-
8/17/2019 EJERCICO Marco Con Contravientos
1/41
Marcos con arriostres diagonales
-
8/17/2019 EJERCICO Marco Con Contravientos
2/41
-
8/17/2019 EJERCICO Marco Con Contravientos
3/41
-
8/17/2019 EJERCICO Marco Con Contravientos
4/41
EJERCICIO
-
8/17/2019 EJERCICO Marco Con Contravientos
5/41
-
8/17/2019 EJERCICO Marco Con Contravientos
6/41
SOLUCIÓN
MARCO
1. NUMERACIÓN DE LAS DEFORMACIONES
Def 1 2 3 4
ux 1 4 0 0
uy 2 5 0 0
∅z 3 6 0 0
2. EC!OR DEFORMACIÓN DEL SIS!EMA
U1x
U1y
[U] =
U2x
U2y
"1z
"2z
Nudo
-
8/17/2019 EJERCICO Marco Con Contravientos
7/41
#. EC!OR ESFUER$OS E%!ERNOS EN LOS NUDOS
F1x 75
F1y 0
[F] = M1z = 0 (Tn)
F2x 75
F2y 0
M2z 0
&. MA!RICES DE RI'IDECES LOCALES DE CADA (ARRA
PARA EL MARCO
(ARRA 1 0 0
A= 1600 !2 11"5#1"5 0
$= 213333#3 !4 0 26#0122%
&= 200 Tn'!2 [1] = 0 3511#66
*= 270 ! +11"5#1"5 0
,= %0 0 +26#0122%
De 3 - 1 0 3511#66
0 1
+1 0
[T1] = 0 0
0 00 0
0 0
0 +1
1 0
-
8/17/2019 EJERCICO Marco Con Contravientos
8/41
[1] = 0 0
0 0
0 0
0 0
(ARRA 2 0 0
A= 1600 !2 11"5#1"5 0
$= 213333#3 !4 0 26#0122%
&= 200 Tn'!2 [2] = 0 3511#66
*= 270 ! +11"5#1"5 0
,= %0 0 +26#0122%
De 4 - 2 0 3511#66
0 1
+1 0
[T2] = 0 0
0 0
-
8/17/2019 EJERCICO Marco Con Contravientos
9/41
0 0
0 0
0 +1
1 0
[2] = 0 0
0 0
0 0
0 0
(ARRA # 1 2A= 1000 !2 571#42"6 0
$= 133333#3 !4 0 7#463557
&= 200 Tn'!2 [&] = 0 1306#122
*= 350 ! +571#42"6 0
,= 0 0 +7#463557
De 1 - 4 0 1306#122
-
8/17/2019 EJERCICO Marco Con Contravientos
10/41
1 0
0 1
[T&] = 0 0
0 0
0 0
0 0
1 0
0 1
[&] = 0 0
0 0
0 0
0 0
PARA LA ARMADURA
-
8/17/2019 EJERCICO Marco Con Contravientos
11/41
(ARRA &
A= 2% !2
&= 2000 Tn'!2 [1] = 131#20%6 +131#20%6
*= 442#0407 !2 +131#20%6 131#20%6
,= 0#657075 .-d
De 3 - 2
[T1] = 0#7%17"2 0#610"03
0 0
0#7%17"2 0
[1] = 0#610"03 0
0 0#7%17"2
0 0#610"03
(ARRA )
A= 2% !2&= 2000 Tn'!2 [1] = 131#20%6 +131#20%6
*= 442#0407 !2 +131#20%6 131#20%6
,= +0#657075 .-d
De 4 - 1
[T1] = 0#7%17"2 +0#610"03
0 0
-
8/17/2019 EJERCICO Marco Con Contravientos
12/41
0#7%17"2 0
[1] = +0#610"03 0
0 0#7%17"2
0 +0#610"03
). MA!RI$ DE RI'IDE$ 'LO(AL DEL SIS!EMA
1 2 3 4 5 6
67%#6%"7 +63#45604 3511#66 +571#42"6 0 0
+63#45604 1241#601 1306#122 0 +7#463557 1306#122
[/] = 3511#66 1306#122 %36"60#7 0 +1306#122 1523"1
+571#42"6 0 0 67%#6%"7 63#45604 3511#66
0 +7#463557 +1306#122 63#45604 1241#601 +1306#122
0 1306#122 1523"1 3511#66 +1306#122 %36"60#7
*. DES+LA$AMIEN!OS 'LO(ALES
0#0057%4 0#000333 +2#0&+005 0#004%"3 +0#0002%1
+1#6&+005
0#000333 0#000"27 +2#1&+006 0#0002%1 +1#4&+005
+1#%&+006
[U] = +2#0&+005 +2#1&+006 1#17&+006 +1#6&+005
1#%2&+006 +1#2&+007
1[ ] [ ] [ ]U K x F
−
=
-
8/17/2019 EJERCICO Marco Con Contravientos
13/41
0#004%"3 0#0002%1 +1#6&+005 0#0057%4 +0#000333
+2#0&+005
+0#0002%1 +1#4&+005 1#%2&+006 +0#000333 0#000"27
2#11&+006
+1#6&+005 +1#%&+006 +1#2&+007 +2#0&+005
2#11&+006 1#17&+006
*. +ROCESO DE RE!ORNO
(ARRA
0 1 0
+1 0 0
1 [u1] = 0 0 10 0 0
0 0 0
0 0 0
0 1 0
+1 0 0
2 [u2] = 0 0 1
0 0 0
0 0 0
0 0 0
1 0 0
0 1 0# [u3] = 0 0 1
0 0 0
0 0 0
0 0 0
-
8/17/2019 EJERCICO Marco Con Contravientos
14/41
& [u4] = 0#7%17"2 0#610"03 0
0 0 0#7%17"2
) [u5] = 0#7%17"2 +0#610"03 0
0 0 0#7%17"2
-
8/17/2019 EJERCICO Marco Con Contravientos
15/41
ARRIOS!RES
-
8/17/2019 EJERCICO Marco Con Contravientos
16/41
0 1 2 3
0 +11"5#1"5 0 0 0
3511#66 0 +26#0122% 3511#66 0
6320%"#" 0 +3511#66 31604%#4 0
0 11"5#1"5 0 0 1
+3511#66 0 26#0122% +3511#66 2
31604%#4 0 +3511#66 6320%"#" 3
0 0 0 0
0 0 0 0
1 0 0 0
0 0 1 00 +1 0 0
0 0 0 1
0 0 0 0 11"5#1"5 0 0
0 0 0 0 0 26#0122% 3511#66
-
8/17/2019 EJERCICO Marco Con Contravientos
17/41
1 0 0 0 x 0 3511#66 6320%"#"
0 0 +1 0 +11"5#1"5 0 0
0 1 0 0 0 +26#0122% +3511#66
0 0 0 1 0 3511#66 31604%#4
0 +26#0122% +3511#66 0 26#0122% +3511#66
11"5#1"5 0 0 +11"5#1"5 0 0
0 3511#66 6320%"#" 0 +3511#66 31604%#4 x
0 26#0122% 3511#66 0 +26#0122% 3511#66
+11"5#1"5 0 0 11"5#1"5 0 0
0 3511#66 31604%#4 0 +3511#66 6320%"#"
0 0 0 1
26#0122% 0 +3511#66 +26#0122%
0 11"5#1"5 0 0
[1] = +3511#66 0 6320%"#" 3511#66
+26#0122% 0 3511#66 26#0122%
0 +11"5#1"5 0 0
+3511#66 0 31604%#4 3511#66
0 4 5 6
0 +11"5#1"5 0 0 0
3511#66 0 +26#0122% 3511#66 0
6320%"#" 0 +3511#66 31604%#4 0
0 11"5#1"5 0 0 4
+3511#66 0 26#0122% +3511#66 5
31604%#4 0 +3511#66 6320%"#" 6
0 0 0 0
0 0 0 0
1 0 0 0
0 0 1 0
-
8/17/2019 EJERCICO Marco Con Contravientos
18/41
0 +1 0 0
0 0 0 1
0 0 0 0 11"5#1"5 0 0
0 0 0 0 0 26#0122% 3511#66
1 0 0 0 x 0 3511#66 6320%"#"
0 0 +1 0 +11"5#1"5 0 0
0 1 0 0 0 +26#0122% +3511#66
0 0 0 1 0 3511#66 31604%#4
0 +26#0122% +3511#66 0 26#0122% +3511#66
11"5#1"5 0 0 +11"5#1"5 0 0
0 3511#66 6320%"#" 0 +3511#66 31604%#4 x
0 26#0122% 3511#66 0 +26#0122% 3511#66
+11"5#1"5 0 0 11"5#1"5 0 0
0 3511#66 31604%#4 0 +3511#66 6320%"#"
0 0 0 4
26#0122% 0 +3511#66 +26#0122%
0 11"5#1"5 0 0
[2] = +3511#66 0 6320%"#" 3511#66
+26#0122% 0 3511#66 26#0122%
0 +11"5#1"5 0 0
+3511#66 0 31604%#4 3511#66
3 4 5 60 +571#42"6 0 0 1
1306#122 0 +7#463557 1306#122 2
304761#% 0 +1306#122 1523"1 3
0 571#42"6 0 0 4
+1306#122 0 7#463557 +1306#122 5
1523"1 0 +1306#122 304761#% 6
-
8/17/2019 EJERCICO Marco Con Contravientos
19/41
0 0 0 0
0 0 0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0 571#42"6 0 0
0 0 0 0 0 7#463557 1306#122
1 0 0 0 x 0 1306#122 304761#%
0 1 0 0 +571#42"6 0 0
0 0 1 0 0 +7#463557 +1306#122
0 0 0 1 0 1306#122 1523"1
571#42"6 0 0 +571#42"6 0 0
0 7#463557 1306#122 0 +7#463557 1306#122
0 1306#122 304761#% 0 +1306#122 1523"1 x
+571#42"6 0 0 571#42"6 0 0
0 +7#463557 +1306#122 0 7#463557 +1306#122
0 1306#122 1523"1 0 +1306#122 304761#%
1 2 3 4
571#42"6 0 0 +571#42"6
0 7#463557 1306#122 0[&] = 0 1306#122 304761#% 0
+571#42"6 0 0 571#42"6
0 +7#463557 +1306#122 0
0 1306#122 1523"1 0
-
8/17/2019 EJERCICO Marco Con Contravientos
20/41
0 0
0#7%17"2 0#610"03
x 131#20%6 +131#20%6 x 0#7%17"2 0#610"03 0 0
+131#20%6 131#20%6 0 0 0#7%17"2 0#610"03
103#""%5 +103#""%5 x 0#7%17"2 0#610"03 0 0
"0#1433 +"0#1433 0 0 0#7%17"2 0#610"03
+103#""%5 103#""%5
+"0#1433 "0#1433
0 0 4 5
"2#257"3 63#45604 +"2#257"3 +63#45604
[1] = 63#45604 4"#%51" +63#45604 +4"#%51"
+"2#257"3 +63#45604 "2#257"3 63#45604
+63#45604 +4"#%51" 63#45604 4"#%51"
0 0
0#7%17"2 +0#610"03
-
8/17/2019 EJERCICO Marco Con Contravientos
21/41
x 131#20%6 +131#20%6 x 0#7%17"2 +0#610"03 0 0
+131#20%6 131#20%6 0 0 0#7%17"2 +0#610"03
103#""%5 +103#""%5 x 0#7%17"2 +0#610"03 0 0
+"0#1433 "0#1433 0 0 0#7%17"2 +0#610"03
+103#""%5 103#""%5
"0#1433 +"0#1433
0 0 1 2
"2#257"3 +63#45604 +"2#257"3 63#45604
[1] = +63#45604 4"#%51" 63#45604 +4"#%51"
+"2#257"3 63#45604 "2#257"3 +63#45604
63#45604 +4"#%51" +63#45604 4"#%51"
1
2
3
4
5
6
75 0#"0"263 1
0 0#046746 2
x 0 = +0#00271" 3
-
8/17/2019 EJERCICO Marco Con Contravientos
22/41
75 0#"0"263 4
0 +0#046746 5
0 +0#00271" 6
DEFORMACIONES LOCALES
0 0 0 0 0
0 0 0 0 0
0 0 0 x 0 = 0
0 1 0 0#"0"263 0#046746
+1 0 0 0#046746 +0#"0"263
0 0 1 +0#00271" +0#00271"
0 0 0 0#"0"263 +0#046746
0 0 0 +0#046746 +0#"0"263
0 0 0 x +0#00271" = +0#00271"
0 1 0 0 0
+1 0 0 0 0
0 0 1 0 0
0 0 0 0#"0"263 0#"0"263
0 0 0 0#046746 0#0467460 0 0 x +0#00271" = +0#00271"
1 0 0 0#"0"263 0#"0"263
0 1 0 +0#046746 +0#046746
0 0 1 +0#00271" +0#00271"
[ ] [ ] [ ]'u T u=
-
8/17/2019 EJERCICO Marco Con Contravientos
23/41
0
0 x 0 = 0
0#610"03 0#"0"263 0#611415
+0#046746
0
0 x 0 = 0
+0#610"03 0#"0"263 0#611415
0#046746
-
8/17/2019 EJERCICO Marco Con Contravientos
24/41
-
8/17/2019 EJERCICO Marco Con Contravientos
25/41
+11"5#1"5 0 0 0 1 0 0
0 +26#0122% 3511#66 +1 0 0 0
-
8/17/2019 EJERCICO Marco Con Contravientos
26/41
0 +3511#66 31604%#4 x 0 0 1 0
11"5#1"5 0 0 0 0 0 0
0 26#0122% +3511#66 0 0 0 +1
0 +3511#66 6320%"#" 0 0 0 0
0 1 0 0 0 0
+1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 1 0
0 0 0 +1 0 0
0 0 0 0 0 1
2 3
0 +3511#66 0
+11"5#1"5 0 0
0 31604%#4 0
0 3511#66 1
11"5#1"5 0 2
0 6320%"#" 3
-
8/17/2019 EJERCICO Marco Con Contravientos
27/41
+11"5#1"5 0 0 0 1 0 0
0 +26#0122% 3511#66 +1 0 0 0
0 +3511#66 31604%#4 x 0 0 1 0
11"5#1"5 0 0 0 0 0 0
0 26#0122% +3511#66 0 0 0 +1
0 +3511#66 6320%"#" 0 0 0 0
0 1 0 0 0 0
+1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 1 0
0 0 0 +1 0 0
0 0 0 0 0 1
5 6
0 +3511#66 0
+11"5#1"5 0 0
0 31604%#4 0
0 3511#66 4
11"5#1"5 0 5
0 6320%"#" 6
-
8/17/2019 EJERCICO Marco Con Contravientos
28/41
+571#42"6 0 0 1 0 0 0
0 +7#463557 1306#122 0 1 0 0
0 +1306#122 1523"1 x 0 0 1 0
571#42"6 0 0 0 0 0 1
0 7#463557 +1306#122 0 0 0 0
0 +1306#122 304761#% 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 1 0
0 0 0 0 0 1
5 6
0 0 1
+7#463557 1306#122 2+1306#122 1523"1 3
0 0 4
7#463557 +1306#122 5
+1306#122 304761#% 6
-
8/17/2019 EJERCICO Marco Con Contravientos
29/41
0
0
4
5
-
8/17/2019 EJERCICO Marco Con Contravientos
30/41
0
0
1
2
-
8/17/2019 EJERCICO Marco Con Contravientos
31/41
FUER$AS LOCALES
11"5#1"5 0 0 +11"5#1"5 0 0
0 26#0122% 3511#66 0 +26#0122% 3511#66
[F1] = 0 3511#66 6320%"#" 0 +3511#66 31604%#4
+11"5#1"5 0 0 11"5#1"5 0 0
0 +26#0122% +3511#66 0 26#0122% +3511#66
0 3511#66 31604%#4 0 +3511#66 6320%"#"
11"5#1"5 0 0 +11"5#1"5 0 0
0 26#0122% 3511#66 0 +26#0122% 3511#66
[F2] = 0 3511#66 6320%"#" 0 +3511#66 31604%#4
+11"5#1"5 0 0 11"5#1"5 0 0
0 +26#0122% +3511#66 0 26#0122% +3511#66
0 3511#66 31604%#4 0 +3511#66 6320%"#"
571#42"6 0 0 +571#42"6 0 0
0 7#463557 1306#122 0 +7#463557 1306#122[F3] = 0 1306#122
304761#% 0 +1306#122 1523"1
+571#42"6 0 0 571#42"6 0 0
0 +7#463557 +1306#122 0 7#463557 +1306#122
0 1306#122 1523"1 0 +1306#122 304761#%
[F'] [k'][u']=
-
8/17/2019 EJERCICO Marco Con Contravientos
32/41
[F4] = 131#20%6 +131#20%6 x 0 =
+131#20%6 131#20%6 0#611415
[F5] = 131#20%6 +131#20%6 x 0 =
+131#20%6 131#20%6 0#611415
-
8/17/2019 EJERCICO Marco Con Contravientos
33/41
-
8/17/2019 EJERCICO Marco Con Contravientos
34/41
0 0
0 0
-
8/17/2019 EJERCICO Marco Con Contravientos
35/41
0 0
1 0
0 0
0 1
-
8/17/2019 EJERCICO Marco Con Contravientos
36/41
0 0
0 0
0 0
1 0
0 0
0 1
-
8/17/2019 EJERCICO Marco Con Contravientos
37/41
0 0
0 0
0 0
0 0
1 0
0 1
-
8/17/2019 EJERCICO Marco Con Contravientos
38/41
-
8/17/2019 EJERCICO Marco Con Contravientos
39/41
-
8/17/2019 EJERCICO Marco Con Contravientos
40/41
0 +55#402""
0 11#4"04
x 0 = 1%7%#351
0#046746 55#402""
+0#"0"263 +11#4"04
+0#00271" 1120#35%
+0#046746 +55#402""
+0#"0"263 +30#56%12
x +0#00271" = +4556#32"
0 55#402""
0 30#56%12
0 +36%7#335
0#"0"263 5#6"&+014
0#046746 +6#40204%x +0#00271" = +1120#35%
0#"0"263 +5#7&+014
+0#046746 6#40204%
+0#00271" +1120#35%
-
8/17/2019 EJERCICO Marco Con Contravientos
41/41
+"0#22356
"0#22356
+"0#22356
"0#22356
