Ejemplo practico de diagramas momento-curvatura y momento rotación para una columnas cuadrada de concreto armado. Los modelos constitutivos de los mat...
Entonces la resistencia en fluencia de la sección para flexión será igual a: Entonces la resistencia nominal de la sección para flexión será igual a: Cc x (Ῡc - k2xc) +/- ΣT's x (d'-Ῡc) + Ts x (d-Ῡc) = My 54104 x 32207 x 3067 x 10558 x 14938 x 63882 x
Cc1 x ( c - k2xc) = T's 2 x (d' 2-Ῡc) = T's 3 x (d' 3-Ῡc) = T's 4 x (d' 4- c ) = T's 5 x (d' 5-Ῡc) = T's 6 x (d' 6-Ῡc) =
12158 8052 383 0 1867 15971 38430 38.43
0.22= 0.25= 0.13= 0.00= 0.13= 0.25= My=
ϕy = εc/c 6.32E-03 ϕy =
La curvatura en fluencia de al sección será gi ual a:
Cc x (Ῡc - a/2) +/- ΣT's x (d'-Ῡc) + Ts x (d-Ῡc) = Mn 90468 x 20896 Cc1 x ( c - a/2 ) = 0.23= 63882 x 15971 T's2 x (d' 2-Ῡc) = 0.25= -23940 x -2993 T's3 x (d' 3-Ῡc) = 0.13= 42588 x 0 T's4 x (d' 4- c ) = 0.00= 23940 x 2993 T's5 x (d' 5-Ῡc) = 0.13= 63882 x 15971 T's6 x (d' 6-Ῡc) = 0.25=
kg-m kg-m kg-m kg-m kg-m kg-m kg-m tn-m
1/m
E nt on ce s t en em os el si gu ei nt er es um en pa ra la se cc ió ne ne qu li bi ri o: ϕy (1/m)
Mn (tn-m)
38.43
6.32E-03
52.84
N=
0.0
d' 2
d' 3
c
f'c
f'cu
P(Mn)
0.145
241
205
0.05
0.18
0.30
0.43
0.55
P(My)
0.218
241
205
0.05
0.18
0.30
0.43
0.55
P(Mcr)
0.300
---
---
---
---
d' 4
---
---
---
---
---
---
---
m
kg/cm2
kg/cm2
m
m
m
A s' 2
f's 2
A's3
15.21
4200
5.70
4200
10.14
4200
5.70
P(My)
15.21
2117
5.70
538
10.14
1041
5.70
---
---
---
f's 4
---
---
---
---
---
cm2
kg/cm2
cm2
kg/cm2
cm2
A's5
---
0.0150 ---
---
---
---
εc
εy
0.0150
0.0021
0.0014
0.0021
εs6
ε's2
0.0420
---
---
ε's3
0.0098
0.0021
0.0001
---
ε's4
0.0031
0.0011 ---
0.0161
0.0003 ---
---
---
z
ε's5 0.0290
0.0005
0.0013
---
---
---
k1
k2
k1xf'c
b
f's 5
Ts6 63882
T's2
63.9
32207
---
---
---
---
---
tn
---
kg
90.5
2E+06
4200
15.21
4200
54104
54.1
2E+06
4200
15.21
4200
---
---
---
---
T's5
---
---
---
T's5
---
---
0.00
14.9
---
tn
kg
εs6
---
---
---
0 3. 00 0
0 0. 01 3
0 3. 00 0
---
---
---
---
---
---
---
---
---
---
---
---
---
---
---
tn
70
700
60
) 600 m N500 k400 ( o t n e300 m o200
0 .0 10
0 .0 20
0 .0 30
0 .0 40 Φ
--- 0 0. 0
0 0. E+ 00
t n-m
c
f'c
f'cu
d' 2
d' 3
P(Mn)
0.212
241
205
0.05
0.18
0.30
0.43
0.55
0.0035
0.0150
0.0150
0.0021
P(My)
0.283
241
205
0.05
0.18
0.30
0.43
0.55
0.0035
0.0150
0.0022
0.0021
P(Mcr)
0.300
---
---
---
---
d' 4
---
---
---
---
---
---
---
m
kg/cm2
kg/cm2
m
m
m
A s' 2
f's 2
A's3
15.21
4200
5.70
4200
10.14
4200
5.70
P(My)
15.21
3678
5.70
1708
10.14
261
5.70
---
---
---
---
---
---
---
cm2
kg/cm2
cm2
kg/cm2
3ER PUNTO:
N=
f's 4
--cm2
A's5
---
---
---
---
---
f's 5
εc
εy
0.0001
N
---
T's2 63882
63.9
ε's4 0.0151
0.0001 ---
---
13.00
0.0011 ---
---
z
ε's5
0.0062
0.0009 ---
---
---
---
T's3
13.00 ---
---
0 .0 80
0 .0 10
0 .0 2 0
k1
k2
k1xf'c
b
Cc1
---
---
kg
0 .0 30
0 . 04 0
(1/m)
132.6
2E+06
4200
15.21
4200
103574
103.6
2E+06
4200
15.21
4200
---
---
---
---
---
T's5
tn
fs6
132588
0.30
---
---
T's5
---
---
0.00
12.7
---
εs6
ε's2
---
--kg/cm2
ε's3
M
0 3. 00 0
0 0. 01 1
---
---
---
---
---
---
---
---
---
---
---
---
---
---
tn
Φ
c
f'c
f'cu
d' 2
d' 3
241
205
0.05
0.18
0.30
0.43
0.55
0.0035
0.0150
0.0150
0.0021
0.273
241
205
0.05
0.18
0.30
0.43
0.55
0.0035
0.0150
0.0021
0.0021
0.300
---
---
---
---
d' 4
---
---
---
---
---
---
---
m
kg/cm2
kg/cm2
m
m
m
P un to
A s' 2
f's 2
A's3
f's 3
P(Mn)
15.21
4200
5.70
f's 4 4200
d' 5
d6
----m
A's5 5.70
εo
εcu
---
---
---
---
---
---
εc
εy
0.0001
εs6
---
ε's2
0.0185
0.0033
0.0007 ---
---
ε's4
0.0043
0.0017 ---
---
ε's3
0.0120
0.0021 ---
---
13.00
0.0012 ---
---
z
ε's5 0.0109
0.0002 ---
13.00 ---
7 . 9E 0- 3 523.465 4 4. E- 04 70.5996
--- 0 0. 0
0 0. E+ 00
m
tn-m
---
k1
k2
k1xf'c
b
4200
N 95.00
Ts6 63882
Ts6 63.9
T's2 63882
T's2 63.9
T's3 23940
T's3 23.9
T's4 42588
42.6
fy
As6
1/m
fs6
0.30
153903
153.9
2E+06
4200
15.21
4200
115.06
0.30
94162
94.2
2E+06
4200
15.21
4200
---
---
---
---
---
---
T's5 23940
Es
208.34
0.3540
---
T's4
Cc1
0.4769
0.4779
---
---
---
---
m
f's 5
Cc1
0.8653
---
T's5 23.9
---
---
---
---
m
kg
tn
Δ
Rev.
εs6
ε's2
ε's3
16.32
¡Revisar!
0 0. 18 5
0 0. 12 0
0 0. 04 3
---
---
---
---
---
---
kg/cm2
kg/cm2
cm2
ε's4
ε's5
Ῡc
0 0. 03 3
0 0. 10 9
0 3. 00 0
M(KN-m)
7 . 1E 0- 2 630.458
5 33. 8
[ Consideracionesdecargaaxial ]
0.246
6 42. 9
--- 7 2. 0
0 3. 00 0
---
--kg/cm2
Ῡc
0 0. 15 1
0 0. 00 1
---
---
--cm2
ε's5
0 0. 06 2
0 0. 00 9
---
--kg/cm2
ε's4
0 0. 02 6
0 0. 01 8
---
--tn
0 0. 11 5
0 0. 02 1
¡Ok!
--kg
0 0. 23 9
¡Ok!
0.00
--kg
Rev.
Δ
23.9
---
---
kg
As6
0.30
121.82
---
---
---
tn
fy
208.34
0.3561
12715
---
Es
0.4769
0.5060
23940
2.6
---
---
tn
42.6
2649
---
---
kg
T's4
42588
9.7
---
Cc1
0.8653
---
---
T's4
23.9
9736
---
tn
T's3 23940
55.9
---
kg
T's2 63.9
55935
---
--tn
Ts6 63.9
63882 ---
--kg/cm2
Ts6 63882
90.00 ---
P(My)
10.14
0 .0 7 0
Φ
ε's3 0.0026
0.0018 ---
---
P(Mn)
4200
0 .0 60
100
(1/m)
ε's2 0.0115
0.0021
---
P(Mcr)
A's4
εs6 0.0239
---
Punto
P(Inicio)
0 .0 50
m
90.00
2231
Diagrama Momento - Curvatura 700
) 600 m - 500 N k ( 400 t n e300 m200 o M
0 0 .0 00
m
4200
cm2
εcu
---
---
--kg/cm2
95.0 tn
εo
---
--m
P(Mn)
---
d6
---
P(Mcr) P(Inicio)
A's4
d' 5
P un to
---
1/m
[ Consideracionesdecargaaxial ]
Punto
f's 3
6 3. E- 0 3
M 100
0 0 .0 00
P(Inicio)
Φ 1 0. E- 0 1
3 8 4. 3
Diagrama Momento -Curvatura
10
90.0 tn
M 5 2 8. 4
4 4. E- 04
m
) m50 n t ( 40 t n e30 m o20 M
N=
--kg/cm2
--- 7 2. 0
Diagrama Momento -Curvatura
2DO PUNTO:
---
--cm2
Ῡc
0 0. 29 0
0 0. 00 5
---
---
--kg/cm2
ε's5
0 0. 16 1
0 0. 00 3
---
kg/cm2
ε's4
0 0. 03 1
0 0. 01 1
---
tn
ε's3
0 0. 09 8
0 0. 02 1
¡Ok!
--kg
ε's2
0 0. 42 0
¡Ok!
0.00
---
---
kg
Rev.
Δ
23.9
---
---
tn
fs6
90468
0.30
---
14938
---
As6
0.30
82.88
23940
10.6
---
fy
208.34
0.3460
---
---
T's4 42.6
10558
---
Es
0.4769
0.3443
---
T's4 42588
3.1
---
kg
T's3 23.9
3067
---
tn
T's3 23940
32.2
---
kg
T's2
63882
63.9 ---
--kg/cm2
Ts6 63.9
63882 ---
Cc1
0.8653
13.00
m
2621
---
Cc1
13.00
---
m
4200
cm2
εcu 0.0150
0.0035 ---
---
--kg/cm2
εo 0.0035
---
--m
P(Mn)
---
d6
---
P(Mcr)
---
A's4
d' 5
P un to
P(Inicio)
f's 3
ϕu (1/m) 1.04E-01
[ Consideracionesdecargaaxial ]
tn
Punto
P(Inicio)
1/m
E nt on ce s t en em os el si gu ei nt e r es um en pa ra la se cc ió ne ne qu li bi ri o:
My (tn-m)
1ER PUNTO:
52837 52.84
Mn= ϕu = εcu/c 1.04E-01 ϕu =
La curvatura en fluencia de al sección será gi ual a:
