Fundamentals of Seismic Design
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
MEEES student: José Velásquez
Fundamentals of Seismic Design
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) 1st floor section. (2) Floors from 2nd to 7th.
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 106 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. A typical moment-curvature run using program Xtract is shown in figure 3.
MEEES student: José Velásquez
Fundamentals of Seismic Design
(a)
(b)
(c)
Figure 2. Material properties. (a) Unconfined concrete. (2) Confined concrete (Mander model). (3) Steel model.
Figure 3. Typical moment-curvature run using the Xtract interface.
MEEES student: José Velásquez
Fundamentals of Seismic Design
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. ci cii ciii civ si sii siii siv
Limit strains Concrete tensile strain Onset of concrete cover spalling Deep of concrete cover spalling Crushing of confined concrete core Steel yielding strain Outermost tensile strain Onset of bar buckling (es-ec)> Long. bar fracture for ec
0.007% -0.400% -0.400% 4.560% 0.219% 1.000% 3.750% 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. MEEES student: José Velásquez
Fundamentals of Seismic Design
MEEES student: José Velásquez
Fundamentals of Seismic Design
Base shear (kN)
Base Shear vs. Drif Ratio
600
sii 500
ciii
Lower bound (100 kN/floor)
cii
Upper bound (500 kN/floor)
si DSII
400
siv cii 300
siii
ciii
sii DSIII ci
si
200
siii DSI
100
siv
ci 0 0.00% 0.00m
0.50%
1.00% 0.20m
1.50%
2.00% 0.40m
2.50% 0.60m
3.00%
3.50% 0.80m
4.00%
Drift ratio 1.00m
Roof displacement Figure 4. Static pushover curve for lower and upper bound axial cases with the definition of damage states.
MEEES student: José Velásquez
Fundamentals of Seismic Design
2. MOMENT-CURVATURE DIAGRAMS OF ALL THE FLOORS Moment-curvature for all stories (lower bound: axial load = 100kN/floor)
1st floor - 700 kN 2nd floor - 600 kN
8000
3rd floor - 500 kN 4th floor - 400 kN
7000
5th floor - 300 kN 6th floor - 200 kN
Moment (kN-m)
6000
7th floor - 100 kN 5000
4000
3000
2000
1000
0 0.00
0.05
0.10
0.15
Curvature x wall length (rad)
Figure 5. Moment-curvature diagrams for all stories and lower bound axial load case of 100 kN/floor.
MEEES student: José Velásquez
0.20
Fundamentals of Seismic Design
Moment-curvature for all stories (upper bound: axial load = 500kN/floor)
1st floor - 3500 kN 2nd floor - 3000 kN
8000
3rd floor - 2500 kN 7000
4th floor - 2000 kN 5th floor - 1500 kN
Moment (kN-m)
6000
6th floor - 1000 kN 7th floor - 500 kN
5000
4000
3000
2000
1000
0 0.00
0.05
0.10
0.15
Curvature x wall length (rad)
Figure 6. Moment-curvature diagrams for all stories and upper bound axial load case of 500 kN/floor.
MEEES student: José Velásquez
0.20
Fundamentals of Seismic Design
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.
MEEES student: José Velásquez
Fundamentals of Seismic Design
Moment-curvature for the base section (upper and lower bounds) 9000
Upper bound (500 kN/m)
sii 8000
cii
Lower bound (100 kN/m)
ciii
si
7000
Moment (kN-
6000
cii
siii
siv
ciii
5000 sii 4000 ci
si
3000
siii
2000 siv =civ
ci 1000 0 0.00
0.01
0.02
0.03
0.04
0.05
0.06
Curvature x Wall length (rad)
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.
MEEES student: José Velásquez
Limite State: ci Limit State Description: Concrete tensile strain = 0.007% Damage State: DSI
Upper axial load: 100 kN/floor Lower axial load: 500 kN/floor
Curvature (rad/m)
Moment diagram (kN-m)
Force distribution (kN/m)
20
20.00
15
15.00
10
10.00
20.00
15.00
10.00
5.00
5.00
5
30.00
20.00
10.00
0 0.00
0.00 3500
3000
2500
2000
1500
1000
500
2.00E-04
0.00 0.00E+00
1.00E-04
0
Deflection (m)
Height (m)
Deflection
23.10 22.30 19.80 19 80 19.00 16.50 15.70 13.20 12.40 9.90 9.10 6.60 5.80 3.30 2.50 0.00
Curvature (rad/m) 0.00E+00 1.40E-07 1 91E-06 1.91E-06 2.93E-06 7.31E-06 9.08E-06 1.56E-05 1.80E-05 2.62E-05 2.90E-05 3.92E-05 4.24E-05 5.35E-05 5.63E-05 6.75E-05
Lower bound (100 kN/floor) Moment (kN-m) Shear (kN) Deflection (m) Curvature (rad/m) 0.00 0.00 0.034 0.00E+00 2.53 6.28 0.033 2.79E-07 41 43 41.43 24 48 24.48 0 029 0.029 4 52E-06 4.52E-06 63.17 29.85 0.028 6.89E-06 157.43 45.19 0.024 1.72E-05 195.38 49.65 0.022 2.13E-05 335.57 62.14 0.018 3.66E-05 386.72 65.68 0.017 4.22E-05 563.43 75.32 0.013 6.15E-05 624.75 77.95 0.012 6.83E-05 828.57 84.74 0.009 9.07E-05 897.06 86.46 0.007 9.82E-05 1118.57 90.39 0.004 1.25E-04 1191.22 91.19 0.003 1.32E-04 1421.00 92.27 0.000 1.61E-04
Upper bound (500 kN/floor) Moment (kN-m) Shear (kN) Deflection (m) 0.00 0.00 0.080 5.92 14.71 0.077 97 06 97.06 57 35 57.35 0 068 0.068 148.00 69.93 0.065 368.81 105.88 0.055 457.72 116.31 0.053 786.15 145.58 0.043 905.97 153.88 0.040 1319.95 176.46 0.031 1463.62 182.62 0.029 1941.11 198.52 0.020 2101.57 202.54 0.017 2620.50 211.76 0.010 2790.69 213.64 0.007 3329.00 216.17 0.000
From foundation (m)
0.026
From foundation (m)
Remaining wall (including hinges, m)
0.008
Remaining wall (including hinges, m)
Total (m)
0.034
20.00
15.00
10.00
0.062 0.019 Total (m)
0.080
5.00
0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00 0.00
Limite State: cii Limit State Description: Onset of concrete cover spalling = -0.4% Damage State: DSI
Upper axial load: 100 kN/floor Lower axial load: 500 kN/floor
Curvature (rad/m)
Moment diagram (kN-m)
Force distribution (kN/m)
20
20.00
15
15.00
10
10.00
20.00
15.00
10.00
5.00
5.00
5
50.00
40.00
30.00
20.00
10.00
1.00E-02
0.00
0 0.00
8000
7000
6000
5000
4000
3000
2000
1000
0 00 0.00 0.00E+00
5.00E-03
0
Deflection (m)
Height (m)
Deflection
23.10 22.30 19.80 19.00 16.50 15.70 13.20 12.40 9.90 9.10 6.60 5.80 3.30 2.50 1.75 0.00
Curvature (rad/m) 0.00E+00 4.66E-07 7.27E-06 1.11E-05 2.76E-05 3.25E-05 1.97E-04 2.63E-04 4.63E-04 4.97E-04 7.00E-04 7.67E-04 1.15E-03 1.52E-03 3.08E-03 3.08E 03 1.07E-02
Lower bound (100 kN/floor) Moment (kN-m) Shear (kN) Deflection (m) 0.00 0.00 0.645 9.52 23.65 0.621 156.01 92.19 0.545 237.89 112.40 0.520 592.82 170.19 0.444 735.74 186.96 0.420 1263.65 234.01 0.344 1456.24 247.34 0.320 2121.68 283.65 0.246 2352.61 293.54 0.222 3120.12 319.10 0.151 3378.04 325.56 0.129 4212.16 340.38 0.062 4485.72 343.40 0.042 4744.10 345.47 0.024 5351.00 347.47 0.000
Curvature (rad/m) 0.00E+00 6.99E-07 1.15E-05 1.76E-05 4.37E-05 5.43E-05 1.02E-04 1.10E-04 3.69E-04 3.51E-04 6.73E-04 6.57E-04 1.05E-03 1.00E-03 1.21E-03 1.21E 03 5.16E-03
Upper bound (500 kN/floor) Moment (kN-m) Shear (kN) Deflection (m) 0.00 0.00 0.445 15.08 37.48 0.429 247.20 146.07 0.376 376.96 178.10 0.359 939.36 269.67 0.307 1165.82 296.25 0.290 2002.33 370.80 0.238 2307.51 391.93 0.221 3361.94 449.46 0.170 3727.86 465.14 0.154 4944.02 505.64 0.105 5352.72 515.87 0.090 6674.43 539.35 0.045 7107.91 544.14 0.032 7517.32 547.42 0.020 8479.00 550.58 0.000
From foundation (m)
0.099
From foundation (m)
Remaining wall (including hinges, m)
0.546
Remaining wall (including hinges, m)
Total (m)
0.645
20.00
15.00
10.00
0.157 0.289 Total (m)
0.445
5.00
0.70 0 70
0.60 0 60
0.50 0 50
0.40 0 40
0.30 0 30
0.20 0 20
0.10 0 10
0.00 0.00 0 00
Limite State: ciii Limit State Description: Deep of concrete cover spalling -0.4% Damage State: DSII
Upper axial load: 100 kN/floor Lower axial load: 500 kN/floor
Curvature (rad/m)
Moment diagram (kN-m)
Force distribution (kN/m)
20
20.00
15
15.00
10
10.00
20.00
15.00
10.00
5.00
5.00
5
50.00
40.00
30.00
20.00
10.00
0.00
0 0.00
8000
7000
6000
5000
4000
3000
2000
1000
1.50E-02
1.00E-02
0 00 0.00 0.00E+00
5.00E-03
0
Deflection (m)
Height (m)
Deflection
23.10 22.30 19.80 19.00 16.50 15.70 13.20 12.40 9.90 9.10 6.60 5.80 3.30 2.50 1.75 0.00
Curvature (rad/m) 0.00E+00 4.66E-07 7.30E-06 1.11E-05 2.78E-05 3.51E-05 1.97E-04 2.70E-04 4.63E-04 5.30E-04 7.00E-04 8.00E-04 1.18E-03 1.70E-03 3.00E-03 3.00E 03 1.28E-02
Lower bound (100 kN/floor) Moment (kN-m) Shear (kN) Deflection (m) 0.00 0.00 0.728 9.63 23.95 0.701 157.96 93.34 0.615 240.87 113.80 0.588 600.24 172.32 0.502 744.95 189.30 0.475 1279.47 236.94 0.390 1474.48 250.44 0.363 2148.24 287.20 0.279 2382.07 297.22 0.253 3159.18 323.10 0.172 3420.33 329.64 0.147 4264.90 344.64 0.071 4541.89 347.70 0.048 4803.50 349.80 0.027 5418.00 351.82 0.000
Curvature (rad/m) 0.00E+00 6.99E-07 1.15E-05 1.75E-05 4.36E-05 5.41E-05 1.01E-04 1.10E-04 3.65E-04 3.47E-04 6.67E-04 6.51E-04 1.04E-03 9.93E-04 1.18E-03 1.18E 03 5.68E-03
Upper bound (500 kN/floor) Moment (kN-m) Shear (kN) Deflection (m) 0.00 0.00 0.464 15.01 37.30 0.446 246.06 145.40 0.392 375.23 177.28 0.374 935.04 268.43 0.320 1160.46 294.89 0.302 1993.12 369.10 0.248 2296.90 390.13 0.231 3346.47 447.39 0.178 3710.72 463.00 0.161 4921.28 503.31 0.110 5328.10 513.50 0.094 6643.73 536.87 0.047 7075.22 541.63 0.033 7482.74 544.91 0.021 8440.00 548.05 0.000
From foundation (m)
0.100
From foundation (m)
Remaining wall (including hinges, m)
0.628
Remaining wall (including hinges, m)
Total (m)
0.728
20.00
15.00
10.00
0.156 0.308 Total (m)
0.464
5.00
0.70 0 70
0.60 0 60
0.50 0 50
0.40 0 40
0.30 0 30
0.20 0 20
0.10 0 10
0.00 0.00 0 00
Limite State: civ Limit State Description: Crushing of confined concrete core 4.56% Damage State: DSIII
Upper axial load: 100 kN/floor Lower axial load: 500 kN/floor
Curvature (rad/m)
Moment diagram (kN-m)
Force distribution (kN/m)
20
20.00
15
15.00
10
10.00
20.00
15.00
10.00
5.00
5.00
5
50.00
40.00
30.00
20.00
10.00
0.00
0 0.00
8000
7000
6000
5000
4000
3000
2000
1000
3.50E-02
3.00E-02
2.50E-02
2.00E-02
1.50E-02
1.00E-02
5.00E-03
0 00 0.00 0.00E+00
0
Deflection (m)
Height (m)
Deflection
23.10 22.30 19.80 19.00 16.50 15.70 13.20 12.40 9.90 9.10 6.60 5.80 3.30 2.50 1.75 0.00
Curvature (rad/m) 0.00E+00 3.73E-07 6.19E-06 9.41E-06 2.35E-05 2.91E-05 1.31E-04 1.97E-04 3.64E-04 4.30E-04 5.67E-04 6.34E-04 7.76E-04 8.45E-04 9.44E-04 9.44E 04 3.64E-02
Lower bound (100 kN/floor) Moment (kN-m) Shear (kN) Deflection (m) 0.00 0.00 1.577 8.09 20.10 1.519 132.59 78.35 1.339 202.19 95.53 1.281 503.86 144.65 1.102 625.33 158.91 1.044 1074.02 198.89 0.864 1237.71 210.23 0.807 1803.29 241.08 0.628 1999.57 249.49 0.572 2651.90 271.22 0.395 2871.11 276.71 0.340 3580.06 289.30 0.167 3812.57 291.87 0.113 4032.17 293.63 0.062 4548.00 295.32 0.000
Curvature (rad/m) 0.00E+00 6.99E-07 1.15E-05 1.75E-05 4.36E-05 5.41E-05 1.01E-04 1.10E-04 3.65E-04 3.47E-04 6.67E-04 6.51E-04 1.04E-03 1.06E-02 1.06E-02 1.06E 02 1.51E-02
Upper bound (500 kN/floor) Moment (kN-m) Shear (kN) Deflection (m) 0.00 0.00 0.843 1.92 4.78 0.811 31.55 18.64 0.712 48.10 22.73 0.681 119.87 34.41 0.582 148.77 37.80 0.551 255.52 47.32 0.452 294.46 50.01 0.421 429.01 57.35 0.323 475.71 59.36 0.292 630.90 64.52 0.197 683.06 65.83 0.167 851.72 68.83 0.076 907.04 69.44 0.048 959.28 69.86 0.025 1082.00 70.26 0.000
From foundation (m)
0.084
From foundation (m)
Remaining wall (including hinges, m)
1.493
Remaining wall (including hinges, m)
Total (m)
1.577
20.00
15.00
10.00
0.020 0.823 Total (m)
0.843
5.00
0.00 1.60 1.50 1.40 1.30 1.20 1.10 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 1 60 1 50 1 40 1 30 1 20 1 10 1 00 0 90 0 80 0 70 0 60 0 50 0 40 0 30 0.20 0 20 0.10 0 10 0.00 0 00
Limite State: si Limit State Description: Steel yielding strain = 0.219% Damage State: DSI
Upper axial load: 100 kN/floor Lower axial load: 500 kN/floor
Curvature (rad/m)
Moment diagram (kN-m)
Force distribution (kN/m)
20
20.00
15
15.00
10
10.00
20.00
15.00
10.00
5.00
5.00
5
40.00
30.00
20.00
10.00
0 0.00
0.00 7000
6000
5000
4000
3000
2000
1000
1.50E-03
1.00E-03
0.00 0.00E+00
5.00E-04
0
Deflection (m)
Height (m)
Deflection
23.10 22.30 19.80 19 80 19.00 16.50 15.70 13.20 12.40 9.90 9.10 6.60 5.80 3.30 2.50 0.00
Curvature (rad/m) 0.00E+00 2.79E-06 5 12E-06 5.12E-06 7.82E-06 1.95E-05 2.18E-05 4.42E-05 5.09E-05 2.95E-04 2.98E-04 4.63E-04 4.67E-04 6.67E-04 6.75E-04 8.43E-04
Lower bound (100 kN/floor) Moment (kN-m) Shear (kN) Deflection (m) Curvature (rad/m) 0.00 0.00 0.159 0.00E+00 6.73 16.72 0.152 6.05E-07 110 29 110.29 65 17 65.17 0 133 0.133 9 69E-06 9.69E-06 168.18 79.46 0.127 1.48E-05 419.11 120.32 0.107 3.68E-05 520.15 132.18 0.101 4.57E-05 893.36 165.44 0.081 8.11E-05 1029.52 174.87 0.075 9.20E-05 1499.97 200.53 0.056 2.29E-04 1663.23 207.53 0.050 2.14E-04 2205.83 225.60 0.033 4.60E-04 2388.17 230.16 0.028 4.35E-04 2977.87 240.64 0.014 7.30E-04 3171.27 242.77 0.010 6.92E-04 3783.00 245.65 0.000 1.01E-03
Upper bound (500 kN/floor) Moment (kN-m) Shear (kN) Deflection (m) 0.00 0.00 0.225 12.68 31.50 0.217 207 81 207.81 122 80 122.80 0 190 0.190 316.90 149.72 0.181 789.69 226.71 0.154 980.07 249.05 0.146 1683.29 311.72 0.119 1939.84 329.48 0.111 2826.26 377.84 0.085 3133.88 391.03 0.077 4156.27 425.07 0.052 4499.84 433.68 0.045 5610.96 453.41 0.023 5975.37 457.44 0.017 7128.00 462.86 0.000
From foundation (m)
0.070
From foundation (m)
Remaining wall (including hinges, m)
0.089
Remaining wall (including hinges, m)
Total (m)
0.159
20.00
15.00
10.00
0.132 0.093 Total (m)
0.225
5.00
0.30
0.20
0.10
0.00 0.00
Limite State: sii Limit State Description: Outermost tensile strain = 1.0% Damage State: DSI
Upper axial load: 100 kN/floor Lower axial load: 500 kN/floor
Curvature (rad/m)
Moment diagram (kN-m)
Force distribution (kN/m)
20
20.00
15
15.00
10
10.00
20.00
15.00
10.00
5.00
5.00
5
50.00
40.00
30.00
20.00
10.00
0.00
0 0.00
8000
7000
6000
5000
4000
3000
2000
1000
4.00E-03
3.00E-03
2.00E-03
0 00 0.00 0.00E+00
1.00E-03
0
Deflection (m)
Height (m)
Deflection
23.10 22.30 19.80 19.00 16.50 15.70 13.20 12.40 9.90 9.10 6.60 5.80 3.30 2.50 1.75 0.00
Curvature (rad/m) 0.00E+00 4.02E-07 6.57E-06 1.00E-05 2.50E-05 3.11E-05 1.64E-04 2.34E-04 3.97E-04 4.64E-04 6.34E-04 7.00E-04 1.01E-03 1.01E-03 3.77E-03 3.77E 03 3.77E-03
Lower bound (100 kN/floor) Moment (kN-m) Shear (kN) Deflection (m) 0.00 0.00 0.368 8.63 21.46 0.354 141.55 83.64 0.309 215.84 101.98 0.295 537.87 154.41 0.250 667.54 169.63 0.236 1146.52 212.32 0.192 1321.26 224.42 0.178 1925.01 257.35 0.134 2134.54 266.34 0.121 2830.90 289.52 0.081 3064.92 295.39 0.068 3821.72 308.83 0.032 4069.93 311.57 0.021 4304.35 313.45 0.013 4855.00 315.26 0.000
Curvature (rad/m) 0.00E+00 6.99E-07 1.15E-05 1.75E-05 4.37E-05 5.42E-05 1.01E-04 1.10E-04 3.67E-04 3.49E-04 6.70E-04 6.54E-04 1.04E-03 9.97E-04 1.19E-03 1.19E 03 3.85E-03
Upper bound (500 kN/floor) Moment (kN-m) Shear (kN) Deflection (m) 0.00 0.00 0.393 15.04 37.38 0.378 246.59 145.71 0.332 376.03 177.66 0.317 937.04 269.01 0.270 1162.94 295.52 0.255 1997.37 369.88 0.209 2301.80 390.96 0.194 3353.61 448.34 0.149 3718.63 463.99 0.135 4931.78 504.39 0.092 5339.46 514.60 0.079 6657.90 538.01 0.040 7090.31 542.79 0.028 7498.70 546.07 0.018 8458.00 549.22 0.000
From foundation (m)
0.090
From foundation (m)
Remaining wall (including hinges, m)
0.279
Remaining wall (including hinges, m)
Total (m)
0.368
20.00
15.00
10.00
0.156 0.237 Total (m)
0.393
5.00
0.40 0 40
0.30 0 30
0.20 0 20
0.10 0 10
0.00 0.00 0 00
Limite State: siii Limit State Description: Onset of bar buckling (es-ec)> 3.75% Damage State: DSII
Upper axial load: 100 kN/floor Lower axial load: 500 kN/floor
Curvature (rad/m)
Moment diagram (kN-m)
Force distribution (kN/m)
20
20.00
15
15.00
10
10.00
20.00
15.00
10.00
5.00
5.00
5
50.00
40.00
30.00
20.00
10.00
0.00
0 0.00
8000
7000
6000
5000
4000
3000
2000
1000
1.50E-02
1.00E-02
0 00 0.00 0.00E+00
5.00E-03
0
Deflection (m)
Height (m)
Deflection
23.10 22.30 19.80 19.00 16.50 15.70 13.20 12.40 9.90 9.10 6.60 5.80 3.30 2.50 1.75 0.00
Curvature (rad/m) 0.00E+00 4.66E-07 7.30E-06 1.11E-05 2.78E-05 3.51E-05 1.97E-04 2.70E-04 4.63E-04 5.30E-04 7.00E-04 8.00E-04 1.18E-03 1.70E-03 3.00E-03 3.00E 03 1.14E-02
Lower bound (100 kN/floor) Moment (kN-m) Shear (kN) Deflection (m) 0.00 0.00 0.674 9.58 23.80 0.648 157.03 92.79 0.569 239.45 113.13 0.543 596.70 171.30 0.464 740.55 188.19 0.439 1271.91 235.54 0.360 1465.77 248.96 0.334 2135.56 285.50 0.257 2368.00 295.46 0.232 3140.52 321.19 0.158 3400.13 327.69 0.135 4239.71 342.60 0.065 4515.06 345.64 0.044 4775.13 347.73 0.025 5386.00 349.74 0.000
Curvature (rad/m) 0.00E+00 6.99E-07 1.15E-05 1.75E-05 4.36E-05 5.41E-05 1.01E-04 1.10E-04 3.65E-04 3.47E-04 6.67E-04 6.51E-04 1.04E-03 3.84E-03 3.84E-03 3.84E 03 1.12E-02
Upper bound (500 kN/floor) Moment (kN-m) Shear (kN) Deflection (m) 0.00 0.00 0.613 4.81 11.95 0.590 78.80 46.57 0.518 120.17 56.78 0.495 299.46 85.97 0.423 371.65 94.44 0.400 638.32 118.21 0.328 735.61 124.94 0.305 1071.74 143.28 0.235 1188.40 148.28 0.212 1576.09 161.19 0.144 1706.38 164.45 0.122 2127.73 171.94 0.058 2265.91 173.46 0.038 2396.43 174.51 0.021 2703.00 175.52 0.000
From foundation (m)
0.100
From foundation (m)
Remaining wall (including hinges, m)
0.574
Remaining wall (including hinges, m)
Total (m)
0.674
20.00
15.00
10.00
0.050 0.564 Total (m)
0.613
5.00
0.70 0 70
0.60 0 60
0.50 0 50
0.40 0 40
0.30 0 30
0.20 0 20
0.10 0 10
0.00 0.00 0 00
Limite State: siv Limit State Description: Long. bar fracture for ec 5% Damage State: DSIII
Upper axial load: 100 kN/floor Lower axial load: 500 kN/floor
Curvature (rad/m)
Moment diagram (kN-m)
Force distribution (kN/m)
20
20.00
15
15.00
10
10.00
20.00
15.00
10.00
5.00
5.00
5
50.00
40.00
30.00
20.00
10.00
0.00
0 0.00
8000
7000
6000
5000
4000
3000
2000
1000
3.50E-02
3.00E-02
2.50E-02
2.00E-02
1.50E-02
1.00E-02
5.00E-03
0 00 0.00 0.00E+00
0
Deflection (m)
Height (m)
Deflection
23.10 22.30 19.80 19.00 16.50 15.70 13.20 12.40 9.90 9.10 6.60 5.80 3.30 2.50 1.75 0.00
Curvature (rad/m) 0.00E+00 2.79E-07 7.31E-06 1.12E-05 2.79E-05 3.52E-05 1.97E-04 2.80E-04 4.63E-04 5.20E-04 7.20E-04 8.00E-04 1.18E-03 1.70E-03 3.00E-03 3.00E 03 1.49E-02
Lower bound (100 kN/floor) Moment (kN-m) Shear (kN) Deflection (m) 0.00 0.00 0.809 9.60 23.87 0.779 157.46 93.05 0.684 240.12 113.45 0.654 598.36 171.78 0.559 742.61 188.71 0.529 1275.45 236.20 0.435 1469.85 249.66 0.405 2141.50 286.30 0.312 2374.59 296.29 0.283 3149.27 322.08 0.193 3409.60 328.60 0.165 4251.52 343.56 0.080 4527.64 346.61 0.054 4788.42 348.70 0.030 5401.00 350.71 0.000
Curvature (rad/m) 0.00E+00 6.99E-07 1.15E-05 1.75E-05 4.36E-05 5.41E-05 1.01E-04 1.10E-04 3.65E-04 3.47E-04 6.67E-04 6.51E-04 1.04E-03 1.06E-02 1.06E-02 1.06E 02 1.51E-02
Upper bound (500 kN/floor) Moment (kN-m) Shear (kN) Deflection (m) 0.00 0.00 0.843 1.92 4.78 0.811 31.55 18.64 0.712 48.10 22.73 0.681 119.87 34.41 0.582 148.77 37.80 0.551 255.52 47.32 0.452 294.46 50.01 0.421 429.01 57.35 0.323 475.71 59.36 0.292 630.90 64.52 0.197 683.06 65.83 0.167 851.72 68.83 0.076 907.04 69.44 0.048 959.28 69.86 0.025 1082.00 70.26 0.000
From foundation (m)
0.100
From foundation (m)
Remaining wall (including hinges, m)
0.709
Remaining wall (including hinges, m)
Total (m)
0.809
20.00
15.00
10.00
0.020 0.823 Total (m)
0.843
5.00
0.00 1.60 1.50 1.40 1.30 1.20 1.10 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 1 60 1 50 1 40 1 30 1 20 1 10 1 00 0 90 0 80 0 70 0 60 0 50 0 40 0 30 0.20 0 20 0.10 0 10 0.00 0 00
