pushover de una placa de 7 pisos
DESCRIPTION
Analisis Pushover de una placa de 7 pisos, mediante el método de estados límiteTRANSCRIPT
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Fundamentals of Seismic Design
MEEES student: Jos Velsquez
FUNDAMENTALS OF SEISMIC DESIGN
Assignment #2
Limit State Analysis
MEEES Student: Jos Martn Velsquez Vargas
E-mail: [email protected]
Professor: Jos Restrepo
Assistant Professor: Matthew Tobolski
October, 2006
Pavia, Italy
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Fundamentals of Seismic Design
MEEES student: Jos Velsquez
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.
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Fundamentals of Seismic Design
MEEES student: Jos Velsquez
(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.
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Fundamentals of Seismic Design
MEEES student: Jos Velsquez
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 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: Jos Velsquez
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Fundamentals of Seismic Design
MEEES student: Jos Velsquez
Base Shear vs. Drif Ratio
ci
si
siicii 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 1.00mRoof displacement
Figure 4. Static pushover curve for lower and upper bound axial cases with the definition of damage states.
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Fundamentals of Seismic Design
MEEES student: Jos Velsquez
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 0.20Curvature x wall length (rad)
M
o
m
e
n
t
(
k
N
-
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
Figure 5. Moment-curvature diagrams for all stories and lower bound axial load case of 100 kN/floor.
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Fundamentals of Seismic Design
MEEES student: Jos Velsquez
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 0.20Curvature x wall length (rad)
M
o
m
e
n
t
(
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
Figure 6. Moment-curvature diagrams for all stories and upper bound axial load case of 500 kN/floor.
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Fundamentals of Seismic Design
MEEES student: Jos Velsquez
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: Jos Velsquez
Moment-curvature for the base section (upper and lower bounds)
si
sii
ci
sici
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 0.06Curvature x Wall length (rad)
Mom
ent (
kN-
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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Limite State: ci Upper axial load: 100 kN/floorLimit State Description: Concrete tensile strain = 0.007% Lower axial load: 500 kN/floorDamage 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 0.08022.30 1.40E-07 2.53 6.28 0.033 2.79E-07 5.92 14.71 0.07719 80 1 91E-06 41 43 24 48 0 029 4 52E-06 97 06 57 35 0 068
Height (m) Upper bound (500 kN/floor)Lower bound (100 kN/floor)
00.0010.0020.0030.00
0.000500100015002000250030003500
0.000.00E+001.00E-042.00E-04
20.00
Deflection (m)
19.80 1.91E-06 41.43 24.48 0.029 4.52E-06 97.06 57.35 0.06819.00 2.93E-06 63.17 29.85 0.028 6.89E-06 148.00 69.93 0.06516.50 7.31E-06 157.43 45.19 0.024 1.72E-05 368.81 105.88 0.05515.70 9.08E-06 195.38 49.65 0.022 2.13E-05 457.72 116.31 0.05313.20 1.56E-05 335.57 62.14 0.018 3.66E-05 786.15 145.58 0.04312.40 1.80E-05 386.72 65.68 0.017 4.22E-05 905.97 153.88 0.0409.90 2.62E-05 563.43 75.32 0.013 6.15E-05 1319.95 176.46 0.0319.10 2.90E-05 624.75 77.95 0.012 6.83E-05 1463.62 182.62 0.0296.60 3.92E-05 828.57 84.74 0.009 9.07E-05 1941.11 198.52 0.0205.80 4.24E-05 897.06 86.46 0.007 9.82E-05 2101.57 202.54 0.0173.30 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 0.0070.00 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 0.080Total (m)De
f
l
e
c
t
i
o
n
Total (m)
From foundation (m)
Remaining wall (including hinges, m)
From foundation (m)
Remaining wall (including hinges, m)
5.00
10.00
0.000.000.010.020.030.040.050.060.070.080.090.10
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Limite State: cii Upper axial load: 100 kN/floorLimit State Description: Onset of concrete cover spalling = -0.4% Lower axial load: 500 kN/floorDamage 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
0 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 0.645 0.00E+00 0.00 0.00 0.44522.30 4.66E-07 9.52 23.65 0.621 6.99E-07 15.08 37.48 0.42919.80 7.27E-06 156.01 92.19 0.545 1.15E-05 247.20 146.07 0.37619.00 1.11E-05 237.89 112.40 0.520 1.76E-05 376.96 178.10 0.359
Height (m) Upper bound (500 kN/floor)Lower bound (100 kN/floor)
00.0010.0020.0030.0040.0050.00
0.00010002000300040005000600070008000
0.000.00E+005.00E-031.00E-02
20.00
Deflection (m)
16.50 2.76E-05 592.82 170.19 0.444 4.37E-05 939.36 269.67 0.30715.70 3.25E-05 735.74 186.96 0.420 5.43E-05 1165.82 296.25 0.29013.20 1.97E-04 1263.65 234.01 0.344 1.02E-04 2002.33 370.80 0.23812.40 2.63E-04 1456.24 247.34 0.320 1.10E-04 2307.51 391.93 0.2219.90 4.63E-04 2121.68 283.65 0.246 3.69E-04 3361.94 449.46 0.1709.10 4.97E-04 2352.61 293.54 0.222 3.51E-04 3727.86 465.14 0.1546.60 7.00E-04 3120.12 319.10 0.151 6.73E-04 4944.02 505.64 0.1055.80 7.67E-04 3378.04 325.56 0.129 6.57E-04 5352.72 515.87 0.0903.30 1.15E-03 4212.16 340.38 0.062 1.05E-03 6674.43 539.35 0.0452.50 1.52E-03 4485.72 343.40 0.042 1.00E-03 7107.91 544.14 0.0321.75 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 0.0200.00 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 0.445Total (m)De
f
l
e
c
t
i
o
n
Total (m)
From foundation (m)
Remaining wall (including hinges, m)
From foundation (m)
Remaining wall (including hinges, m)
0.00
5.00
10.00
0 000 100 200 300 400 500 600 700.00
0.000.100.200.300.400.500.600.70
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Limite State: ciii Upper axial load: 100 kN/floorLimit State Description: Deep of concrete cover spalling -0.4% Lower axial load: 500 kN/floorDamage State: DSII
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
0 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 0.728 0.00E+00 0.00 0.00 0.46422.30 4.66E-07 9.63 23.95 0.701 6.99E-07 15.01 37.30 0.44619.80 7.30E-06 157.96 93.34 0.615 1.15E-05 246.06 145.40 0.39219.00 1.11E-05 240.87 113.80 0.588 1.75E-05 375.23 177.28 0.374
Height (m) Upper bound (500 kN/floor)Lower bound (100 kN/floor)
00.0010.0020.0030.0040.0050.00
0.00010002000300040005000600070008000
0.000.00E+005.00E-031.00E-021.50E-02
20.00
Deflection (m)
16.50 2.78E-05 600.24 172.32 0.502 4.36E-05 935.04 268.43 0.32015.70 3.51E-05 744.95 189.30 0.475 5.41E-05 1160.46 294.89 0.30213.20 1.97E-04 1279.47 236.94 0.390 1.01E-04 1993.12 369.10 0.24812.40 2.70E-04 1474.48 250.44 0.363 1.10E-04 2296.90 390.13 0.2319.90 4.63E-04 2148.24 287.20 0.279 3.65E-04 3346.47 447.39 0.1789.10 5.30E-04 2382.07 297.22 0.253 3.47E-04 3710.72 463.00 0.1616.60 7.00E-04 3159.18 323.10 0.172 6.67E-04 4921.28 503.31 0.1105.80 8.00E-04 3420.33 329.64 0.147 6.51E-04 5328.10 513.50 0.0943.30 1.18E-03 4264.90 344.64 0.071 1.04E-03 6643.73 536.87 0.0472.50 1.70E-03 4541.89 347.70 0.048 9.93E-04 7075.22 541.63 0.0331.75 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 0.0210.00 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 0.464Total (m)De
f
l
e
c
t
i
o
n
Total (m)
From foundation (m)
Remaining wall (including hinges, m)
From foundation (m)
Remaining wall (including hinges, m)
0.00
5.00
10.00
0 000 100 200 300 400 500 600 700.00
0.000.100.200.300.400.500.600.70
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Limite State: civ Upper axial load: 100 kN/floorLimit State Description: Crushing of confined concrete core 4.56% Lower axial load: 500 kN/floorDamage State: DSIII
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
0 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 1.577 0.00E+00 0.00 0.00 0.84322.30 3.73E-07 8.09 20.10 1.519 6.99E-07 1.92 4.78 0.81119.80 6.19E-06 132.59 78.35 1.339 1.15E-05 31.55 18.64 0.71219.00 9.41E-06 202.19 95.53 1.281 1.75E-05 48.10 22.73 0.681
Height (m) Upper bound (500 kN/floor)Lower bound (100 kN/floor)
00.0010.0020.0030.0040.0050.00
0.00010002000300040005000600070008000
0.000.00E+005.00E-031.00E-021.50E-022.00E-022.50E-023.00E-023.50E-02
20.00
Deflection (m)
16.50 2.35E-05 503.86 144.65 1.102 4.36E-05 119.87 34.41 0.58215.70 2.91E-05 625.33 158.91 1.044 5.41E-05 148.77 37.80 0.55113.20 1.31E-04 1074.02 198.89 0.864 1.01E-04 255.52 47.32 0.45212.40 1.97E-04 1237.71 210.23 0.807 1.10E-04 294.46 50.01 0.4219.90 3.64E-04 1803.29 241.08 0.628 3.65E-04 429.01 57.35 0.3239.10 4.30E-04 1999.57 249.49 0.572 3.47E-04 475.71 59.36 0.2926.60 5.67E-04 2651.90 271.22 0.395 6.67E-04 630.90 64.52 0.1975.80 6.34E-04 2871.11 276.71 0.340 6.51E-04 683.06 65.83 0.1673.30 7.76E-04 3580.06 289.30 0.167 1.04E-03 851.72 68.83 0.0762.50 8.45E-04 3812.57 291.87 0.113 1.06E-02 907.04 69.44 0.0481.75 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 0.0250.00 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 0.843Total (m)De
f
l
e
c
t
i
o
n
Total (m)
From foundation (m)
Remaining wall (including hinges, m)
From foundation (m)
Remaining wall (including hinges, m)
0.00
5.00
10.00
0 000 100 200 300 400 500 600 700 800 901 001 101 201 301 401 501 600.00
0.000.100.200.300.400.500.600.700.800.901.001.101.201.301.401.501.60
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Limite State: si Upper axial load: 100 kN/floorLimit State Description: Steel yielding strain = 0.219% Lower axial load: 500 kN/floorDamage 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 0.159 0.00E+00 0.00 0.00 0.22522.30 2.79E-06 6.73 16.72 0.152 6.05E-07 12.68 31.50 0.21719 80 5 12E-06 110 29 65 17 0 133 9 69E-06 207 81 122 80 0 190
Height (m) Upper bound (500 kN/floor)Lower bound (100 kN/floor)
00.0010.0020.0030.0040.00
0.0001000200030004000500060007000
0.000.00E+005.00E-041.00E-031.50E-03
20.00
Deflection (m)
19.80 5.12E-06 110.29 65.17 0.133 9.69E-06 207.81 122.80 0.19019.00 7.82E-06 168.18 79.46 0.127 1.48E-05 316.90 149.72 0.18116.50 1.95E-05 419.11 120.32 0.107 3.68E-05 789.69 226.71 0.15415.70 2.18E-05 520.15 132.18 0.101 4.57E-05 980.07 249.05 0.14613.20 4.42E-05 893.36 165.44 0.081 8.11E-05 1683.29 311.72 0.11912.40 5.09E-05 1029.52 174.87 0.075 9.20E-05 1939.84 329.48 0.1119.90 2.95E-04 1499.97 200.53 0.056 2.29E-04 2826.26 377.84 0.0859.10 2.98E-04 1663.23 207.53 0.050 2.14E-04 3133.88 391.03 0.0776.60 4.63E-04 2205.83 225.60 0.033 4.60E-04 4156.27 425.07 0.0525.80 4.67E-04 2388.17 230.16 0.028 4.35E-04 4499.84 433.68 0.0453.30 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 0.0170.00 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 0.225Total (m)De
f
l
e
c
t
i
o
n
Total (m)
From foundation (m)
Remaining wall (including hinges, m)
From foundation (m)
Remaining wall (including hinges, m)
5.00
10.00
0.000.000.100.200.30
-
Limite State: sii Upper axial load: 100 kN/floorLimit State Description: Outermost tensile strain = 1.0% Lower axial load: 500 kN/floorDamage 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
0 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 0.368 0.00E+00 0.00 0.00 0.39322.30 4.02E-07 8.63 21.46 0.354 6.99E-07 15.04 37.38 0.37819.80 6.57E-06 141.55 83.64 0.309 1.15E-05 246.59 145.71 0.33219.00 1.00E-05 215.84 101.98 0.295 1.75E-05 376.03 177.66 0.317
Height (m) Upper bound (500 kN/floor)Lower bound (100 kN/floor)
00.0010.0020.0030.0040.0050.00
0.00010002000300040005000600070008000
0.000.00E+001.00E-032.00E-033.00E-034.00E-03
20.00
Deflection (m)
16.50 2.50E-05 537.87 154.41 0.250 4.37E-05 937.04 269.01 0.27015.70 3.11E-05 667.54 169.63 0.236 5.42E-05 1162.94 295.52 0.25513.20 1.64E-04 1146.52 212.32 0.192 1.01E-04 1997.37 369.88 0.20912.40 2.34E-04 1321.26 224.42 0.178 1.10E-04 2301.80 390.96 0.1949.90 3.97E-04 1925.01 257.35 0.134 3.67E-04 3353.61 448.34 0.1499.10 4.64E-04 2134.54 266.34 0.121 3.49E-04 3718.63 463.99 0.1356.60 6.34E-04 2830.90 289.52 0.081 6.70E-04 4931.78 504.39 0.0925.80 7.00E-04 3064.92 295.39 0.068 6.54E-04 5339.46 514.60 0.0793.30 1.01E-03 3821.72 308.83 0.032 1.04E-03 6657.90 538.01 0.0402.50 1.01E-03 4069.93 311.57 0.021 9.97E-04 7090.31 542.79 0.0281.75 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 0.0180.00 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 0.393Total (m)De
f
l
e
c
t
i
o
n
Total (m)
From foundation (m)
Remaining wall (including hinges, m)
From foundation (m)
Remaining wall (including hinges, m)
0.00
5.00
10.00
0 000 100 200 300 400.00
0.000.100.200.300.40
-
Limite State: siii Upper axial load: 100 kN/floorLimit State Description: Onset of bar buckling (es-ec)> 3.75% Lower axial load: 500 kN/floorDamage State: DSII
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
0 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 0.674 0.00E+00 0.00 0.00 0.61322.30 4.66E-07 9.58 23.80 0.648 6.99E-07 4.81 11.95 0.59019.80 7.30E-06 157.03 92.79 0.569 1.15E-05 78.80 46.57 0.51819.00 1.11E-05 239.45 113.13 0.543 1.75E-05 120.17 56.78 0.495
Height (m) Upper bound (500 kN/floor)Lower bound (100 kN/floor)
00.0010.0020.0030.0040.0050.00
0.00010002000300040005000600070008000
0.000.00E+005.00E-031.00E-021.50E-02
20.00
Deflection (m)
16.50 2.78E-05 596.70 171.30 0.464 4.36E-05 299.46 85.97 0.42315.70 3.51E-05 740.55 188.19 0.439 5.41E-05 371.65 94.44 0.40013.20 1.97E-04 1271.91 235.54 0.360 1.01E-04 638.32 118.21 0.32812.40 2.70E-04 1465.77 248.96 0.334 1.10E-04 735.61 124.94 0.3059.90 4.63E-04 2135.56 285.50 0.257 3.65E-04 1071.74 143.28 0.2359.10 5.30E-04 2368.00 295.46 0.232 3.47E-04 1188.40 148.28 0.2126.60 7.00E-04 3140.52 321.19 0.158 6.67E-04 1576.09 161.19 0.1445.80 8.00E-04 3400.13 327.69 0.135 6.51E-04 1706.38 164.45 0.1223.30 1.18E-03 4239.71 342.60 0.065 1.04E-03 2127.73 171.94 0.0582.50 1.70E-03 4515.06 345.64 0.044 3.84E-03 2265.91 173.46 0.0381.75 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 0.0210.00 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 0.613Total (m)De
f
l
e
c
t
i
o
n
Total (m)
From foundation (m)
Remaining wall (including hinges, m)
From foundation (m)
Remaining wall (including hinges, m)
0.00
5.00
10.00
0 000 100 200 300 400 500 600 700.00
0.000.100.200.300.400.500.600.70
-
Limite State: siv Upper axial load: 100 kN/floorLimit State Description: Long. bar fracture for ec 5% Lower axial load: 500 kN/floorDamage State: DSIII
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
0 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 0.809 0.00E+00 0.00 0.00 0.84322.30 2.79E-07 9.60 23.87 0.779 6.99E-07 1.92 4.78 0.81119.80 7.31E-06 157.46 93.05 0.684 1.15E-05 31.55 18.64 0.71219.00 1.12E-05 240.12 113.45 0.654 1.75E-05 48.10 22.73 0.681
Height (m) Upper bound (500 kN/floor)Lower bound (100 kN/floor)
00.0010.0020.0030.0040.0050.00
0.00010002000300040005000600070008000
0.000.00E+005.00E-031.00E-021.50E-022.00E-022.50E-023.00E-023.50E-02
20.00
Deflection (m)
16.50 2.79E-05 598.36 171.78 0.559 4.36E-05 119.87 34.41 0.58215.70 3.52E-05 742.61 188.71 0.529 5.41E-05 148.77 37.80 0.55113.20 1.97E-04 1275.45 236.20 0.435 1.01E-04 255.52 47.32 0.45212.40 2.80E-04 1469.85 249.66 0.405 1.10E-04 294.46 50.01 0.4219.90 4.63E-04 2141.50 286.30 0.312 3.65E-04 429.01 57.35 0.3239.10 5.20E-04 2374.59 296.29 0.283 3.47E-04 475.71 59.36 0.2926.60 7.20E-04 3149.27 322.08 0.193 6.67E-04 630.90 64.52 0.1975.80 8.00E-04 3409.60 328.60 0.165 6.51E-04 683.06 65.83 0.1673.30 1.18E-03 4251.52 343.56 0.080 1.04E-03 851.72 68.83 0.0762.50 1.70E-03 4527.64 346.61 0.054 1.06E-02 907.04 69.44 0.0481.75 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 0.0250.00 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 0.843Total (m)De
f
l
e
c
t
i
o
n
Total (m)
From foundation (m)
Remaining wall (including hinges, m)
From foundation (m)
Remaining wall (including hinges, m)
0.00
5.00
10.00
0 000 100 200 300 400 500 600 700 800 901 001 101 201 301 401 501 600.00
0.000.100.200.300.400.500.600.700.800.901.001.101.201.301.401.501.60