8/17/2019 Portico Plano Comprobacion Con SAP
1/155
METODO MATRICIAL DE RIGIDEZ POR SISTEMATIZA
ANALIZAR EL PORTICO PLANO MOSTRADO
E = 2.00E+06 Tn/m2
ELEM B H AX AY L
m m m m m
1 0.4 0.4 5 4 6.403124242 0.4 0.4 -4 4 5.65685425
NUDOS Y ELEMENTOS sis!m" #$%&"$
MATRIZ DE TRANSFORMACION [A]
8/17/2019 Portico Plano Comprobacion Con SAP
2/155
1 2 3 4 5
1 0 0 0 0
0 1 0 0 0
[A]1 = 0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
0 0 0 0 0
1 2 3 4 5
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 0 1
0 0 0 0 0
MATRIZ DE RIGIDEZ DEL ELEMENTO [k]i sis!m" $%'"$
[A]2 =
8/17/2019 Portico Plano Comprobacion Con SAP
3/155
()*i
(,* !$ !$!m!n% !n '%%!n""s $%'"$!s
45.60 0 0 -45.60
0 15.03 624.3 0
()*1 0 624.3 2665.3 0
-45.60 0 0 45.60
0 -15.03 -624.3 0
0 624.3 1332.68 0
56568.54 0 0 -56568.54
0 282.84 800.00 0
()*2 0 800.00 3016. 0
-56568.54 0 0 56568.54
0 -282.84 -800.00 0
0 800.00 1508.4 0
MATRIZ DE TRANSFORMACION [R]i !s $" m"i ! "ns%m"
0 0
0 0
(R*i 0 0 1 0
0 0 0
0 0 0
0 0 0 0
0.8086881 0.6246505 0 0
-0.6246505 0.8086881 0 0
COS α SEN α
-SEN α COS α
COS α
-SEN α
8/17/2019 Portico Plano Comprobacion Con SAP
4/155
0 0 0 0.8086881
0 0 0 -0.6246505
0 0 0 0
-0.01068 0.01068 0 0
-0.01068 -0.01068 0 0(R*2 0 0 1 0
0 0 0 -0.01068
0 0 0 -0.01068
0 0 0 0
MATRIZ DE RIGIDEZ DEL ELEMENTO [k*]i !n i!''i%n !$ sis!m" #$
1 2 3 4
3054.04 24283.21 -30.05 -3054.04
24283.21 1621.5 48.5 -24283.21
()*1 -30.05 48.5 2665.3 30.05
-3054.04 -24283.21 30.05 3054.04
-24283.21 -1621.5 -48.5 24283.21
-30.05 48.5 1332.68 30.05
8 4
28425.6 -28142.85 -565.6 -28425.6
-28142.85 28425.6 -565.6 28142.85
()*2 -565.6 -565.6 3016. 565.6
-28425.6 28142.85 565.6 28425.6
28142.85 -28425.6 565.6 -28142.85
-565.6 -565.6 1508.4 565.6
ENSAMBLAE DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA [!]
1 2 3 4 5
3054.04 24283.21 -30.05 -3054.04 -24283.21
24283.21 1621.5 48.5 -24283.21 -1621.5
-30.05 48.5 2665.3 30.05 -48.5
-3054.04 -24283.21 30.05 3054.04 24283.21
[!]1 = -24283.21 -1621.5 -48.5 24283.21 1621.5
-30.05 48.5 1332.68 30.05 -48.5
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
1 2 3 4 5
0 0 0 0 0
*[
8/17/2019 Portico Plano Comprobacion Con SAP
5/155
0 0 0 0 0
0 0 0 0 0
0 0 0 28425.6 -28142.85
[!]2 = 0 0 0 -28142.85 28425.6
0 0 0 565.6 565.6
0 0 0 -28425.6 28142.85
0 0 0 28142.85 -28425.60 0 0 565.6 565.6
1 2 3 4 5
3054.04 24283.21 -30.05 -3054.04 -24283.21
24283.21 1621.5 48.5 -24283.21 -1621.5
-30.05 48.5 2665.3 30.05 -48.5
-3054.04 -24283.21 30.05 584.3 -385.64
[!] = -24283.21 -1621.5 -48.5 -385.64 4804.2
-30.05 48.5 1332.68 55.4 8.12
- - - -28425.6 28142.85
- - - 28142.85 -28425.6
- - - 565.6 565.6
FUERZAS DE EMPOTRAMIENTO "#$% &' ($$)&'++, -$(+-&,
ELEM ./ .0 AX AY L
T'm T'm m m m
1 0 0 5 4 6.40312424
2 -6 0 -4 4 5.65685425
- 1
- 2
9:%71 - 3 9:%72
- 4
- 5
- 6
FUERZAS DE EMPOTRAMIENTO "#*$% &' ($$)&'+
- 1
- 2
9:%71 - 3 9:%72
- 4
- 5
- 6
FUERZAS DE FIACION "R%
9:07
! (R* T
! ; 9:
07
!
8/17/2019 Portico Plano Comprobacion Con SAP
6/155
- 1
- 2
- 3
- 4
9R71 - 5 9R72
- 6
-
- 8
-
9R7 (A* T!
; 9:07!
8/17/2019 Portico Plano Comprobacion Con SAP
7/155
9R7 9R71 + 9R72
- 1
- 2
- 3
-0.00 4
9R7 12.00 5 9
8/17/2019 Portico Plano Comprobacion Con SAP
8/155
- 2
- 6
9D7 6.62E-06 4
-2.4E-04 5
-1.41E-03 6
- 7
- 8 - 9
CALCULO DE REACCIONES
9
6.34 1 -
4.00 2 -
9
8/17/2019 Portico Plano Comprobacion Con SAP
9/155
0.84 5
-3.62 6
?@ERZAS INTERNAS PRIMARIAS 9:%7 !m%"mi!n%
- 1
- 2
9:%71 - 3 9:%72
- 4
- 5
- 6
?@ERZAS INTERNAS TOTALES 9:7
"#4%& = "#:%& ; "#%&
.45 1
-0.84 2
9:71 -1.5 3 9:72
-.45 4
0.84 5
-3.62 6
8/17/2019 Portico Plano Comprobacion Con SAP
10/155
ION TOTAL
A I EAL < EIL EIL2 12 EIL6
m2 m< T' T'>m T' T'm
0.16 0.00213333 45.60 2665.3 624.3 15.030.16 0.00213333 56568.54 3016. 800.00 282.84
8/17/2019 Portico Plano Comprobacion Con SAP
11/155
6 8
0 0 0 0 1
0 0 0 0 2
0 0 0 0 3
0 0 0 0 4
0 0 0 0 5
1 0 0 0 6
6 8
0 1 0 0
0 0 1 0 8
0 0 0 1
0 0 0 0 4
0 0 0 0 5
1 0 0 0 6
8/17/2019 Portico Plano Comprobacion Con SAP
12/155
0 0
-15.03 624.3
-624.3 1332.68
0 0
15.03 -624.3
-624.3 2665.3
0 0
-282.84 800.00
-800.00 1508.4
0 0
282.84 -800.00
-800.00 3016.
i%n!s ! !"s
0 0
0 0
0 0
0
0
0 1
0 0
0 0
SEN α
COS α
8/17/2019 Portico Plano Comprobacion Con SAP
13/155
0.6246505 0
0.8086881 0
0 1
0 0
0 00 0
0.01068 0
-0.01068 0
0 1
&"$ ! '%%!n""s
5 6
-24283.21 -30.05 1
-1621.5 48.5 2
-48.5 1332.68 3
24283.21 30.05 4
1621.5 -48.5 5
-48.5 2665.3 6
5 6
28142.85 -565.6
-28425.6 -565.6 8
565.6 1508.4
-28142.85 565.6 4
28425.6 565.6 5
565.6 3016. 6
6 8
-30.05 0 0 0 1
48.5 0 0 0 2
1332.68 0 0 0 3
30.05 0 0 0 4
-48.5 0 0 0 5
2665.3 0 0 0 6
0 0 0 0
0 0 0 0 8
0 0 0 0
6 8
0 0 0 0 1
(B* 7 * 7{ ^ [ {
7{ ^ [ * 7{
8/17/2019 Portico Plano Comprobacion Con SAP
14/155
0 0 0 0 2
0 0 0 0 3
565.6 -28425.6 28142.85 565.6 4
565.6 28142.85 -28425.6 565.6 5
3016. -565.6 -565.6 1508.4 6
-565.6 28425.6 -28142.85 -565.6
-565.6 -28142.85 28425.6 -565.6 8 1508.4 -565.6 -565.6 3016.
6 8
-30.05 - - - 1
48.5 - - - 2
1332.68 - - - 3
55.4 -28425.6 28142.85 565.6 4
8.12 28142.85 -28425.6 565.6 5
5682.35 -565.6 -565.6 1508.4 6
-565.6 28425.6 -28142.85 -565.6
-565.6 -28142.85 28425.6 -565.6 8
1508.4 -565.6 -565.6 3016.
. .? @L2 12 @L2 @? L 2
T'm T'm T'>m T' T'
0 0 - - -
-3 3 -8.00 -8.4 8.4
8.4
-8.4 8
-8.00
8.4 4
-8.4 5
8.00 6
+, -$3+-&,
-0.00
12.00 8
-8.00
-0.00 4
12.00 5
8.00 6
8/17/2019 Portico Plano Comprobacion Con SAP
15/155
- 1
- 2
- 3
-0.00 4
12.00 5
8.00 6
-0.00
12.00 8
-8.00
8/17/2019 Portico Plano Comprobacion Con SAP
16/155
- 1
- 2
- 3
0.00 4
-12.00 5
-8.00 6 0.00
-12.00 8
8.00
6 8 1
-30.05 - - - 1 -
48.5 - - - 2 -
1332.68 - - - 3 -
55.4 -28425.6 28142.85 565.6 4 0.00
8.12 28142.85 -28425.6 565.6 5 -12.00
5682.35 -565.6 -565.6 1508.4 6 -8.00
-565.6 28425.6 -28142.85 -565.6 0.00
-565.6 -28142.85 28425.6 -565.6 8 -12.00
1508.4 -565.6 -565.6 3016. 8.00
$$)&'++, )&,4)i'i+,
6 7 8 9 1
30.05 -28425.6 28142.85 565.6 4 0.00
-48.5 28142.85 -28425.6 565.6 5 -12.00
1332.68 -565.6 -565.6 1508.4 6 -8.00
-30.05 - - - 1 -
48.5 - - - 2 -
2665.3 - - - 6 -
- 28425.6 -28142.85 -565.6 7 0.00
- -28142.85 28425.6 -565.6 8 -12.00
- -565.6 -565.6 3016. 9 8.00
0.00 6.62E-06 4
-12.00 9D7 -2.4E-04 5
-8.00 -1.41E-03 6
9D7 (,* -1; 9
8/17/2019 Portico Plano Comprobacion Con SAP
17/155
9
8/17/2019 Portico Plano Comprobacion Con SAP
18/155
1.1 5
-4.38 6
8.4
-8.4 8
-8.00
8.4 4
-8.4 5
8.00 6
18.63
-.66 8
-10.26
-1.66 4
-.31 5
3.62 6
8/17/2019 Portico Plano Comprobacion Con SAP
19/155
8/17/2019 Portico Plano Comprobacion Con SAP
20/155
8/17/2019 Portico Plano Comprobacion Con SAP
21/155
8/17/2019 Portico Plano Comprobacion Con SAP
22/155
8/17/2019 Portico Plano Comprobacion Con SAP
23/155
8/17/2019 Portico Plano Comprobacion Con SAP
24/155
8/17/2019 Portico Plano Comprobacion Con SAP
25/155
9
8/17/2019 Portico Plano Comprobacion Con SAP
26/155
8/17/2019 Portico Plano Comprobacion Con SAP
27/155
8/17/2019 Portico Plano Comprobacion Con SAP
28/155
8/17/2019 Portico Plano Comprobacion Con SAP
29/155
8/17/2019 Portico Plano Comprobacion Con SAP
30/155
8/17/2019 Portico Plano Comprobacion Con SAP
31/155
8/17/2019 Portico Plano Comprobacion Con SAP
32/155
8/17/2019 Portico Plano Comprobacion Con SAP
33/155
8/17/2019 Portico Plano Comprobacion Con SAP
34/155
8/17/2019 Portico Plano Comprobacion Con SAP
35/155
8/17/2019 Portico Plano Comprobacion Con SAP
36/155
8/17/2019 Portico Plano Comprobacion Con SAP
37/155
8/17/2019 Portico Plano Comprobacion Con SAP
38/155
8/17/2019 Portico Plano Comprobacion Con SAP
39/155
8/17/2019 Portico Plano Comprobacion Con SAP
40/155
8/17/2019 Portico Plano Comprobacion Con SAP
41/155
8/17/2019 Portico Plano Comprobacion Con SAP
42/155
8/17/2019 Portico Plano Comprobacion Con SAP
43/155
8/17/2019 Portico Plano Comprobacion Con SAP
44/155
8/17/2019 Portico Plano Comprobacion Con SAP
45/155
8/17/2019 Portico Plano Comprobacion Con SAP
46/155
E = 10000000 Tn/m2
ELEM B H AX AY L
m m m m m
1 0.4 0.4 0 4 4
2 0.4 0.4 5 0 5
3 0.4 0.4 3 -4 5
8/17/2019 Portico Plano Comprobacion Con SAP
47/155
MATRIZ DE TRANSFORMACION [A]
1 2 3 4 5
1 0 0 0 0
0 1 0 0 0
[A]1 = 0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
0 0 0 0 0
1 2 3 4 5
0 0 0 1 0
0 0 0 0 1
[A]2 = 0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
1 2 3 4 5
0 0 0 0 0
0 0 0 0 0
[A]6 = 0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
MATRIZ DE RIGIDEZ DEL ELEMENTO [k]i sis!m" $%'"$
8/17/2019 Portico Plano Comprobacion Con SAP
48/155
()*i
(,* !$ !$!m!n% !n '%%!n""s $%'"$!s30000 0 0 -30000
0 18.5 38 0
()*1 0 38 100 0
-30000 0 0 30000
0 -18.5 -3.5 0
0 38 50 0
24000 0 0 -240000 .6 24 0
()*2 0 24 80 0
-24000 0 0 24000
0 -.6 -24 0
0 24 40 0
8/17/2019 Portico Plano Comprobacion Con SAP
49/155
24000 0 0 -24000
0 .6 24 0
()*3 0 24 80 0
-24000 0 0 24000
0 -.6 -24 0
0 24 40 0
MATRIZ DE TRANSFORMACION [R]i !s $" m"i ! "ns%m"'i%
0 0
0 0
(R*i 0 0 1 0
0 0 0
0 0 0
0 0 0 0
0.00 1.00 0 0
-1.00 0.00 0 0
(R*1 0 0 1 0
0 0 0 0.00
0 0 0 -1.00
0 0 0 0
1.00 0.00 0 0
0.00 1.00 0 0
(R*2 0 0 1 0
0 0 0 1.00
0 0 0 0.00
0 0 0 0
0.60 -0.80 0 0
0.80 0.60 0 0
(R*3 0 0 1 0
0 0 0 0.60
0 0 0 0.80
0 0 0 0
COS α SEN α
-SEN α COS α
COS α
-SEN α
8/17/2019 Portico Plano Comprobacion Con SAP
50/155
MATRIZ DE RIGIDEZ DEL ELEMENTO [k*]i !n i!''i%n !$ sis!m" #$%&
1 2 3 4
18.5 - -3.50 -18.5
- 30000.00 - -()*1 -3.50 - 100.00 3.50
-18.5 - 3.50 18.5
- -30000.00 - -
-3.50 - 50.00 3.50
4 5 6
24000.00 - - -24000.00
- .60 24.00 -()*2 - 24.00 80.00 -
-24000.00 - - 24000.00
- -.60 -24.00 -
- 24.00 40.00 -
8 10
8646.14 -11515.3 1.20 -8646.14
-11515.3 15363.46 14.40 11515.3
()*3 1.20 14.40 80.00 -1.20
-8646.14 11515.3 -1.20 8646.14
11515.3 -15363.46 -14.40 -11515.3
1.20 14.40 40.00 -1.20
ENSAMBLAE DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA [!]
1 2 3 4
18.5 0 -3.5 -18.5
0 30000 0 0
-3.5 0 100 3.5
-18.5 0 3.5 18.5
0 -30000 0 0
[!]1 = -3.5 0 50 3.5
8/17/2019 Portico Plano Comprobacion Con SAP
51/155
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
1 2 3 4
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 24000
0 0 0 0
[!]2 = 0 0 0 00 0 0 -24000
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
1 2 3 40 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
[!]6= 0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 00 0 0 0
0 0 0 0
1 2 3 4
18.5 0 -3.5 -18.5
0 30000 0 0
8/17/2019 Portico Plano Comprobacion Con SAP
52/155
-3.5 0 100 3.5
-18.5 0 3.5 24018.5
0 -30000 0 0
-3.5 0 50 3.5
[!] = 0 0 0 -24000
0 0 0 0
0 0 0 00 0 0 0
0 0 0 0
0 0 0 0
REORDENANDO LAS FILAS Y COLUMNAS
($$)&'++, -i3)&,
< 7 8
24018.5 0 3.5 -24000 0
0 3000.6 24 0 -.63.5 24 180 0 -24
-24000 0 0 32646.144 -11515.32
0 -.6 -24 -11515.32 1533.056
[!] = 0 24 40 1.2 -.6
-18.5 0 -3.5 0 0
0 -30000 0 0 0
3.5 0 50 0 0
0 0 0 -8646.144 11515.32
0 0 0 11515.32 -15363.456
0 0 0 1.2 14.4
HALLAMOS EL 5ECTOR DE CARGA "%
+--+m$, &- &(4$) & (+)+, )im+)i+, &m$4)+mi&'4$, "R%1
"" $" &"" 1
10 1
6 2
9:071 4 3
0 4
6 5
-4 6
8/17/2019 Portico Plano Comprobacion Con SAP
53/155
FUERZAS DE EMPOTRAMIENTO "#*$%
1
-6 1
0 2
4 39:%71 -6 4
0 5
-4 6
FUERZAS DE FIACION "R%
1
-6 1
0 2
4 3-6 4
0 5
9R71 -4 6
0
0 8
0
0 10
0 11
0 12
1
-6 1
0 2
4 3
-6 4
0.416 5"R%1= -3.36 6
2
5.084 8
0.565
2 10
1.5 11
-3.125 12
9:07
! (R* T
! ; 9:
07
!
!n%n'!s "R%1 9R71 + 9R72 + 9R73
8/17/2019 Portico Plano Comprobacion Con SAP
54/155
+--+m$, &- &(4$) & (+)+, ($m-&m&'4+)i+, '$+-&, "R%2
1
0 10 2
0 3
-4 4
0 5
"R%2= 0 6
0
0 8
3
0 10
0 110 12
"%= > ["R%2 ; "R%1]
1
6 1
0 2
-4 310 <
-0.416
3.36
TOTAL "%= -2 7
-5.084 8
-3.565 9
-2 10
-1.5 11
3.125 12
CALCULO DE LOS DESPLAZAMIENTOS
9,7
4 5 6
24018.5 0 3.5 -24000
8/17/2019 Portico Plano Comprobacion Con SAP
55/155
0 3000.6 24 0
3.5 24 180 0
[!]= -24000 0 0 32646.144
0 -.6 -24 -11515.32
0 24 40 1.2
5ECTOR DE DESPLAZAMIENTOS
1
0 1
0 2
0 3
0.1106123 4
2.84440E-005 50.014160448 6
9D7 0.11036061
0.082343528 8
-0.0341314535
0 10
0 11
0 12
CALCULO DE REACCIONES
9
1
-2.606535236 1
-0.853322623 2
9
8/17/2019 Portico Plano Comprobacion Con SAP
56/155
0 2
0 3
971 0.1106123 4 972
2.84441E-005 5
0.01416045 6
DESPLAZAMIENTO EN ELEMENTOS "% &' ($$)&'
"%& = [R]& / "*%&
0 1
0 2
0 3
971 2.84441E-005 4 972
-0.1106123 5
0.01416045 6
?@ERZAS INTERNAS COMPLEMENTARIAS 9:7 &' ($$)&'
"#%& = [!]& / "%&
-0.853322623 1
2.606535236 2
4.858844351 3
9:71 0.853322623 4 9:72
-2.606535236 5
5.562651 6
?@ERZAS INTERNAS PRIMARIAS 9:%7 !m%"mi!n%
0 1
6 2
9:071 4 3 9:072
0 4
6 5
-4 6
?@ERZAS INTERNAS TOTALES 9:7 '%%!n""s $%'"
"#4%& = "#:%& ; "
-0.853 1 ";i"$
8.60 2 '%"n!
8/17/2019 Portico Plano Comprobacion Con SAP
57/155
8.85 3 m%m!n%
9:71 0.853 4 ";i"$ 9:72
3.33 5 '%"n!
1.56 6 m%m!n%
i"#"m" ! !" ";i"$
!s$""mi!n% !$ n% 2
8/17/2019 Portico Plano Comprobacion Con SAP
58/155
8/17/2019 Portico Plano Comprobacion Con SAP
59/155
A I EAL < EIL EIL2 12 EIL6
m2 m< T' T'>m T' T'm
0.012 0.00001 30000 100 38 1
0.012 0.00001 24000 80 24 10
0.012 0.00001 24000 80 24 10
8/17/2019 Portico Plano Comprobacion Con SAP
60/155
6 8 10 11
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
1 0 0 0 0 0
6 8 10 11
0 0 0 0 0 0
0 0 0 0 0 0
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
6 8 10 11
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
0 0 0 0 0 0
8/17/2019 Portico Plano Comprobacion Con SAP
61/155
0 0
-18.5 3.5
-3.5 50
0 0
18.5 -3.5
-3.5 100
0 0-.6 24
-24 40
0 0
.6 -24
-24 80
8/17/2019 Portico Plano Comprobacion Con SAP
62/155
0 0
-.6 24
-24 40
0 0
.6 -24
-24 80
!s ! !"s
0 0
0 0
0 0
0
0
0 1
0 0
0 0
0 0
1.00 0
0.00 0
0 1
0 0
0 0
0 0
0.00 0
1.00 0
0 1
0 0
0 0
0 0
-0.80 0
0.60 0
0 1
SEN α
COS α
8/17/2019 Portico Plano Comprobacion Con SAP
63/155
$ ! '%%!n""s
5 6
- -3.50 1
-30000.00 - 2 - 50.00 3
- 3.50 4
30000.00 - 5
- 100.00 6
8
- - 4
-.60 24.00 5 -24.00 40.00 6
- -
.60 -24.00 8
-24.00 80.00
11 12
11515.3 1.20
-15363.46 14.40 8
-14.40 40.00
-11515.3 -1.20 10
15363.46 -14.40 11
-14.40 80.00 12
5 6 8 10
0 -3.5 0 0 0 0
-30000 0 0 0 0 0
0 50 0 0 0 0
0 3.5 0 0 0 0
30000 0 0 0 0 0
0 100 0 0 0 0
(B* 7 * 7{ ^ [ {
* 7 B* 7[ { ^ [ {
8/17/2019 Portico Plano Comprobacion Con SAP
64/155
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
5 6 8 10
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 -24000 0 0 0
.6 24 0 -.6 24 0
24 80 0 -24 40 00 0 24000 0 0 0
-.6 -24 0 .6 -24 0
24 40 0 -24 80 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
5 6 8 100 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 8646.144 -11515.32 1.2 -8646.144
0 0 -11515.32 15363.456 14.4 11515.32
0 0 1.2 14.4 80 -1.2
0 0 -8646.144 11515.32 -1.2 8646.1440 0 11515.32 -15363.456 -14.4 -11515.32
0 0 1.2 14.4 40 -1.2
5 6 8 10
0 -3.5 0 0 0 0
-30000 0 0 0 0 0
8/17/2019 Portico Plano Comprobacion Con SAP
65/155
0 50 0 0 0 0
0 3.5 -24000 0 0 0
3000.6 24 0 -.6 24 0
24 180 0 -24 40 0
0 0 32646.144 -11515.32 1.2 -8646.144
-.6 -24 -11515.32 1533.056 -.6 11515.32
24 40 1.2 -.6 160 -1.20 0 -8646.144 11515.32 -1.2 8646.144
0 0 11515.32 -15363.456 -14.4 -11515.32
0 0 1.2 14.4 40 -1.2
9 1 2 6 1: 11
0 -18.5 0 3.5 0 0
24 0 -30000 0 0 040 -3.5 0 50 0 0
1.2 0 0 0 -8646.144 11515.32
-.6 0 0 0 11515.32 -15363.456
160 0 0 0 -1.2 -14.4
0 18.5 0 -3.5 0 0
0 0 30000 0 0 0
0 -3.5 0 100 0 0
-1.2 0 0 0 8646.144 -11515.32
-14.4 0 0 0 -11515.32 15363.456
40 0 0 0 -1.2 -14.4
"" $" &"" 2 "" $" &""
20 4
0.416 5
9:072 0.64 6 9:073
0
3.584 8
-2.56
8/17/2019 Portico Plano Comprobacion Con SAP
66/155
&' ($$)&'++, -$3+-&,
2
0 4
0.416 5
0.64 69:%72 0 9:%72
3.584 8
-2.56
2
0 1
0 2
0 30 4
0.416 5
9R72 0.64 6 9R73
0
3.584 8
-2.56
0 10
0 11
0 12
8/17/2019 Portico Plano Comprobacion Con SAP
67/155
10 4
-0.416 5
3.36 6-2
-5.084 8
-3.565
6 1
0 2
-4 3
9
8/17/2019 Portico Plano Comprobacion Con SAP
68/155
-.6 24 5
-24 40 6 9
8/17/2019 Portico Plano Comprobacion Con SAP
69/155
2.84440E-005 5 0.08234353 8
0.014160448 6 -0.03413145
0.11036061 973 0 10
0.082343528 8 0 11
-0.0341314535 0 12
++, -$(+-&,
0.1106123 4 0.00034661
2.84440E-005 5 0.13013 8
0.014160448 6 -0.03413145
0.11036061 973 0 10
0.082343528 8 0 11
-0.0341314535 0 12
++, -$(+-&,
.33464644 4 8.318366
-1.263226231 5 0.502824 8
-2.2026513 6 0.5431652
-.33464644 9:73 -8.318366 10
1.263226231 8 -0.502824 11
-4.13316524 1.35466 12
0 4 0
0.416 5 2.5 8
0.64 6 9:073 3.125
0 0 10
3.584 8 2.5 11
-2.56 -3.125 12
$!s
#%&
.33 4 ";i"$ 8.31
-0.853 5 '%"n! 3.003 8
8/17/2019 Portico Plano Comprobacion Con SAP
70/155
-1.56 6 m%m!n% 3.6
-.33 ";i"$ 9:73 -8.31 10
4.853 8 '%"n! 1. 11
-6.6 m%m!n% -1.185 12
i"#"
8/17/2019 Portico Plano Comprobacion Con SAP
71/155
8/17/2019 Portico Plano Comprobacion Con SAP
72/155
C$,&'$, Di)&(4$)&,
0.00 1.00
1.00 0.00
0.60 -0.80
l = cos( ) m = sen( )
8/17/2019 Portico Plano Comprobacion Con SAP
73/155
12
0 1
0 2
0 3
0 4
0 5
0 6
12
0 4
0 5
0 6
0
0 8
0
12
0
0 8
0
0 10
0 11
1 12
8/17/2019 Portico Plano Comprobacion Con SAP
74/155
8/17/2019 Portico Plano Comprobacion Con SAP
75/155
8/17/2019 Portico Plano Comprobacion Con SAP
76/155
11 12
0 0 1
0 0 2
0 0 3
0 0 4
0 0 5
0 0 6
8/17/2019 Portico Plano Comprobacion Con SAP
77/155
0 0
0 0 8
0 0
0 0 10
0 0 11
0 0 12
11 12
0 0 1
0 0 2
0 0 3
0 0 4
0 0 5
0 0 60 0
0 0 8
0 0
0 0 10
0 0 11
0 0 12
11 120 0 1
0 0 2
0 0 3
0 0 4
0 0 5
0 0 6
11515.32 1.2
-15363.456 14.4 8
-14.4 40
-11515.32 -1.2 1015363.456 -14.4 11
-14.4 80 12
11 12
0 0 1
0 0 2
8/17/2019 Portico Plano Comprobacion Con SAP
78/155
0 0 3
0 0 4
0 0 5
0 0 6
11515.32 1.2
-15363.456 14.4 8
-14.4 40 -11515.32 -1.2 10
15363.456 -14.4 11
-14.4 80 12
12
0 <
0 0
1.2 7
14.4 8
40 9
0 1
0 2
0 6
-1.2 1:
-14.4 11
80 12
3
30
2.5 8
3.125
0 10
2.5 11
-3.125 12
8/17/2019 Portico Plano Comprobacion Con SAP
79/155
3
2
1.5 8
3.125 2 10
1.5 11
-3.125 12
3
0 1
0 2
0 30 4
0 5
0 6
2
1.5 8
3.125
2 10
1.5 11
-3.125 12
8/17/2019 Portico Plano Comprobacion Con SAP
80/155
10 4 0.110612
9D7 (,* -1; 9
8/17/2019 Portico Plano Comprobacion Con SAP
81/155
-0.416 5 2.8444E-005
3.36 6 9D7 0.0141604
-2 0.1103606
-5.084 8 0.08234353
-3.565 -0.03413145
9
8/17/2019 Portico Plano Comprobacion Con SAP
82/155
";i"$
'%"n!
8/17/2019 Portico Plano Comprobacion Con SAP
83/155
m%m!n%
";i"$
'%"n!
m%m!n%
" ! !" '%"n!
!s$""mi!n% !$ n%3
8/17/2019 Portico Plano Comprobacion Con SAP
84/155
8/17/2019 Portico Plano Comprobacion Con SAP
85/155
8/17/2019 Portico Plano Comprobacion Con SAP
86/155
8/17/2019 Portico Plano Comprobacion Con SAP
87/155
8/17/2019 Portico Plano Comprobacion Con SAP
88/155
8/17/2019 Portico Plano Comprobacion Con SAP
89/155
8/17/2019 Portico Plano Comprobacion Con SAP
90/155
8/17/2019 Portico Plano Comprobacion Con SAP
91/155
8/17/2019 Portico Plano Comprobacion Con SAP
92/155
8/17/2019 Portico Plano Comprobacion Con SAP
93/155
4
8/17/2019 Portico Plano Comprobacion Con SAP
94/155
5
6
8
8/17/2019 Portico Plano Comprobacion Con SAP
95/155
8/17/2019 Portico Plano Comprobacion Con SAP
96/155
i"#"m" ! m%m!n% !'%
8/17/2019 Portico Plano Comprobacion Con SAP
97/155
8/17/2019 Portico Plano Comprobacion Con SAP
98/155
8/17/2019 Portico Plano Comprobacion Con SAP
99/155
8/17/2019 Portico Plano Comprobacion Con SAP
100/155
8/17/2019 Portico Plano Comprobacion Con SAP
101/155
8/17/2019 Portico Plano Comprobacion Con SAP
102/155
8/17/2019 Portico Plano Comprobacion Con SAP
103/155
8/17/2019 Portico Plano Comprobacion Con SAP
104/155
8/17/2019 Portico Plano Comprobacion Con SAP
105/155
8/17/2019 Portico Plano Comprobacion Con SAP
106/155
8/17/2019 Portico Plano Comprobacion Con SAP
107/155
8/17/2019 Portico Plano Comprobacion Con SAP
108/155
8/17/2019 Portico Plano Comprobacion Con SAP
109/155
8/17/2019 Portico Plano Comprobacion Con SAP
110/155
8/17/2019 Portico Plano Comprobacion Con SAP
111/155
E = 1 Tn/m2
ELEM B H AX AY L
m m m m m
1 0.4 0.4 0.6 0.8 1
8/17/2019 Portico Plano Comprobacion Con SAP
112/155
MATRIZ DE TRANSFORMACION [A]
1 2 3 4 5
1 0 0 0 0
0 1 0 0 0
[A]1 = 0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
0 0 0 0 0
MATRIZ DE RIGIDEZ DEL ELEMENTO [k]i sis!m" $%'"$
()*i
8/17/2019 Portico Plano Comprobacion Con SAP
113/155
(,* !$ !$!m!n% !n '%%!n""s $%'"$!s
5 0 0 -5
0 12.00 6 0
()*1 0 6 4 0
-5 0 0 5
0 -12 -6 0
0 6 2 0
MATRIZ DE TRANSFORMACION [R]i !s $" m"i ! "ns%m"'i%
0 0
0 0
(R*i 0 0 1 0
0 0 0
0 0 0
0 0 0 0
0.60 0.80 0 0
-0.80 0.60 0 0
(R*1 0 0 1 0
0 0 0 0.60
0 0 0 -0.80
0 0 0 0
MATRIZ DE RIGIDEZ DEL ELEMENTO [k*]i !n i!''i%n !$ sis!m" #$%&
1 2 3 4
.48 -3.36 -4.80 -.48
-3.36 .52 3.60 3.36
()*1 -4.80 3.60 4.00 4.80
-.48 3.36 4.80 .48
COS α SEN α
-SEN α COS α
COS α
-SEN α
8/17/2019 Portico Plano Comprobacion Con SAP
114/155
3.36 -.52 -3.60 -3.36
-4.80 3.60 2.00 4.80
ENSAMBLAE DE LA MATRIZ DE RIGIDEZ DE LA ESTRUCTURA [!]
1 2 3 4
.48 -3.36 -4.8 -.48
-3.36 .52 3.6 3.36
-4.8 3.6 4 4.8
[!]1 = -.48 3.36 4.8 .48
3.36 -.52 -3.6 -3.36
-4.8 3.6 2 4.8
1 2 3 4
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 0.8
RT 0 0 0 -0.6
0 0 0 0
1 2 3 4
.48 -3.36 -4.8 -5.568
-3.36 .52 3.6 -1.824
-4.8 3.6 4 1.68
[!]*1 = -5.568 -1.824 1.68 5.5488
8.36 -8.032 -5.6 -1.8816
-4.8 3.6 2 1.68
0
0
0
0
-10
0
* = RT
8/17/2019 Portico Plano Comprobacion Con SAP
115/155
0
0
0
* -6
-8
0
MATRIZ REDUCIDA
3 4 6
4 1.68 2 3
! 1.68 5.55 1.68 4
2 1.68 4 6
0 3
-6 4
0 6
D = !>1
0.3645 3
D -1.301 4
0.3645 6
0 1
0 2
0.3645 3
%"$ D -1.301 4
0 5
0.3645 6
* = !* D*
3.4 1
4. 2
0.000 3
8/17/2019 Portico Plano Comprobacion Con SAP
116/155
%"$ * -5.8 4
-1.50 5 9
8/17/2019 Portico Plano Comprobacion Con SAP
117/155
DESPLAZAMIENTO EN ELEMENTOS "*% &' ($$)&'
"*%& = [A]& / "D%
0 1
0 2
0.3644884145 3
971 -1.30144334 4
0 5
0.3644884145 6
DESPLAZAMIENTO EN ELEMENTOS "% &' ($$)&'
"%& = [R]& / "*%&
0.00000 1
0.00000 2
0.3644 3
971 -0.8105 4
1.04140 5
0.3644 6
?@ERZAS INTERNAS COMPLEMENTARIAS 9:7 &' ($$)&'
"#%& = [!]& / "%&
3.052330122 1
-8.1228846655 2
-4.061442332 3
9:71 -3.052330122 4
8.1228846655 5
-4.061442332 6
?@ERZAS INTERNAS PRIMARIAS 9:%7 !m%"mi!n%
0 1
8/17/2019 Portico Plano Comprobacion Con SAP
118/155
0 2
9:071 0 3
0 4
0 5
0 6
?@ERZAS INTERNAS TOTALES 9:7 '%%!n""s $%'""#4%& = "#:%& ; "#
3.05 1 ";i"$
-8.123 2 '%"n!
-4.061 3 m%m!n%
9:71 -3.05 4 ";i"$
8.123 5 '%"n!
-4.061 6 m%m!n%
i"#"m" ! !" ";i"$
!s$""mi!n% !$ n% 2
8/17/2019 Portico Plano Comprobacion Con SAP
119/155
8/17/2019 Portico Plano Comprobacion Con SAP
120/155
A I EAL < EIL EIL2 12 EIL6
m2 m< T' T'>m T' T'm
5 1 5 4 6 12
8/17/2019 Portico Plano Comprobacion Con SAP
121/155
6
0 1
0 2
0 3
0 4
0 5
1 6
8/17/2019 Portico Plano Comprobacion Con SAP
122/155
0 0
-12 6
-6 2
0 0
12 -6
-6 4
!s ! !"s
0 0
0 0
0 0
0
0
0 1
0 0
0 0
0 0
0.80 0
0.60 0
0 1
$ ! '%%!n""s
5 6
3.36 -4.80 1
-.52 3.60 2
-3.60 2.00 3
-3.36 4.80 4
SEN α
COS α
(B* 9 7 ( * 9 7
8/17/2019 Portico Plano Comprobacion Con SAP
123/155
.52 -3.60 5
-3.60 4.00 6
5 6
3.36 -4.8 1
-.52 3.6 2
-3.6 2 3
-3.36 4.8 4
.52 -3.6 5
-3.6 4 6
5 6
0 0 1
0 0 2
0 0 3
0.6 0 4
0.8 0 5
0 1 6
5 6
8.36 -4.8 1
-8.032 3.6 2
-5.6 2 3
-1.8816 1.68 4
11.4512 -5.6 5
-5.6 4 6
( * 9 7 ( B * 9 7
8/17/2019 Portico Plano Comprobacion Con SAP
124/155
0.000 3
-5.8 4
0.000 6
8/17/2019 Portico Plano Comprobacion Con SAP
125/155
3.4 1
4. 2
-1.50 5
)&,4)i'i+,2 5
3
4
6
1
2
5
0.000 3
9
8/17/2019 Portico Plano Comprobacion Con SAP
126/155
+, -$3+-&,
++, -$(+-&,
++, -$(+-&,
8/17/2019 Portico Plano Comprobacion Con SAP
127/155
8/17/2019 Portico Plano Comprobacion Con SAP
128/155
8/17/2019 Portico Plano Comprobacion Con SAP
129/155
C$,&'$, Di)&(4$)&,
0.60 0.80
l = cos( ) m = sen( )
8/17/2019 Portico Plano Comprobacion Con SAP
130/155
8/17/2019 Portico Plano Comprobacion Con SAP
131/155
8/17/2019 Portico Plano Comprobacion Con SAP
132/155
8/17/2019 Portico Plano Comprobacion Con SAP
133/155
8/17/2019 Portico Plano Comprobacion Con SAP
134/155
0.3644 3
-1.3014 4
0.3644 6
7T 9
8/17/2019 Portico Plano Comprobacion Con SAP
135/155
8/17/2019 Portico Plano Comprobacion Con SAP
136/155
m" ! !" '%"n!
!s$""mi!n% !$ n%3
8/17/2019 Portico Plano Comprobacion Con SAP
137/155
8/17/2019 Portico Plano Comprobacion Con SAP
138/155
8/17/2019 Portico Plano Comprobacion Con SAP
139/155
8/17/2019 Portico Plano Comprobacion Con SAP
140/155
8/17/2019 Portico Plano Comprobacion Con SAP
141/155
8/17/2019 Portico Plano Comprobacion Con SAP
142/155
8/17/2019 Portico Plano Comprobacion Con SAP
143/155
8/17/2019 Portico Plano Comprobacion Con SAP
144/155
8/17/2019 Portico Plano Comprobacion Con SAP
145/155
i"#"m" ! m%m!n% !'%
8/17/2019 Portico Plano Comprobacion Con SAP
146/155
8/17/2019 Portico Plano Comprobacion Con SAP
147/155
8/17/2019 Portico Plano Comprobacion Con SAP
148/155
8/17/2019 Portico Plano Comprobacion Con SAP
149/155
8/17/2019 Portico Plano Comprobacion Con SAP
150/155
8/17/2019 Portico Plano Comprobacion Con SAP
151/155
8/17/2019 Portico Plano Comprobacion Con SAP
152/155
8/17/2019 Portico Plano Comprobacion Con SAP
153/155
8/17/2019 Portico Plano Comprobacion Con SAP
154/155
8/17/2019 Portico Plano Comprobacion Con SAP
155/155