lecture 2 - examples of strengthening building · ... addition of rc shear walls is ... during a...

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2 October 2015Dr. Pramin NorachanManager, Structural Engineering Unit, AIT Consulting

Presentation Outline

1. Introduction

2. Global Retrofitting

3. Local Retrofitting

4. Example 1: 5-Story RC School Building

5. Example 2: 4-Story RC Hotel Building

6. Example 3: 55-Story High-Rise Building

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Dr. Pramin Norachan 4

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Dr. Pramin Norachan 5JSCE, Concrete Engineering Series No.28, 1998. (In Japanese)


Global

Local

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The design philosophy for strengthening can be divided into two approaches.

The first approach is the system strengthening (global strengthening) which new elements are added to a building to enhance its global stiffness.

With an increase in the stiffness, the natural period of vibration of the building is to decrease. This will result in a decrease in the amount of horizontal displacement that must be achieved by the building to resist earthquakes.

Moreover, addition of new members to the building shall mostly increase the horizontal load capacity of the building as well. Therefore, the increased capacity will require greater ground motions to allow the building to develop a yielding behavior.

Thus, it can be said that the system strengthening does not only prevent collapsing but also delays structural damages.


The second approach is element strengthening (local strengthening) which is a method based on the insufficient capacities of members due to the sustained damages without undertaking major changes in the load-deformation relationship of the building.

It should also be noted that there will be no significant changes in the displacement demand after the member strengthening.

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Among the global strengthening methods, addition of RC shear walls is the most popular one.

The installation of RC shear walls greatly improves lateral load capacityand stiffness of the structure.

In the strengthening method with shear walls, the existing partition walls in the building are removed and high strength reinforced concrete shear walls are built instead.

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Shear walls have to be constructed from the foundation level and there may not need to strengthen other components.

The shear walls can resist majority of the earthquake loads and limits the displacement behavior of the building.


Under enormous cyclic forces during a seismic effect, Buckling Restrained Brace (BRB) which is system based strengthening techniques (global strengthening) devices can be used to increase the resistance of frame structures by providing energy dissipation and introducing nonlinear behavior.

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Testing and evaluating are required for designing and ensuring quality control.

The structures are susceptible to collapse or large lateral displacements due to earthquake ground motions and require special attention to limit the displacement.

This displacement can be brought into limit by providing BRB in the structure.


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Passive control systems reduce structural vibration and associatedforces through energy dissipation devices that do not require external power. These devices utilize the motion of the structure to develop counteracting control forces and absorb a portion of the input seismic energy.

Active control systems, however, enhance structural response through control forces developed by force delivery devices that rely on external power to operate. The actuator forces are controlled by real time controllers that process the information obtained from sensors within the structure.

Semi-active control systems combine passive and active control devices and are sometimes used to optimize the structural performance with minimal external power requirements.

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The seismic base isolation technology involves placing flexible isolation systems.between the foundation and the superstructure.

By means of their flexibility and energy absorption capability, the isolation systems reflect and absorb part of the earthquake input energy before this energy is fully transmitted to the superstructure, reducing the energy dissipation demand on the superstructure.


Base isolation causes the natural period of the structure to increase and results in increased displacements across the isolation level and reduced accelerations and displacements in the superstructure during an earthquake.

Base isolation is fundamentally concerned to reduce the horizontal seismic forces.

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A typical base isolation system is evolved by the use of rubber bearing located at the base of the building.

Rubber bearing consist of laminated layers of rubber and steel plates.

The main advantage are good protection against earthquake due to decrease shear.Superstructure will need no reinforcement.

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There are several options for the jacketing of concrete members which are element based strengthening techniques (local strengthening).

Usually, the exiting member is wrapped with a jacket of concrete reinforced with longitudinal steel bars and ties, or with weld wire fabric.

Based on this method, axial strength, bending strength, and stiffness of the original column are increased.


Reinforcement concrete jacketing can be used as a repair of strengthening scheme.

If there is damage in some of the existing members, they should be repaired before jacketing.

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Jacketing of beams is recommended for several purposes as it gives continuity to the columnsand increases the strength and stiffness of the structure.

While jacketing a beam, its flexural resistance must be carefully computed to avoid the creation of a strong beam‐weak column system.


Jacketing of beam may be carried out under different ways, the most common are one-sided jackets or 3- and 4-sided jackets.

The beam should be jacketed through its whole length.

The reinforcement has also been added to increase beam flexural capacity moderately and to produce high joint shear stresses.

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The steel jacket retrofit has been used as a method to enhance the shear strength and ductility of square reinforced concrete (RC) columns in existing buildings

Local strengthening of columns has been frequently accomplished by jacketing with steel plates.

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FRP composite materials have experienced a continuous increase of use in structural strengthening and repair applications around the world in the last fifteen years. In general, applications that allow complete wrapping of the member with FRP have proven to be effective.


Wrapping of columns to increase their load and deformation capacity is the most effective and most commonly used method of retrofitting with composites.

However, certain performance and failure mode issues regarding different wrapping configuration and fiber orientations.

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Influence of shear strengthening and anchorage on FRP strengthened beam behavior under cyclic loading by using FRP plates in various configurations.

It can be seen from this figure that flexural strengthening of beams without proper attention to brittle shear and debonding failure modes not only renders the strengthening application ineffective, but also harms the member by decreasing its ductility.

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Seismic performance review of an existing 5-story RC frame-Infill wall school building and comparison of various retrofit options is presented here.

Rastriya Higher Secondary School Building, Nepal


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Stage I: Collecting As-built Building InformationThe architectural and structural drawings of the building are provided by the client. However, it is understood that the drawings for the extension part of the building are not available. On-site measurements and investigation are carried out to collect the as-built information of extension part.

Stage II: Performance Based Evaluation for the Existing BuildingPerformance based evaluation is carried out to check the seismic performance of the existing building using the as-built information from the previous stage.

Stage III: Performance Based Evaluation for the Strengthened BuildingsPerformance based evaluation is carried out to check the seismic performance of the strengthened buildings based on common strengthening techniques used by practical engineers.

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IS 1893:2002

NBC 105:1994

Nepal


Response spectrum for seismic zone V (Z = 0.36) based on type III of subsoil (soft soil), specified in IS 1893:2002, approximately equivalent to the response spectrum with 1.1 of seismic zone factor, mentioned in NBC 105:1994.

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Spectral A

cceleration, Sa (g)

Natural Period (s)

Response Spectra

DBE

MCE

T1T2T3T4T5T6

MCE level response spectrum is estimated by increasing the spectra values of DBE level response spectrum by 2.0 times.

Modal pushover analysis (MPA) is conducted to determine the inelastic response of the building.

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Nonlinear Components- Columns (Fiber hinges)- Girders (Moment hinges)- Infill walls

(Tension/Compression limits)

Linear Component- Slab

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Modeling Parameters and Numerical Acceptance Criteria for Nonlinear Procedures-Reinforced Concrete Beams

(Table 6-7, ASCE 41-06, Supplement No. 1)


Moment hinge

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Column fiber sections


1. Perform modal analysis to get periods (T1, T2,…,Tn). The combination of participating mass based on selected modes must greater than 90%.

2. Read the spectral curve according to the periods

3. Find the modal participation factor for each mode,

4. Find the amplitude of each mode at the roof,

5. Find the spectral displacement for each mode,

6. Find the target displacement,

7. Push the structure based on each modal load pattern according to its target displacement.

8. Combine the results based on the modal combination rules, such as SRSS.

m

mroof

mdS

mroof

2 2 2, 1 2 ...b SRSS b b bnV V V V

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Mode Period Sa Sd Φi Γi Target Disp Story Joint Dir Dir

Sec m/sec2 m m m Text Text Text Text

1 0.90 5.18 0.107 0.076 26.61 0.217 ROOF P1-7 Y U2

2 0.86 5.45 0.102 0.078 14.70 0.118 ROOF P3-7 Y U2

3 0.66 6.94 0.077 0.045 29.15 0.100 ROOF 184 X U1

4 0.33 8.93 0.024 0.089 7.22 0.015 ROOF P1-7 Y U2

5 0.30 8.93 0.020 0.086 8.56 0.015 ROOF P3-7 Y U2

6 0.23 8.93 0.011 0.044 10.12 0.005 ROOF 186 X U1

m

m

m

roofd

m roof

SPF

2

2

1 1

n n

m i im i imi i

W W W

2

2m m

md a

TS S g

m m mroof d m roofS


12.48.2

13.710.9

34.3

27.1

16.2

9.2

68.6

54.0

28.4

15.0

0

20

40

60

80

X Y

Bas

e S

hear

(%

)

Along Direction

Base Shear Percentage in Total Weight of Building

Euivalent Statics

RSA-DBE(inelastic)

RSA-DBE(elastic)

MPA-DBE

RSA-MCE

MPA-MCE

Seismic weight of building at the ground level = 10,500 kN

2.4

3.6

MCE (Linear, RS)

MCE (Nonlinear, MPA)

xy

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1

2

3

4

5

6

‐4000 ‐2000 0 2000 4000

Story Level

Shear Force (KN)

Story Shear in X‐Direction

DBE

MCE

1

2

3

4

5

6

‐3000 ‐2000 ‐1000 0 1000 2000 3000

Story Level

Shear Force (KN)

Story Shear in Y‐Direction

DBE

MCE

xy


Girder Rotation CriteriaMCE

No. %

ϴp < 0.005 (Good range) 219 98.6%

0.005< ϴp <0.01 (IO) 2 0.9%

0.01< ϴp <0.02 (LS) 1 0.5%

ϴp >0.02 (CP) 0 0.0%

Total 222 100.0%

It is found that two girders perform at the Immediate Occupancy (IO), and only a girder performs at the Life safety (LS). However, none of the girders are beyond the Collapse Prevention (CP).

The shear capacity of many girders seems to be adequate to resist the probable shear demand with 90% of D/C smaller than one

Girder Shear CriteriaMCE

No. %

DC<1 (Good range) 202 91.0%

1<DC<1.2 (Overstressed) 1 0.5%

1.2<DC<1.5 (Overstressed) 0 0.0%

DC>1.5 (Overstressed) 19 8.6%

Total 222 100.0%

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Shear D/C Ratios of Girders in Ground Level (MCE)

Shear D/C Ratios of Girders in Level 1 (MCE)


Column PMM CriteriaMCE

No. %





Total 124 100.0%

Column Shear CriteriaMCE

No. %





Total 124 100.0%

Most columns have insufficient shear capacity to resist the shear demand for MCE levels. Therefore, it is recommended that the retrofit for shear capacity of these columns must be done.

In terms of axial-flexural interaction capacity, many columns are generally acceptable for DBE level while several columns seem to be overstressed under earthquakes at MCE level.

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The first fundamental mode is coupled both X and Y direction (torsion) due to unsymmetrical configuration of the building as expected.

ModeNatural Period

(s)UX UY RZ

1 0.90 2.0% 63.8% 20.9%

2 0.86 9.4% 19.5% 45.4%

3 0.67 76.6% 0.1% 14.7%

4 0.32 0.4% 4.7% 0.5%

5 0.30 0.3% 6.6% 9.3%

6 0.23 9.2% 0.0% 0.9%

Total 97.8% 94.7% 91.7%

Modal Participation Mass Ratios


For repairing and strengthening of the existing building, three common strengthening techniques used by practical engineers, column jacketing, adding steel braces and adding new shear walls were used to improve the seismic performance of the existing building.

Then, the efficiency of each strengthening method was investigated on the basis of member strength and deformation.

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There are several options for the jacketing of concrete members which are element based strengthening techniques (local strengthening).

Usually, the exiting member is wrapped with a jacket of concrete reinforced with longitudinal steel bars and ties, or with weld wire fabric.

Based on this method, axial strength, bending strength, and stiffness of the original column are increased.


Reinforcement concrete jacketing can be used as a repair of strengthening scheme. If there is damage in some of the existing members, they should be repaired before jacketing.

The details of concrete jacketing with longitudinal steel bars are illustrated in the following figure.

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Among the global strengthening methods, addition of RC shear walls is the most popular one. Many researchers have focused on the addition of RC shear walls and found that the installation of RC shear walls greatly improves lateral load capacity and stiffness of the structure.

In the strengthening method with shear walls, the existing partition walls in the building are removed and high strength reinforced concrete shear walls are built instead.


In this method, shear walls have to be constructed the foundation level and there may not need to strengthen other components. The shear walls bear majority of the earthquake loads and limits the displacement behavior of the building.

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Under enormous cyclic forces during a seismic effect, Buckling Restrained Brace (BRB) which is system based strengthening techniques (global strengthening) devices can be used to increase the resistance of frame structures by providing energy dissipation and introducing nonlinear behavior.

Testing and evaluating are required for designing and ensuring quality control.


The structures are susceptible to collapse or large lateral displacements due to earthquake ground motions and require special attention to limit the displacement. This displacement can be brought into limit by providing BRB in the structure.

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The existing building is increased stiffness by column jacketing, adding shear walls and BRB which is the main reason in reducing time period when compared with that of the existing building.

Shear wall and BRB can contribute more stiffness than column jacketing.

Mode Natural Period (s)

Original Jacketing SW BRB

1 0.90 0.76 0.43 0.52

2 0.85 0.72 0.39 0.50

3 0.66 0.54 0.30 0.41

4 0.32 0.25 0.17 0.18

5 0.30 0.24 0.15 0.18

6 0.22 0.18 0.15 0.16


The pushover curves for all buildings in Y direction (weak direction) which represent the relationship between base shear and roof displacement are plotted in the following figure.

0

1000

2000

3000

4000

5000

0.00 0.05 0.10 0.15 0.20 0.25

Base Shear (KN)

Roof Displacement (m)

Pushover Curves for Different Buildings

ExistingColumn JacketingSWBRB

The results show all strengthening methods increased the building base shear, while they reduced the maximum roof displacement.

The shear walls were more effective than other strengthening methods in this purpose.

In the term of ductility, the results show that column jacketing technique caused the highest ductility, while shear walls significantly reduced the ductility.

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Base shear resulting from modal pushover analysis (MPA) at MCE levels of different strengthened buildings are summarized in the following figure.

28.4

15.0

45.0

26.5

48.5

40.340.9

34.4

0

10

20

30

40

50

60

X Y

Base Shear (%

)

Along Direction


MPA‐Existing MPA‐Jacketing MPA‐SW MPA‐BRB

Results showed that base shear of all strengthened buildings are increased approximately 1.5 times in X-direction and 2 times in Y-direction, respectively.

Column jacketing, adding shear walls and BRB cause the increase in the structural base shear because they contribute more stiffness to the existing building.


1

2

3

4

5

6

‐6000 ‐4000 ‐2000 0 2000 4000 6000

Story Level

Shear Force (KN)

Story Shear in X‐Direction

Existing

Jacketing

SW

BRB

1

2

3

4

5

6

‐6000 ‐4000 ‐2000 0 2000 4000 6000

Story Level

Shear Force (KN)

Story Shear in Y‐Direction

Existing

Jacketing

SW

BRB

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0

1

2

3

4

5

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

Sto

ry L

evel

Displacement (m)

MPA - MCE - Story Displacement (X)

Original

Jacketing

SW

BRB

Limit(H/200)

0

1

2

3

4

5

-0.30 -0.20 -0.10 0.00 0.10 0.20 0.30

Sto

ry L

evel

Displacement (m)

MPA - MCE - Story Displacement (Y)

Original

Jacketing

SW

BRB

Limit(H/200)

The story displacement and story drift for the buildings with shear walls (SW) and BRB are significantly decreased.


Based on the results, the shear capacity of many girders seems to be adequate to resist the probable shear demand with approximately 90% of D/C smaller than one.

Even thought the seismic performance existing structure is improved by using column jacketing, adding shear wall or BRB, it cannot avoid shear failure in girders because girders are primary structure which are used to transfer loads to vertical members.

Thus, it is recommended that only some girders about 10% need to be strengthened to resist shear demand. The strengthening method can perform by using concrete girder jacketing or CFRP.

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In terms of shear capacity, for the building with column jacketing is the most effective method to resist shear demand under MCE earthquake level, while many columns of the other strengthened buildings seem to be insufficient to resist the shear demand.

Therefore, it is recommended that the retrofit for shear capacity of columns have to be provided for only few columns for the column jacketing building, while most columns of the other strengthened buildings need to be strengthened.


The axial‐flexural interaction capacity of buildings with column jacketing, shear wall or BRB seem to be improved.

However, some columns need to be retrofitted to increase the capacity to resist these biaxial demand forces.

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Girders:

Flexural deformation of all girders generally acceptable for both DBE and MCE level earthquakes, while few girders seem to be inadequate to resist the demand forces at MCE level. However, the retrofitting for girder flexure is negligible. For girder shear capacity, only 10% of girders need to be strengthened to resist shear demand.


Columns:

For shear capacity, most columns are insufficient to resist the shear demand for both earthquake levels. Thus, it is recommended almost all columns need to be strengthened to increase shear capacities.

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Columns:

Moreover, in terms of axial‐flexural interaction capacity, approximately 50% of columns seem to be overstressed under earthquakes at MCE level. Therefore, these columns need to be strengthened to resist the biaxial demand force.


For strengthening of the existing building, three common strengthening techniques were used to improve the seismic performances of the existing building.

• Column jacketing (local strengthening approach)• Adding new shear walls, SW (global strengthening approach)• Adding bucking restrained braces, BRB (global strengthening approach)

With increase in the stiffness for all three strengthening methods, results show that the natural period of vibration of the building is reduced, while the base shear is increased.

The story displacement and story drift for the buildings with shear walls (SW) and BRB are significantly decreased.

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Shear and axial‐flexural interaction capacities of columns seem to be reduced because new shear walls and BRB can help to resist some shear demand. However, local strengthening is still required for both girders and columns.

However, in the case of the column jacketing, shears capacities of the girders and tension, compression, shear and axial‐flexural interaction capacities of columns seem to be adequate to resist demand forces under MCE earthquake level.

In conclusion, the results indicate that displacement at roof and story drift are within the limitation. Therefore, adding new shear walls and BRB may not be necessary because the local strengthening is still required for both girders and columns.

Moreover, in general, adding new shear walls are more expensive since additional foundation should be provided in this method. Therefore, based on these results, it might be concluded that the column jacketing is the most effective and the most economic strengthening method for this building. However, there are still 16% of girders that need to be strengthened to increase their shear capacity.


In addition, to verify the accuracy of modal pushover method (MPA), time-history analysis (THA) was also carried for comparison of the base shear.The existing building and the strengthened building including BRB were selected for this comparison. The results show that the base shear based on modal pushover is slightly different from that based on time-history analysis.

The ground motions used for time-history analysis are scaled to match with the target response spectrum for MCE earthquake level.

‐0.10

‐0.05

0.00

0.05

0.10

0 10 20 30 40 50 60

Ground Acceleration

(g)

Time (sec)

1776

1776‐FN 1776‐FP

(1) Target Spectrum(2) Searching for ground motions (3) Scaling

ground motions to the target

spectrum

(4) Using scaled ground motions for time-history analysis

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‐0.2

0.0

0.2

0 5 10 15 20 25Ground

Acceleration (g)

Time (sec)

719

719‐FN 719‐FP

‐0.1

0.0

0.1

0 5 10 15 20 25 30 35Ground

Acceleration (g)

Time (sec)

792

792‐FN 792‐FP

‐0.5

0.0

0.5

0 5 10 15 20 25 30

Ground Acceleration

(g)

Time (sec)

949

949‐FN 949‐FP‐0.40

‐0.20

0.00

0.20

0.40

0 5 10 15 20 25 30 35

Ground Acceleration

(g)

Time (sec)

988

988‐FN 988‐FP

‐0.20

‐0.10

0.00

0.10

0.20

0 10 20 30 40 50

Ground Acceleration

(g)

Time (sec)

1034

1034‐FN 1034‐FP‐0.50

0.00

0.50

0 5 10 15 20 25 30Ground Acceleration

(g)

Time (sec)

184

184‐FN 184‐FP

‐0.10

0.00

0.10

0 10 20 30 40 50 60Ground

Acceleration (g)

Time (sec)

1776

1776‐FN

1776‐FP


28.4

15.0

27.0

17.6

40.9

34.4

41.6

35.7

0

10

20

30

40

50

60

X Y

Base Shear (%)

Along Direction


MPA‐ExistingTHA‐ExistingMPA‐BRBTHA‐BRB

Comparison of base shear at the ground level between modal Pushover (MPA) and time history analysis (THA) for the existing building (Original) and the strengthened building using BRB

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38,537

24,840

39167

26911

4931044302

51090

37461

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

X Y

Moment (kN‐m

)

Along Direction

Comparison of Moment

MPA‐Existing

THA‐Existing

MPA‐BRB

THA‐BRB

Comparison of base moment at the ground level between modal Pushover (MPA) and time history analysis (THA) for the existing building (Original) and the strengthened building using BRB

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Seismic Performance Evaluation of Lal Durbar Convention Center building of Yak and Yeti Hotel, Kathmandu, Nepal, 18 April 2013.

Lal Durbar Convention Centre (LDCC) building was constructed in 1999. It is a four-story building with one basement.


0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Spectral A

cceleration, Sa (g)

Natural Period (s)

Response Spectra

DBE

MCE

T1T2T3T4T5T6

This seismic zone provides the response spectrum approximately equivalent to that for seismic zone V, mentioned in IS 1893:2002. DBE elastic level response spectrum is approximately increased from the value of DBE inelastic level response spectrum by 2.5 times. In addition, the factor 2 is used so as to increase DBE elastic level response spectrum to MCE level response spectrum.

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The proposed shear wall locations The revised shear wall locations


The proposed shear wall locations

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The revised shear wall locations


Nonlinear Components- Shear walls (layered shell)- Columns (Fiber hinges)- Girders (Moment hinges)

Linear Component- Slab

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Section (1)

Unconfined concrete

Confined concrete

Confined concrete

Section (2)

Section (3)

Steel

As1

As2

As3


Top bar

Bottom bar

ConcreteSection (1)

SECTION 1

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12.2 12.5

30.5 31.2

22.6 23.5

61.0 62.3

36.639.7

0

10

20

30

40

50

60

70

X Y

Base Shear (%

)

Along Direction


RSA‐DBE(inelastic)

RSA‐DBE

MPOA‐DBE

RSA‐MCE

MPOA‐MCE

Seismic weight of building at the ground level = 71,300 kN

1.7 1.6

MCE (Linear, RS)

MCE (Nonlinear, MPA)


A

Formation of Plastic Hinges for the First Mode of Modal Pushover Analysis (MCE level) with the Target Displacement 9.0 cm.

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The Roxas Triangle Tower is located in Paseo de Roxas St, Makati City, Philippines. It is a high-rise residential tower, which is 55-story high-rise building with 4-story of below grade parking. The building is reinforced concrete building. The lateral forces are mainly resisted by the reinforced concrete structure core built around the elevator shaft and special moment resisting frames connecting the core.

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Sample Backbone Curve for Unconfined Concrete

Sample Backbone Curve for Confined Concrete

Sample Backbone Curve for Reinforcement Steel

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Nonlinear fiber sections of shear walls

Shear hinge of coupling beam


3.43%2.73%2.61%

2.20%

8.72%

7.42%

17.39%

14.84%

8.51% 8.21%

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

X Y

Base Shear (%)

Along Direcrtion

Base Shear Percentage of Total Weight of Building

Wind*1.6(CODE)

Service

RSA‐DBE

RSA‐MCE

NLTHA‐MCE

2.0 1.8

MCE (Linear, RS)

MCE (Nonlinear, THA)

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0

5

10

15

20

25

30

35

40

45

50

55

‐0.006 ‐0.004 ‐0.002 0.000 0.002 0.004

Story Level

Axial Strain (mm/mm)

Wall Axial Strain (SW7, S18)

ARC

DAY

HRC

LCN

SCE

STG

TCU

Average

Steel YieldingStrain

Max. Comp.Strain Limit


0

10

20

30

40

50

60

‐30000 ‐20000 ‐10000 0 10000 20000 30000

Story Level

Shear Force (KN)

Wall Shear (SW5‐2)

AJC

LGP

PER

STG

STL

TAB

UNIO

Average

Capacity

MaximumLimit Capacity

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0

10

20

30

40

50

60

‐30000 ‐20000 ‐10000 0 10000 20000 30000

Story Level

Shear Force (KN)

Wall Shear (SW5‐2)

AJC

LGP

PER

STG

STL

TAB

UNIO

Average

Capacity

MaximumLimitCapacity

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lecture 2 - examples of strengthening building · ... addition of rc shear walls is ... during a...

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