analisis estructural matrices excel
TRANSCRIPT
-
8/16/2019 analisis estructural matrices excel
1/37
3. Hallar los desplazamientos, fuerzas y esfuerzos.
E =
A =
P =Q =
K Barra θ Longitud CK1 0 25 1.0
K2 20 25 0.0
K3 !5 35 0.
K! 0 25 1.0
K5 "0 25 0.0
#al$ulo de %i&idez
K1 = 1.00 0.00
0.00 0.0
!000 ' (1.00 0.00
0.00 0.0
0 00 0
0 0
0 0
K2 =
0 0
0 1
0 0
1 ( 2
1 ( !
! ( 2
! ( 3
3 ( 2
-
8/16/2019 analisis estructural matrices excel
2/37
!000 ' 0 0
0 0
0 0
0 0
0 (1
K3 =0 0
0 0
0 0
2)5.1!2)* ' 0 0
0 0
0 0
0 0
0 0
K! =0 0
0 0
0 0
!000 ' 0 0
0 0
0 0
0 0
0 0
K5 =
0 0
0 0
0 0
!000 ' 0 0
0 0
0 0
0 0
0 0
ensam+aldo
!000 0 (!000 0
0 !000 0 0
(!000 0 5!2).51!2)51! 1!2).51!2)*
0 0 1!2).51!2)51! (251.!2)51
0 0 0 0
0 0 0 !000
0 0 (1!2).51!2)51! (1!2).51!2"
-
8/16/2019 analisis estructural matrices excel
3/37
0 (!000 (1!2).51!2)51! (1!2).51!2"
5!2).51!2)51! 1!2).51!2)*
1!2).51!2)51! (251.!2)51
(1!2).51!2)51! (1!2).51!2"(1!2).51!2)51! (1!2).51!2"
inersa
0.0001""1* 5.20)33E(005
5.20)333333E(005 (0.0003020)3
5.20)333333E(005 (5.20)3E(005
5.20)333333E(005 (5.20)3E(005
desplazamientos u2 (0.253125
2 0.32)125u! 0.32)125
! (1.11)5
enton$es
-1 !000 0
-2 0 !000
-3 (!000 0
-! = 0 0
-5 0 0
-* 0 0
- 0 0
-) 0 (!000
-uerzas
-1 = 1012.50
-2 = !*).50
-3 = 300.00
-! = 0.00
-5 = (1312.50
-* = 1312.50
- = 0.00
-) = (*000.00
-
8/16/2019 analisis estructural matrices excel
4/37
200 /pa 200000000 K
0.0005m2
3000K*000K
S C2 S2 SC0.0 1.00 0.0 0.00
(1.0 0.00 1.0 0.00
0. 0.50 0.5 0.50
0.0 1.00 0.0 0.00
1.0 0.00 1.0 0.00
(1.00 0.00 0 0 0
0.00 0.0 0 0 0
1.00 0.00 0 0 0
0.00 0.0 0 0 0
0 0 0 0 00 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
-
8/16/2019 analisis estructural matrices excel
5/37
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 0.5 0 0 (0.5
0.5 0.5 0 0 (0.5
0 0 0 0 0
0 0 0 0 0
(0.5 (0.5 0 0 0.5
(0.5 (0.5 0 0 0.5
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 1 0 (1
0 0 0 0 0
0 0 (1 0 1
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 1 0 (1 0
0 0 0 0 0
0 (1 0 1 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0
0 0 0 (!000
0 0 (1!2).51!3 (1!2).51!3
0 0 (1!2).51!3 (1!2).51!3
!000 0 (!000 0
0 0 0 0
(!000 0 5!2).51!3 1!2).51!3
-
8/16/2019 analisis estructural matrices excel
6/37
0 0 1!2).51!3 5!2).51!3
(1!2).51!2)51! (1!2).51!2)51! u2
(1!2).51!2)51! (1!2).51!2)51! ' 2 =
5!2).51!2)51! 1!2).51!2)51! u!1!2).51!2)51! 5!2).51!2)51! !
5.20)333333E(005 5.20)333333E(005 300
(5.20)33333E(005 (5.20)33333E(005 ' 0 =
0.0001""1* (5.20)33333E(005 0
(5.20)33333E(005 0.0001""1* (*000
(!000 0 0 0 0
0 0 0 0 0
5!2).51!2)51! 1!2).51!2)51! 0 0 (1!2).51!3
1!2).51!2)51! (251.!2)51!2)* 0 0 (1!2).51!3
0 0 !000 0 (!000
0 !000 0 0 0
(1!2).51!2)51! (1!2).51!2)51! (!000 0 5!2).51!3
(1!2).51!2)51! (1!2).51!2)51! 0 0 1!2).51!3
-
8/16/2019 analisis estructural matrices excel
7/37
-
8/16/2019 analisis estructural matrices excel
8/37
0 = 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
1 0 (!000 0
0 0 0 0
0 0 0 0
(0.5 0 0 1!2).51!3
(0.5 = 0 0 1!2).51!3
0 0 0 0
0 0 0 0
0.5 0 0 (1!2).51!3
0.5 0 0 (1!2).51!3
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 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
u1 -1
1 -y1
u2 3000
2 0
u3 -3
3 -y3
u! 0
=
-
8/16/2019 analisis estructural matrices excel
9/37
! (*000
300
0
0(*000
u2
2
u!
!
0 0
(!000 0
(1!2).51!3 (0.253125
(1!2).51!3 ' 0.32)125
0 0
0 0
1!2).51!3 0.32)125
5!2).51!3 (1.11)5
-
8/16/2019 analisis estructural matrices excel
10/37
0 0 0 0 0
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 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 (!000
0 0 0 0 0
-
8/16/2019 analisis estructural matrices excel
11/37
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 !000
0 0 0 0 0
0 0 0 0 0
1!2).51!3 0 0 (1!2).51!3 (1!2).51!3
1!2).51!3 0 0 (1!2).51!3 (1!2).51!3
0 0 0 0 0
0 0 0 0 0
(1!2).51!3 0 0 1!2).51!3 1!2).51!3
(1!2).51!3 0 0 1!2).51!3 1!2).51!3
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 !000 0 (!000 0
0 0 0 0 0
0 (!000 0 !000 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
!000 0 (!000 0 0
0 0 0 0 0
(!000 0 !000 0 0
0 0 0 0 0
0 0 0 0 0
-
8/16/2019 analisis estructural matrices excel
12/37
-
8/16/2019 analisis estructural matrices excel
13/37
!. Halla los desplazameintos, fuerzas y esfuerzas en la $aso
K Barra θ LongitudK1 *0 12
K2 "0 10
K3 0 *
K! 0 *
K5 120 12
K* "0 10
Hallamos la ri&idez
u1 1
u1 0.25 0.!33
1 0.!33 0.5
u2 0 0
2 0 0
u3 0 0
1= 5000 3 0 0
u! (0.25 (0.!33! (0.!33 (0.5
u5 0 0
5 0 0
1 ( !
1 ( 5
5 ( !
! ( 3
2 ( !
2 ( 3
-
8/16/2019 analisis estructural matrices excel
14/37
u1 1
u1 0 0
1 0 1
u2 0 0
2 0 0
2= *000 u3 0 0
3 0 0u! 0 0
! 0 0
u5 0 0
5 0 (1
u1 1
u1 0.00 0.001 0.00 0.00
u2 0.00 0.00
K3= 10000 2 0.00 0.00
u3 0.00 0.00
3 0.00 0.00
u! 0.00 0.00
! 0.00 0.00
u5 0.00 0.00
5 0.00 0.00
u1 1
u1 0 0
1 0 0
u2 0 0
2 0 0
!= 10000 u3 0 0
3 0 0
u! 0 0
! 0 0
u5 0 0
5 0 0
-
8/16/2019 analisis estructural matrices excel
15/37
u1 1
u1 0 0
1 0 0
u2 0 0
2 0 05= 5000 u3 0 0
3 0 0
u! 0 0
! 0 0
u5 0 0
5 0 0
u1 1
u1 0.0 0.0
1 0.0 0.0
u2 0.0 0.0
2 0.0 0.0
*= *000 u3 0.0 0.0
3 0.0 0.0
u! 0.0 0.0
! 0.0 0.0
u5 0.0 0.0
5 0.0 0.0
ensam+aldo
1250.00 21*5.00 0.00
21*5 "50.00 0.00
0 0.00 1250.00
0 0.00 (2150.00
0 0.00 0.00
0 0.00 0.00
(1250 (21*5.00 (1250.00
(21*5 (350.00 2150.00
0 0.00 0.00
0 (*000.00 0.00
-
8/16/2019 analisis estructural matrices excel
16/37
1250.00 (2150.00
(2150.00 "50.00
0.00 0.00
0.00 (*000.00
(1250.00 2150.002150.00 (350.00
inersa
0.05"230 0.03301"1"02
0.03301"1"02 0.01"530*
".""""2***E(005 (5.32"100E(005
0.03301"1"02 0.01"530*
".""""2***E(005 (5.32"100E(005
(5.32"100E(005 0.0002"""")
u1 0
1 0
esplazamiento u2 1)2.20!111*")
2 "*.)*0)23020*
u3 3.00!111*")
3 "*.)*0)23020*
u! 2.20!111*")
! (3.13"1*""!
u5 0
5 0
Enton$es
-1 1250.00
-2 21*5.00
-3 0.00
-! 0.00
-5 = 0.00
-* 0.00
- (1250.00
-) (21*5.00
-" 0.00
-10 0.00
-uerzas
-1 = !0!1.1
-2 = 000.00
-3 = 10000.00
-! = (12000.00
-
8/16/2019 analisis estructural matrices excel
17/37
-5 = )000.00
-* = 0.00
- = 0.00
-) = 5000.00
-" = (220!1.1
-10 = 0.00
-
8/16/2019 analisis estructural matrices excel
18/37
E = 200 /pa 200000000
A = 0.0003 m2
P = 12000 KQ = 10000 K
% = )000
4 = 5000
C S C2 S20.5 0.) 0.25 0.50
0.0 1.00 0.00 1.000
1.0 0.00 1.00 0.000
1.0 0.00 1.00 0.000
(0.5 0.) 0.25 0.50
0.0 1.00 0.00 1.000
u2 2 u3 3
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 00 0 0 0
0 0 0 0
0 0 0 0
-
8/16/2019 analisis estructural matrices excel
19/37
u2 2 u3 3
0 0 0 0
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
0 0 0 0
0 0 0 0
u2 2 u3 3
0.00 0.00 0.00 0.000.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
u2 2 u3 3
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 1 0
0 0 0 0
0 0 (1 0
0 0 0 0
0 0 0 0
0 0 0 0
-
8/16/2019 analisis estructural matrices excel
20/37
u2 2 u3 3
0 0 0 0
0 0 0 0
0.25 (0.!3 0 0
(0.!3 0.5 0 00 0 0 0
0 0 0 0
(0.25 0.!3 0 0
0.!3 (0.5 0 0
0 0 0 0
0 0 0 0
u2 2 u3 3
0 0 0 0
0 0 0 0
0 0 0 0
0 1 0 (1
0 0 0 0
0 (1 0 1
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0.00 0.00 0.00 (1250.00
0.00 0.00 0.00 (21*5.00
(2150.00 0.00 0.00 (1250.00
"50.00 0.00 (*000.00 2150.00
0.00 10000.00 0.00 (10000.00
(*000.00 0.00 *000.00 0.00
2150.00 (10000.00 0.00 22500.00
(350.00 0.00 0.00 15.00
0.00 0.00 0.00 (10000.00
0.00 0.00 0.00 0.00
-
8/16/2019 analisis estructural matrices excel
21/37
0.00 0.00 (1250.00 2150.00
0.00 (*000.00 2150.00 (350.00
10000.00 0.00 (10000.00 0.00
0.00 *000.00 0.00 0.00
(10000.00 0.00 22500.00 15.000.00 0.00 15.00 500.00
".""""2***E(005 0.03301"1"02 ".""""2***E(005 (5.32"100E(005
(5.32"100E(005 0.01"530* (5.32"100E(005 0.0002"""")
0.0001"""""3 (5.32"100E(005 ".""""2***E(005 (5.32"100E(005
(5.32"100E(005 0.01"*"!33 (5.32"100E(005 0.0002"""")
".""""2***E(005 (5.32"100E(005 ".""""2***E(005 (5.32"100E(005
(5.32"100E(005 0.0002"""") (5.32"100E(005 0.0002"""")
21*5.00 0.00 0.00 0.00
"50.00 0.00 0.00 0.00
0.00 1250.00 (2150.00 0.00
0.00 (2150.00 "50.00 0.00
0.00 0.00 0.00 10000.00
0.00 0.00 (*000.00 0.00
(21*5.00 (1250.00 2150.00 (10000.00
(350.00 2150.00 (350.00 0.00
0.00 0.00 0.00 0.00
(*000.00 0.00 0.00 0.00
-
8/16/2019 analisis estructural matrices excel
22/37
-
8/16/2019 analisis estructural matrices excel
23/37
K
CS0.!3
0.00
0.00
0.00
(0.!3
0.00
u! ! u5 5
(0.25 (0.!33 0 0
(0.!33 (0.5 0 0
0 0 0 0
0 0 0 0
0 0 0 0 =
0 0 0 0
0.25 0.!33 0 00.!33 0.5 0 0
0 0 0 0
0 0 0 0
-
8/16/2019 analisis estructural matrices excel
24/37
u! ! u5 5
0 0 0 0
0 0 0 (1
0 0 0 0
0 0 0 0
0 0 0 0 =
0 0 0 00 0 0 0
0 0 0 0
0 0 0 0
0 0 0 1
u! ! u5 5
0.00 0.00 0 00.00 0.00 0 0
0 0.00 0 0
0 0.00 0 0 =
0 0.00 0 0
0 0.00 0 0
1.00 0.00 (1.00 0
0.00 0.00 0 0
(1 0.00 1 0
0 0.00 0 0
u! ! u5 5
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
(1 0 0 0 =
0 0 0 0
1 0 0 0
0.0 0 0 0
0 0 0 0
0 0 0 0
-
8/16/2019 analisis estructural matrices excel
25/37
u! ! u5 5
0 0 0 0
0 0 0 0
(0.25 0.!3 0 0
0.!3 (0.5 0 00.0 0.0 0 0 =
0.0 0.0 0 0
0.25 (0.!3 0 0
(0.! 0.5 0 0
0 0 0 0
0 0 0 0
u! ! u5 5
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 0 0.0 0.0
0 0 0.0 0.0
0 0 0.0 0.0
0 0 0.0 0.0
(21*5.00 0.00 0.00 u1 -1
(350.00 0.00 (*000.00 1 -y1
2150.00 0.00 0.00 u2 10000
(350.00 0.00 0.00 2 (12000
0.00 0.00 0.00 ' u3 )000
0.00 0.00 0.00 3 0
15.00 (10000.00 0.00 u! 0
500.00 0.00 0.00 ! 5000
0.00 10000.00 0.00 u5 -5
0.00 0.00 *000.00 5 -y5
=
-
8/16/2019 analisis estructural matrices excel
26/37
u2 10000
2 (12000
u3 = )000
3 0
u! 0! 5000
10000 u2
(12000 2
' )000 = u3
0 3
0 u!
5000 !
0.00 (1250.00 (21*5.00 0.00 0.00
0.00 (21*5.00 (350.00 0.00 (*000.00
0.00 (1250.00 2150.00 0.00 0.00
(*000.00 2150.00 (350.00 0.00 0.00
0.00 (10000.00 0.00 0.00 0.00 '
*000.00 0.00 0.00 0.00 0.00
0.00 22500.00 15.00 (10000.00 0.00
0.00 15.00 500.00 0.00 0.00
0.00 (10000.00 0.00 10000.00 0.00
0.00 0.00 0.00 0.00 *000.00
-
8/16/2019 analisis estructural matrices excel
27/37
-
8/16/2019 analisis estructural matrices excel
28/37
1250.00 21*5.00 0.00 0.00 0.00 0.00
21*5.00 350.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00
(1250.00 (21*5.00 0.00 0.00 0.00 0.00(21*5.00 (350.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00
-
8/16/2019 analisis estructural matrices excel
29/37
0 0 0 0 0 0
0 *000 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 00 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 (*000 0 0 0 0
0 0 0 0 0 00 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 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 0 0 0
0 0 0 0 10000 0
0 0 0 0 0 0
0 0 0 0 (10000 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
-
8/16/2019 analisis estructural matrices excel
30/37
0 0 0 0 0 0
0 0 0 0 0 0
0 0 1250 (2150 0 0
0 0 (2150 350 0 00 0 0 0 0 0
0 0 0 0 0 0
0 0 (1250 2150 0 0
0 0 2150 (350 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 *000 0 (*000
0 0 0 0 0 0
0 0 0 (*000 0 *000
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
-
8/16/2019 analisis estructural matrices excel
31/37
0.00
0.00
1)2.20
"*.)*
3.00
"*.)*
2.20
(3.1!
0.00
0.00
-
8/16/2019 analisis estructural matrices excel
32/37
-
8/16/2019 analisis estructural matrices excel
33/37
(1250.00 (21*5.00 0.00 0.00
(21*5.00 (350.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
1250.00 21*5.00 0.00 0.0021*5.00 350.00 0.00 0.00
0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00
-
8/16/2019 analisis estructural matrices excel
34/37
0 0 0 0
0 0 0 (*000
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 00 0 0 0
0 0 0 0
0 0 0 0
0 0 0 *000
0 0 0 00 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
10000 0 (10000 0
0 0 0 0
(10000 0 10000 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
(10000 0 0 0
0 0 0 0
10000 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
-
8/16/2019 analisis estructural matrices excel
35/37
0 0 0 0
0 0 0 0
(1250 2150 0 0
2150 (350 0 00 0 0 0
0 0 0 0
1250 (2150 0 0
(2150 350 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 0
0 0 0 0
0 0 0 0
0 0 0 0
-
8/16/2019 analisis estructural matrices excel
36/37
-
8/16/2019 analisis estructural matrices excel
37/37