ANALISIS MATRICIAL DE PORTICOS EXCEL

MATRICES DE RIGIDEZ Columnas Barra x12 y12 m12 x21 y21 m21

1

x23 y23 m23 x32 y32 m32

2

x34 y34 m34 x43 y43 m43

3

x56 y56 m56 x65 y65 m65 Barra x67 y67

0.005 A=

3

E=

### I=

4

E=

### I=

5

6

E=

### I=

6

7 253.125 0

E= 0 45000

### I=

-506.3 -253 0 0

0 -45000

u2 v2 θ2 u3 v3 θ3

0.001 A= u3 v3 θ3 u4 v4 θ4

0.001 A=

253.125 0 -506.3 -253 0 -506 0 45000 0 0 -45000 0 -506.25 0 1350 506.3 0 675 -253.125 0 506.25 253.1 0 506.3 0 -45000 0 0 45000 0 -506.25 0 675 506.3 0 1350

=

u1 v1 θ1 u2 v2 θ2

0.001 A=

253.125 0 -506.3 -253 0 -506 0 45000 0 0 -45000 0 -506.25 0 1350 506.3 0 675 -253.125 0 506.25 253.1 0 506.3 0 -45000 0 0 45000 0 -506.25 0 675 506.3 0 1350

=

Barra

### I=

253.125 0 -506.3 -253 0 -506 0 45000 0 0 -45000 0 -506.25 0 1350 506.3 0 675 -253.125 0 506.25 253.1 0 506.3 0 -45000 0 0 45000 0 -506.25 0 675 506.3 0 1350

=

Barra

E=

19531.25 0 -39063 ### 0 ### 0 450000 0 0 ### 0 -39062.5 0 ### 39063 0 52083 -19531.25 0 39063 19531 0 39063 0 -450000 0 0 450000 0 -39062.5 0 52083 39063 0 ###

=

Barra

2

u5 v5 θ5 u6 v6 θ6

0.001 A= -506 0

u6 v6

0.09

+

0.09

+

0.09

+

0.09

+

0.09

m67 x76 y76 m76

=

Barra x78 y78 m78 x87 y87 m87

7

9

x1011 y1011 m1011 x1110 y1110 m1110

10

x1112 y1112 m1112 x1211 y1211 m1211

### I=

10

E=

### I=

11

E=

### I=

11

12

E=

### I=

u7 v7 θ7 u8 v8 θ8

0.001 A= u9 v9 θ9 u10 v10 θ10

0.001 A= u10 v10 θ10 u11 v11 θ11

0.001 A=

253.125 0 -506.3 -253 0 -506 0 45000 0 0 -45000 0 -506.25 0 1350 506.3 0 675 -253.125 0 506.25 253.1 0 506.3 0 -45000 0 0 45000 0 -506.25 0 675 506.3 0 1350

=

θ6 u7 v7 θ7

0.001 A=

253.125 0 -506.3 -253 0 -506 0 45000 0 0 -45000 0 -506.25 0 1350 506.3 0 675 -253.125 0 506.25 253.1 0 506.3 0 -45000 0 0 45000 0 -506.25 0 675 506.3 0 1350

=

Barra

E=

253.125 0 -506.3 -253 0 -506 0 45000 0 0 -45000 0 -506.25 0 1350 506.3 0 675 -253.125 0 506.25 253.1 0 506.3 0 -45000 0 0 45000 0 -506.25 0 675 506.3 0 1350

=

Barra

8

253.125 0 -506.3 -253 0 -506 0 45000 0 0 -45000 0 -506.25 0 1350 506.3 0 675 -253.125 0 506.25 253.1 0 506.3 0 -45000 0 0 45000 0 -506.25 0 675 506.3 0 1350

=

Barra x910 y910 m910 x109 y109 m109

-506.25 0 1350 506.3 0 675 -253.125 0 506.25 253.1 0 506.3 0 -45000 0 0 45000 0 -506.25 0 675 506.3 0 1350

u11 v11 θ11 u12 v12 θ12

+

0.09

+

0.09

+

0.09

+

0.09

+

Vigas Barra

2

6

E=

### I=

0.005 A=

0.18

x26 y26 m26 x62 y62 m62

=

Barra x37 y37 m37 x73 y73 m73

3

4

Barra x610 y610 m610 x106 y106 m106

6

=

Barra x711 y711 m711 x117 y117 m117 Barra

7

8

0 4800 7200 0 -4800 7200

0 2025 4050 0 -2025 4050

12

0 2025 4050 0 -2025 4050

### I=

### I=

u6 v6 θ6 u10 v10 θ10

0.005 A=

0 ### 0 0 4050 0 -2025 4050 10800 0 -4050 5400 0 90000 0 0 -4050 0 2025 -4050 5400 0 -4050 10800 E=

u4 v4 θ4 u8 v8 θ8

0.005 A=

0 ### 0 0 4050 0 -2025 4050 10800 0 -4050 5400 0 90000 0 0 -4050 0 2025 -4050 5400 0 -4050 10800 E=

u3 v3 θ3 u7 v7 θ7

0.005 A=

0 0 -4800 7200 -7200 7200 0 0 4800 -7200 -7200 14400

### I=

u2 v2 θ2 u6 v6 θ6

0.005 A=

0 0 -4800 7200 -7200 7200 0 0 4800 -7200 -7200 14400

### I=

0 ### 7200 0 14400 0 0 ### -7200 0 7200 0 E=

0 0 -4800 7200 -7200 7200 0 0 4800 -7200 -7200 14400

### I=

0 ### 7200 0 14400 0 0 ### -7200 0 7200 0 E=

11 90000 0 0 -90000 0 0

=

0 4800 7200 0 -4800 7200

10 90000 0 0 -90000 0 0

0 ### 7200 0 14400 0 0 ### -7200 0 7200 0 E=

8 120000 0 0 -120000 0 0

=

0 4800 7200 0 -4800 7200

7 120000 0 0 -120000 0 0

=

Barra x48 y48 m48 x84 y84 m84

120000 0 0 -120000 0 0

u7 v7 θ7 u11 v11 θ11

0.005 A=

+

0.18

+

0.18

+

0.18

+

0.18

+

0.18

x812 y812 m812 x128 y128 m128

=

90000 0 0 -90000 0 0

0 2025 4050 0 -2025 4050

0 ### 0 0 4050 0 -2025 4050 10800 0 -4050 5400 0 90000 0 0 -4050 0 2025 -4050 5400 0 -4050 10800

2 X2 Y2 M2 X3 Y3 M3 X4 Y4 M4 X6 Y6 M6 X7 Y7 M7 X8 Y8 M8 X10 Y10 M10 X11 Y11 M11 X12 Y12 M12

3

139784.4 0 38556 -253 0 0 499800 7200 0 -45000 38556.25 7200 ### 506.3 0

### 0 0

u8 v8 θ8 u12 v12 θ12

+

4 -506 0 675

0 0 -4800 -7200 7200 7200

EI=

###

AE=

###

L=

4

EI=

1350

AE=

###

L=

4

EI=

1350

AE=

###

L=

4

EI=

1350

AE=

###

L=

4

EI=

1350

AE=

###

L=

4

EI=

1350

AE=

###

L=

4

EI=

1350

AE=

###

L=

4

EI=

1350

AE=

###

L=

4

EI=

1350

AE=

###

L=

4

EI=

10800

AE=

###

L=

3

0 7.5 3.75 0 7.5 -3.75 EI=

10800

AE=

###

L=

3

EI=

10800

AE=

###

L=

3

EI=

10800

AE=

###

L=

4

EI=

10800

AE=

###

L=

4

EI=

10800

AE=

###

L=

4

0 7.5 3.75 0 7.5 -3.75

0 7.5 3.75 0 7.5 -3.75

0 10 6.667 0 10 -6.667

0 10 6.667 0 10 -6.667

0 10 6.667 0 10 -6.667

4

6 -120000 0 0 -4800 0 -7200

-253.125 0 -506.25

7

8

10

0 7200 7200

0 506.3 210506.25 0 0 -253 ### 0 0 96825 -3150 0 0 675 0 -3150 27900 506.3

0 ### 0

-506 0 675

10

11

-90000 0 0 -2025 0 -4050

12

0 4050 5400

MATRICES DE RIGIDEZ Columnas Barra x12 y12 m12 x21 y21 m21

1

x23 y23 m23 x32 y32 m32

2

x34 y34 m34 x43 y43 m43

3

x56 y56 m56 x65 y65 m65 Barra x67 y67

0.005 A=

3

E=

### I=

4

E=

### I=

5

6

E=

### I=

6

7 253.125 0

E= 0 45000

### I=

-506.3 -253 0 0

0 -45000

u2 v2 θ2 u3 v3 θ3

0.001 A= u3 v3 θ3 u4 v4 θ4

0.001 A=

253.125 0 -506.3 -253 0 -506 0 45000 0 0 -45000 0 -506.25 0 1350 506.3 0 675 -253.125 0 506.25 253.1 0 506.3 0 -45000 0 0 45000 0 -506.25 0 675 506.3 0 1350

=

u1 v1 θ1 u2 v2 θ2

0.001 A=

253.125 0 -506.3 -253 0 -506 0 45000 0 0 -45000 0 -506.25 0 1350 506.3 0 675 -253.125 0 506.25 253.1 0 506.3 0 -45000 0 0 45000 0 -506.25 0 675 506.3 0 1350

=

Barra

### I=

253.125 0 -506.3 -253 0 -506 0 45000 0 0 -45000 0 -506.25 0 1350 506.3 0 675 -253.125 0 506.25 253.1 0 506.3 0 -45000 0 0 45000 0 -506.25 0 675 506.3 0 1350

=

Barra

E=

19531.25 0 -39063 ### 0 ### 0 450000 0 0 ### 0 -39062.5 0 ### 39063 0 52083 -19531.25 0 39063 19531 0 39063 0 -450000 0 0 450000 0 -39062.5 0 52083 39063 0 ###

=

Barra

2

u5 v5 θ5 u6 v6 θ6

0.001 A= -506 0

u6 v6

0.09

+

0.09

+

0.09

+

0.09

+

0.09

m67 x76 y76 m76

=

Barra x78 y78 m78 x87 y87 m87

7

9

x1011 y1011 m1011 x1110 y1110 m1110

10

x1112 y1112 m1112 x1211 y1211 m1211

### I=

10

E=

### I=

11

E=

### I=

11

12

E=

### I=

u7 v7 θ7 u8 v8 θ8

0.001 A= u9 v9 θ9 u10 v10 θ10

0.001 A= u10 v10 θ10 u11 v11 θ11

0.001 A=

253.125 0 -506.3 -253 0 -506 0 45000 0 0 -45000 0 -506.25 0 1350 506.3 0 675 -253.125 0 506.25 253.1 0 506.3 0 -45000 0 0 45000 0 -506.25 0 675 506.3 0 1350

=

θ6 u7 v7 θ7

0.001 A=

253.125 0 -506.3 -253 0 -506 0 45000 0 0 -45000 0 -506.25 0 1350 506.3 0 675 -253.125 0 506.25 253.1 0 506.3 0 -45000 0 0 45000 0 -506.25 0 675 506.3 0 1350

=

Barra

E=

253.125 0 -506.3 -253 0 -506 0 45000 0 0 -45000 0 -506.25 0 1350 506.3 0 675 -253.125 0 506.25 253.1 0 506.3 0 -45000 0 0 45000 0 -506.25 0 675 506.3 0 1350

=

Barra

8

253.125 0 -506.3 -253 0 -506 0 45000 0 0 -45000 0 -506.25 0 1350 506.3 0 675 -253.125 0 506.25 253.1 0 506.3 0 -45000 0 0 45000 0 -506.25 0 675 506.3 0 1350

=

Barra x910 y910 m910 x109 y109 m109

-506.25 0 1350 506.3 0 675 -253.125 0 506.25 253.1 0 506.3 0 -45000 0 0 45000 0 -506.25 0 675 506.3 0 1350

u11 v11 θ11 u12 v12 θ12

+

0.09

+

0.09

+

0.09

+

0.09

+

Vigas Barra

2

6

E=

### I=

0.005 A=

0.18

x26 y26 m26 x62 y62 m62

=

Barra x37 y37 m37 x73 y73 m73

3

4

Barra x610 y610 m610 x106 y106 m106

6

=

Barra x711 y711 m711 x117 y117 m117 Barra

7

8

0 4800 7200 0 -4800 7200

0 2025 4050 0 -2025 4050

12

0 2025 4050 0 -2025 4050

### I=

### I=

u6 v6 θ6 u10 v10 θ10

0.005 A=

0 ### 0 0 4050 0 -2025 4050 10800 0 -4050 5400 0 90000 0 0 -4050 0 2025 -4050 5400 0 -4050 10800 E=

u4 v4 θ4 u8 v8 θ8

0.005 A=

0 ### 0 0 4050 0 -2025 4050 10800 0 -4050 5400 0 90000 0 0 -4050 0 2025 -4050 5400 0 -4050 10800 E=

u3 v3 θ3 u7 v7 θ7

0.005 A=

0 0 -4800 7200 -7200 7200 0 0 4800 -7200 -7200 14400

### I=

u2 v2 θ2 u6 v6 θ6

0.005 A=

0 0 -4800 7200 -7200 7200 0 0 4800 -7200 -7200 14400

### I=

0 ### 7200 0 14400 0 0 ### -7200 0 7200 0 E=

0 0 -4800 7200 -7200 7200 0 0 4800 -7200 -7200 14400

### I=

0 ### 7200 0 14400 0 0 ### -7200 0 7200 0 E=

11 90000 0 0 -90000 0 0

=

0 4800 7200 0 -4800 7200

10 90000 0 0 -90000 0 0

0 ### 7200 0 14400 0 0 ### -7200 0 7200 0 E=

8 120000 0 0 -120000 0 0

=

0 4800 7200 0 -4800 7200

7 120000 0 0 -120000 0 0

=

Barra x48 y48 m48 x84 y84 m84

120000 0 0 -120000 0 0

u7 v7 θ7 u11 v11 θ11

0.005 A=

+

0.18

+

0.18

+

0.18

+

0.18

+

0.18

x812 y812 m812 x128 y128 m128

=

90000 0 0 -90000 0 0

0 2025 4050 0 -2025 4050

0 ### 0 0 4050 0 -2025 4050 10800 0 -4050 5400 0 90000 0 0 -4050 0 2025 -4050 5400 0 -4050 10800

2 X2 Y2 M2 X3 Y3 M3 X4 Y4 M4 X6 Y6 M6 X7 Y7 M7 X8 Y8 M8 X10 Y10 M10 X11 Y11 M11 X12 Y12 M12

3

139784.4 0 38556 -253 0 0 499800 7200 0 -45000 38556.25 7200 ### 506.3 0

### 0 0

u8 v8 θ8 u12 v12 θ12

+

4 -506 0 675

0 0 -4800 -7200 7200 7200

EI=

###

AE=

###

L=

4

EI=

1350

AE=

###

L=

4

EI=

1350

AE=

###

L=

4

EI=

1350

AE=

###

L=

4

EI=

1350

AE=

###

L=

4

EI=

1350

AE=

###

L=

4

EI=

1350

AE=

###

L=

4

EI=

1350

AE=

###

L=

4

EI=

1350

AE=

###

L=

4

EI=

10800

AE=

###

L=

3

0 7.5 3.75 0 7.5 -3.75 EI=

10800

AE=

###

L=

3

EI=

10800

AE=

###

L=

3

EI=

10800

AE=

###

L=

4

EI=

10800

AE=

###

L=

4

EI=

10800

AE=

###

L=

4

0 7.5 3.75 0 7.5 -3.75

0 7.5 3.75 0 7.5 -3.75

0 10 6.667 0 10 -6.667

0 10 6.667 0 10 -6.667

0 10 6.667 0 10 -6.667

4

6 -120000 0 0 -4800 0 -7200

-253.125 0 -506.25

7

8

10

0 7200 7200

0 506.3 210506.25 0 0 -253 ### 0 0 96825 -3150 0 0 675 0 -3150 27900 506.3

0 ### 0

-506 0 675

10

11

-90000 0 0 -2025 0 -4050

12

0 4050 5400