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