metodo kani
Post on 14-Jan-2016
45 Views
Preview:
DESCRIPTION
TRANSCRIPT
DATOSplanta baja planta alta
w(B-E;E-H)= 15 Ton/m w(C-D;D-I)=8
ALTURA(A-B)= 4
m
ALTURA(B-C)= 3ALTURA(F-E)= 4 ALTURA(E-D)= 3
ALTURA(G-H)= 4 ALTURA(H-I)= 3
b= 40 cm b= 30h= 40 cm h= 30L= 4 m L= 3
DISTANCIA(B-E)= 5 m DISTANCIA(C-D)= 5
DISTANCIA(E-H)= 7 m DISTANCIA(D-I)= 7
b= 30 cm b= 25
h= 40 cm h= 35
L(B-E)= 5 m L(B-E)= 5
L(E-H)= 7 m L(E-H)= 7
0 0 15.289811840 7 30.5796236806432 0
30.57962368 7 35.06399656191 0
68.80415328 7 35.06399656191 468.80415328 0 36.5080693366853 468.80415328 4 36.5080693366853 7
0 4 30.5796236806432 730.57962368 4 68.8041532814471 030.57962368 7 57.71 030.57962368 0 57.71 4
0 0 53.51 44.540893767 0 53.51 7.00
4.540893767 4 68.8041532814471 7.005.733808052 4.005.733808052 7.00
0 7.00
0 0 29.59586448899050 7 0 0
62.15131543 7 6.05452502232243 0130.2218038 7 -12.1090500446449 4
130.2218038 0 8.2880617136772 4130.2218038 4 -8.91 7
0 4 0 762.15131543 4 62.15131542688 062.15131543 7 68.13 062.15131543 0 50.19 4130.2218038 0 70.6022208286348 4
115.42 0 52.82 7159.82 4 62.15131542688 7
108.689113 4154.56 7
130.2218038 7
DATOSplanta alta
Ton/m8 Ton/m
m C D I
cm
cm 3 15 Ton/mmm B E H
m
cm 4cm
m A F G
m
5 7
40.000 0 0 1760 92 0 1930 176 5 153
12 176 5 20512 0 12 14912 92 12 176
0 925 925 1765 0
0.00 920 125
5 50.175 146
12 41.12
12 92
0 0 5 ### 600 168 6.44 1680 168 8.67 148 5 90
12 168 ### 168 5 152
12 168 12 ### 12 ###12 0 0 ### 12 90
0 90 0.74 90 0 11012 90 2.21 73.7 0 90
5 0 3.68 90 0 1775 168 5 ### 0 1680 ### 5 ### 5 202
0.62 168 6.44 90 5 1682.11 159 8.61 54.8 12 1923.60 168 ### 90 12 168
5 ### 12 ###
0 2 4 6 8 10 12 14
CORTANTE EN VIGAS
0
1
2
3
4
5
6
7
8
CORTANTE EN COLUMNAS
0
1
2
3
4
5
6
7
8
MOMENTOS EN COLUMNAS
0 2 4 6 8 10 12 14
MOMENTOS EN VIGAS
0 2 4 6 8 10 12 14
CORTANTE EN VIGAS
0 2 4 6 8 10 12 14
MOMENTOS EN VIGAS
0
1
2
3
4
5
6
7
8
MOMENTOS EN COLUMNAS
0 2 4 6 8 10 12 14
MOMENTOS EN VIGAS
0 2 4 6 8 10 12 14
MOMENTOS EN VIGAS
INERCIA I = b*h^3
12
PLANTA ALTACOLUMNA(B-C;E-D;H-I
I = 0.3 * 0.3 ^ 312
VIGA (C-D;D-I)
I = 0.25 * 0.35 ^ 3
12
PLANTA BAJACOLUMNA(A-B;F-E;G-H)
I = 0.4 * 0.4 ^ 3
12
VIGA (B-E;E-H)
I =0.3 * 0.4 ^ 3
12
RIGIDEZ
PLANTA ALTA
VIGAS
C-D K= I = 0.000893229166666666 = 0.000178645833333333L 5
D-I K= I = 0.000893229166666666 = 0.000127604166666667L 7
COLUMNAS(B-C;E-D;H-I)
K= I = 0.000675 = 0.000225
K=𝑰/𝑳
L=
3= 0.000225
PLANTA BAJAVIGAS
B-E K= I = 0.0016 = 0.00032L 5
E-H K= I = 0.0016 = 0.000228571428571429L 7
COLUMNAS(A-B;F-E;G-H)
K= I = 0.00213333333333333 = 0.000533333333333334L 4
CALCULO DE LOS FACTORES DE DISTRIBUCION
NUDOS CONCURRENTES EN 4 BARRAS
= 0.000675 NUDO E
0.00032 + 0.000533333
= 0.000893229
- 1 * 0.000322 0.001306905
-1
*0.000533333
= 0.002133333 2 0.001306905
- 1 * 0.000228571
= 0.00162 0.001306905
- 1 * 0.000225
2 0.001306905
PLANTA ALTA NUDOS CONCURRENTES EN 3 BARRAS
NUDO B
0.000178645833333333 0.000533333 + 0.000225
- 1 * 0.000533333
0.000127604166666667 2 0.001078333
- 1 * 0.000225
2 0.001078333
0.000225 - 1 * 0.00032
βEB=
βEF=
βEH=
βED=
βBA=
βBC=
βBE=
∑▒𝐾=
∑▒𝐾=
0.0002250.000225 -2
*0.001078333
NUDO H
PLANTA BAJA0.000533333 + 0.000228571
- 1 * 0.000533333
0.00032 2 0.000986905
- 1 * 0.000228571
0.000228571428571429 2 0.000986905
- 1 * 0.0002252 0.000986905
NUDO D
0.0005333333333333340.000225 + 0.000178646
-1
*0.000225
2 0.00053125
- 1 * 0.0001786462 0.00053125
-1
*0.000127604
2 0.00053125
NUDOS CONCURRENTES EN 2 BARRAS
NUDO C
0.000225 +
- 1 * 0.000225
2 0.000403646
- 1 * 0.0001786462 0.000403646
NUDO I
0.000225 +
βHG=
βHE=
βHI=
βDE=
βDC=
βDI=
βCB=
βCD=
∑▒𝐾=
∑▒𝐾=
∑▒𝐾=
∑▒𝐾=
- 1 * 0.0002252 0.000352604
- 1 * 0.0001276042 0.000352604
βIH=
βID=
CALCULO DE LOS FACTORES DE DISTRIBUCIONMOMENTO DE EMPOTRAMIENTO
NUDOS CONCURRENTES EN 4 BARRASPLANTA ALTA
+ 0.000228571 + 0.000225 = 0.001306905
= -0.12243
= -0.20404
= -0.08745
= -0.08608 PLANTA BAJA
NUDOS CONCURRENTES EN 3 BARRAS
+ 0.00032 = 0.001078333
= -0.24730
= -0.10433
= -0.14838
ḾCD=
ḾDC=
ḾDI=
ḾID=
ḾBE=
ḾEB=
ḾEH=
ḾHE=
β=- 𝟏/𝟐∗𝑲/(∑𝑲)
= -0.14838
+ 0.000225 = 0.000986905
= -0.27021
= -0.11580
= -0.11399
+ 0.000127604 = 0.00053125
= -0.21176
= -0.16814
= -0.12010
NUDOS CONCURRENTES EN 2 BARRAS
0.000178646 = 0.000403646
= -0.27871
= -0.22129
0.000127604 = 0.000352604
= -0.31905
= -0.18095
MOMENTO DE EMPOTRAMIENTO
PLANTA ALTA
-8 * 5 ^ 2
= -16.666666712
+ 8 * 5 ^ 2 = 16.6666666712
-8 * 7 ^ 2
= -32.666666712
+ 8 * 7 ^ 2 = 32.6666666712
PLANTA BAJA
-
15 * 5 ^ 2
= -31.25
12
+ 15 * 5 ^ 2 = 31.2512
- 15 * 7 ^ 2 = -61.2512
+15 * 7 ^ 2
= 61.2512
MOMENTO DE EMPOTRAMIENTO ITERACIONES
M'ik=β*(Ḿi + EM'ki)PLANTA ALTA
I CICLOTon/m
NUDO MOMENTO
BM'ik= -0.24730 * ( -31.25
Ton/m M'ik= -0.10433 * ( -31.25M'ik= -0.14838 * ( -31.25
E
M'ik= -0.20404 * ( -30
Ton/mM'ik= -0.08608 * ( -30
M'ik= -0.12243 * ( -30
M'ik= -0.08745 * ( -30
Ton/mH
M'ik= -0.27021 * ( 61.25
M'ik= -0.11399 * ( 61.25
M'ik= -0.11580 * ( 61.25
PLANTA BAJA I M'ik= -0.31905 * ( 32.66666667
M'ik= -0.18095 * ( 32.66666667
Ton/mD
M'ik= -0.21176 * ( -16.00
M'ik= -0.12010 * ( -16.00
M'ik= -0.16814 * ( -16.00
Ton/m C M'ik= -0.27871 * ( -16.6666667
M'ik= -0.22129 * ( -16.6666667
II CICLOTon/m
BM'ik= -0.24730 * ( -31.25
M'ik= -0.10433 * ( -31.25
Ton/mM'ik= -0.14838 * ( -31.25
E
M'ik= -0.20404 * ( -30
M'ik= -0.08608 * ( -30M'ik= -0.12243 * ( -30
M'ik= -0.08745 * ( -30
HM'ik= -0.27021 * ( 61.25M'ik= -0.11399 * ( 61.25M'ik= -0.11580 * ( 61.25
I M'ik= -0.31905 * ( 32.66666667M'ik= -0.18095 * ( 32.66666667
DM'ik= -0.21176 * ( -16.00M'ik= -0.12010 * ( -16.00M'ik= -0.16814 * ( -16.00
C M'ik= -0.27871 * ( -16.6666667M'ik= -0.22129 * ( -16.6666667
III CICLO
BM'ik= -0.24730 * ( -31.25M'ik= -0.10433 * ( -31.25M'ik= -0.14838 * ( -31.25
E
M'ik= -0.20404 * ( -30M'ik= -0.08608 * ( -30
M'ik= -0.12243 * ( -30
M'ik= -0.08745 * ( -30
HM'ik= -0.27021 * ( 61.25
M'ik= -0.11399 * ( 61.25M'ik= -0.11580 * ( 61.25
IM'ik= -0.31905 * ( 32.66666667
M'ik= -0.18095 * ( 32.66666667
DM'ik= -0.21176 * ( -16.00M'ik= -0.12010 * ( -16.00M'ik= -0.16814 * ( -16.00
C M'ik= -0.27871 * ( -16.6666667
M'ik= -0.22129 * ( -16.6666667
IV CICLO
BM'ik= -0.24730 * ( -31.25
M'ik= -0.10433 * ( -31.25M'ik= -0.14838 * ( -31.25
E
M'ik= -0.20404 * ( -30M'ik= -0.08608 * ( -30M'ik= -0.12243 * ( -30M'ik= -0.08745 * ( -30
HM'ik= -0.27021 * ( 61.25M'ik= -0.11399 * ( 61.25
H
M'ik= -0.11580 * ( 61.25
I M'ik= -0.31905 * ( 32.66666667M'ik= -0.18095 * ( 32.66666667
DM'ik= -0.21176 * ( -16.00M'ik= -0.12010 * ( -16.00M'ik= -0.16814 * ( -16.00
C M'ik= -0.27871 * ( -16.6666667M'ik= -0.22129 * ( -16.6666667
V CICLO
BM'ik= -0.24730 * ( -31.25M'ik= -0.10433 * ( -31.25M'ik= -0.14838 * ( -31.25
E
M'ik= -0.20404 * ( -30M'ik= -0.08608 * ( -30M'ik= -0.12243 * ( -30M'ik= -0.08745 * ( -30
HM'ik= -0.27021 * ( 61.25M'ik= -0.11399 * ( 61.25M'ik= -0.11580 * ( 61.25
I M'ik= -0.31905 * ( 32.66666667M'ik= -0.18095 * ( 32.66666667
DM'ik= -0.21176 * ( -16.00M'ik= -0.12010 * ( -16.00M'ik= -0.16814 * ( -16.00
C M'ik= -0.27871 * ( -16.6666667M'ik= -0.22129 * ( -16.6666667
VI CICLO
BM'ik= -0.24730 * ( -31.25M'ik= -0.10433 * ( -31.25M'ik= -0.14838 * ( -31.25
E
M'ik= -0.20404 * ( -30M'ik= -0.08608 * ( -30M'ik= -0.12243 * ( -30M'ik= -0.08745 * ( -30
HM'ik= -0.27021 * ( 61.25M'ik= -0.11399 * ( 61.25M'ik= -0.11580 * ( 61.25
I M'ik= -0.31905 * ( 32.66666667M'ik= -0.18095 * ( 32.66666667
DM'ik= -0.21176 * ( -16.00M'ik= -0.12010 * ( -16.00M'ik= -0.16814 * ( -16.00
C M'ik= -0.27871 * ( -16.6666667
CM'ik= -0.22129 * ( -16.6666667
VII CICLO
BM'ik= -0.24730 * ( -31.25M'ik= -0.10433 * ( -31.25M'ik= -0.14838 * ( -31.25
E
M'ik= -0.20404 * ( -30M'ik= -0.08608 * ( -30M'ik= -0.12243 * ( -30M'ik= -0.08745 * ( -30
HM'ik= -0.27021 * ( 61.25M'ik= -0.11399 * ( 61.25M'ik= -0.11580 * ( 61.25
I M'ik= -0.31905 * ( 32.66666667M'ik= -0.18095 * ( 32.66666667
DM'ik= -0.21176 * ( -16.00M'ik= -0.12010 * ( -16.00M'ik= -0.16814 * ( -16.00
CM'ik= -0.27871 * ( -16.6666667M'ik= -0.22129 * ( -16.6666667
ITERACIONES
M'ik=β*(Ḿi + EM'ki)
I CICLO
+ 0 ) = 7.73
+ 0 ) = 3.26+ 0 ) = 4.64+ 4.64 ) = 5.18+ 4.64 ) = 2.18
+ 4.64 ) = 3.11
+ 4.64 ) = 2.22
+ 2.22 ) = -17.15
+ 2.22 ) = -7.23
+ 2.22 ) = -7.35
+ -7.23 ) = -8.11
+ -7.23 ) = -4.60
+ -4.60 + 2.18 ) = 3.90
+ -4.60 + 2.18 ) = 2.21
+ -4.60 + 2.18 ) = 3.10
+ 3.10 + 3.26 ) = 2.87
+ 3.10 + 3.26 ) = 2.28
II CICLO+ 3.11 + 2.87 ) = 6.25
+ 3.11 + 2.87 ) = 2.64
+ 3.11 + 2.87 ) = 3.75
+ 3.75 + 3.90 + -7.35 6.06
+ 3.75 + 3.90 + -7.35 2.56+ 3.75 + 3.90 + -7.35 3.64
+ 3.75 + 3.90 + -7.35 2.60
+ 2.60 + -8.11 = -15.06+ 2.60 + -8.11 = -6.35+ 2.60 + -8.11 = -6.45
+ -6.35 + 2.21 = -9.10+ -6.35 + 2.21 = -5.16
+ -5.16 + 2.56 + 2.28 3.46+ -5.16 + 2.56 + 2.28 1.96+ -5.16 + 2.56 + 2.28 2.74
+ 2.74 + 2.64 ) = 3.15+ 2.74 + 2.64 ) = 2.50
III CICLO+ 3.64 + 3.15 ) = 6.05+ 3.64 + 3.15 ) = 2.55+ 3.64 + 3.15 ) = 3.63+ 3.63 + 3.46 + -6.45 5.99+ 3.63 + 3.46 + -6.45 2.53
+ 3.63 + 3.46 + -6.45 3.60
+ 3.63 + 3.46 + -6.45 2.57+ 2.57 + -9.10 = -14.78
+ 2.57 + -9.10 = -6.24+ 2.57 + -9.10 = -6.34+ -6.24 + 1.96 = -9.06
+ -6.24 + 1.96 = -5.14
+ -5.14 + 2.53 + 2.50 3.41+ -5.14 + 2.53 + 2.50 1.93+ -5.14 + 2.53 + 2.50 2.71
+ 2.71 + 2.55 ) = 3.18
+ 2.71 + 2.55 ) = 2.52
IV CICLO+ 3.60 + 3.18 ) = 6.05
+ 3.60 + 3.18 ) = 2.55+ 3.60 + 3.18 ) = 3.63
+ 3.63 + 3.41 + -6.34 5.98+ 3.63 + 3.41 + -6.34 2.52+ 3.63 + 3.41 + -6.34 3.59+ 3.63 + 3.41 + -6.34 2.56+ 2.56 + -9.06 = -14.79+ 2.56 + -9.06 = -6.24
+ 2.56 + -9.06 = -6.34+ -6.24 + 1.93 = -9.05+ -6.24 + 1.93 = -5.13
+ -5.13 + 2.52 + 2.52 3.41+ -5.13 + 2.52 + 2.52 1.93+ -5.13 + 2.52 + 2.52 2.70+ 2.70 + 2.55 ) = 3.18+ 2.70 + 2.55 ) = 2.52
V CICLO+ 3.59 + 3.18 ) = 6.05+ 3.59 + 3.18 ) = 2.55+ 3.59 + 3.18 ) = 3.63+ 3.63 + 3.41 + -6.34 5.98+ 3.63 + 3.41 + -6.34 2.52+ 3.63 + 3.41 + -6.34 3.59+ 3.63 + 3.41 + -6.34 2.56+ 2.56 + -9.05 = -14.80+ 2.56 + -9.05 = -6.24+ 2.56 + -9.05 = -6.34+ -6.24 + 1.93 = -9.05+ -6.24 + 1.93 = -5.13+ -5.13 + 2.52 + 2.52 3.41+ -5.13 + 2.52 + 2.52 1.93+ -5.13 + 2.52 + 2.52 2.70+ 2.70 + 2.55 ) = 3.18+ 2.70 + 2.55 ) = 2.52
VI CICLO+ 3.59 + 3.18 ) = 6.05+ 3.59 + 3.18 ) = 2.55+ 3.59 + 3.18 ) = 3.63+ 3.63 + 3.41 + -6.34 5.98+ 3.63 + 3.41 + -6.34 2.52+ 3.63 + 3.41 + -6.34 3.59+ 3.63 + 3.41 + -6.34 2.56+ 2.56 + -9.05 = -14.80+ 2.56 + -9.05 = -6.24+ 2.56 + -9.05 = -6.34+ -6.24 + 1.93 = -9.05+ -6.24 + 1.93 = -5.13+ -5.13 + 2.52 + 2.52 3.41+ -5.13 + 2.52 + 2.52 1.93+ -5.13 + 2.52 + 2.52 2.70+ 2.70 + 2.55 ) = 3.18
+ 2.70 + 2.55 ) = 2.52
VII CICLO+ 3.59 + 3.18 ) = 6.05+ 3.59 + 3.18 ) = 2.55+ 3.59 + 3.18 ) = 3.63+ 3.63 + 3.41 + -6.34 5.98+ 3.63 + 3.41 + -6.34 2.52+ 3.63 + 3.41 + -6.34 3.59+ 3.63 + 3.41 + -6.34 2.56+ 2.56 + -9.05 = -14.80+ 2.56 + -9.05 = -6.24+ 2.56 + -9.05 = -6.34+ -6.24 + 1.93 = -9.05+ -6.24 + 1.93 = -5.13+ -5.13 + 2.52 + 2.52 3.41+ -5.13 + 2.52 + 2.52 1.93+ -5.13 + 2.52 + 2.52 2.70+ 2.70 + 2.55 ) = 3.18+ 2.70 + 2.55 ) = 2.52
ITERACIONESC
I CICLO
-0.2
2129
03
-16.6666667 -16.66666672.28
-0.2787097 2.50
2.87 2.523.15 2.523.18 2.523.18 2.52
8.2880617 3.18 2.52
2.55 3.18 -8.912.55 3.18
2.55 8.912.55
2.55
2.64
B 3.26
-0.1043277
-0.1
4837
71
-31.25 -31.25
4.64
II CICLO -0.2473 3.75
7.73 3.63
6.25 3.63
6.05 3.63
6.05 3.63
6.05 3.63
6.05 -20.406.05
12.10905
A 6.054525
III CICLO
IV CICLO
V CICLO
VI CICLO
VII CICLO
D
-0.1
6813
73
-0.1
2009
8
16.66666667 -16.00 -32.66666673.10 2.21
2.74 -0.2117647 1.96
2.71 3.90 1.932.70 3.46 1.932.70 3.41 1.932.70 3.41 1.93
2.70 3.41 8.4509054 1.93
24.60 3.41 2.52 -33.933.41 2.52
9.33 2.52
2.52
2.53
2.56
E 2.18
-0.08608125
-0.1
2243
-0.0
8744
7622
5177
628
31.25 -30 -61.25
3.11 2.22
3.64 -0.20404445 2.60
3.60 5.18 2.57
3.59 6.06 2.56
3.59 5.99 2.56
3.59 5.98 2.56
3.59 5.98 2.56
42.06 5.98 -62.475.98
11.96
F 5.98
I
-0.1
8094
53
32.66666667 32.66666667-4.60
-5.16 -0.3190547
-5.14 -8.11-5.13 -9.10-5.13 -9.06-5.13 -9.05
-5.13 -9.05 -21.5326924.34 -9.05 -6.24
-9.05 -6.24
-24.34 -6.24
-6.24
-6.24
-6.35
-7.23 H
-0.1139928
-0.1
1580
22
61.25 61.25
-7.35
-6.45 -0.2702051
-6.34 -17.15
-6.34 -15.06
-6.34 -14.78
-6.34 -14.79
-6.34 -14.80
51.13 -14.80-14.80
-29.60
-14.80 G
MOMENTOS FINALES
Mik= Ḿik + 2*M'ik + Mki
NUDO B
MAB= 0 + 2 * 0 + 6.05MBA= 0 + 2 * 6.05 + 0
MBC= 0 + 2 * 2.55 + 3.18
MBE= -31.25 + 2 * 3.63 + 3.59
NUDO EMFE= 0 + 2 * 0 + 5.98
MEF= 0 + 2 * 5.98 + 0
MED= 0 + 2 * 2.52 + 3.41
MEB= 31.25 + 2 * 3.59 + 3.63
MEH= -61.25 + 2 * 2.56 + -6.34
NUDO HMGH= 0 + 2 * 0.00 + -14.80
MHG= 0 + 2 * -14.80 + 0.00
MHI= 0 + 2 * -6.24 + -9.05
MHE= 61.25 + 2 * -6.34 + 2.56
NUDO IMIH= 0 + 2 * -9.05 + -6.24
MID= 32.66666667 + 2 * -5.13 + 1.93
NUDO DMDI= -32.6666667 + 2 * 1.93 + -5.13
MDC= 16.66666667 + 2 * 2.70 + 2.52
MDE= 0 + 2 * 3.41 + 2.52
NUDO C
MCD= -16.6666667 + 2 * 2.52 + 2.70MCB= 0 + 2 * 3.18 + 2.55
MOMENTOS FINALES VALORES CRITICOS PARA VIGAS
VIGA Mfi MFj L(m)
Mik= Ḿik + 2*M'ik + MkiBE -20.40 42.06 5 4.332127697
NUDO BEH -62.47 51.13 7 -1.61977412
= 6.054525022 CD -8.91 24.60 5 3.137278429= 12.10905004 DI -33.93 24.34 7 -1.37106285
= 8.288061714
= -20.3970726
NUDO E= 5.979163842
= 11.95832768
= 8.450905402
= 42.05771113
= -62.4669742
NUDO H= -14.7979322
= -29.5958645
= -21.5326908
= 51.1285553
NUDO I= -24.3367447
= 24.33673841
NUDO D= -33.93
24.60
= 9.33
NUDO C
Rh=(∆M)/L
= -8.91= 8.91
VALORES CRITICOS PARA VIGAS
Ṝi Ṝj Ri=Ṝi±Rh Rj=Ṝj±Rh Xo=Rj/W Mmax=Rj^2/2W-MFj
37.5 37.5 33.1678723 41.8321277 2.788808513 16.273185788869 1.47
52.5 52.5 54.11977412 50.88022588 3.392015058 35.1646908738397 2.1720 20 16.86272157 23.13727843 2.892159804 8.8585987314491 1.4928 28 29.37106285 26.62893715 3.328617143 19.9820299457552 2.24
VALORES CRITICOS EN COLUMNAS
COLUMNAMFi MFj h V=(Mfi+MFj)/hPIE CABEZA
AB 6.054525022 12.10905004 4 4.541
BC 8.288061714 8.91 3 5.734
FE 5.98 11.96 4 4.484
ED 8.450905402 9.33 3 5.928
GH -14.80 -29.60 4 -11.10
HI -21.5326908 -24.34 3 -15.29
𝑋𝑖=√(2𝑀𝑚𝑎𝑥/𝑊)
VALORES CRITICOS PARA VIGAS
X=X0+Xi X=X0-Xi
1.47 4.261818393 1.315798634
2.17 5.557338464 1.2266916531.49 4.380329714 1.4039898932.24 5.563680339 1.093553948
𝑋𝑖=√(2𝑀𝑚𝑎𝑥/𝑊)
33.167872354.119774116.862721629.371062941.832127750.880225923.137278426.628937154.1197741
VALORES CRITICOS EN COLUMNAS
top related