Matriz de rigidez para placas.xlsx

T R A B A J O D E A N Á L I S I S E S T R U C T UR UR A L I I  

MATRIZ DE RIGIDEZ DE UNA VIGA CON UN BRAZO RIGIDO

0.00E+00

≤

ok 0.3

X

0. 5

10

0. 5

placa

4

placa

5 1 0.3

1

1

2

1.5 P-1

1 placa 0 co colu lumn mna a

0.3 1. 5 P-2

Datos : F'c I P-1 I P-2 As P-1 As P-2 Ø P- 1

= = = = = = placa

210 Kg/cm2 0.084 m4 0.084 m4 5/6 *A total = 5/6 *A total = 12 * I   = 0.4*As * h^2

3/8 3/8 0.374 primer piso

Ø P-2

= placa

12 * I   0.4*As * h^2

0.374 primer piso

=

E I V-1 G

=

2173706.512 0.0031 869482. 6048

=

m2 m2

3 1

FIGURA ESTRUCTURAL ( Solo los ejes )

5

5

4

2

   1   -

   2   -

   P

   P

4.25

7

6 10

8

0 . 75

5

11

0 . 75

Primer Nivel Nivel " P - 1 "

6 7 8 5 1 2

6 7 8 20870.67 0 -44350.183 0 230157.16 0 -44350.18 0 137398.61 -20870.67 0 44350.183 0 -230157.16 0 -44350.18 0 51089.672

5 -20870.674 0 44350.183 20870.674 0 44350.183

1 2 0 -44350.2 -230157 0 0 51089.67 0 44350.18 230157 0 0 137398.6

Primer Nivel Nivel " P - 2 "

9 10 11 5 3 4

9 10 11 20870.67 0 -44350.183 0 230157.16 0 -44350.18 0 137398.61 -20870.67 0 44350.183 0 -230157.16 0 -44350.18 0 51089.672

5 3 4 -20870.674 0 -44350.2 0 -230157 0 44350.183 0 51089.67 20870.674 0 44350.18 0 230157 0 44350.183 0 137398.6

Primer Nivel " V - 1 " 1 2 3 652.11 652.1120 20 2119.3 2119.3638 638 -652.1 -652.1120 120 1 2119.3638 8246.4991 8246.4991 -2119 -2119.3638 .3638 2   2119.3638 3 -652.1120 -652.1120 -2119.363 -2119.3638 8 652.1120 652.1120 4   2119.3638 2119.3638 5529.3659 5529.3659 -2119 -2119.3638 .3638

1 2

1 230809.3 2119.4

2 2119.4 145645.1

3 -652.1 -2119.4

4 2119.3 2119.3638 638 5529.3659 5529.3659 -2119.363 -2119.3638 8 8246.4991 8246.4991

4 2119.4 5529.4

5 0.0 44350.2

6 0.0 -44350.2

7 -230157.2 0.0

8 0.0 51089.7

9 0.0 0.0

10 0.0 0.0

11 11 0.0 0.0

9

Tn/m2 m4 Tn/m2

0.007

Qf=

3 4 5 6 7 8 9 10 11

-652.1 2119.4 0.0   0.0 -230157.2   0.0   0.0 0.0 0.0

1 2 3 4 5

0 0 0 0 10

-2119.4 5529.4 44350.2 -44350.2 0.0 51089.7 0.0 0.0 0.0

230809.3 -2119.4 0.0 0.0 0.0 0.0 0.0 -230157.2 0.0

-2119.4 145645.1 44350.2 0.0 0.0 0.0 -44350.2 0.0 51089.7

0.0 0.0 44350.2 0.0 41741.3 -20870.7 -20870.7 20870.7 0.0 0.0 44350.2 -44350.2 -20870.7 0.0 0.0 0.0 44350.2 0.0

{Df}=

0.0 -230157.2 0.0 -44350.2 0.0 51089.7 -20870.7 0.0 44350.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 20870.7 0.0 -44350.2 0.0 230157.2 0.0 -44350.2 0.0 137398.6

1 2 3 4 5 4.34E-06 -1.61E-07 9.29E-09 -1.61E-07 3.42E-07 -1.61E-07 1.24E-05 1.61E-07 5.23E-06 -1.87E-05 9.29E-09 1.61E-07 4.34E-06 1.61E-07 -3.42E-07 -1.61E-07 5.23E-06 1.61E-07 1.24E-05 -1.87E-05 3.42E-07 -1.87E-05 -3.42E-07 -1.87E-05 6.37E-05

1 2 3 4 5

Kff -¹ =

0.0 0.0 0.0 0.0 0.0 44350.2 0.0 -44350.2 230157.2 0.0 0.0 137398.6 0.0 0.0 0.0 0.0 0.0 0.0

[ K ff ] -¹ * [ {Qf} - {K fr} * {Dr} ] Dr= 0

{Df}=

[ K ff ] -¹ * {Qf}

1   3.42E-06 2   -1.87E-04 3   -3.42E-06 4   -1.87E-04 5   6.37E-04

Df=

{R}=

[ Krf ] *{Df} [ + {K rr} * {Dr} Dr= 0

{R}=

[ Krf ] *{Df}

6 7 8 9 10 11

Reaccion=

Chequeo: ∆ r1=

  -5.000   -0.788   18.690   -5.000   0.788   18.690

0.00E+00 0.00E+00

6.4E-04 6.37E-04 6.37E-04

∆ r2= ∆ r2=

-

0.00E+00

Primer Nivel : ∆r

* 0.75 * R

≤

0.007

≤

0.007

H 0.00E+00 4.25

*0.75*

6

0.00000000000E+00 ok

≤

0.007