܽ ൌ

ଵ ଶǤଵଶ

Spectral Reduction Factor for Velocity, ܴܵ‫ ݒ‬ൌ

ଵ ଵǤ଺ହ

ሺ͵Ǥʹͳ െ ͲǤ͸ͺ ௘ ߚ௘௙௙ ሻ

(10)

ሺʹǤ͵ͳ െ ͲǤͶͳ݈‫݃݋‬௘ ߚ௘௙௙ ሻ

(11)

Where, βeff = Effective Damping βE = Elastic Damping = 5% considered βH =Hysteresis damping (post Yielding Response obtained from hysteresis loop ͳ ߚா ൌ ൈ Ͷߨ ߚ஽ ͳ ‫ܧ‬ௗ௜௦௦௣ ൌ൬ ‫כ‬ ൰ Ͷߨ ‫ܧ‬௦௧௢௥௘ௗ

The intersection or performance point is obtained from the capacity and demand curved as shown in Figure 6 to determine the probability of exceeding of damage for the particular spectral displacement. The performance points are tabulated in Table 1.

Performance Points

Table 1. Performance Points by two methods IS 456:2000

IS 13920:1993

Sa(m/s2)

0.172

0.2

Sd(cm)

2.32

2

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G. Navya and Pankaj Agarwal / Procedia Engineering 144 (2016) 1364 – 1372 damped response spectra capacity curve

(a)

(b)

0.6

Sa(m/s2)

Sa(m/s2)

0.8 0.4 0.2

0.8

0.6 0.4 0.2 0

0

Sd(Cm)

0

20

40

Sd (cm)

0

60

20

40

60

Fig.6: Performance point of the building according to (a) IS 456 : 2000 (b) IS 1893(Part 1) : 2002

2.1 Determination of Fragility curves For a particular damage state as defined by the Park, Ang and Wen (1965) shown in the Table 2. The maximum drift displacement is calculated using equation (12) and the obtained mean spectral displacements along with the assumed Standard deviation of the log normal values (ߚௗ௦ ) as given in Table (3). Thus the cumulative probability was found out from Eq. (13) Table 2: Damage states corresponding to the range of damage Indices Range of Damage Index Damage State DI൑0.1

None

0.1 ൑DI ൑0.20

Slight

0.20 ൑DI ൑0.40

Moderate

0.40 ൑DI ൑1.00

Extensive

DI ൒ 1.00

Complete

‫ܫ‬஽ ൌ

ௗ೘ ିௗ೤ ௗೠ ିௗ೤

൅

ఉ೐ ‫ ׬‬ௗா

(12)

ி೤ ௗೠ

Where, dm = Maximum Displacement due to point of maximum capacity du = Ultimate Displacement due to monotonic loading dy =Yield Displacement βe =Parameter representing the cyclic loading strength reduction factor dE =Incremental energy dissipated Fy =Longitudinal reinforcement yielding force. Table 3: Standard deviation of the natural logarithm Values for different damage states Damage state Slight Moderate Extensive Complete Collapse ઺‫ܛ܌‬

0.65

0.75

݀ ܲ ቂ ௦ൗܵ ቃ ൌ ߶ ൤ ௗ

0.85 ଵ

ఉ೏ೞ

ௌ

೏ ݈݊ തതതതതതതതത ൨

௦೏ǡೄ೏ೞ

0.95

(13)

Where, ‫ݏ‬ௗǡௌௗ௦ = Median value of spectral displacement at which the building reaches the threshold of the damage state, ds ߚௗ௦ = Standard deviation of the natural logarithm of spectral displacement of damage state, ds and

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߶ = Standard normal cumulative distribution function. (a)

(b)

1 0.8 0.6 0.4 0.2 0 0

20

1.2 1

Probability of Exceedence


1.2

40

0.8 slight moderate extensive collapse

0.6 0.4 0.2 0

0

10

20

30

40

50

Spectral Displacement(Cm)


Fig.7: Fragility Curves of the building according to (a) IS 456 : 2000 (b) IS 1893(Part 1) : 2002

3. Seismic Vulnerability Assessment of the Retrofitted Building It is observed that the expected damage in building design as per IS 456:2000 is almost collapse zone whereas building designed as per IS 1893 (Part 1): 2002 is in the moderate to extensive zone. There is an urge to retrofit these buildings with steel bracings. The bracings are provided with the steel members and are diagonally connected in the form of X at the location as shown in figure 8. Figure 9 shows the pushover curves of the building after retrofitting with steel bracing and the fragility curve under both the schemes are shown in Figure 10.The performance of the retrofitted building is shown in Table 4 (b)

1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00

Spectral Acceleration (Sa)

Spectral Acceleration (Sa)

(a)

0.00

20.00

40.00

1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00 0.00

60.00

20.00

40.00

60.00

Spectral Displacement (Sd) original buiding bracings

Spectral Displacement (Sd)

Fig.8 : Comparison of capacity curves before and after retrofitting of building according to (a) IS 456 : 2000 (b) IS 1893(Part 1) : 2002 Table 4: Performance points of retrofitted building by using steel bracings Performance Points IS 456:2000 IS 13920:1993 Sa(m/s2)

0.19

6.4

Sd(cm)

3.3

8

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G. Navya and Pankaj Agarwal / Procedia Engineering 144 (2016) 1364 – 1372 (b) 1.2

1.2



(a)

1 0.8

0.6 0.4 0.2

1 0.8 0.6

slight moderate Extensive collapse

0.4 0.2 0

0 0

0

20 40 Spectral Displacement(Cm)

20 40 Spectral Displacement(Cm)

60

Fig.9: Fragility curves designed by IS 456 : 2000 of (a) Original building (b) Retrofitted building


1.2

(b)

1.2 1 0.8 0.6

slight moderate extensive collapse

0.4 0.2 0 0

10

20

30


40

50


(a)

1 0.8 0.6 0.4 0.2 0 0

20

40

60

Spectral Displacement (Cm)

Fig.10: Fragility curves designed by IS 13920 : 2002 of (a) Original building (b) Retrofitted building

Conclusions x

Pushover analysis of the building designed as per IS 1893 (Part 1): 2002 on the basis of confined plastic hinge regions performs much satisfactorily as compared to un-confined condition. Fragility curves also indicate that conventionally designed building is more vulnerable as compared to building designed with seismic provisions related to confinement at the possible location of plastic hinges.

x

Fragility analysis indicates that the conventionally designed building under MCE condition corresponding to Zone IV indicates that the highest probability (97.68%) is under the category of extensive damage. However, building designed as per IS 1893 (Part 1): 2002 suffers moderate damage under the same level of seismic hazard.

x

There is a significant reduction in the seismic vulnerability of the building after retrofitting of building with steel bracing. The fragility analysis indicates that the probability of damage under collapse and extensive state of damage reduces considerably after retrofitting of building.

References [1] [2] [3]

Reitherman, Robert , Earthquakes and Engineers , International History, Reston, VA ,2012, ASCE, press, pp. 486-487 . Mander, J.B., Priestly, M.J.N., and Park, R.,Observed Stress – strain behavior of confined concrete , Journal of Structural Engineering , Vol.114, No. 8, 1988. Seismic Evaluation and Retrofitting of concrete buildings. Applied Technology Council -40, Redwood city, Vol 1,Report No.SSC 9601,1996

1372 [4] [5]

G. Navya and Pankaj Agarwal / Procedia Engineering 144 (2016) 1364 – 1372 Fajfar P., Fischinger M.,Non-linear seismic analysis of RC buildings –Implications of a case study, European Earthquake Engineering , 1987,Vol. 1, No. 1 ,pp. 31-43 . IS 13920:1993, Ductile Detailing of Reinforced concrete structures subjected to seismic forces-Code of practice, Bureau of Indian standards ,1993.