on 28 february 2011 - firdausadnan.files.wordpress.com...seen in the middle of city. this map is...

(Project Rainbow II)

NATURAL HAZARD AND RISK ENGINEERING (NHRE) WS 2010/2011

By Firdaus (91128)

This report is submitted as a part of subject of Evaluation and Re‐Design of Structures

On 28 February 2011

CONTENTS

1. General 1 2. Modeling of the Structural System 3

2.1 Interpretation of the Structural System in view of Earthquake Resistant 3

2.2 Reliable Numerical Model 4

2.2.1 Layout and Geometry 5

2.2.2 Cross Sections 7

2.2.3 Material Properties and Load Cases 11

2.2.4 Masses and Distributed Loads 13

2.3 Identification of Dynamic response Characteristics 17

3. Capacity Curve, Spectra and Damage States 19

3.1 Check the effect of different horizontal Load Pattern 19

3.2 Application of Capacity Spectrum Method 20

3.3 Limit States 26

3.4 Critical Acceleration Levels in Dependence of Subsoil Conditions 32

4. Prediction of Structural Damage Corresponding to the Seismic Impact 36

4.1 According to the 1999 Düzce Earthquake 36

4.2 Comparison of Predicted with Observed Damage 39

5. Application of Strengthening and Retrofitting Measures 41

5.1 Modeling of Strengthening Measures 41

5.1.1 Reinforced Concrete Columns 42

5.1.2 Column Flexural Strengthening 44

5.1.3 Column Ductility Improvement and Shear Strengthening 47

5.2 Evaluation of the applied strengthening method on the basis the analysis results 51

6. Conclusions and Recommendations 54

7. References 55

8. Annex 1 56

1

EVALUATION AND RE‐DESIGN OF STRUCTURES

1. General

The 1999 İzmit earthquake was a 7.6 magnitude earthquake that struck northwestern Turkey on August

17, 1999, at about 3:02am local time. The event lasted for 37 seconds, killing around 17 thousand people

and leaving approximately half a million people homeless. The nearby city of Izmit was very badly

damaged.

An official Turkish estimate of October 19, 1999, placed the toll at 17,127 killed and 43,959 injured, but

many sources suggest the actual figure may have been closer to 45,000 dead and a similar number

injured. Reports from September 1999 show that 120,000 poorly engineered houses were damaged

beyond repair, 50,000 houses were heavily damaged, 2,000 other buildings collapsed and 4,000 other

buildings were heavily damaged. 600,000 people were left homeless after the earthquake.

Bolu is a province in north western in the Black Sea region of Turkey, midpoint between the large cities

of Istanbul and Ankara. It covers an area of 7,410 km², and the population is 271,545. This is an

attractive forested mountain district centre on the city of Bolu, which has a long history.

The objective of this project is to

1. Evaluate the vulnerability and slightly damaged of RC frame structures, which were affected by

the 1999 Düzce earthquake.

2. Determine the capacity of the building, predict and compare the damage under the occurred

seismic action.

3. Apply some strengthening measures onto the reconstructed building.

The pictures below describe the shaking map which was generated by Mapinfo version 10.5. It can be

clearly seen that the earthquake source was situated at the land and it was really near to the main cities.

2

Figure 1. Shaking map of The 1999 İzmit earthquake

Figure 2. Detail of Intensity zone due to the 1999 İzmit earthquake

3

Based on the task, position of Bolu 15 is Latitude : 40.739479° and Longitude : 31.611561°.

In the map below, the topography of Bolu city is situated at the valley and the building (Red box) can be

seen in the middle of city. This map is generated by using ArcGIS v.9.2 and Sketchup software.

Figure 3. 3D Perspective with respect to topography by using ArcGIS and sketchup

2. Modeling of the Structural System 2.1. Interpretation of the Structural System in view of Earthquake Resistant

Nowadays, Earthquakes are very difficult to predict when it will occur and where it is. Therefore, the

only way to prevent structural damage against a seismic loading in earthquake areas is through

proper design and construction. For that purpose, it is important to sufficiently understand seismic

activity, dynamic effect and related building response. The dynamic response of a building against

an earthquake vibration is an important structural aspect which directly affects the structural

resistance and consequently the hazard level. Not only the direct member displacements and

member strength must be considered in structural analysis, but also second order effects caused by

large displacements due to cyclic loading.

In order to design an earthquake resistant steel building, engineers can choose different methods

and structural components capable to withstand lateral loads. These structural elements can be:

shear walls, concentrically or eccentrically braced frames, moment resisting frames, diaphragms,

truss systems and other similar systems. The determination of an appropriate earth resisting system

4

also is dependent upon the building design's architectural concept. Therefore, the designer

responsible for making an earthquake resistant building must develop a comprehensive structural

system that will address the requirements of earthquake safety, building cost, building use, and

importantly the architectural design.

Figure 4. This building is reconstructed

by RC‐Frame with Shear wall (Blue).

These shear wall are necessary to

resist earthquake force from weak

direction. We could install it as a lift

access.

2.2. Reliable Numerical Model

PERFORM 3D is a highly focused nonlinear software tool for earthquake resistant design.

Complex structures, including those with intricate shear wall layouts, can be analyzed

nonlinearly using a wide variety of deformation‐based and strength‐based limit states.

PERFORM 3D provides powerful performance based design capabilities, and can calculate

demand/capacity (usage) ratios for all components and all limit states. Performance assessment

based on ATC‐40, FEMA‐356 or ATC‐440 is fully automated.

PERFORM 3D output includes usage ratio plots, pushover diagrams, energy balance displays, as

well as mode shapes, deflected shapes, and time history records of displacements and forces.

5

2.2.1. Layout and Geometry The task (Bolu 15) given, consists of portal frame (column and beam) without wall. The layout of this building is:

Figure 5. Layout of Bolu 15 Building

The 3D perspective of this building can be seen in the figure 6 below:

6

Figure 6. 3D perspective of Bolu 15 Building Detail of each element properties is following below:

Table 1. Element properties of Bolu 15

Elements b h A (m2) γ (kg/m3) W (kg/m) W (kg/cm) W (kN/cm)

A Column_20x100 0.2 1 0.2 2400 480 4.8 0.048B Column_25x60 0.25 0.6 0.15 2400 360 3.6 0.036C Column_25x70 0.25 0.7 0.175 2400 420 4.2 0.042D Column_30x70 0.3 0.7 0.21 2400 504 5.04 0.050E Column_20x190 0.2 1.9 0.38 2400 912 9.12 0.091

beam_20x50 0.2 0.5 0.1 2400 240 2.4 0.024

2.6 m

2.6 m

2.6 m

2.6 m

7

2.2.2. Cross Sections

Every element has own cross section stiffness and material properties. The table below is describing the detail of cross section properties for Bolu 15.

Table 2. Section stiffness for each element

There are two types of fiber cross section for beam and column elements, namely the “Beam

Inelastic Fiber Section” and the “Column Inelastic Fiber Section”. In this project, we just use

column element for all sections which is limited 60 fibers for each section. Column sections use

the fiber properties for bending about both axes, and account for P‐M‐M interaction.

The following material types are currently allowed for the fibers :

1. steel material

2. tension‐only material

3. buckling material

4. Concrete material.

The detail of fibers for each section is illustrated in the figures below:

Dimension

Section stiffness

1 Axial Area (cm2) 2000 1500 1750 2100 1000 3800

2 Shear area Axis 2 (cm2) 1666.7 1250 1458.3 1750 833.33 3166.5

3 Shear area axis 3 (cm2) 1666.7 1250 1458.3 1750 833.33 3166.54 Torsional Inertia 233690 242680 294690 485080 104760 4567105 bending Inertia Axis 2 66667 78125 91146 157500 33333 1266706 bending Inertia Axis 3 1666700 450000 714580 857500 208330 1.14E+07Material properties

1 Young's Modulus (kN/cm2) 3350 3350 3350 3350 3350 33502 Poisson's ratio 0.2 0.2 0.2 0.2 0.2 0.2

3 Shear Modulus (kN/cm2) 1395.8 1395.8 1395.8 1395.8 1395.8 1675

C ‐ 20x190 cm (E)

C ‐ 20x100 cm (A)

C ‐ 25x60 cm (B)

C ‐ 25x70 cm (C)

C ‐ 30x70 cm (D)

B ‐ 20x50 cm

8

Figure 7. Fiber position in column 20 cm x 100 cm

9



10


Figure 11. Fiber position in beam 20 cm x 50 cm

2. Th

co

C

be

.2.3. Mater

he table belo

onsists of 3

orrelation be

elow:

Stress

Figure 1

rial Propertie

ow explains th

element typ

etween stres

Figure

s (kN/cm2)

2. Fiber posit

s and Load Ca

he material p

pes, which a

ss and strain

e 13. Relation

tion in column

ases

properties for

are steel ba

for each el

n between Str

n 20 cm x 190

r all material

r, cover con

ement could

ress and Strai

0 cm

types in Bolu

ncrete and c

d be illustrate

in

u 15. Each ele

onfined conc

ed by the p

Strain (cm)

11

ement

crete.

icture

12

Table 3. Detail of Stress and Strain for each material type.

There are 2 load types are applied onto the elements, which are Dead Load and Live Load. These

loads are distributed on the slab and additional elements. The beam element accommodates all

these loads into line load along the beam span.

The table below is explaining the detail of Load Cases in Bolu 15.

material Properties SteelCover

concreteConfined Concrete

Young's Modulus [kN/cm2] 20000 3350 3350KH/KO pos 0.003KH/KO neg 0.179 0.313

Tension StressesFY (kN/cm2) 50FU (kN/cm2) 55

Compression StressesFY (kN/cm2) 2.8 2.92FU (kN/cm2) 3.5 4.05

Tension StrainsDU (cm) 0.078DX (cm) 0.088DL (cm) 0.08DR (cm) 0.082FR/FU 0.01

Compression StrainsDU (cm) 0.002 0.00195DX (cm) 0.006 0.0412DL (cm) 0.0025 0.0054DR (cm) 0.005 0.03914FR/FU 0.01 0.8

Tension CapacitiesLevel 1 0.0025 0.0022 0.00392Level 2 0.08 0.004Level 3 0.006

Compression CapacitiesLevel 1 0.0022 0.00392Level 2 0.004Level 3 0.006

Strength Loss Interaction 1

13

Table 4. Detail Load cases in Bolu 15

2.2.4. Masses and Distributed Loads

Bolu 15 building is analyzed by considering non linear behavior where we have to investigate the masses (m), damping (c) and stiffness (k). These parameters are related into an equation which is declared in the following below:

mx¨(t) + cx˙ (t) + kx(t) = f(t)

Mass is a main factor to determine mode shape due to dynamic load. Mode shape is related to the frequency/period which is generated by a vibration (lateral load). In perform 3D, we are doing a push over analysis where we apply a lateral load to determine maximum capacity from a building.

The table below describes the masses distribution for each node which is illustrated in the figure 14.

Position Type of Loadthickness

(m)γ

(kN/m3)q

(kN/m2)L (m)

floor_span_1 RC floor 0.16 24 3.84 4.1 15.744 kN/mPlaster and covering 1.25 4.1 5.125 kN/mLightweight partitions 1.25 4.1 5.125 kN/mTotal Dead Load 6.34 25.994 kN/mLive Load 2 4.1 8.2 kN/m

floor_span_2 RC floor 0.16 24 3.84 3.1 11.904 kN/mPlaster and covering 1.25 3.1 3.875 kN/mLightweight partitions 1.25 3.1 3.875 kN/mTotal Dead Load 6.34 19.654 kN/mLive Load 2 3.1 6.2 kN/m

floor_span_3 RC floor 0.16 24 3.84 3.2 12.288 kN/mPlaster and covering 1.25 3.2 4 kN/mLightweight partitions 1.25 3.2 4 kN/mTotal Dead Load 6.34 20.288 kN/mLive Load 2 3.2 6.4 kN/m

roof_span_1 Dead Load 0.2 24 4.8 4.1 19.68 kN/mSnow 1.25 4.1 5.125 kN/mTotal Dead Load 6.05

roof_span_2 Dead Load 0.2 24 4.8 3.1 14.88 kN/mSnow 1.25 3.1 3.875 kN/mTotal Dead Load 6.05

roof_span_3 Dead Load 0.2 24 4.8 3.2 15.36 kN/mSnow 1.25 3.2 4 kN/mTotal Dead Load 6.05

Load

14

Table 5. Masses distribution at Bolu 15

Masses at every point above are assigned for all joint in Bolu 15 building. Dead Load masses are

assigned for all storeys, whereas the Live Load masses are not assigned for 4th storey since there

is no activity at the top storey.

Slab loads transmitted to beams can be calculated from the areas limited by lines bisecting the

angles at the corners of any panel as shown in figure 15. These loads are of

triangular/trapezoidal pattern. Transforming these loads to equivalent uniform distributed loads

is allowed by the code.

L1 L2 ADead

Load (kN)Live Load

(kN)

Dead Load on the Roof

(kN)Point A 2.05 2.45 5.02 31.84 10.05 30.39Point B 3.60 2.45 8.82 55.92 17.64 53.36Point C 3.15 2.45 7.72 48.93 15.44 46.69Point D 1.60 2.45 3.92 24.85 7.84 23.72Point E 2.05 3.80 7.79 49.39 15.58 47.13Point F 3.60 3.80 13.68 86.73 27.36 82.76Point G 3.15 3.80 11.97 75.89 23.94 72.42Point H 1.60 3.80 6.08 38.55 12.16 36.78Point I 2.05 2.65 5.43 34.44 10.87 32.87Point J 3.60 2.65 9.54 60.48 19.08 57.72Point K 3.15 2.65 8.35 52.92 16.70 50.50Point L 1.60 2.65 4.24 26.88 8.48 25.65Point M 2.05 2.75 5.64 35.74 11.28 34.11Point N 3.60 2.75 9.90 62.77 19.80 59.90Point O 3.15 2.75 8.66 54.92 17.33 52.41Point P 1.60 2.75 4.40 27.90 8.80 26.62Point Q 2.05 2.85 5.84 37.04 11.69 35.35Point R 3.60 2.85 10.26 65.05 20.52 62.07Point S 3.15 2.85 8.98 56.92 17.96 54.31Point T 1.60 2.85 4.56 28.91 9.12 27.59Point U 2.05 2.20 4.51 28.59 9.02 27.29Point V 3.60 1.85 6.66 42.22 13.32 40.29Point W 3.15 1.85 5.83 36.95 11.66 35.26Point X 1.60 1.40 2.24 14.20 4.48 13.55

15

Figure 14. Slab zone for vertical load at the point

Figure 15. Load Distribution from slab to beams

Based on the method above, these tables are detail of loading calculation from the slab to the beams.

4.1 3.1 3.2

4.9

2.7

2.6

2.9

2.83.7

4.4

A B C D

E F G H

K L

M N

I

O

J

P

Q R S T

UV

W X

16

Table 6. Triangular/trapezoidal loads

Table 7. Line Loads for H1 Direction

slab Types b (m) h (m) L1 (m) L2 (m) A (m2)L

(m)Dead Load

(kN/m)Live Load

(kN/m)1.1 triangular 4.1 2.05 4.2025 4.1 6.19 1.95

trapezoidal 2.05 4.9 0.8 5.8425 4.9 5.32 1.681.2 triangular 3.1 1.55 2.4025 3.1 8.18 2.58








trapezoidal 0.8 2.6 1 1.44 2.6 11.45 3.614.1 triangular 4.1 1.025 2.10125 4.1 12.37 3.90






trapezoidal 0.8 2.8 1.2 1.6 2.8 11.10 3.50

BeamDead Load

(kN/m)

Live Load (kN/m)

Dead Load

(kN/cm)

Live Load (kN/cm)

A-B 6.19 1.95 0.062 0.020B-C 8.18 2.58 0.082 0.026C-D 7.93 2.50 0.079 0.025E-F 18.56 5.85 0.186 0.059F-G 24.54 7.74 0.245 0.077G-H 23.78 7.50 0.238 0.075I-J 24.74 7.80 0.247 0.078J-K 32.72 10.32 0.327 0.103K-L 31.70 10.00 0.317 0.100M-N 24.74 7.80 0.247 0.078N-O 32.72 10.32 0.327 0.103O-P 31.70 10.00 0.317 0.100Q-R 24.74 7.80 0.247 0.078R-S 32.72 10.32 0.327 0.103S-T 31.70 10.00 0.317 0.100U-V 12.37 3.90 0.124 0.039V-W 16.36 5.16 0.164 0.052W-X 15.85 5.00 0.159 0.050

17

Table 8. Line Loads for H2 Direction

2.3. Identification of Dynamic response Characteristics

The structure behaves 3‐dimensionally against earthquake ground motion, therefore the response

characteristics are necessary to be reflected to the design of structures. As the first step of a

breakthrough on the 3‐dimentional Reinforced Concrete (RC) column response behaviors, we focus on

the bilateral behavior.

The experimental results showed that the effect of bilateral excitation of the column was found to be

significant on the non‐linear response behavior of the column. Furthermore, it was found that the fiber

element model analysis could simulate the experimental results well before the deterioration of the

strength of the columns caused by the buckling of longitudinal reinforcement and the peeling of cover

concrete.

The figure below describes two drift directions which are used to do Pushover analysis. We are pushing

the building corresponding to the limit of the drift.

BeamDead Load

(kN/m)

Live Load (kN/m)

Dead Load

(kN/cm)

Live Load (kN/cm)

A-E 5.32 1.68 0.053 0.017B-F 11.30 3.56 0.113 0.036C-G 11.87 3.74 0.119 0.037D-H 5.88 1.86 0.059 0.019E-I 9.97 3.15 0.100 0.031F-J 21.44 6.76 0.214 0.068G-K 22.74 7.17 0.227 0.072H-L 11.26 3.55 0.113 0.036I-M 10.21 3.22 0.102 0.032J-N 21.87 6.90 0.219 0.069K-O 23.10 7.29 0.231 0.073L-P 11.45 3.61 0.114 0.036M-Q 9.57 3.02 0.096 0.030N-R 20.73 6.54 0.207 0.065O-S 22.11 6.97 0.221 0.070P-T 10.94 3.45 0.109 0.035Q-U 9.76 3.08 0.098 0.031R-V 21.07 6.65 0.211 0.066S-W 22.41 7.07 0.224 0.071T-X 11.10 3.50 0.111 0.035

18

Figure 16. Drift directions at one corner

Drift at H1 Direction Drift at H2 Direction

3. Capa 3.1. C

Struct

displa

The g

for pu

than H

Limit

SteeSteeConcConc

city Curve, S

Check the eff

tural capacity

acement curv

raph below d

ushover at H

H2 direction.

Ta

t State at H1 Di

l Yieldingl Ultimatecrete Spallingcrete Degradat

Spectra and

ect of differe

y is represent

e is by trackin

describes capa

1 direction is

Figure 17

ble 9. Base Sh

irection

Ref. D

%0.0.0.

tion 0.

d Damage St

ent horizonta

ted by a push

ng the base s

acity curve fo

s higher than

7. Capacity Cu

hear and refe

Drift Base Shea

kN.005 283.03.013 551.13.007 394.44.008 430.55

tates

l Load Patter

hover curve. T

hear and the

or 2 push ove

n H2 direction

urve from 2 p

erence drift fr

Lim

ar

31 Ste37 Ste46 Con51 Con

rn

The most con

roof displace

r directions. A

n. It means,

push over ana

rom 2 push ov

mit State at H2

eel Yieldingeel Ultimatencrete Spallingncrete Degrad

nvenient way

ement.

As shown in t

stiffness at H

alysis

ver analysis

Direction

Ref. Dr

%0.1440.418

g 0.193ation 0.240

y to plot the f

the graph, du

H1 direction i

rift Base Shear

kN4% 986.2898% 1746.9803% 1180.4600% 1352.451

19

force‐

ctility

is less

r

9001

20

Table 10. Detail Base shear value for each reference drift from 2 push over analysis

3.2. Application of Capacity Spectrum Method

The Capacity Spectrum Method (CSM) is a procedure that can be applied to Performance‐Based

Seismic Design which gives a realistic assessment of how a structure will perform when subjected to

either particular or generalized earthquake ground motion. By converting the base shears and roof

displacements from a non‐linear pushover to equivalent spectral accelerations and displacements

and superimposing an earthquake demand curve, the non‐linear pushover becomes a capacity

spectrum.

Ref. Drift F (KN) Ref. Drift F (KN) Ref. Drift F (KN)

0.00% 0 1.20% 556.3774 0.00% 00.00% 3.867924 1.25% 549.0917 0.00% 9.1451090.05% 51.97622 1.29% 535.0541 0.05% 479.10770.10% 90.22143 1.35% 551.1366 0.10% 765.16720.15% 122.2763 1.39% 533.1299 0.14% 986.28930.20% 150.1437 1.44% 546.6237 0.19% 1180.460.25% 177.4794 1.50% 558.7481 0.24% 1352.4510.30% 203.3567 1.55% 570.6151 0.29% 1511.0750.35% 230.1396 1.60% 581.4202 0.34% 1649.3880.40% 256.4514 1.65% 591.7467 0.38% 1734.3530.45% 283.0313 1.70% 562.7814 0.42% 1746.980.50% 307.4047 1.74% 577.0224 0.48% 1791.7240.55% 329.9739 1.79% 588.2768 0.52% 1745.0240.60% 351.804 1.85% 598.5183 0.57% 1755.9310.65% 372.6557 1.89% 597.0939 0.62% 1785.5990.70% 394.446 1.94% 579.803 0.66% 1775.8440.75% 415.4799 1.99% 594.1616 0.73% 1750.7780.80% 430.5507 2.04% 604.0106 0.77% 1770.0390.85% 448.6069 2.09% 606.8904 0.83% 1749.2290.90% 467.3284 2.14% 600.9731 0.87% 1741.7540.95% 484.1482 2.19% 610.2912 0.90% 1728.3481.00% 499.6085 2.23% 584.1528 0.97% 1680.121.05% 514.6893 2.28% 593.8748 1.01% 1666.1641.10% 529.7755 2.33% 577.6529 1.05% 1686.3561.15% 543.2078 2.38% 584.0585

H2 DirectionH1 Direction

To us

of bas

of the

The o

lowes

e the capacit

se shear and

e capacity cur

output from e

st frequency (

y spectrum m

roof displace

rve in Acceler

Figure 18.

xcitation load

(2.8 rad) or th

Table 11

Mode Numbe

Period

Frequency

method it is n

ement to wha

ration‐Displac

Capacity Spe

d is the funda

he highest pe

1. Period and

er 1

0.36

2.80

ecessary to c

at is called a c

cement Respo

ctrum from 2

amental frequ

riod (0.36 sec

d frequency d

2 3

0.34 0.3

2.97 3.3

convert the ca

capacity spect

onse Spectra

2 push over a

uency or perio

cond).

ue to excitati

4

30 0.25

39 3.95

apacity curve

trum, which i

(ADRS) forma

nalysis

od which is d

ion load

5

0.24

4.14

e, which is in t

is a represent

at.

efined as the

21

terms

tation

22

Table 12. Detail Response Spectrum value for H1 and H2 Direction

Sd (cm) Sa (g) Sa (cm/s2) Area (cm2) Sd (cm) Sa (g) Sa (cm/s2) Area (cm2)

0.000 0.000 0.000 0.000 0.017 0.003 2.463 0.000

0.031 0.006 5.438 0.085 1.181 0.134 131.743 78.152

0.443 0.073 71.942 15.921 2.216 0.213 208.653 176.029

0.843 0.124 121.989 38.790 3.106 0.272 266.616 211.672

1.228 0.165 162.338 54.811 3.957 0.323 316.795 248.007

1.587 0.201 196.804 64.413 4.784 0.368 360.896 280.374

1.956 0.235 230.602 78.886 5.656 0.409 401.218 332.313

2.318 0.267 262.525 89.188 6.584 0.444 435.995 388.508

2.705 0.301 295.692 107.901 7.599 0.466 457.760 453.620

3.095 0.335 328.631 121.970 8.906 0.466 457.180 597.998

3.500 0.369 362.097 139.783 10.656 0.476 466.897 808.381

3.888 0.400 392.586 146.340 12.002 0.459 450.633 617.415

4.264 0.429 420.642 152.919 12.944 0.458 449.281 423.905

4.648 0.456 447.579 166.535 13.882 0.464 454.979 424.012

5.028 0.482 473.216 175.228 14.850 0.460 451.815 439.147

5.436 0.509 500.024 198.646 15.540 0.448 440.144 307.521

5.848 0.536 525.574 211.058 16.115 0.452 443.646 254.253

6.210 0.552 541.355 192.919 16.783 0.443 435.169 293.366

6.600 0.573 562.516 215.266 17.263 0.439 430.879 208.064

7.009 0.596 584.673 234.634 17.819 0.436 427.876 238.627

7.386 0.616 604.500 224.445 18.852 0.422 414.512 435.153

7.758 0.634 622.413 227.800 19.283 0.418 410.124 177.618

8.139 0.652 639.561 240.664 19.859 0.422 414.057 237.315

8.527 0.669 656.427 251.665 ∑ 7631.449

8.896 0.684 671.032 244.641

9.273 0.698 684.996 255.740

9.592 0.677 664.108 215.342

9.925 0.645 633.325 216.123

10.354 0.664 651.235 275.304

10.707 0.631 618.897 223.943

11.111 0.645 633.505 253.367

11.517 0.658 646.252 259.445

11.922 0.671 658.619 264.054

12.299 0.682 669.747 250.669

12.676 0.693 680.191 254.295

13.088 0.650 638.240 272.111

13.437 0.668 655.219 225.379

13.827 0.680 666.943 258.026

14.216 0.690 677.247 261.593

14.612 0.685 672.582 267.165

15.001 0.657 644.473 256.042

15.397 0.673 660.217 258.068

15.783 0.682 669.794 256.798

16.163 0.683 670.247 254.427

16.575 0.673 660.876 274.564

16.931 0.684 671.051 237.209

17.465 0.650 637.664 349.237

17.861 0.660 648.226 254.838

18.321 0.638 626.219 292.874

18.701 0.645 633.062 239.043

∑ 10020.162

H1 Direction H2 Direction

23

A previous version of the seismic hazard map for the DA‐CH countries (Germany D, Austria A,

Switzerland CH, et al. Grünthal 1998) was commissioned by the German Institute for Building

Technology (DIBt) as the basis for the map of seismic zones of the DIN 4149 (amended 2005) and for

the National Annex to Eurocode 8.

Elastic Response Spectra DIN 4149 (2002) is drawn by following the equilibrium below:

As shown in Table 13, five different subsoil classes (A‐E) are defined. The main distinguishing feature

is the average shear wave velocity Vs,30 that exists in the uppermost 30 meters of the subsoil layers.

If Vs,30 is not available, the Standard Penetration Test blow‐count NSPT should be used for site

classification. The value cu describes the shear strength of the soil that has not been drained.

Table 13. Subsoil characteristic according to EC8

Equivalent linearization is used as a part of a nonlinear static procedure that models the nonlinear

response of a building with a SDOF oscillator, the objective is to estimate the maximum

displacement response of the nonlinear system with an “equivalent” linear system using an effective

period, Teff, and effective damping, βeff.

Effective viscous damping values (βeff), expressed as a percentage of critical damping, for all

hysteretic model types and alpha values have the following form:

For 1 < μ < 4

βeff = A(μ‐1)2 + B(μ‐1)3 + β0

T = 0 Se (T) = ag * S

TA < T < TB Se (T) = ag * S * [1 + T/TB * (η * β0 - 1)]

TB < T < TC Se (T) = ag * S * η * β0

TC < T < TD Se (T) = ag * S * η * β0 * TC/ T

TD < T Se (T) = ag * S * η * β0 * (TC * TD)/ T²

24

For 4 < μ < 6.5

βeff = C + D(μ‐1) + β0

For μ > 6.5

( )( )

2

020

1 1

1eff

eff

TFE

TF

μβ β

μ

⎡ ⎤− − ⎛ ⎞⎢ ⎥= +⎜ ⎟⎢ ⎥−⎡ ⎤ ⎝ ⎠⎣ ⎦⎣ ⎦

Effective period values for all hysteretic model types and alpha values have the following form:

For 1 < μ < 4

Teff = [G(μ‐1)2 + H(μ‐1)3 +1]T0

For 4 < μ < 6.5

Teff = [I + J(μ‐1) + 1]T0

For μ > 6.5

( ) 01 1 1

1 2effT K TLμ

μ

⎧ ⎫⎡ ⎤−⎪ ⎪= − +⎢ ⎥⎨ ⎬+ −⎢ ⎥⎪ ⎪⎣ ⎦⎩ ⎭

Values of the coefficients in the equations for effective damping (βeff) and period (Teff ) of the

model oscillators are tabulated in Table 14 and table 15.

Table 14. Coefficient for use in equations for effective period

Model alpha [%] G H I J K L

Bilinear hysteretic BLH 0 0.11 ‐0.017 0.27 0.09 0.57 0Bilinear hysteretic BLH 2 0.10 ‐0.014 0.17 0.12 0.67 0.02Bilinear hysteretic BLH 5 0.11 ‐0.018 0.09 0.14 0.77 0.05Bilinear hysteretic BLH 10 0.13 ‐0.022 0.27 0.10 0.87 0.1Bilinear hysteretic BLH 20 0.10 ‐0.015 0.17 0.094 0.98 0.2

Stiffness degrading STDG 0 0.17 ‐0.032 0.10 0.19 0.85 0Stiffness degrading STDG 2 0.18 ‐0.034 0.22 0.16 0.88 0.02Stiffness degrading STDG 5 0.18 ‐0.037 0.15 0.16 0.92 0.05Stiffness degrading STDG 10 0.17 ‐0.034 0.26 0.12 0.97 0.1Stiffness degrading STDG 20 0.13 ‐0.027 0.11 0.11 1.00 0.2Stiffness degrading STDG ‐3 0.18 ‐0.033 0.17 0.18 0.76 ‐0.03Stiffness degrading STDG ‐5 0.20 ‐0.038 0.25 0.17 0.71 ‐0.05

25

Table 15. Coefficient for use in equations for effective damping

MADRS (Modified Acceleration‐Displacement Response Spectrum) method estimates the maximum

displacement response of nonlinear system with an equivalent linear system using the effective

period (Teff) and effective damping (βeff). The effective linear parameters are functions of the

capacity spectrum, the corresponding initial period and damping, and the ductility demand (μ).

The use of effective period and damping generate a maximum displacement that coincides with the

intersection of the radial effective period line and the ADRS demand. The intersection point is

presented by the amax and dmax.

Figure 19. MADRS for use with secant period

Model alpha [%] A B C D E F

Bilinear hysteretic BLH 0 3.2 ‐0.66 11 0.12 19 0.73Bilinear hysteretic BLH 2 3.3 ‐0.64 9.4 1.1 19 0.42Bilinear hysteretic BLH 5 4.2 ‐0.83 10 1.6 22 0.4Bilinear hysteretic BLH 10 5.1 ‐1.1 12 1.6 24 0.36Bilinear hysteretic BLH 20 4.6 ‐0.99 12 1.1 25 0.37

Stiffness degrading STDG 0 5.1 ‐1.1 12 1.4 20 0.62Stiffness degrading STDG 2 5.3 ‐1.2 11 1.6 20 0.51Stiffness degrading STDG 5 5.6 ‐1.3 10 1.8 20 0.38Stiffness degrading STDG 10 5.3 ‐1.2 9.2 1.9 21 0.37Stiffness degrading STDG 20 4.6 ‐1 9.6 1.3 23 0.34Stiffness degrading STDG ‐3 5.3 ‐1.2 14 0.69 24 0.9Stiffness degrading STDG ‐5 5.6 ‐1.3 14 0.61 22 0.9

26

MADRS demand curve is obtained by multiplying the ordinates of the ADRS demand corresponding

to the effective damping (βeff) by the modification factor M.

2 2 2

0

sec 0 sec

eff effT T TMT T T

⎛ ⎞ ⎛ ⎞ ⎛ ⎞= =⎜ ⎟ ⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠ ⎝ ⎠ where

( )2

0

sec

1 1TT

α μμ

+ −⎛ ⎞=⎜ ⎟

⎝ ⎠

α is the post‐elastic stiffness and u is the ductility demand and given by

pi y

pi y

y

y

a ad d

ad

α

⎛ ⎞−⎜ ⎟⎜ ⎟−⎝ ⎠=

pi

y

dd

μ =

Spectral reduction factors are applied to obtain reduced demand spectra for the appropriate level of

effective damping (βeff). In the MADRS method, these factors are termed damping coefficients,

B(βeff), and used to adjust spectral acceleration ordinates given as follow:

( ) ( )( )

0aa

eff

SS

Bβ β=

45.6 ln ( %)eff

Binβ

=−

3.3. Limit States

A nonlinear analysis can produce a huge volume of analysis results. If you make effective use of limit

states you can distill the results down to a few usage ratios that can tell you whether the structure

satisfies the performance requirements. The limit states type are following below:

• Deformation limit states, based on deformation capacities for inelastic components.

• Strength limit states, based on strength capacities for elastic components and strength

sections.

• Drift limit states, based on drifts.

• Deflection limit states, based on deflections.

• Shear strength limit states for structure sections.

27

1. Steel Yielding

The yield strength or yield point of a material is defined in engineering and materials science as

the stress at which a material begins to deform plastically. Prior to the yield point the material

will deform elastically and will return to its original shape when the applied stress is removed.

Once the yield point is passed some fraction of the deformation will be permanent and non‐

reversible.

2. Steel Ultimate

Ultimate tensile strength (UTS), often shortened to tensile strength (TS) or ultimate strength,is

the maximum stress that a material can withstand while being stretched or pulled

before necking, which is when the specimen's cross‐section starts to significantly contract.

3. Concrete Spalling

Spalling concrete is concrete which breaks up, flakes, or becomes pitted. This is usually the

result of a combination of poor installation and environmental factors which stress the concrete,

causing it to become damaged. On a low level, concrete spalling can be purely cosmetic in

nature. However, it can also result in structural damage such as damage to reinforcing bars

positioned inside the concrete. For this reason, it is important to address spalling concrete when

it first starts to appear.

4. Concrete Degradation

Concrete degradation may have various causes. Concrete can be damaged by fire, aggregate

expansion, sea water effects, bacterial corrosion, calcium leaching, physical damage and

chemical damage (from carbonation, chlorides, sulfates and distilled water). This process

adversely affects concrete exposed to these damaging stimuli.

The result of pushover analysis for each limit state is:

28

Table 16. Response Spectrum for each Limit State

A bilinear representation of the capacity spectrum is needed to estimate the effective damping

and appropriate reduction of spectral demand. Construction of the bilinear representation

requires definition of the point api and dpi. This point is the trial performance point which is

estimated by the engineer to develop a reduced demand response spectrum.

The graphs below are bilinear representation for each limit state which are calculated for H1

and H2 direction.

Table 17 below is an example of calculation for determining effective damping, effective period,

MADRS and damping coefficient (B). These parameters are defined to determine critical

acceleration level. The others calculation details are enclosed in the Annex 1.

Results for each Limit State at H1 DirectionDisplacement

cm g cm/s2

Steel Yielding 3.500 0.369 362.1Steel Ultimate 10.354 0.664 651.2Concrete Spalling 5.436 0.509 500.0Concrete Degradation 6.210 0.552 541.4

Results for each Limit State at H2 DirectionDisplacement

cm g cm/s2

Steel Yielding 3.106 0.272 266.6Steel Ultimate 8.906 0.466 457.2Concrete Spalling 3.957 0.323 316.8Concrete Degradation 4.784 0.368 360.9

Acceleration

Acceleration

Figure 20. Bilinnear vs Capacity sspectrum for pusshover analysis att H1 direction

29

Figure 21. Bilinnear vs Capacity s

spectrum for pusshover analysis att H2 direction

30

31

Table 17. An example calculation for determining Effective damping and period

Steel Yielding

Steel Ultimate

Concrete Spalling

Concrete Degradation

d0 cm 0 0.000 0.000 0.000

dy cm 0.5 4.000 0.600 0.700

dpi cm 3.500 10.354 5.436 6.210

a0 cm/s20 0.000 0.000 0.000

ay cm/s297 485.000 120.000 140.000

api cm/s2362.1 651.235 500.024 541.355

Ay cm2 24.250 970.000 36.000 49.000

Api cm2 688.663 3609.881 1499.347 1877.008A1 cm2 712.913 4579.881 1535.347 1926.008A2 cm2 711.748 4557.015 1551.416 1955.393Diff. cm2 0.164 0.502 -1.036 -1.503To sec 0.451 0.571 0.444 0.444α (%) 45.548 21.577 39.288 36.423α (%) 20.000 20.000 20.000 20.000

A 4.600 4.600 4.600 4.600B ‐0.990 ‐0.990 ‐0.990 ‐0.990C 12.000 12.000 12.000 12.000D 1.100 1.100 1.100 1.100E 25.000 25.000 25.000 25.000F 0.370 0.370 0.370 0.370G 0.100 0.100 0.100 0.100H ‐0.015 ‐0.015 ‐0.015 ‐0.015I 0.170 0.170 0.170 0.170J 0.094 0.094 0.094 0.094K 0.980 0.980 0.980 0.980L 0.200 0.200 0.200 0.200

β0 = 5.000 5.000 5.000 5.000

η = 1.000 1.000 1.000 1.000

Sub Soil A A A A

Vs,30 >800 >800 >800 >800S 1.000 1.000 1.000 1.000TB 0.150 0.150 0.150 0.150TC 0.400 0.400 0.400 0.400

TD 2.000 2.000 2.000 2.000μ 7.000 2.589 9.061 8.871

Teff = 0.775 0.680 0.805 0.802

βeff = 23.253 12.639 23.284 23.352M = 50.985 17.994 58.748 58.141B = 1.630 1.306 1.631 1.633

B / M = 0.032 0.073 0.028 0.028ag cm/sec2 2264.804 1794.821 3601.789 3854.624

TB < T < TC g 2.308 1.829 3.670 3.927ag cm/sec2 4386.576 3052.491 7246.960 7725.189

TC < T < TD g 4.469 3.110 7.384 7.871ag cm/sec2 1699.225 1038.288 2916.241 3096.465

TD < T g 1.731 1.058 2.971 3.155

Soil Type

ICo

eff. Eff. Dam

ping

Coeff. Eff. Period

32

3.4. Critical Acceleration Levels in Dependence of Subsoil Conditions

Critical Acceleration Level is related to Peak Ground Acceleration (PGA) where it is a measure of

earthquake acceleration on the ground and an important input parameter for earthquake

engineering.

Tables below are summaries of critical acceleration level for each Limit State at different sub

soil condition which follows seismic code DIN 4149.

Table 18. Critical Acceleration Level for pushover analysis at H1 Direction

Steel Yielding

(g)

Steel Ultimate

(g)

Concrete Spalling

(g)


(g)

Soil Type

I

Sub Soil A TB < T < TC 2.31 1.83 3.67 3.93

TC < T < TD 4.47 3.11 7.38 7.87TD < T 1.73 1.06 2.97 3.15

Soil Type

I

Sub Soil A

Sub Soil B TB < T < TC 1.92 1.52 3.06 3.27

TC < T < TD 2.98 2.07 4.92 5.25TD < T 1.15 0.71 1.98 2.10

Soil Type

I Sub Soil B

Sub Soil C TB < T < TC 2.01 1.59 3.19 3.42

TC < T < TD 2.59 1.80 4.28 4.56TD < T 1.00 0.61 1.72 1.83

Soil Type

I

Sub Soil C

Sub Soil D TB < T < TC 1.71 1.35 2.72 2.91

TC < T < TD 1.66 1.15 2.73 2.92TD < T 0.64 0.39 1.10 1.17

Soil Type

I

Sub Soil D

Sub Soil E TB < T < TC 1.65 1.31 2.62 2.81

TC < T < TD 2.55 1.78 4.22 4.50TD < T 0.99 0.60 1.70 1.80

Soil Type

ISoil Type

II

Sub Soil A

Sub Soil E

TB < T < TC 2.31 1.83 3.67 3.93TC < T < TD 7.15 4.98 11.81 12.59TD < T 4.62 2.82 7.92 8.41

Soil Type

II

Sub Soil A

Sub Soil B TB < T < TC 1.71 1.35 2.72 2.91

TC < T < TD 5.30 3.69 8.75 9.33TD < T 3.42 2.09 5.87 6.23

Soil Type

II Sub Soil B

Sub Soil C TB < T < TC 1.54 1.22 2.45 2.62

TC < T < TD 4.77 3.32 7.88 8.40TD < T 3.08 1.88 5.28 5.61

Soil Type

II

Sub Soil C

Sub Soil D TB < T < TC 1.28 1.02 2.04 2.18

TC < T < TD 3.31 2.30 5.47 5.83TD < T 2.14 1.31 3.67 3.90

Soil Type

II

Sub Soil D

Sub Soil E TB < T < TC 1.44 1.14 2.29 2.45

TC < T < TD 4.47 3.11 7.38 7.87TD < T 2.89 1.76 4.95 5.26

Soil Type

II

Sub Soil E

33

Table 19. Critical Acceleration Level for pushover analysis at H2 Direction

Based on two tables above, it can be clearly seen that Critical Acceleration Level for pushover

analysis at H1 Direction is relatively higher than H2 Direction.

These values are different due to the regularity of the building. According to the layout, the

stiffness of the building at H2 direction is higher than H1 direction. Therefore, the critical

acceleration value at H1 direction is higher than H2 direction.

Steel Yielding

(g)

Steel Ultimate

(g)

Concrete Spalling

(g)


(g)

Soil Type

ISub Soil A TB < T < TC 1.17 2.10 1.57 2.06

TC < T < TD 2.42 4.24 3.25 4.43TD < T 1.00 1.71 1.34 1.90

TB < T < TC 0.97 1.75 1.31 1.72TC < T < TD 1.61 2.83 2.16 2.95TD < T 0.67 1.14 0.89 1.27

TB < T < TC 1.02 1.83 1.37 1.80TC < T < TD 1.40 2.46 1.88 2.57TD < T 0.58 0.99 0.78 1.10

TB < T < TC 0.87 1.56 1.16 1.53TC < T < TD 0.89 1.57 1.20 1.64TD < T 0.37 0.64 0.50 0.70

Soil Type

ISub Soil A

Sub Soil B

Sub Soil C

Sub Soil D

Sub Soil E TB < T < TC 0.83 1.50 1.12 1.47

TC < T < TD 1.38 2.42 1.85 2.53TD < T 0.57 0.98 0.77 1.09

Soil Type

I

Sub Soil E

Soil Type

II

Sub Soil A TB < T < TC 1.17 2.10 1.57 2.06

TC < T < TD 3.87 6.79 5.19 7.09TD < T 2.66 4.57 3.57 5.07

Soil Type

II

Sub Soil A

Sub Soil B TB < T < TC 0.87 1.56 1.16 1.53

TC < T < TD 2.86 5.03 3.85 5.25TD < T 1.97 3.39 2.65 3.76

Soil Type

II Sub Soil B

Sub Soil C TB < T < TC 0.78 1.40 1.05 1.38

TC < T < TD 2.58 4.53 3.46 4.73TD < T 1.78 3.05 2.38 3.38

Soil Type

II

Sub Soil C

Sub Soil D TB < T < TC 0.65 1.17 0.87 1.15

TC < T < TD 1.79 3.14 2.40 3.28TD < T 1.23 2.12 1.65 2.35

Soil Type

II

Sub Soil D

Sub Soil E TB < T < TC 0.73 0.42 1.29 1.61

TC < T < TD 2.42 0.99 4.53 5.80TD < T 1.67 0.48 3.31 4.36

Soil Type

II

Sub Soil E

Figure 22. Crritical Acceleratioon Level for pushoover analysis at HH1 Direction

34

Figure 23. Crritical Acceleratioon Level for pushoover analysis at HH2 Direction

35

36

4. Prediction of Structural Damage Corresponding to the Seismic Impact 4.1. According to the 1999 Düzce Earthquake

The Düzce earthquake of 1999 was an earthquake that occurred on 12 November 1999 at 18.57

local time (16.57 UTC} with a moment magnitude of 7.2, causing damage and 894 fatalities

in Duzce, Turkey. The epicenter was approx. 100 km (62 mi) to the east of the moment magnitude

7.4 1999 İzmit earthquake of 17 August, 1999, which killed over 17,000 people.

A total of 1,202 buildings were surveyed. Approximately 90% of them were 1‐ to 6‐story reinforced

concrete structures. The data gathered can be classified into two groups. The first group of data was

obtained through a sampling process that will be referred to as the ‘‘general survey.’’ The purpose

of this type of survey was to investigate the spatial distribution of the damage within a city. The

information recorded for each structure surveyed included damage rating, number of stories,

pictures, and location. A total of 1,021 buildings were surveyed in this manner in Bolu and Du¨zce.

The damage scale used to categorize all the buildings surveyed refers to structural members only.

The damage of a structure was labeled ‘‘light’’ if characterized by hairline inclined and flexural

cracks. Structures with wider cracks and spalling of concrete were classified as structures with

‘‘moderate damage.’’ Structures with local structural failures were classified as structures with

‘‘severe damage.’’

Figure 24. Map of Turkey and locations of the epicenters and surveyed cities.

37

Figure 25 . Distribution of damage in Düzce.

Figure 26. Distribution of damage in Bolu.

38

Figure 27. General survey results for Düzce and Bolu.

39

4.2. Comparison of Predicted with Observed Damage

In spite of their relatively poor construction quality, many buildings that were close to the rupture,

but not directly on it, did not suffer serious damage. Available attenuation relationships for

earthquake ground motion parameters such as peak ground acceleration would lead to a different

conclusion. Existing attenuation relationships (Anderson 2000, Rathje 2003) would indicate that

within a certain distance to fault line (approximately 1 to 20 km) peak ground acceleration

‘‘saturates.’’ Beyond the saturation zone PGA would be expected to decrease.

Observations made after the 1999 Turkey earthquakes indicate that ground acceleration decreased

in the vicinity of the fault line. There is no sufficient data to discern the boundaries of the zone

where structural damage seemed to indicate lower acceleration demands. It is clear, however, that

this is a relatively narrow zone whose width may be in the order of tens to hundreds of meters.

Figure 28. Failure of a shear wall in Bolu. Figure 29. Typical example of captive columns.

Figure 30. Column failure, Bolu government hospital.

40

According to the figure below, red boundary is indicating the expected failure area which is

usually called “Strong Column Weak Beam” mechanism. This figure was taken from Perform 3D

which uses Bolu 15 as a model. It can be clearly seen that the red indicator in the boundary is

the critical element which should be retrofitted or strengthened by additional elements, for

instance steel bar, cover concrete or steel plate.

Figure 31. Deflected shape according to combination all limit states for H1 direction

Minimum usage ratio for each color: 0.0 0.4 0.6 0.8 1

Zone A and B are unexpected failure mechanism where the column and beam have the critical

condition at the same time. This situation will cause soft storey effect at the 2nd storey, whereas

zone C indicates expected failure mechanism, where beam element will collapse before column.

On the other word, Strong Column weak Beam mechanism is fulfilled at zone C. It means, we do

not need to retrofit this joint due to predicted earthquake.

Zone D is comparable to a damage case in the figure 31 above. As we can see in the green

boundary, there is red line near to the foundation. It indicates the critical zone which should be

strengthened by additional cross bar. It is required to increase moment resistance capacity due

to excitation load.

Drift H1 Direction

Zone A Zone B

Zone C

Zone D

41

5. Application of Strengthening and Retrofitting Measures 5.1. Modeling of Strengthening Measures

Seismic Strengthening (retrofitting) is an action taken to upgrade the seismic resistance of an

existing building so that it becomes safer under future earthquakes. This can be in the form of

providing seismic bands, eliminating sources of weakness or concentrations of large mass and

openings in walls, adding shear walls or strong column points in walls, bracing roofs and floors to be

able to act as horizontal diaphragms, adequately connecting roofs to walls and columns and also

connecting between walls and foundations.

It is known that certain types of building structures and a few specific components of these have

repeatedly failed in earthquakes and are prime candidates for renovation and strengthening. Some

of these are:

• Buildings with irregular configurations such as those with abrupt changes in stiffness, large

floor openings, very large floor heights etc.

• Buildings or structures on sites prone to liquefaction

• Buildings with walls of un‐reinforced masonry, which tend to crack and crumble under

severe ground motions.

• Building with lack of ties between walls and floors or roofs

• Buildings with non‐ductile concrete frames, where shear failure at beam‐column joints and

column failures are common.

• Concrete buildings in which insufficient lengths of bar anchorage are used.

• Concrete buildings with flat‐slab framing, which can be severely affected by large storey

drifts.

Before commencing any repairs it is important to

• Determine the materials which have been used in the damaged building

• Carry out a detailed foundation check;

• Carry out a detailed structural assessment of the damaged building with particular attention

to vulnerable elements of the structure.

42

Methods of retrofitting reinforced concrete columns include:

• Complete or partial replacement.

• Addition of supplemental columns.

• Shear or flexural strengthening.

• Improvement of column ductility.

The most popular of these methods is ductility improvement, which is possible using one or more of

the following techniques:

• Steel jacketing.

• Active confinement by prestressing wire.

• Active or passive confinement by a composite fiber/epoxy jacket.

• Reinforced concrete jacketing.

5.1.1. Reinforced Concrete Columns

Total or partial column replacement will require placement of temporary shoring to carry the

weight of the bridge while the column is being removed and replaced. This shoring must

generally be capable of resisting the horizontal loads produced by small earthquakes.

5.1.1.1. Total Replacement

Total column replacement will sometimes be the most appropriate method for retrofitting the

bridge substructure. It will usually be necessary to modify or replace both the footing supporting

the column and the pier cap to which the column is connected. In fact, it is often the need to

replace the foundation, or strengthen the pier cap, that mandates column replacement in the

first place. Replacement should also be considered when the column is damaged or

deteriorated, column flexural capacity is grossly inadequate, or where space limitations or

architectural considerations preclude other retrofitting alternatives.

43

Figure 32. An example of total replacement

5.1.1.2. Partial Column Replacement

Partial column replacement involves the removal of surface concrete in the region of the

potential plastic hinge zone. The main vertical column reinforcement is cut and replaced by

machined ‘fuse bars’ that are, in turn, connected to the existing main steel outside of the

plastic hinge zone. The connection is made by welded splice plates to which threaded

couplers are welded so that the fuse bars can be replaced in the future.

44

Figure33. An example for partial column replacement

5.1.2. Column Flexural Strengthening

Three methods for increasing column strength are:

5.1.2.1. Concrete Overlays

Applying full or partial height concrete overlays to the face of an existing column can

increase a column’s flexural strength. A sufficient number of dowels must be provided for

shear transfer between the overlay and the existing column and a roughened contact

surface can also help in this regard.

45

Figure 34. An example for concrete overlays

5.1.2.2. Added Reinforcement in Conjunction with Steel Shell

The strength of an existing column can also be increased by adding extra longitudinal

reinforcement in the grout space between a steel shell and the column. This will require

adequate shear transfer between the grout and the existing column, which can generally be

assured by roughening the existing concrete surface or providing drilled and grouted dowels

on the surface of the existing column.

46

Figure 35. An Example for Added Reinforcement in Conjunction with Steel Shell

5.1.2.3. Composite Steel Shell

A steel shell can also contribute to flexural strength if sufficient shear transfer is provided

between the shell and the grout. This is done by coating the inside of the steel shell with an

epoxy adhesive impregnated with grit. Steel shear rings, on the inside of the shell, consisting

of welded reinforcing bar hoops, steel bars, or weld beads can also be used for this purpose.

High strength adhesives can be used to bond steel plates to the surface of the existing

column.

47

Figure 36. An example for Composite Steel Shell

5.1.3. Column Ductility Improvement and Shear Strengthening

One of the principal reasons for the low ductility of existing reinforced concrete columns was

the practice of using starter bars at the base of columns where plastic hinges are likely to form.

Failure in the splice between the starter bars and the longitudinal reinforcement generally

occurs when the concrete surrounding the reinforcing bars splits due to radial stresses that are

produced as the deformed bar tries to pull out of the concrete socket into which it is cast. Once

split, the concrete socket dilates and allows the bar to pull free.

5.1.3.1. Steel Jacketing

This technique was originally developed for circular columns, it is currently the preferred

method used by Caltrans for the seismic retrofits of bridge columns.

48

A steel jacket is effective as passive confinement, but confinement is not provided until the

radial expansion of the concrete column induces circumferential stresses in the steel shell.

This radial expansion occurs as a result of bulging caused by high axial compression strains in

the concrete and dilation around longitudinal reinforcement caused by vertical cracking

near the bar splices. Similar radial dilation occurs with the development of diagonal shear

cracks in the concrete of the column.

Figure 37. An example for Steel Jacketing

For rectangular columns, the recommended procedure is to use an oval jacket, which provides

continuous confining action similar to that for a circular column. Because of increased space

between the shell and the existing column, small sized aggregate is added to the grout that is

placed in the gap between the column and the shell.

49

Figure 38. Steel oval jacketing for rectangular column

5.1.3.2. Fiber Composite Jacketing

There are a number of proprietary techniques for jacketing or wrapping deficient concrete

columns that use advanced fiber composites to increase the flexural ductility and shear

strength, and to correct lap splice length deficiencies at ends of columns. These composites

are usually high strength glass (E‐glass), carbon, or aramid fibers oriented primarily in the

circumferential direction of the column, and bound in a polyester, vinyl ester, or epoxy resin

matrix. The resulting material has anisotropic properties, which allows the flexural ductility,

splice strength and shear strength of a column to be improved without significantly affecting

flexural strength and stiffness. Since the properties of a cured composite laminate depend

on the particular fiber and resin combination, it is advisable to use only components that

have been developed for use as part of a system and thoroughly tested. Detailed guidance

on the use of composites for column wraps is available in ACI’s Design and Construction of

Externally Bonded FRP Systems for Strengthening Concrete Structures (ACI, 2002).

Mechanical properties of fibers used in modern fiber‐reinforced plastic composites.

50

Table 20. Type of fiber‐reinforced plastic composites

Plates of fiber reinforced plastics (FRP) can be used instead of steel plates. The advantage with

FRP plate is the avoidance of corrosion problem, which is a problem for steel plates. FRP plates

are most popular in the retrofitting of bridges as FRP is resistant to corrosion caused by acids,

alkalis and salts. Both glass fiber reinforced plastic (GFRP) and carbon fiber reinforced plastic

(CFRP) are used for retrofitting purposes.

Figure 39. An example for Fiber Composite Jacketing

Large number of cracks of various sizes is generated in the concrete structures due to

earthquake. There are three basic methods of crack repair: to ‘glue’ the cracked concrete back

together by epoxy injection or grouting, to ‘stitch’ the cracked concrete with dowels or to

enlarge the crack and ‘caulk’ it with a flexible or semi rigid sealant.

Jacketing, pinning, stitching, strapping etc. are some of the methods of retrofitting distressed

structural elements. Depending on the types of distress and the importance of the structure an

appropriate type of retrofitting technique is adopted.

51

5.2. Evaluation of the applied strengthening method on the basis the analysis results

The following are the highlights of proposed retrofit based on the performance based design

methodology.

• Reinforced concrete infill of a few openings to prevent soft story mechanisms from

developing.

• Fiber Reinforced Polymer (FRP) pier wraps to strength the existing piers where significant

shear demands are present.

• FRP chords to strengthen the diaphragm at higher floor levels.

The deflected shape figures below are defined from pushover analysis at H1 and H2 direction. Color

indicators are representative from combination of all limit states which was explained above. Based

on the color indicators below, it can be clearly seen that there is soft storey mechanism effect at H1

Direction which is illustrated in circle A at figure 40. Whereas at H2 Direction occurs collapse

mechanism which is indicated red line alone column (rectangular B) at figure 41.

Minimum usage ratio for each color : 0.0 0.4 0.6 0.8 1


Figure 40. Deflected shape of pushover analysis for H1 direction

Figure 41. Deflected shape of pushover analysis for H2 direction

A

B

52

In order to indicate the failure mechanism more detail for every limit state, the figure 42 is

describing the deflected shape at frame 1 (H1 Direction) for steel ultimate limit state. The frame

below is could be retrofitted by using some methods which have been explained above.


Figure 42. Deflected shape at frame 1 (H1 Direction) for all limit states.

According to figure 42 and figure 43, there are 2 retrofit types for strengthening the structure

due to dynamic load. FRP Catch Mechanism (FRP C.M) is installed at soft storey zone potential

which is necessary to support these joints due to lateral loads. In addition, concrete overlay is

also given at the first storey for strengthening this area due to lack of “Strong Column Weak

Beam” mechanism.

These retrofit types should be investigated by using Finite Element Software, for instance,

ANSYS, ABAQUS and ADINA. If we use Perform 3D, it does not give us specific result with respect

to non linear behavior. But we could create a model where the element properties between

existing frame and additional retrofit element are combined and simplified into a new element.

FRP Catch Mechanism

Concrete Overlay

53


Figure 43. Deflected shape at frame 1 (H2 Direction) for all limit states.

FRP Catch Mechanism

Concrete Overlay

Example of Retrofitting

These cross se ctions below are defined from Frame A which was determined as a critical frame due to Pushover analysis. According to the explanation in proceed paragraph above, frame A undergo the critical condition where the soft storey occures at the second level. It could be strenghtened by adding the additional cover concrete on the existing column and steel bars such the figures below.

All material properties for retrofitting element are similar to the existing element.

Figure A. Exisitng cross section of column (25 x 60 cm) and retrofitting element

Figure B.Equivalent element after combining the existing and retrofitting element.

25 Y 3.125 1

5

1.6 0.8

7.570

X

535

25 Y 6.25

5

2.4 0.8

1570

X

535

Additional Cover Concrete (5cm)

Additional steel bar (1 cm)

Equivalent steel bar (2.4 cm)

Whereas, the new reinforcement area is given as table below:

Table 1. Equivalent bar area after retrofitting

Figure C. Limit states overview for H1 direction by using the strengthening element

Figure D. Limit State at Frame A after strengthening by additonal concrete cover at Column A and B

Existing Bar (cm)

number of barAdditional Bar (cm)

number of bar

expected bar

Equivalent Area (cm2)/Quarter

Diameter (cm) 1.6 2 1 4Area (cm2) 2.01 4.02 0.79 3.14

3.00 2.4

FRAME A

COLUMN A

COLUMN B

Figure E. Exisitng cross section of column (25 x 60 cm) and retrofitting element

Figure F. Equivalent element after combining the existing and retrofitting element.

25 Y 3.125 1

5

1.6 0.8

8.7580

X

535

25 Y 6.25

5

2.4 0.8

17.580

X

535

Additional Cover Concrete (5cm)

Additional steel bar (1 cm)

Equivalent steel bar (2.4 cm)

Figure G. Limit states overview for H2 direction by using the strengthening element

Figure H. Limit State at Frame A after strengthening by additonal concrete cover at Column A and B

FRAME A

COLUMN A

COLUMN B

Having applying the retrofitting element on the columns at frame A, the period of structure is smaller than the previous period. It means, the structure retrofitted is stiffer than before and it can resist the earthquake load stronger than existing structure.

Table 2. Comparison the period between before and after strengthening

The curve below could be a representative for distinguishing the structure capacity before and after retrofitting. It can be clearly seen that the capacity curve after retrofitting is higher than before. It means, the adding of the concrete cover is in according with the expectation where the retrofitting is given to increase the high capacity for the building due to the earthquake load.

Figure I. Comparison of Capacity Curve before retrofitting and after retrofitting

Mode Shape

period before retrofitting

period after retrofitting

1 0.36 0.33162 0.34 0.29793 0.30 0.28664 0.25 0.23895 0.24 0.2174

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25

Sa (g)

Sd (cm)

Capacity Curve

H1 Direction after retrofitting H2 Direction after retrofitting

H1 Direction before retrofitting H2 Direction before retrofitting

54

6. Conclusions and Recommendations 1. Fundamental period of the building is relatively lower than the standard with respect to the

number of storey’s. Masonry as non structural element should be added into account to

increase total masses in order to rise the fundamental period.

2. Layout of beam should be checked to the existing building in order to find the real evaluation for

retrofitting/strengthening.

3. The position of reference drift at H1 and H2 direction should be investigated at some nodes.

4. The load case of pushover analysis should not just consider modal analysis, but also different

load type, for instance, uniform load and triangular load.

5. Critical Acceleration value should be compared to the existing dynamic soil investigation which

has done at that building.

6. Pushover analysis result for each limit state should be checked to initial steps which has been

determined before doing the analysis.

7. Position of fibers at every cross section should accommodate two way direction loads, and fiber

numbers for each element are not exceed from 60 fibers.

8. Capacity spectrum from Perform 3D should be compared to different structural software, for

instance, ETABS 2000, SAP 2000 and ANSYS 9. It is necessary to make sure the analysis result

which was given by Perform 3D.

9. Critical acceleration values are different due to the regularity of the building. According to the

layout, the stiffness of the building at H2 direction is higher than H1 direction. Therefore, the

critical acceleration value at H1 direction is higher than H2 direction.

10. Ductility for pushover at H1 direction is higher than H2 direction. It means, stiffness at H1

direction is less than H2 direction.

55

References

ATC 40 (1996). Seismic evaluation and retrofit of concrete buildings. Applied Technology council, Redwood City, California. Boore, D.M., and Atkinson, G. M., 2008. Ground‐motion prediction equations, for the average horizontal component of PGA, PGV, and 5%‐damped PSA at spectral periods between 0.01 s and 10.0 s, Earthquake Spectra 24, 99‐138. Eurocode 8 (2003), Design of Structures for Earthquake Resistance, Draft No. 6, European Committee for Standardization, Brussels. Fajfar P. (2000), A non linear analysis method for performance based seismic design, Earthquake Spectra, 16,3, pp. 573‐591. FEMA, (1999), “HAZUS99 user and technical manuals”. Federal Emergency Management Agency Report: HAZUS 1999, Washington D.C., USA. FEMA 440, (2005). “Improvement of nonlinear static seismic analysis procedures”. Federal Emergency Management Agency (FEMA) Report no. 440, Applied Technology Council, Washington D.C., USA. FEMA 356, (2000), Pre‐standard for the Seismic Rehabilitation of Buildings, U.S. Grünthal, G. (editor) (1998). European macroseismic scale 1998. Cahiers du Center Europeen de GEodynamique et de Seismologie. Conseil de l’Europa. Luxembourg, 1998. IBC (2006), „Internternational Building Code“, International Code Council, USA. Computer and Structures, Inc, (2008), Perform 3D user’s Guide, U.S Earthquake Engineering Research Institute (EERI), 1999. The Izmit (Kocaeli), Turley earthquake of August 17, 1999, EERI Special Earthquake Report, Newslatter insert, October.

56

Annex I

57

Table 21. Detail calculation of Critical Acceleration for each sub soil type I at H1 Direction

η = 1.000 1.000 1.000 1.000 Steel Yielding

Steel Ultimate

Concrete Spalling


Steel Yielding

Steel Ultimate

Concrete Spalling


Steel Yielding

Steel Ultimate

Concrete Spalling


Steel Yielding

Steel Ultimate

Concrete Spalling


Sub Soil A A A A B B B B C C C C D D D D E E E E

Vs,30 >800 >800 >800 >800 360‐800 360‐800 360‐800 360‐800 180‐360 180‐360 180‐360 180‐360 <180 <180 <180 <180 0.000 0.000 0.000 0.000S 1.000 1.000 1.000 1.000 1.200 1.200 1.200 1.200 1.150 1.150 1.150 1.150 1.350 1.350 1.350 1.350 1.400 1.400 1.400 1.400

TB 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.150 0.150 0.150 0.150

TC 0.400 0.400 0.400 0.400 0.500 0.500 0.500 0.500 0.600 0.600 0.600 0.600 0.800 0.800 0.800 0.800 0.500 0.500 0.500 0.500

TD 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000μ 7.000 2.589 9.061 8.871 7.000 2.589 9.061 8.871 7.000 2.589 9.061 8.871 7.000 2.589 9.061 8.871 7.000 2.589 9.061 8.871

Teff = 0.775 0.680 0.805 0.802 0.775 0.680 0.805 0.802 0.775 0.680 0.805 0.802 0.775 0.680 0.805 0.802 0.775 0.680 0.805 0.802

βeff = 23.253 12.639 23.284 23.352 23.253 12.639 23.284 23.352 23.253 12.639 23.284 23.352 23.253 12.639 23.284 23.352 23.253 12.639 23.284 23.352M = 50.985 17.994 58.748 58.141 50.985 17.994 58.748 58.141 50.985 17.994 58.748 58.141 50.985 17.994 58.748 58.141 50.985 17.994 58.748 58.141B = 1.630 1.306 1.631 1.633 1.630 1.306 1.631 1.633 1.630 1.306 1.631 1.633 1.630 1.306 1.631 1.633 1.630 1.306 1.631 1.633

B / M = 0.032 0.073 0.028 0.028 0.032 0.073 0.028 0.028 0.032 0.073 0.028 0.028 0.032 0.073 0.028 0.028 0.032 0.073 0.028 0.028

ag cm/sec2 2264.804 1794.821 3601.789 3854.624 1887.336 1495.684 3001.491 3212.187 1969.395 1560.714 3131.991 3351.847 1677.632 1329.497 2667.992 2855.277 1617.717 1282.015 2572.707 2753.303

TB < T < TC g 2.308 1.829 3.670 3.927 1.923 1.524 3.058 3.273 2.007 1.590 3.191 3.415 1.709 1.355 2.718 2.909 1.648 1.306 2.621 2.805

ag cm/sec2 4386.576 3052.491 7246.960 7725.189 2924.384 2034.994 4831.307 5150.126 2542.943 1769.560 4201.136 4478.370 1624.658 1130.552 2684.059 2861.181 2506.615 1744.281 4141.120 4414.393

TC < T < TD g 4.469 3.110 7.384 7.871 2.980 2.073 4.923 5.247 2.591 1.803 4.281 4.563 1.655 1.152 2.735 2.915 2.554 1.777 4.219 4.498

ag cm/sec2 1699.225 1038.288 2916.241 3096.465 1132.816 692.192 1944.161 2064.310 985.058 601.906 1690.575 1795.052 629.342 384.551 1080.089 1146.839 970.986 593.307 1666.424 1769.408

TD < T g 1.731 1.058 2.971 3.155 1.154 0.705 1.981 2.103 1.004 0.613 1.723 1.829 0.641 0.392 1.101 1.169 0.989 0.605 1.698 1.803

Soil Type

I

58

Table 22. Detail calculation of Critical Acceleration for each sub soil type II at H1 Direction

η = 1.000 1.000 1.000 1.000 Steel Yielding

Steel Ultimate

Concrete Spalling


Steel Yielding

Steel Ultimate

Concrete Spalling


Steel Yielding

Steel Ultimate

Concrete Spalling


Steel Yielding

Steel Ultimate

Concrete Spalling



Vs,30 >800 >800 >800 >800 360‐800 360‐800 360‐800 360‐800 180‐360 180‐360 180‐360 180‐360 <180 <180 <180 <180 0.000 0.000 0.000 0.000S 1.000 1.000 1.000 1.000 1.350 1.350 1.350 1.350 1.500 1.500 1.500 1.500 1.800 1.800 1.800 1.800 1.600 1.600 1.600 1.600

TB 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.050 0.050 0.050 0.050

TC 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.300 0.300 0.300 0.300 0.250 0.250 0.250 0.250

TD 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200μ 7.000 2.589 9.061 8.871 7.000 2.589 9.061 8.871 7.000 2.589 9.061 8.871 7.000 2.589 9.061 8.871 7.000 2.589 9.061 8.871

Teff = 0.775 0.680 0.805 0.802 0.775 0.680 0.805 0.802 0.775 0.680 0.805 0.802 0.775 0.680 0.805 0.802 0.775 0.680 0.805 0.802

βeff = 23.253 12.639 23.284 23.352 23.253 12.639 23.284 23.352 23.253 12.639 23.284 23.352 23.253 12.639 23.284 23.352 23.253 12.639 23.284 23.352M = 50.985 17.994 58.748 58.141 50.985 17.994 58.748 58.141 50.985 17.994 58.748 58.141 50.985 17.994 58.748 58.141 50.985 17.994 58.748 58.141B = 1.630 1.306 1.631 1.633 1.630 1.306 1.631 1.633 1.630 1.306 1.631 1.633 1.630 1.306 1.631 1.633 1.630 1.306 1.631 1.633

B / M = 0.032 0.073 0.028 0.028 0.032 0.073 0.028 0.028 0.032 0.073 0.028 0.028 0.032 0.073 0.028 0.028 0.032 0.073 0.028 0.028

ag cm/sec2 2264.804 1794.821 3601.789 3854.624 1677.632 1329.497 2667.992 2855.277 1509.869 1196.547 2401.193 2569.750 1258.224 997.123 2000.994 2141.458 1415.502 1121.763 2251.118 2409.140

TB < T < TC g 2.308 1.829 3.670 3.927 1.709 1.355 2.718 2.909 1.538 1.219 2.447 2.618 1.282 1.016 2.039 2.182 1.442 1.143 2.294 2.455

ag cm/sec2 7018.522 4883.986 11595.136 12360.302 5198.905 3617.767 8588.990 9155.779 4679.015 3255.990 7730.091 8240.201 3249.316 2261.104 5368.119 5722.362 4386.576 3052.491 7246.960 7725.189

TC < T < TD g 7.151 4.976 11.814 12.594 5.297 3.686 8.751 9.329 4.767 3.318 7.876 8.396 3.311 2.304 5.470 5.831 4.469 3.110 7.384 7.871

ag cm/sec2 4531.266 2768.767 7776.643 8257.239 3356.493 2050.938 5760.476 6116.473 3020.844 1845.845 5184.429 5504.826 2097.808 1281.837 3600.298 3822.796 2832.041 1730.479 4860.402 5160.774

TD < T g 4.617 2.821 7.924 8.413 3.420 2.090 5.869 6.232 3.078 1.881 5.282 5.609 2.137 1.306 3.668 3.895 2.886 1.763 4.952 5.258

Soil Type

II

59

Table 23. Detail calculation of Critical Acceleration for each sub soil type I at H2 Direction

η = 1.000 1.000 1.000 1.000 Steel Yielding

Steel Ultimate

Concrete Spalling


Steel Yielding

Steel Ultimate

Concrete Spalling


Steel Yielding

Steel Ultimate

Concrete Spalling


Steel Yielding

Steel Ultimate

Concrete Spalling



Vs,30 >800 >800 >800 >800 360‐800 360‐800 360‐800 360‐800 180‐360 180‐360 180‐360 180‐360 <180 <180 <180 <180 0.000 0.000 0.000 0.000

S 1.000 1.000 1.000 1.000 1.200 1.200 1.200 1.200 1.150 1.150 1.150 1.150 1.350 1.350 1.350 1.350 1.400 1.400 1.400 1.400

TB 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.200 0.150 0.150 0.150 0.150

TC 0.400 0.400 0.400 0.400 0.500 0.500 0.500 0.500 0.600 0.600 0.600 0.600 0.800 0.800 0.800 0.800 0.500 0.500 0.500 0.500

TD 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000

μ 3.883 4.453 4.946 5.980 3.883 4.453 4.946 5.980 3.883 4.453 4.946 5.980 3.883 4.453 4.946 5.980 3.883 4.453 4.946 5.980

Teff = 0.827 0.808 0.826 0.858 0.827 0.808 0.826 0.858 0.827 0.808 0.826 0.858 0.827 0.808 0.826 0.858 0.827 0.808 0.826 0.858

βeff = 19.511 20.799 21.340 22.478 19.511 20.799 21.340 22.478 19.511 20.799 21.340 22.478 19.511 20.799 21.340 22.478 19.511 20.799 21.340 22.478

M = 32.720 35.146 38.365 45.143 32.720 35.146 38.365 45.143 32.720 35.146 38.365 45.143 32.720 35.146 38.365 45.143 32.720 35.146 38.365 45.143B = 1.521 1.559 1.575 1.608 1.521 1.559 1.575 1.608 1.521 1.559 1.575 1.608 1.521 1.559 1.575 1.608 1.521 1.559 1.575 1.608

B / M = 0.046 0.044 0.041 0.036 0.046 0.044 0.041 0.036 0.046 0.044 0.041 0.036 0.046 0.044 0.041 0.036 0.046 0.044 0.041 0.036

ag cm/sec2 1146.756 2060.814 1543.187 2026.255 955.630 1717.345 1285.990 1688.546 997.179 1792.012 1341.902 1761.961 849.449 1526.529 1143.102 1500.930 819.111 1472.010 1102.277 1447.325

TB < T < TC g 1.168 2.100 1.572 2.065 0.974 1.750 1.310 1.720 1.016 1.826 1.367 1.795 0.866 1.555 1.165 1.529 0.835 1.500 1.123 1.475

ag cm/sec2 2371.149 4164.062 3185.366 4348.654 1580.766 2776.041 2123.578 2899.103 1374.579 2413.949 1846.589 2520.959 878.203 1542.245 1179.765 1610.613 1354.942 2379.464 1820.209 2484.945

TC < T < TD g 2.416 4.243 3.246 4.431 1.611 2.829 2.164 2.954 1.401 2.460 1.881 2.569 0.895 1.571 1.202 1.641 1.381 2.424 1.855 2.532

ag cm/sec2 980.565 1682.774 1315.013 1866.575 653.710 1121.849 876.675 1244.384 568.444 975.521 762.326 1082.073 363.172 623.250 487.042 691.324 560.323 961.585 751.436 1066.614

TD < T g 0.999 1.715 1.340 1.902 0.666 1.143 0.893 1.268 0.579 0.994 0.777 1.103 0.370 0.635 0.496 0.704 0.571 0.980 0.766 1.087

Soil Type

I

60

Table 24. Detail calculation of Critical Acceleration for each sub soil type II at H2 Direction

η = 1.000 1.000 1.000 1.000 Steel Yielding

Steel Ultimate

Concrete Spalling


Steel Yielding

Steel Ultimate

Concrete Spalling


Steel Yielding

Steel Ultimate

Concrete Spalling


Steel Yielding

Steel Ultimate

Concrete Spalling



Vs,30 >800 >800 >800 >800 360‐800 360‐800 360‐800 360‐800 180‐360 180‐360 180‐360 180‐360 <180 <180 <180 <180 0.000 0.000 0.000 0.000

S 1.000 1.000 1.000 1.000 1.350 1.350 1.350 1.350 1.500 1.500 1.500 1.500 1.800 1.800 1.800 1.800 1.600 1.600 1.600 1.600

TB 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.050 0.050 0.050 0.050

TC 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.300 0.300 0.300 0.300 0.250 0.250 0.250 0.250

TD 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200 1.200μ 3.883 4.453 4.946 5.980 3.883 4.453 4.946 5.980 3.883 4.453 4.946 5.980 3.883 4.453 4.946 5.980 3.883 1.978 5.980 7.070

Teff = 0.827 0.808 0.826 0.858 0.827 0.808 0.826 0.858 0.827 0.808 0.826 0.858 0.827 0.808 0.826 0.858 0.827 0.585 0.878 0.902

βeff = 19.511 20.799 21.340 22.478 19.511 20.799 21.340 22.478 19.511 20.799 21.340 22.478 19.511 20.799 21.340 22.478 19.511 8.475 22.478 23.297M = 32.720 35.146 38.365 45.143 32.720 35.146 38.365 45.143 32.720 35.146 38.365 45.143 32.720 35.146 38.365 45.143 32.720 12.163 45.143 51.298B = 1.521 1.559 1.575 1.608 1.521 1.559 1.575 1.608 1.521 1.559 1.575 1.608 1.521 1.559 1.575 1.608 1.521 1.155 1.608 1.632

B / M = 0.046 0.044 0.041 0.036 0.046 0.044 0.041 0.036 0.046 0.044 0.041 0.036 0.046 0.044 0.041 0.036 0.046 0.095 0.036 0.032

ag cm/sec2 1146.756 2060.814 1543.187 2026.255 849.449 1526.529 1143.102 1500.930 764.504 1373.876 1028.792 1350.837 637.087 1144.896 857.326 1125.697 716.723 416.955 1266.410 1576.854

TB < T < TC g 1.168 2.100 1.572 2.065 0.866 1.555 1.165 1.529 0.779 1.400 1.048 1.376 0.649 1.167 0.874 1.147 0.730 0.425 1.290 1.607

ag cm/sec2 3793.838 6662.500 5096.586 6957.846 2810.250 4935.185 3775.249 5153.960 2529.225 4441.666 3397.724 4638.564 1756.406 3084.491 2359.531 3221.225 2371.149 975.555 4446.389 5689.770

TC < T < TD g 3.866 6.788 5.193 7.089 2.863 5.028 3.847 5.251 2.577 4.526 3.462 4.726 1.790 3.143 2.404 3.282 2.416 0.994 4.530 5.797

ag cm/sec2 2614.841 4487.397 3506.702 4977.534 1936.919 3323.998 2597.557 3687.062 1743.227 2991.598 2337.801 3318.356 1210.575 2077.498 1623.473 2304.414 1634.276 475.525 3252.366 4277.170

TD < T g 2.664 4.572 3.573 5.072 1.974 3.387 2.647 3.757 1.776 3.048 2.382 3.381 1.233 2.117 1.654 2.348 1.665 0.485 3.314 4.358

Soil Type

II

on 28 february 2011 - firdausadnan.files.wordpress.com...seen in the middle of city. this map is...

Documents