ejercicio 1
DESCRIPTION
Ejercicio resuelto de análisis estructural IITRANSCRIPT
EJERCICIO 1 A.E II
5 tn
3 tn/m10
3.5 tn1.5
44
66
2I, A=20I 2I, A=20I
5
5 tn
3 tn/m10
3.5 tn1.5
2I, A=20I 2I, A=20I
5
jA/L
[k']= E 00
-A/L00
cosø-senø
[T]= 00
11 22
11 22
4
6
A C
B D
E
44
66
00
2.- ENUMERACION DE LAS DEFORMACIONES
Def. 1ux 0uy 0Øz 0
VECTOR DEFORMACION DEL SISTEMA
U=
3.-FUERZAS EFECTIVAS EN COORD. GLOBALES
FUERZAS EXT. EN NUDOS
M3zU4xU4yM4zU5x
Nudo|
U5yM5zU6xU6y
F= M6zU7xU7yM7zU8xU8yM8zU9xU9yM9z
4.-FUERZAS DE EMPOTRAMIENTO PERFECTO DE BARRA 5
MAB= 0.00MBA= 0.00MBD= -2.50MDB= 3.75MCD= 0.00MDC= 0.00MDE= 0.00MED= 0.00MEF= -20.83MFE= 20.83MFG= 0.00MGF= 0.00MGH= 0.00MHG= 0.00MDG= -7.35MGD= 3.15
FUERZAS EXT. EN NUDOS
03.50000000
F= 05000-25-31.25
6-7 RIGIDEZ EN LAS BARRAS
BARRA 1 AA= 20I= 2E= 1L= 4ø= 90 0.50 PI
000
[k'1]= 0000
0.00
-1[T1]= 0
000
6.13E-1710
TRANSP [Ti]= 000
[ki]=TRANSP[Ti]*[k'i]*[Ti]
0 - -
[k2]= - - - -
BARRA 2 CA= 20I= 2E= 1L= 4ø= 90 0.50 PI
000
[k'1]= 0000
0.00 -1
[T1]= 0000
6.13E-1710
TRANSP [Ti]= 000
[ki]=TRANSP[Ti]*[k'i]*[Ti]
0 - -
[k2]= - - - -
BARRA 3 HA= 20I= 2E= 1L= 4ø= 90 0.50 PI
000
[k'1]= 00
00
0.00 -1
[T1]= 0000
0.00 1
TRANSP [Ti]= 0000
[ki]=TRANSP[Ti]*[k'i]*[Ti]
0 - - -
[ki]= - - -
BARRA 4 BA= 20I= 1E= 1L= 5ø= 0 0.00 PI
1040
[k'1]= 0-4
00
1.00 -
[T1]= - - - -
1.00 0
TRANSP [Ti]= 0000
[ki]=TRANSP[Ti]*[k'i]*[Ti]
10 4.00 - -
[ki]= -4.00 - -
BARRA 5 DA= 20I= 1E= 1L= 5ø= 0 0.00 PI
1340
[k'1]= 0-400
1.00 0
[T1]= 0000
1.00 00
TRANSP [Ti]= 000
[ki]=TRANSP[Ti]*[k'i]*[Ti]
13 4.000 - -
[k5]= -4.000 - -
BARRA 6 DA= 20I= 2E= 1L= 3.5ø= 90 0.50 PI
135.710.00
[k'1]= 0.00-5.710.000.00
0.00 -1
[T1]= 0000
0.00 10
TRANSP [Ti]= 000
[ki]=TRANSP[Ti]*[k'i]*[Ti]
130.5597667638 0.00 -0.98
[ki]= -0.56 -0.00 -0.98
BARRA 7 G
A= 20I= 2E= 1L= 3.5ø= 90 0.50 PI
165.710.00
[k'1]= 0.00-5.710.000.00
0.00 -1
[T1]= 0000
0.00 10
TRANSP [Ti]= 000
[ki]=TRANSP[Ti]*[k'i]*[Ti]
16 0.56 0.00 -0.98
[ki]= -0.56 -0.00 -0.98
BARRA 8 EA= 20I= 1E= 1L= 5ø= 0 0.00 PI
1940
[k'1]= 0-400
1.00 0
[T1]= 0000
1.00 00
TRANSP [Ti]= 000
[ki]=TRANSP[Ti]*[k'i]*[Ti]
19 4.000
- -
[ki]= -4.000 - -
ENSAMBLAMOS LA MATRIZ GLOBAL
9 10 11 12
2.00 0 0 0
0 4.38 0.00 0.75
0 0.00 5.10 0.24
0 0.75 0.24 2.80
0 -4.00 - -
0 - -0.10 -0.24
0 - 0.24 0.40
0.75 0 0 0 -0.00 0 0 0
1 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0
0.8007 -0.6023 -0.0111-0.6023 2.1011 0.0381-0.0111 0.0381 0.19810.1503 -0.5257 -0.0249-0.6306 1.9496 0.03700.0096 -0.0053 0.00300.0893 -0.2860 -0.0145-0.7101 1.9305 0.0373
0.0015 -0.0328 -0.0012-0.0689 -0.2433 -0.0058
{U}= -0.6966 2.5641 0.06200.0093 0.0016 0.0033-0.0153 -0.0791 -0.0022-0.6877 2.5607 0.06140.0018 -0.0398 -0.00140.0198 -0.1029 -0.0056
CALCULARÁ LAS DEFORMACIONES EN COORDENDAS LOCALES PARA LA BARRA
PRIMERO SE CALCULARÁ LAS DEFORMACIONES EN COORDENDAS LOCALES PARA LA BARRA
BARRA 1
u1'xju1'yj
{u1'}= Ø1ju1'xku1'ykØ1k
{u1'}=
BARRA 1 1A 20I 2E 1L 4φ 90 0.50 PI
[F'1]=
BARRA 2
u1'xju1'yj
{u1'}= Ø1ju1'xku1'ykØ1k
{u1'}=
BARRA AIELφ
BARRA 3
u1'xju1'yj
{u1'}= Ø1ju1'xku1'ykØ1k
{u1'}=
BARRA 3 3A 20I 2E 1L 4φ 90 0.50 PI
[K'3]=
BARRA 4
U4xU4y
{u1'}= Φ4zU5xU5yΦ5z
{u1'}=
BARRA 4 4A 20I 1E 1L 5φ 0 0.00 PI
[K'4]=
BARRA 5
U5xU5y
{u1'}= Φ5zU6xU6yΦ6z
{u1'}=
BARRA 5 5A 20I 1E 1L 5φ 0 0.00 PI
[K'5]=
BARRA 6
U5xU5y
{u1'}= Φ5z =U7xU7yΦ7z
{u1'}=
BARRA 6 5A 20I 2E 1L 3.5φ 90 0.50 PI
[K'6]=
BARRA 7
U6xU6y
{u1'}= Φ6z =U8xU8yΦ8z
{u1'}=
BARRA 7 6A 20I 2E 1L 3.5φ 90 0.50 PI
[K'6]=
BARRA 8
U7xU7y
{u1'}= Φ7z =U8xU8yΦ8z
{u1'}=
BARRA 8 7A 20I 1E 1L 5φ 0 0.00 PI rad
1940
0[K'5]= -4
00
F FEP
BARRA 1
N1 -0.53tn 0.00tn
V1 4.36tn 0.00tn
M1 12.44tn 0.00tn
N4 0.53tn 0.00tn
V4 -4.36tn 0.00tn
M4 5.01tn 0.00tn
BARRA 2
N2 30.87tn 0.00tn
V2 4.24tn 0.00tn
M2 12.33tn 0.00tn
N5 -30.87tn 0.00tn
V5 -4.24tn 0.00tn
M5 4.64tn 0.00tn
BARRA 3
N3 62.16tn 0.00tn
V3 -0.11tn 0.00tn
M3 0.00tn 0.00tn
N6 -62.16tn 0.00tn
V6 0.11tn 0.00tn
M6 -0.43tn 0.00tn
BARRA 4
N4 -0.86tn 0.00tn
V4 -3.03tn 2.50tn
M4 -7.51tn 2.50tn
N5 0.86tn 0.00tn
V5 3.03tn 5.00tn
M5 -7.62tn -3.75tn
BARRA 5
N5 -4.41tn 0.00tn
V5 -2.98tn 7.00tn
M5 -7.54tn 7.35tn
N6 4.41tn 0.00tn
V6 2.98tn 3.00tn
M6 -7.36tn -3.15tn
BARRA 6
N5 18.82tn 0.00tn
V5 0.69tn 0.00tn
M5 6.92tn 0.00tn
N7 -18.82tn 0.00tn
V7 -0.69tn 0.00tn
M7 -4.49tn 0.00tn
BARRA 7
N6 56.18tn 0.00tn
V6 4.31tn 0.00tn
M6 10.94tn 0.00tn
N8 -56.18tn 0.00tn
V8 -4.31tn 0.00tn
M8 4.13tn 0.00tn
BARRA 8
N7 4.31tn 0.00tn
V7 -6.18tn 25.00tn
M7 -16.34tn 20.83tn
N8 -4.31tn -5.00tn
V8 6.18tn 25.00tn
M8 -14.55tn -20.83tn
EJERCICIO 1 A.E II
COLUMNAS A = 20 , E = 1 , I = 2
COLUMNAS
A = 20 , E = 1 , I = 2
10 tn/m
I, A=20I2.5
3.5tn
I, A=20I
55
77
88
42I, A=20I
5
25 tn10 tn/m
31.25 tn/m
I, A=20I
3.5tn
I, A=20I
42I, A=20I
5
j j k k k0 0 -A/L 0 0
12I/L^3 6I/L^2 0 -12I/L^3 6I/L^26I/L^2 4I/L 0 -6I/L^2 2I/L
0 0 A/L 0 0-12I/L^3 -6I/L^2 0 12I/L^3 -6I/L^26I/L^2 2I/L 0 -6I/L^2 4I/L
senø 0 0 0 0cosø 0 0 0 0
0 1 0 0 00 0 cosø senø 0
33
33
55
7
8 F
G
H
77
88
0 0 -senø cosø 00 0 0 0 1
2.- ENUMERACION DE LAS DEFORMACIONES
2 3 4 5 60 0 10 13 160 0 11 14 170 9 12 15 18
16 INCOGNITAS
VECTOR DEFORMACION DEL SISTEMA
Φ3z 9U4x 10U4y 11Φ4z 12U5x 13U5y 14Φ5z 15U6x 16U6y 17Φ6z 18U7x 19U7y 20Φ7z 21U8x 22U8y 23Φ8z 24
FUERZAS EFECTIVAS EN COORD. GLOBALES
FUERZAS EXT. EN NUDOS FUERZA DE EMP. PERFECTO
M3zU4xU4yM4zU5x
U5yM5zU6xU6y
+ M6zU7xU7yM7zU8xU8yM8zU9xU9yM9z
FUERZAS DE EMPOTRAMIENTO PERFECTO DE BARRA 5
BARRA 4
0 10-2.5 11
-2.50 12F4= 0 13
-5 143.75 15
FUERZAS EXT. EN NUDOS FUERZA DE EMP. PERFECTO
0.0 90.0 10-2.5 11-2.5 120.0 13-12.0 14-3.6 150.0 16-3.0 17
+ 3.2 180.0 19-25.0 20-20.8 210.0 22-25.0 2320.8 24
B
rad
0 0 10 11 120 0 0 0 00 0 0 0 00 0 0 0 00 0 5 0 00 0 0 0.375 -0.750 0 0 -0.75 2
1 0 0 0 0
0.00 0 0 0 00 1 0 0 00 0 0.00 1 00 0 -1 0.00 00 0 0 0 1
-1 0 0 0 06.126E-17 0 0 0 0
0 1 0 0 00 0 6.1257423E-017 -1 00 0 1 6.125742E-017 00 0 0 0 1
TRANSP[Ti]*[k'i]*[Ti]
0 0 10 11 12 - - - - - - - - - -
- - - - - - - 0.375 0.000 0.750 - - 0.000 5.000 -0.000 - - 0.750 -0.000 2.000
D
rad
0 0 13 14 150 0 0 0 00 0 0 0 00 0 0 0 00 0 5 0 00 0 0 0.375 -0.750 0 0 -0.75 2
1 0 0 0 0 0.00 0 0 0 0
0 1 0 0 00 0 0.00 1 00 0 -1 0.00 00 0 0 0 1
-1 0 0 0 06.126E-17 0 0 0 0
0 1 0 0 00 0 6.1257423E-017 -1 00 0 1 6.125742E-017 00 0 0 0 1
TRANSP[Ti]*[k'i]*[Ti]
0 0 13 14 15 - - - - - - - - - -
- - - - - - - 0.375 0.000 0.750 - - 0.000 5.000 -0.000 - - 0.750 -0.000 2.000
G
rad
0 9 16 17 180 0 0 0 00 0 0 0 00 2 0 -0.75 10 0 5 0 0
0 -0.75 0 0.375 -0.750 1 0 -0.75 2
1 0 0 0 0 0.00 0 0 0 0
0 1 0 0 00 0 0.00 1 00 0 -1 0.00 00 0 0 0 1
-1 0 0 0 0 0.00 0 0 0 0
0 1 0 0 00 0 0.00 -1 00 0 1 0.00 00 0 0 0 1
TRANSP[Ti]*[k'i]*[Ti]
0 9 16 17 18 - - - - - - - - - - - 2.00 0.75 -0.00 1.00
- 0.75 0.38 0.00 0.75 - -0.00 0.00 5.00 -0.00 - 1.00 0.75 -0.00 2.00
D
rad
11 12 13 13 150 0 -4 0 0
0.096 0.096 0 -0.096 0.240.24 0.8 0 -0.24 0.4
0 0 4 0 0
-0.096 -0.24 0 0.096 -0.240.24 0.4 0 -0.24 0.8
- - ### - ### 1.00 - ### - ### - 1.00 - ### - - - 1.00 - - - - - 1.00 - - - ### - 1.00
0 0 0 0 0 1.00 0 0 0 0
0 1 0 0 00 0 1.00 0 00 0 0 1.00 00 0 0 0 1
TRANSP[Ti]*[k'i]*[Ti]
11 12 13 13 15 - - -4.00 - - 0.10 0.10 - -0.10 0.24 0.24 0.80 - -0.24 0.40
- - 4.00 - - -0.10 -0.24 - 0.10 -0.24 0.24 0.40 - -0.24 0.80
G
rad
14 15 16 17 180 0 -4 0 0
0.096 0.096 0 -0.096 0.24
0.24 0.8 0 -0.24 0.40 0 4 0 0
-0.096 -0.24 0 0.096 -0.240.24 0.4 0 -0.24 0.8
0 0 0 0 0 1.00 0 0 0 0
0 1 0 0 00 0 1.00 0 00 0 0 1.00 00 0 0 0 1
0 0 0 0 0 1.00 0 0 0 0
0 1 0 0 00 0 1.00 0 00 0 0 1.00 00 0 0 0 1
TRANSP[Ti]*[k'i]*[Ti]
14 15 16 17 18 - - -4.000 - - 0.096 0.096 - -0.096 0.240 0.240 0.800 - -0.240 0.400
- - 4.000 - - -0.096 -0.240 - 0.096 -0.240 0.240 0.400 - -0.240 0.800
E
rad
14 15 19 20 210.00 0.00 -5.71 0.00 0.000.56 0.56 0.00 -0.56 0.980.98 2.29 0.00 -0.98 1.140.00 0.00 5.71 0.00 0.00-0.56 -0.98 0.00 0.56 -0.980.98 1.14 0.00 -0.98 2.29
1 0 0 0 0 0.00 0 0 0 0
0 1 0 0 00 0 0.00 1 00 0 -1 0.00 00 0 0 0 1
-1 0 0 0 0 0.00 0 0 0 0
0 1 0 0 00 0 0.00 -1 00 0 1 0.00 00 0 0 0 1
TRANSP[Ti]*[k'i]*[Ti]
14 15 19 20 21 0.00 -0.56 -0.56 -0.00 -0.98 5.71 0.00 -0.00 -5.71 0.00 0.00 2.29 0.98 -0.00 1.14
-0.00 0.98 0.56 0.00 0.98 -5.71 -0.00 0.00 5.71 -0.00 0.00 1.14 0.98 -0.00 2.29
F
rad
17 18 22 23 240.00 0.00 -5.71 0.00 0.000.56 0.56 0.00 -0.56 0.980.98 2.29 0.00 -0.98 1.140.00 0.00 5.71 0.00 0.00-0.56 -0.98 0.00 0.56 -0.980.98 1.14 0.00 -0.98 2.29
1 0 0 0 0 0.00 0 0 0 0
0 1 0 0 00 0 0.00 1 00 0 -1 0.00 00 0 0 0 1
-1 0 0 0 0 0.00 0 0 0 0
0 1 0 0 00 0 0.00 -1 00 0 1 0.00 00 0 0 0 1
TRANSP[Ti]*[k'i]*[Ti]
17 18 22 23 24 0.00 -0.56 -0.56 -0.00 -0.98 5.71 0.00 -0.00 -5.71 0.00 0.00 2.29 0.98 -0.00 1.14
-0.00 0.98 0.56 0.00 0.98 -5.71 -0.00 0.00 5.71 -0.00 0.00 1.14 0.98 -0.00 2.29
F
rad
20 21 22 23 240 0 -4 0 0
0.096 0.096 0 -0.096 0.240.24 0.8 0 -0.24 0.4
0 0 4 0 0-0.096 -0.24 0 0.096 -0.240.24 0.4 0 -0.24 0.8
0 0 0 0 0 1.00 0 0 0 0
0 1 0 0 00 0 1.00 0 00 0 0 1.00 00 0 0 0 1
0 0 0 0 0 1.00 0 0 0 0
0 1 0 0 00 0 1.00 0 00 0 0 1.00 00 0 0 0 1
TRANSP[Ti]*[k'i]*[Ti]
20 21 22 23 24 - - -4.000 - -
0.096 0.096 - -0.096 0.240 0.240 0.800 - -0.240 0.400
- - 4.000 - - -0.096 -0.240 - 0.096 -0.240 0.240 0.400 - -0.240 0.800
ENSAMBLAMOS LA MATRIZ GLOBAL
13 14 15 16 17
0 0 0 0.75 -4.6E-017
-4.00 - - 0 0
- -0.10 0.24 0 0
- -0.24 0.40 0 0
8.93 0.00 -0.23 -4.00 -
0.00 10.91 - - -0.10
-0.23 - 5.89 - -0.24
-4.00 - - 4.93 0.00 - -0.10 -0.24 0.00 10.81 - 0.24 0.40 -0.23 -0.24 -0.56 -0.00 0.98 0 0 -0.00 -5.71 -0.00 0 0 -0.98 0.00 1.14 0 0
0 0 0 -0.56 -0.00 0 0 0 -0.00 -5.71 0 0 0 -0.98 0.00
{F}=[K]*{U}
0.03.5
-2.5-2.50.0
-12.0-3.6
0.0 = k-3.03.25.0
-25.0-20.8
0.0-50.0-10.4
{U}= [K]^-1*{F}
0.1503 -0.6306 0.0096 0.0893 -0.7101-0.5257 1.9496 -0.0053 -0.2860 1.9305-0.0249 0.0370 0.0030 -0.0145 0.03730.4960 -0.4819 0.0185 0.0393 -0.4751-0.4819 2.0420 -0.0023 -0.3054 2.02240.0185 -0.0023 0.1936 -0.0055 -0.00150.0393 -0.3054 -0.0055 0.2663 -0.3175-0.4751 2.0224 -0.0015 -0.3175 2.2428
0.0063 -0.0347 0.0033 0.0200 -0.03580.0556 -0.2557 -0.0181 0.0595 -0.2619
-0.5857 2.6947 0.0697 -0.7035 2.81400.0172 0.0050 0.1929 -0.0097 0.00610.0161 -0.0835 -0.0321 0.0179 -0.1282-0.5866 2.6908 0.0706 -0.6896 2.81570.0077 -0.0421 0.0040 0.0242 -0.04340.0120 -0.1103 -0.0267 0.0964 -0.0721
Φ3zU4xU4yΦ4zU5xU5yΦ5z
{U}= U6xU6yΦ6zU7xU7yΦ7zU8xU8yΦ8z
CALCULARÁ LAS DEFORMACIONES EN COORDENDAS LOCALES PARA LA BARRA
{u'}= [T]*{U} DEFORMACIONES LOCALES EN CADA BARRA
{F'}= [k']*{u'} FUERZAS EN LOS ELEMENTOS MECÁNICOS CADA BARRA
PRIMERO SE CALCULARÁ LAS DEFORMACIONES EN COORDENDAS LOCALES PARA LA BARRA
0.000 00.000 0
= [T] * 0.000 0 = 26.49 10 0.11 11 -7.43 12
0.00.0
1 0.0 deformaciones locales barra 1EI 0.1
-26.5-7.4
4
rad
1 2 3 10 115 0 0 -5 00 0.375 0.75 0 -0.375
0 0.75 2 0 -0.75-5 0 0 5 00 -0.375 -0.75 0 0.3750 0.75 1 0 -0.750
0.000 00.000 0
= [T] * 0.000 0 = 26.70 13 -6.17 14 -7.69 15
0.00.0
1 0.0 deformaciones locales barra 2EI -6.2
-26.7-7.7
2 2 520214
90 0.50 PI rad
4 5 65 0 00 0.375 0.75
0 0.75 2[K'2]= -5 0 0
0 -0.375 -0.750 0.75 1
0.000 00.000 0
= [T] * -6.809 9 = 27.80 16 -12.43 17 -7.24 18
0.00.0
1 -6.8 deformaciones locales barra 3EI -12.4
-27.8-7.2
6
rad
7 8 9 16 175 0 0 -5 00 0.375 0.75 0 -0.375
0 0.75 2 0 -0.75-5 0 0 5 00 -0.375 -0.75 0 0.375
0 0.75 1 0 -0.750
26.485 100.105 11
= [T] * -7.427 12 =26.701 13-6.173 14-7.691 15
26.50.1
1 -7.4 deformaciones locales barra 4EI 26.7
-6.2-7.7
5
rad
10 11 12 13 144 0 0 -4 00 0.096 0.24 0 -0.096
0 0.24 0.8 0 -0.24-4 0 0 4 0
0 -0.096 -0.24 0 0.0960 0.24 0.4 0 -0.240
26.701 13-6.173 14
= [T] * -7.691 15 =27.804 16
-12.432 17-7.236 18
26.7-6.2
1 -7.7 deformaciones locales barra 5EI 27.8
-12.4-7.2
6
rad
13 14 15 16 174 0 0 -4 00 0.096 0.24 0 -0.096
0 0.24 0.8 0 -0.24
-4 0 0 4 00 -0.096 -0.24 0 0.0960 0.24 0.4 0 -0.240
26.701 13 0.00 -6.173 14 -1.00
[T] * -7.691 15 = - 72.323 19 - -9.467 20 -
-17.672 21 -
-6.2-26.7
1 -7.7 deformaciones locales barra 6EI -9.5
-72.3-17.7
7
rad
13 14 15 19 205.71 0.00 0.00 -5.71 0.000.00 0.56 0.98 0.00 -0.56
0.00 0.98 2.29 0.00 -0.98-5.71 0.00 0.00 5.71 0.00
0.00 -0.56 -0.98 0.00 0.560.00 0.98 1.14 0.00 -0.98
0.00 27.804 17 -1.00
-12.432 17 -
[T] * -7.236 18 = - 71.246 22 -
-22.263 24 - -13.191 24
-12.4-27.8
1 -7.2 deformaciones locales barra 7EI -22.3
-71.2-13.2
8
rad
16 17 18 22 235.714 0.000 0.000 -5.714 0.0000.000 0.560 0.980 0.000 -0.560
0.000 0.980 2.286 0.000 -0.980-5.714 0.000 0.000 5.714 0.000
0.000 -0.560 -0.980 0.000 0.5600.000 0.980 1.143 0.000 -0.980
1.00 72.323 19 - -9.467 20 -
[T] * -17.672 21 = - 71.246 22 -
-22.263 23 - -13.191 24
72.3-9.5
1 -17.7 deformaciones locales barra 8EI 71.2
-22.3-13.2
8
20 21 22 23 240 0 -4 0 0
0.096 0.24 0 -0.096 0.24
0.24 0.8 0 -0.24 0.40 0 4 0 0
-0.096 -0.24 0 0.096 -0.2400.24 0.4 0 -0.240 0.8
FUERZAS FINALES
BARRA 1
-0.53tn4.36tn
12.44tn0.53tn
-4.36tn5.01tn
BARRA 2
30.87tn4.24tn
12.33tn-30.87tn-4.24tn4.64tn
BARRA 3
62.16tn-0.11tn0.00tn
-62.16tn0.11tn-0.43tn
BARRA 4
-0.86tn-0.53tn-5.01tn0.86tn8.03tn
-11.37tn
BARRA 5
-4.41tn4.02tn-0.19tn4.41tn5.98tn
-10.51tn
BARRA 6
18.82tn0.69tn6.92tn
-18.82tn-0.69tn-4.49tn
BARRA 7
56.18tn4.31tn
10.94tn-56.18tn
-4.31tn4.13tn
BARRA 8
4.31tn18.82tn
4.49tn-9.31tn31.18tn-35.38tn
COLUMNAS A = 20 , E = 1 , I = 2
COLUMNAS
A = 20 , E = 1 , I = 2
jjjkkk
7 819 2220 2321 24
16 INCOGNITAS
BARRA 5 BARRA 8
0 13 0-7 14 -25
-7.35 15 -20.83F5= 0 16 F8= 0
-3 17 -253.15 18 20.83
F.EFECTIVA EN NUDOS
0.0 93.5 10
-2.5 11-2.5 120.0 13
-12.0 14-3.6 150.0 16
= -3.0 17
3.2 185.0 19
-25.0 20-20.8 21
0.0 22-50.0 23-10.4 24
000101112
00
0
101112
000131415
00
0
131415
00916
1718
009
16
1718
10111213
1315
101112
13
1315
1314
15161718
131415
16
1718
131415192021
131415
19
2021
161718222324
161718
22
2324
192021222324
19
2021
22
2324
18 19 20 21 22
1 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
- -0.56 -0.00 -0.98 0
0.24 -0.00 -5.71 0.00 0
0.40 0.98 -0.00 1.14 0
-0.23 0 0 0 -0.56 -0.24 0 0 0 -0.00 5.09 0 0 0 0.98
0 4.56 0 0.98 -4.00 0 0 5.81 0.24 - 0 0.98 0.24 3.09 -
0.98 -4.00 - - 4.56 -0.00 - -0.10 -0.24 0.00 1.14 - 0.24 0.40 0.98
Φ3zU4xU4yΦ4zU5xU5yΦ5z
x U6xU6yΦ6zU7xU7yΦ7zU8xU8yΦ8z
0.0015 -0.0689 -0.6966 0.0093 -0.0153-0.0328 -0.2433 2.5641 0.0016 -0.0791-0.0012 -0.0058 0.0620 0.0033 -0.00220.0063 0.0556 -0.5857 0.0172 0.0161-0.0347 -0.2557 2.6947 0.0050 -0.08350.0033 -0.0181 0.0697 0.1929 -0.03210.0200 0.0595 -0.7035 -0.0097 0.0179-0.0358 -0.2619 2.8140 0.0061 -0.1282
0.1979 0.0239 -0.1318 0.0038 0.03430.0239 0.3342 -0.7174 -0.0232 0.1267
-0.1318 -0.7174 6.2911 0.1288 -0.81270.0038 -0.0232 0.1288 0.3664 -0.05710.0343 0.1267 -0.8127 -0.0571 0.5454-0.1321 -0.7364 6.1731 0.1297 -0.77680.1974 0.0289 -0.1908 0.0053 0.05930.0323 0.0145 -0.7202 -0.0513 0.0973
-6.81 926.49 100.11 11-7.43 1226.70 13-6.17 14
= -7.69 15
27.80 16-12.43 17-7.24 1872.32 19-9.47 20-17.67 2171.25 22-22.26 23-13.19 24
CALCULARÁ LAS DEFORMACIONES EN COORDENDAS LOCALES PARA LA BARRA
DEFORMACIONES LOCALES EN CADA BARRA
FUERZAS EN LOS ELEMENTOS MECÁNICOS CADA BARRA
0.00 1.00 - - -
-1.00 0.00 - - - - - 1.00 - -
- - - 0.00 1.00 - - - -1.00 0.00 - - - - -
deformaciones locales barra 1
120 1 0.0
0.75 2 0.0
1 3 * 0.00 10 0.1
-0.750 11 -26.52 12 -7.4
0.00 1.00 - ### - -1.00 0.00 - ### - - ### 1.00 - -
- ### - 0.00 1.00
- ### - -1.00 0.00 - ### - ### -
deformaciones locales barra 2
13 14 15-5 0 0 40 -0.375 0.75 5
0 -0.75 1 6 *5 0 0 130 0.375 -0.750 140 -0.750 2 15
0.00 1.00 - ### - -1.00 0.00 - ### - - ### 1.00 - -
- ### - 0.00 1.00 - ### - -1.00 0.00 - ### - ### -
deformaciones locales barra 3
180 7 0.0
0.75 8 0.0
1 9 * -6.80 16 -12.4
-0.750 17 -27.8
2 18 -7.2
1.00 - - - - - 1.00 - - - - - 1.00 - -
- - - 1.00 - - - - - 1.00 - - - - -
deformaciones locales barra 4
150 10 26.5
0.24 11 0.1
0.4 12 * -7.40 13 26.7
-0.240 14 -6.20.8 15 -7.7
1.00 - - - - - 1.00 - - - - - 1.00 - -
- - - 1.00 - - - - - 1.00 - - - - -
deformaciones locales barra 5
180 13 26.7
0.24 14 -6.2
0.4 15 * -7.7
0 16 27.8-0.240 17 -12.4
0.8 18 -7.2
1.00 - - - - 0.00 - - - -
- 1.00 - - - - - 0.00 1.00 - - - -1.00 0.00 - - - - - 1.00
210.00 13 -6.20.98 14 -26.7
1.14 15 * -7.70.00 19 -9.5
-0.98 20 -72.32.29 21 -17.7
1.00 - - - - 0.00 - - - - - 1.00 - - -
- - 0.00 1.00 - - - -1.00 0.00 - - - - - 1.00
240.000 16 -12.40.980 17 -27.8
1.143 18 * -7.20.000 22 -22.3
-0.980 23 -71.22.286 24 -13.2
- - - - - 1.00 - - - - - 1.00 - - -
- - 1.00 - - - - - 1.00 - - - - - 1.00
19 72.320 -9.5
21 * -17.7 =22 71.223 -22.324 -13.2
VERIFICACION DE MOMENTO EN CADA NUDO
NUDO SUMATORIA
4 0.00 Ok !5 0.00
6 0.00
7 0.00
8 0.00
∑M nudos = 0
192021222324 3.5 tn
2I, A=20I1
A
B
A
10
1112
13
1415
19
2021
22
2324
16
1718
9
A
B D
C H
6
E F
1 2 3
4 5
6 7
8
1
45
2 3
G
7 8
23 24
0 0 9
0 0 10
0 0 11
0 0 12
0 0 13
0 0 14
0 0 15
-0.00 -0.98 16 -5.71 0.00 17 -0.00 1.14 18 - - 19 -0.10 0.24 20 -0.24 0.40 21 0.00 0.98 22 5.81 -0.24 23 -0.24 3.09 24
-0.6877 0.0018 0.01982.5607 -0.0398 -0.10290.0614 -0.0014 -0.0056-0.5866 0.0077 0.01202.6908 -0.0421 -0.11030.0706 0.0040 -0.0267-0.6896 0.0242 0.09642.8157 -0.0434 -0.0721
-0.1321 0.1974 0.0323 x-0.7364 0.0289 0.0145
6.1731 -0.1908 -0.72020.1297 0.0053 -0.0513-0.7768 0.0593 0.09736.3013 -0.1911 -0.7581-0.1911 0.3711 0.0570-0.7581 0.0570 0.5323
- 0.000 0
- 0.000 0 - 0.000 0
- x 26.485 10 - 0.105 11 1.00 -7.427 12
-0.53tn 14.36tn 2
= 12.44tn 30.53tn 10
-4.36tn 115.01tn 12
- 0.000 0 - 0.000 0 - 0.000 0
- x 26.701 13 - -6.173 14 1.00 -7.691 15
0.0 30.87tn 40.0 4.24tn 5
0.0 = 12.33tn 6-6.2 -30.87tn 13
-26.7 -4.24tn 14-7.7 4.64tn 15
- 0.000 0 - 0.000 0 - -6.809 9
- x 27.804 16 - -12.432 17 1.00 -7.236 18
62.16tn 7-0.11tn 8
= 0.00tn 9-62.16tn 16
0.11tn 17
-0.43tn 18
- 26.485 10 - 0.105 11 - -7.427 12
- x 26.701 13 - -6.173 14 1.00 -7.691 15
-0.86tn 10-3.03tn 11
= -7.51tn 120.86tn 13
3.03tn 14-7.62tn 15
- 26.701 13 - -6.173 14 - -7.691 15
- x 27.804 16 - -12.432 17 1.00 -7.236 18
-4.41tn 13-2.98tn 14
= -7.54tn 15
4.41tn 162.98tn 17
-7.36tn 18
26.701 13-6.173 14
-7.691 15x 72.323 19
-9.467 20-17.672 21
18.82tn 130.69tn 14
= 6.92tn 15-18.82tn 19
-0.69tn 20-4.49tn 21
27.804 17-12.432 17
-7.236 18
x 71.246 22-22.263 24-13.191 24
56.18tn 164.31tn 17
= 10.94tn 18-56.18tn 22
-4.31tn 234.13tn 24
72.323 19-9.467 20
-17.672 21
x 71.246 22-22.263 23-13.191 24
4.31tn 19-6.18tn 20
-16.34tn 21-4.31tn 226.18tn 23
-14.55tn 24
25 tn10 tn/m
31.255 tn
I, A=20I
3 tn/m 3.510 tn
1.5 I, A=20I
42I, A=20I 2I, A=20I2
3
4
5
6 7
8
C
D
E F
G
H
5 5
C
10
1112
13
1415
19
2021
22
2324
16
1718
9
A
B D
C H
6
E F
1 2 3
4 5
6 7
8
1
45
2 3
G
7 8
0.03.5
-2.5-2.50.0
-12.0-3.60.0
-3.03.2
5.0-25.0-20.8
0.0-50.0-10.4
tn/m
