Ejemplo_1_-_Pushover_de_una_placa_de_7_pisos.pdf

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FUNDAMENTALS OF SEISMIC DESIGN

Assignment #2

Limit State Analysis

MEEES Student:

José Martín Velásquez Vargas

E-mail:

[email protected]

Professor: José

Restrepo

Assistant Professor: Matthew Tobolski

October, 2006

Pavia, Italy

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Fundamentals of Seismic Design

MEEES student: José Velásquez

PROBLEM 4

Description of the problem

A static pushover analysis is performed by hand on a cantilever wall, in order to determine the

base shear vs. top story displacement relationship. The structure has a total of 7 stories with a

clear height of 2.5m between floors with an 800mm slab at each level. The cross sections of

the wall are shown in figure 1 bellow.

Figure

1 . Cross sections of the slabs. (1) 1

st

_{floor section. (2) Floors from 2}

nd

_{to 7}

th

_.

The pushover analysis is performed for two load cases with lower and upper bound axial loads

of 100 kN/floor and 500 kN/floor, respectively. It has also been determined that an

appropriate rotational soil spring has a stiffness of 1.25 x 10

6

_{kN-m/rad representing the use}

of a pile foundation.

The moment-curvature relationships for all the floors and both load axial bounds are

developed by means of the Xtract program (Imbsen and Associated, 2006). The geometry, the

material properties, the reinforcement distribution and the confinement properties are all

shown in figures 1 and 2.

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(a)

(b)

(c)

Figure 2. Material properties. (a) Unconfined concrete. (2) Confined concrete (Mander model). (3) Steel model.

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Fundamentals of Seismic Design

MEEES student: José Velásquez

1. STATIC PUSHOVER CURVES

In order to plot the pushover curves, the following limit strains are considered for the

materials.

Table 1. Strain limits for the pushover analysis.

Limit strains

ci

Concrete tensile strain

0.007%

cii

Onset of concrete cover spalling

-0.400%

ciii

Deep of concrete cover spalling

-0.400%

civ

Crushing of confined concrete core

4.560%

si

Steel yielding strain

0.219%

sii

Outermost tensile strain

1.000%

siii

Onset of bar buckling (es-ec)>

3.750%

siv

Long. bar fracture for ec<=-0.004

and (es-ec)>

5.000%

A displacement controlled pushover analysis is performed over the critical section (base

section). In summary the steps followed to plot the pushover curves were:

• In an increasing way, a limit strain is defined and its correspondent curvature is

read from the moment-curvature relationship at the base. Also the related moment

from this diagram is read.

• With the moment at the base, the load distribution is calculated and the bending

moment diagram for the entire wall. In this analysis, a triangular-shaped distributed

load is assumed along the height of the wall.

• From the moments at every floor, the corresponding curvatures are read from

their moment-curvature relationships.

• Once the curvature diagram is plotted, by means of numerical integration, the

displacement associated with the current limit strain is computed.

These steps are repeated for all the limit strains. From the case sii, plasticity is already

considered to be developed and 2 hinges are assumed to be concentrated at the first floor.

Also when unloading takes place at the base, the other sections are considered to unload with

the yielding stiffness.

The pushover curves are shown in figure 4. Damage states are defined based on the strain

limits. In the upper load ciii could be considered as the actual ultimate stage because this is

when unloading takes place and it is expected that the wall perform unstable behavior. This

means ductility for the upper bound case is much lower than that of the lower bound case.

However, it is clearly seen that for the upper bound case the strength is increased.

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Fundamentals of Seismic Design

MEEES student: José Velásquez

Base Shear vs. Drif Ratio

ci

si

sii

cii

siii

ciii

siv

ci

si

sii

cii

0

100

200

300

400

500

600 0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

4.00%

Drift ratio

Lower bound (100 kN/floor)

Upper bound (500 kN/floor)

DSI

DSII

DSIII

ciii

siii

siv

Base shear (kN)

0.00m

0.20m

0.40m

0.60m

0.80m

1.00m

Roof displacement

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MEEES student: José Velásquez

2. MOMENT-CURVATURE DIAGRAMS OF ALL THE FLOORS

Moment-curvature for all stories (lower bound: axial load = 100kN/floor)

0 1000

2000

3000

4000

5000

6000

7000

8000

0.00

0.05

0.10

0.15

0.20 Curvature x wall length (rad)

M

o

ment (kN

-m)

1st floor - 700 kN

2nd floor - 600 kN

3rd floor - 500 kN

4th floor - 400 kN

5th floor - 300 kN

6th floor - 200 kN

7th floor - 100 kN

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Fundamentals of Seismic Design

MEEES student: José Velásquez

Moment-curvature for all stories (upper bound: axial load = 500kN/floor)

0 1000

2000

3000

4000

5000

6000

7000

8000

0.00

0.05

0.10

0.15

0.20 Curvature x wall length (rad)

Mome

nt

(k

N

-m)

1st floor - 3500 kN

2nd floor - 3000 kN

3rd floor - 2500 kN

4th floor - 2000 kN

5th floor - 1500 kN

6th floor - 1000 kN

7th floor - 500 kN

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In figures 5 and 6 moment-curvatures diagrams are plotted for all 7 floors and both axial load

cases. The curvatures are normalized to the wall length.

For the lower bound case the moment strength goes from 8000 to 5000 kN-m as the height

increases. However the ultimate curvature in the first floor is appreciately decreased due to the

high axial load.

For the upper bound case the moment strength goes from 8500 to 4000 kN-m as the height

increases. However the ultimate curvature in the first floor is significantly decreased due to the

high axial load. This gives and idea that plastic hinges may develop in the second floor as well

due to the low ductility of the first floor.

3. STRAIN LIMITS DEFINITION FOR THE BASE OF THE WALL

The strain limits from table 1 are identified for the base section and for axial load cases. Both

plots are shown in figure 7

In the lower bound curve, siv takes place before civ. This means that the steel fractures before

the concrete can keep on using its remaining strength. Since there is no tell at this stage, the

section cannot resist moment anymore. This is way, the moment-curvature diagram is taken

until siv only.

In the upper bound curve, loss of strength is developed. In this case ciii must be taken as the

ultimate practical stage. This is due to the fact that when the section loses strength it usually

has an unstable behavior and the ductility cannot be well developed. Just for theoretical

analysis, all the limits are shown in figure 7.

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Fundamentals of Seismic Design

MEEES student: José Velásquez

Moment-curvature for the base section (upper and lower bounds)

si sii ci si ci cii ciii =civ siii siv cii ciii sii siii siv 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 0.00 0.01 0.02 0.03 0.04 0.05 0.06

Curvature x Wall length (rad)

Mo m e n t ( k N -Upper bound (500 kN/m) Lower bound (100 kN/m)

Figure 7. Strain limits for the base section and lower and upper bound axial load cases.

4. STEP-BY-STEP RESULTS

In the following figures, for each strain limit state it is shown the first mode distribution

(triangular-shaped), the bending moment diagram, the associated curvature distribution (based

on moment-curvature for each floor) for both load cases, and the displacement profile. The

displacements are derived by means of Integration.

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Limit State Description: Concrete tensile strain = 0.007% Lower axial load: 500 kN/floor

Damage State: DSI

Force distribution (kN/m) Moment diagram (kN-m) Curvature (rad/m)

15 20 15.00 20.00 15.00 20.00 5 10 5.00 10.00 5.00 10.00

Curvature (rad/m) Moment (kN-m) Shear (kN) Deflection (m) Curvature (rad/m) Moment (kN-m) Shear (kN) Deflection (m)

23.10 0.00E+00 0.00 0.00 0.034 0.00E+00 0.00 0.00 0.080

22.30 1.40E-07 2.53 6.28 0.033 2.79E-07 5.92 14.71 0.077

19 80 1 91E-06 41 43 24 48 0 029 4 52E-06 97 06 57 35 0 068

Height (m) Lower bound (100 kN/floor) Upper bound (500 kN/floor)

0 0.00 10.00 20.00 30.00 0.00 0 500 1000 1500 2000 2500 3000 3500 0.00 0.00E+00 1.00E-04 2.00E-04 20.00 Deflection (m) 19.80 1.91E-06 41.43 24.48 0.029 4.52E-06 97.06 57.35 0.068 19.00 2.93E-06 63.17 29.85 0.028 6.89E-06 148.00 69.93 0.065 16.50 7.31E-06 157.43 45.19 0.024 1.72E-05 368.81 105.88 0.055 15.70 9.08E-06 195.38 49.65 0.022 2.13E-05 457.72 116.31 0.053 13.20 1.56E-05 335.57 62.14 0.018 3.66E-05 786.15 145.58 0.043 12.40 1.80E-05 386.72 65.68 0.017 4.22E-05 905.97 153.88 0.040 9.90 2.62E-05 563.43 75.32 0.013 6.15E-05 1319.95 176.46 0.031 9.10 2.90E-05 624.75 77.95 0.012 6.83E-05 1463.62 182.62 0.029 6.60 3.92E-05 828.57 84.74 0.009 9.07E-05 1941.11 198.52 0.020 5.80 4.24E-05 897.06 86.46 0.007 9.82E-05 2101.57 202.54 0.017 3.30 5.35E-05 1118.57 90.39 0.004 1.25E-04 2620.50 211.76 0.010 15.00 20.00 2.50 5.63E-05 1191.22 91.19 0.003 1.32E-04 2790.69 213.64 0.007 0.00 6.75E-05 1421.00 92.27 0.000 1.61E-04 3329.00 216.17 0.000 0.026 0.062 0.008 0.019 0.034 0.080 Total (m) Def lect io n Total (m) From foundation (m)

Remaining wall (including hinges, m) From foundation (m)

Remaining wall (including hinges, m)

5.00 10.00 0.00 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

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Limite State: cii Upper axial load: 100 kN/floor

Limit State Description: Onset of concrete cover spalling = -0.4% Lower axial load: 500 kN/floor

15 20 15.00 20.00 15.00 20.00 5 10 5.00 10.00 0 00 5.00 10.00

23.10 0.00E+00 0.00 0.00 0.645 0.00E+00 0.00 0.00 0.445

22.30 4.66E-07 9.52 23.65 0.621 6.99E-07 15.08 37.48 0.429

19.80 7.27E-06 156.01 92.19 0.545 1.15E-05 247.20 146.07 0.376

19.00 1.11E-05 237.89 112.40 0.520 1.76E-05 376.96 178.10 0.359

0 0.00 10.00 20.00 30.00 40.00 50.00 0.00 0 1000 2000 3000 4000 5000 6000 7000 8000 0.00 0.00E+00 5.00E-03 1.00E-02 20.00 Deflection (m) 16.50 2.76E-05 592.82 170.19 0.444 4.37E-05 939.36 269.67 0.307 15.70 3.25E-05 735.74 186.96 0.420 5.43E-05 1165.82 296.25 0.290 13.20 1.97E-04 1263.65 234.01 0.344 1.02E-04 2002.33 370.80 0.238 12.40 2.63E-04 1456.24 247.34 0.320 1.10E-04 2307.51 391.93 0.221 9.90 4.63E-04 2121.68 283.65 0.246 3.69E-04 3361.94 449.46 0.170 9.10 4.97E-04 2352.61 293.54 0.222 3.51E-04 3727.86 465.14 0.154 6.60 7.00E-04 3120.12 319.10 0.151 6.73E-04 4944.02 505.64 0.105 5.80 7.67E-04 3378.04 325.56 0.129 6.57E-04 5352.72 515.87 0.090 3.30 1.15E-03 4212.16 340.38 0.062 1.05E-03 6674.43 539.35 0.045 2.50 1.52E-03 4485.72 343.40 0.042 1.00E-03 7107.91 544.14 0.032 1.75 3.08E-03 4744.10 345.47 0.024 1.21E-03 7517.32 547.42 0.020 10.00 15.00 1.75 3.08E 03 4744.10 345.47 0.024 1.21E 03 7517.32 547.42 0.020 0.00 1.07E-02 5351.00 347.47 0.000 5.16E-03 8479.00 550.58 0.000 0.099 0.157 0.546 0.289 0.645 0.445 Total (m) Deflection Total (m) From foundation (m)

0.00 5.00 10.00 0 00 0 10 0 20 0 30 0 40 0 50 0 60 0 70 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

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Limit State Description: Deep of concrete cover spalling -0.4% Lower axial load: 500 kN/floor

Damage State: DSII

15 20 15.00 20.00 15.00 20.00 5 10 5.00 10.00 0 00 5.00 10.00

23.10 0.00E+00 0.00 0.00 0.728 0.00E+00 0.00 0.00 0.464

22.30 4.66E-07 9.63 23.95 0.701 6.99E-07 15.01 37.30 0.446

19.80 7.30E-06 157.96 93.34 0.615 1.15E-05 246.06 145.40 0.392

19.00 1.11E-05 240.87 113.80 0.588 1.75E-05 375.23 177.28 0.374

0 0.00 10.00 20.00 30.00 40.00 50.00 0.00 0 1000 2000 3000 4000 5000 6000 7000 8000 0.00 0.00E+00 5.00E-03 1.00E-02 1.50E-02 20.00 Deflection (m) 16.50 2.78E-05 600.24 172.32 0.502 4.36E-05 935.04 268.43 0.320 15.70 3.51E-05 744.95 189.30 0.475 5.41E-05 1160.46 294.89 0.302 13.20 1.97E-04 1279.47 236.94 0.390 1.01E-04 1993.12 369.10 0.248 12.40 2.70E-04 1474.48 250.44 0.363 1.10E-04 2296.90 390.13 0.231 9.90 4.63E-04 2148.24 287.20 0.279 3.65E-04 3346.47 447.39 0.178 9.10 5.30E-04 2382.07 297.22 0.253 3.47E-04 3710.72 463.00 0.161 6.60 7.00E-04 3159.18 323.10 0.172 6.67E-04 4921.28 503.31 0.110 5.80 8.00E-04 3420.33 329.64 0.147 6.51E-04 5328.10 513.50 0.094 3.30 1.18E-03 4264.90 344.64 0.071 1.04E-03 6643.73 536.87 0.047 2.50 1.70E-03 4541.89 347.70 0.048 9.93E-04 7075.22 541.63 0.033 1.75 3.00E-03 4803.50 349.80 0.027 1.18E-03 7482.74 544.91 0.021 10.00 15.00 1.75 3.00E 03 4803.50 349.80 0.027 1.18E 03 7482.74 544.91 0.021 0.00 1.28E-02 5418.00 351.82 0.000 5.68E-03 8440.00 548.05 0.000 0.100 0.156 0.628 0.308 0.728 0.464 Total (m) Deflection Total (m) From foundation (m)

0.00 5.00 10.00 0 00 0 10 0 20 0 30 0 40 0 50 0 60 0 70 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

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Limite State: civ Upper axial load: 100 kN/floor

Limit State Description: Crushing of confined concrete core 4.56% Lower axial load: 500 kN/floor

Damage State: DSIII

15 20 15.00 20.00 15.00 20.00 5 10 5.00 10.00 0 00 5.00 10.00

23.10 0.00E+00 0.00 0.00 1.577 0.00E+00 0.00 0.00 0.843

22.30 3.73E-07 8.09 20.10 1.519 6.99E-07 1.92 4.78 0.811

19.80 6.19E-06 132.59 78.35 1.339 1.15E-05 31.55 18.64 0.712

19.00 9.41E-06 202.19 95.53 1.281 1.75E-05 48.10 22.73 0.681

0 0.00 10.00 20.00 30.00 40.00 50.00 0.00 0 1000 2000 3000 4000 5000 6000 7000 8000 0.00 0.00E+00 5.00E-03 1.00E-02 1.50E-02 2.00E-02 2.50E-02 3.00E-02 3.50E-02 20.00 Deflection (m) 16.50 2.35E-05 503.86 144.65 1.102 4.36E-05 119.87 34.41 0.582 15.70 2.91E-05 625.33 158.91 1.044 5.41E-05 148.77 37.80 0.551 13.20 1.31E-04 1074.02 198.89 0.864 1.01E-04 255.52 47.32 0.452 12.40 1.97E-04 1237.71 210.23 0.807 1.10E-04 294.46 50.01 0.421 9.90 3.64E-04 1803.29 241.08 0.628 3.65E-04 429.01 57.35 0.323 9.10 4.30E-04 1999.57 249.49 0.572 3.47E-04 475.71 59.36 0.292 6.60 5.67E-04 2651.90 271.22 0.395 6.67E-04 630.90 64.52 0.197 5.80 6.34E-04 2871.11 276.71 0.340 6.51E-04 683.06 65.83 0.167 3.30 7.76E-04 3580.06 289.30 0.167 1.04E-03 851.72 68.83 0.076 2.50 8.45E-04 3812.57 291.87 0.113 1.06E-02 907.04 69.44 0.048 1.75 9.44E-04 4032.17 293.63 0.062 1.06E-02 959.28 69.86 0.025 10.00 15.00 1.75 9.44E 04 4032.17 293.63 0.062 1.06E 02 959.28 69.86 0.025 0.00 3.64E-02 4548.00 295.32 0.000 1.51E-02 1082.00 70.26 0.000 0.084 0.020 1.493 0.823 1.577 0.843 Total (m) Deflection Total (m) From foundation (m)

0.00 5.00 10.00 0 00 0 10 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 1 00 1 10 1 20 1 30 1 40 1 50 1 60 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60

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Limit State Description: Steel yielding strain = 0.219% Lower axial load: 500 kN/floor

15 20 15.00 20.00 15.00 20.00 5 10 5.00 10.00 5.00 10.00

23.10 0.00E+00 0.00 0.00 0.159 0.00E+00 0.00 0.00 0.225

22.30 2.79E-06 6.73 16.72 0.152 6.05E-07 12.68 31.50 0.217

19 80 5 12E-06 110 29 65 17 0 133 9 69E-06 207 81 122 80 0 190

0 0.00 10.00 20.00 30.00 40.00 0.00 0 1000 2000 3000 4000 5000 6000 7000 0.00 0.00E+00 5.00E-04 1.00E-03 1.50E-03 20.00 Deflection (m) 19.80 5.12E-06 110.29 65.17 0.133 9.69E-06 207.81 122.80 0.190 19.00 7.82E-06 168.18 79.46 0.127 1.48E-05 316.90 149.72 0.181 16.50 1.95E-05 419.11 120.32 0.107 3.68E-05 789.69 226.71 0.154 15.70 2.18E-05 520.15 132.18 0.101 4.57E-05 980.07 249.05 0.146 13.20 4.42E-05 893.36 165.44 0.081 8.11E-05 1683.29 311.72 0.119 12.40 5.09E-05 1029.52 174.87 0.075 9.20E-05 1939.84 329.48 0.111 9.90 2.95E-04 1499.97 200.53 0.056 2.29E-04 2826.26 377.84 0.085 9.10 2.98E-04 1663.23 207.53 0.050 2.14E-04 3133.88 391.03 0.077 6.60 4.63E-04 2205.83 225.60 0.033 4.60E-04 4156.27 425.07 0.052 5.80 4.67E-04 2388.17 230.16 0.028 4.35E-04 4499.84 433.68 0.045 3.30 6.67E-04 2977.87 240.64 0.014 7.30E-04 5610.96 453.41 0.023 15.00 20.00 2.50 6.75E-04 3171.27 242.77 0.010 6.92E-04 5975.37 457.44 0.017 0.00 8.43E-04 3783.00 245.65 0.000 1.01E-03 7128.00 462.86 0.000 0.070 0.132 0.089 0.093 0.159 0.225 Total (m) Def lect io n Total (m) From foundation (m)

5.00 10.00 0.00 0.00 0.10 0.20 0.30

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Limite State: sii Upper axial load: 100 kN/floor

Limit State Description: Outermost tensile strain = 1.0% Lower axial load: 500 kN/floor

15 20 15.00 20.00 15.00 20.00 5 10 5.00 10.00 0 00 5.00 10.00

23.10 0.00E+00 0.00 0.00 0.368 0.00E+00 0.00 0.00 0.393

22.30 4.02E-07 8.63 21.46 0.354 6.99E-07 15.04 37.38 0.378

19.80 6.57E-06 141.55 83.64 0.309 1.15E-05 246.59 145.71 0.332

19.00 1.00E-05 215.84 101.98 0.295 1.75E-05 376.03 177.66 0.317

0 0.00 10.00 20.00 30.00 40.00 50.00 0.00 0 1000 2000 3000 4000 5000 6000 7000 8000 0.00 0.00E+00 1.00E-03 2.00E-03 3.00E-03 4.00E-03 20.00 Deflection (m) 16.50 2.50E-05 537.87 154.41 0.250 4.37E-05 937.04 269.01 0.270 15.70 3.11E-05 667.54 169.63 0.236 5.42E-05 1162.94 295.52 0.255 13.20 1.64E-04 1146.52 212.32 0.192 1.01E-04 1997.37 369.88 0.209 12.40 2.34E-04 1321.26 224.42 0.178 1.10E-04 2301.80 390.96 0.194 9.90 3.97E-04 1925.01 257.35 0.134 3.67E-04 3353.61 448.34 0.149 9.10 4.64E-04 2134.54 266.34 0.121 3.49E-04 3718.63 463.99 0.135 6.60 6.34E-04 2830.90 289.52 0.081 6.70E-04 4931.78 504.39 0.092 5.80 7.00E-04 3064.92 295.39 0.068 6.54E-04 5339.46 514.60 0.079 3.30 1.01E-03 3821.72 308.83 0.032 1.04E-03 6657.90 538.01 0.040 2.50 1.01E-03 4069.93 311.57 0.021 9.97E-04 7090.31 542.79 0.028 1.75 3.77E-03 4304.35 313.45 0.013 1.19E-03 7498.70 546.07 0.018 10.00 15.00 1.75 3.77E 03 4304.35 313.45 0.013 1.19E 03 7498.70 546.07 0.018 0.00 3.77E-03 4855.00 315.26 0.000 3.85E-03 8458.00 549.22 0.000 0.090 0.156 0.279 0.237 0.368 0.393 Total (m) Deflection Total (m) From foundation (m)

0.00 5.00 10.00 0 00 0 10 0 20 0 30 0 40 0.00 0.00 0.10 0.20 0.30 0.40

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Limit State Description: Onset of bar buckling (es-ec)> 3.75% Lower axial load: 500 kN/floor

Damage State: DSII

15 20 15.00 20.00 15.00 20.00 5 10 5.00 10.00 0 00 5.00 10.00

23.10 0.00E+00 0.00 0.00 0.674 0.00E+00 0.00 0.00 0.613

22.30 4.66E-07 9.58 23.80 0.648 6.99E-07 4.81 11.95 0.590

19.80 7.30E-06 157.03 92.79 0.569 1.15E-05 78.80 46.57 0.518

19.00 1.11E-05 239.45 113.13 0.543 1.75E-05 120.17 56.78 0.495

0 0.00 10.00 20.00 30.00 40.00 50.00 0.00 0 1000 2000 3000 4000 5000 6000 7000 8000 0.00 0.00E+00 5.00E-03 1.00E-02 1.50E-02 20.00 Deflection (m) 16.50 2.78E-05 596.70 171.30 0.464 4.36E-05 299.46 85.97 0.423 15.70 3.51E-05 740.55 188.19 0.439 5.41E-05 371.65 94.44 0.400 13.20 1.97E-04 1271.91 235.54 0.360 1.01E-04 638.32 118.21 0.328 12.40 2.70E-04 1465.77 248.96 0.334 1.10E-04 735.61 124.94 0.305 9.90 4.63E-04 2135.56 285.50 0.257 3.65E-04 1071.74 143.28 0.235 9.10 5.30E-04 2368.00 295.46 0.232 3.47E-04 1188.40 148.28 0.212 6.60 7.00E-04 3140.52 321.19 0.158 6.67E-04 1576.09 161.19 0.144 5.80 8.00E-04 3400.13 327.69 0.135 6.51E-04 1706.38 164.45 0.122 3.30 1.18E-03 4239.71 342.60 0.065 1.04E-03 2127.73 171.94 0.058 2.50 1.70E-03 4515.06 345.64 0.044 3.84E-03 2265.91 173.46 0.038 1.75 3.00E-03 4775.13 347.73 0.025 3.84E-03 2396.43 174.51 0.021 10.00 15.00 1.75 3.00E 03 4775.13 347.73 0.025 3.84E 03 2396.43 174.51 0.021 0.00 1.14E-02 5386.00 349.74 0.000 1.12E-02 2703.00 175.52 0.000 0.100 0.050 0.574 0.564 0.674 0.613 Total (m) Deflection Total (m) From foundation (m)

0.00 5.00 10.00 0 00 0 10 0 20 0 30 0 40 0 50 0 60 0 70 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

(18)

Limite State: siv Upper axial load: 100 kN/floor

Limit State Description: Long. bar fracture for ec<=-0.004 and (es-ec)> 5% Lower axial load: 500 kN/floor

Damage State: DSIII

15 20 15.00 20.00 15.00 20.00 5 10 5.00 10.00 0 00 5.00 10.00

23.10 0.00E+00 0.00 0.00 0.809 0.00E+00 0.00 0.00 0.843

22.30 2.79E-07 9.60 23.87 0.779 6.99E-07 1.92 4.78 0.811

19.80 7.31E-06 157.46 93.05 0.684 1.15E-05 31.55 18.64 0.712

19.00 1.12E-05 240.12 113.45 0.654 1.75E-05 48.10 22.73 0.681

0 0.00 10.00 20.00 30.00 40.00 50.00 0.00 0 1000 2000 3000 4000 5000 6000 7000 8000 0.00 0.00E+00 5.00E-03 1.00E-02 1.50E-02 2.00E-02 2.50E-02 3.00E-02 3.50E-02 20.00 Deflection (m) 16.50 2.79E-05 598.36 171.78 0.559 4.36E-05 119.87 34.41 0.582 15.70 3.52E-05 742.61 188.71 0.529 5.41E-05 148.77 37.80 0.551 13.20 1.97E-04 1275.45 236.20 0.435 1.01E-04 255.52 47.32 0.452 12.40 2.80E-04 1469.85 249.66 0.405 1.10E-04 294.46 50.01 0.421 9.90 4.63E-04 2141.50 286.30 0.312 3.65E-04 429.01 57.35 0.323 9.10 5.20E-04 2374.59 296.29 0.283 3.47E-04 475.71 59.36 0.292 6.60 7.20E-04 3149.27 322.08 0.193 6.67E-04 630.90 64.52 0.197 5.80 8.00E-04 3409.60 328.60 0.165 6.51E-04 683.06 65.83 0.167 3.30 1.18E-03 4251.52 343.56 0.080 1.04E-03 851.72 68.83 0.076 2.50 1.70E-03 4527.64 346.61 0.054 1.06E-02 907.04 69.44 0.048 1.75 3.00E-03 4788.42 348.70 0.030 1.06E-02 959.28 69.86 0.025 10.00 15.00 1.75 3.00E 03 4788.42 348.70 0.030 1.06E 02 959.28 69.86 0.025 0.00 1.49E-02 5401.00 350.71 0.000 1.51E-02 1082.00 70.26 0.000 0.100 0.020 0.709 0.823 0.809 0.843 Total (m) Deflection Total (m) From foundation (m)

0.00 5.00 10.00 0 00 0 10 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 1 00 1 10 1 20 1 30 1 40 1 50 1 60 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60