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Tabla Resumen Barra B (MM) H (MM) Área (MM) Inercia (MM)

This document contains calculations and results for the structural analysis of 3 bars (Bar 1, Bar 2, Bar 3) under a load. Key results include: - The stiffness matrix [K] for the assembled system of 3 bars - The inverse stiffness matrix [K]-1 - Calculated forces {F}, reactions {R}, and deformations {D} for each bar The analysis determines the internal forces, reactions, and deformations of the 3 bar structure.

Uploaded by

Juan Carlos Chuquilin Zamora
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© © All Rights Reserved
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31 views17 pages

Tabla Resumen Barra B (MM) H (MM) Área (MM) Inercia (MM)

This document contains calculations and results for the structural analysis of 3 bars (Bar 1, Bar 2, Bar 3) under a load. Key results include: - The stiffness matrix [K] for the assembled system of 3 bars - The inverse stiffness matrix [K]-1 - Calculated forces {F}, reactions {R}, and deformations {D} for each bar The analysis determines the internal forces, reactions, and deformations of the 3 bar structure.

Uploaded by

Juan Carlos Chuquilin Zamora
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as XLSX, PDF, TXT or read online on Scribd
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0 kN

TABLA RESUMEN

Barra b (mm) h (mm) Área (mm2) Inercia (mm4)


1 0.3 0.5 0.15 0.00313
2 0.3 0.5 0.15 0.00313
3 0.4 0.4 0.16 0.00213
E 2200000 kN/mm2

BARRA N° 01:
𝐴𝐸/𝐿= 12𝐸𝐼/𝐿^3 =
110000 3055.556

MATRICES

110000 0 0
0 3055.56 4583.33
0 4583.33 9166.666666667
[k1] =
-110000 0 0
0 -3055.56 -4583.33
0 4583.33 4583.333333333

110000.00 0.00 0.00


0.00 3055.56 4583.33
0.00 4583.33 9167
[k1][λ1][λ1]T =
-110000.00 0.00 0.00
0.00 -3055.56 -4583.33
0.00 4583.33 4583
kaa
[K1] =
kba

BARRA N° 02:
𝐴𝐸/𝐿= 12𝐸𝐼/𝐿^3 =
110000.00 3055.556

MATRICES

110000.00 0.00 0.00


0.00 3055.56 4583.33
0.00 4583.33 9166.67
[k2] =
-110000.00 0.00 0.00
0.00 -3055.56 -4583.33
0.00 4583.33 4583.33

110000.00 0.00 0.00


0.00 3055.56 4583.33
0.00 4583.33 9166.67
[k2][λ2][λ2]T =
-110000.00 0.00 0.00
0.00 -3055.56 -4583.33
0.00 4583.33 4583.33

kaa
[K2] =
kba

BARRA N° 03:
𝐴𝐸/𝐿= 12𝐸𝐼/𝐿^3 =
88000.00 880.00

MATRICES

88000 0 0
0 880.00 1760.00
0 1760.00 4693.333333333
[k3] =
-88000 0 0
0 -880.00 -1760.00
0 1760.00 2346.666666667

880.00 0.00 -1760.00


0.00 88000.00 0.00
-1760.00 0.00 4693.33
[k3][λ3][λ3]T =
-880.00 0.00 1760.00
0.00 -88000.00 0.00
-1760.00 0.00 2346.67

kaa
[K3] =
kba

MATRIZ DE ENSAMBLAJE

1 2 3
1 k1aa k1ab 0
2 k1ba k1bb + k2aa k2ab
3 0 k2ba k2bb + k3aa
4 0 0 k3ba

ENSAMBLAJE

1 2
1 110000 0
2 0 3056
3 0 4583
4 -110000 0
[K] = 5 0 -3056
6 0 4583
7 0 0
8 0 0
9 0 0
10 0 0
11 0 0
12 0 0

Nueva Matriz

1 2
1 110000.00 0.00
2 0.00 3055.56
3 0.00 4583.33
4 -110000.00 0.00
[K] = 6 0.00 4583.33
9 0.00 0.00
12 0.00 0.00
5 0.00 -3055.56
7 0.00 0.00
8 0.00 0.00
10 0.00 0.00
11 0.00 0.00
Matriz Inversa

1 2
1 0.0000 0.000000
2 0.0000000 0.002507
3 0.00000 -0.001054
[K]-1 =
4 0.0000 0.000000
6 0.0000000 -0.00039942
9 0.00000 0.000144
12 0.00000 -0.000072

Fuerzas

0 0 1
WL/2 2.31 2
{q2p} = WL2/12 1.15 3
0 0 7
WL/2 2.31 8
-WL2/12 -1.15 9

0 1
2.31 2
{F2p} = 1.15 3
[λ2]x{q2p} = 0 7
2.31 8
-1.15 9

Fuerzas E

0.00 1
2.31 2
1.15 3
0 4
{FE1} = 0.00 5
0.00 6
0 7
2.31 8
-1.15 9
0 10
0 11
0 12

Deformaciones

{D} = 1 0.00000000
[K]-1 x 2 0.00440278
{FL} = 3 -0.00171927
4 0.00000000
6 -0.00071258
9 0.00016679
12 -0.00008339

Valor de KRL

1 2
5 0.00 -3055.56
{KRL} = 7 0.00 0.00
8 0.00 0.00
10 0.00 0.00
11 0.00 0.00

Reacciones

5 -4.8086
7 -0.1468
{RC} = 8 2.5015 {RP} =
{KRL} x {D} = 10 0.1468
11 0.0000

Deformaciones

1 0.00000
2 0.00440
3 -0.00172
4 0.0000000
{D} = 5 0.0000000
6 -0.0007126
7 0.0000000
8 0.0000000
9 0.0001668
10 0
11 0
12 -0.0000834

Deformaciones Barra 1

0.00000
0.00000
-0.00071
{D1] =
0.0000000
0.0044028
-0.0017193

Deformaciones Barra 2

0.0000000
0.0044028
-0.0017193
{D2] =
0.0000000
0.0000000
0.0001668

Deformaciones Barra 3

0.0000000
0.0000000
-0.0000834
{D2] =
0
0
-0.0017193
kN

1.54 Tn/m

Longitud (mm) θ
3.00 0°
3.00 0°
4.00 90 °

6𝐸𝐼/𝐿^2 = 4𝐸𝐼/𝐿= 2𝐸𝐼/𝐿=


4583.33 9166.66666667

-110000 0 0 1.00
0 -3055.56 4583.33 0.00
0 -4583.33 4583.33333333 [λ1] = 0
110000 0 0 0
0 3055.56 -4583.33 0
0 -4583.33 9166.66666667 0

-110000.00 0.00 0.00 1.00


0.00 -3055.56 4583.33 0
0.00 -4583.33 4583 [λ1]T = 0
110000.00 0.00 0.00 0
0.00 3055.56 -4583.33 0
0.00 -4583.33 9167 0
kab
kbb

6𝐸𝐼/𝐿^2 = 4𝐸𝐼/𝐿= 2𝐸𝐼/𝐿=


4583.33 9166.67

-110000.00 0.00 0.00 1.00


0.00 -3055.56 4583.33 0.00
0.00 -4583.33 4583.33 [λ2] = 0
110000.00 0.00 0.00 0
0.00 3055.56 -4583.33 0
0.00 -4583.33 9166.67 0

-110000.00 0.00 0.00 1.00


0.00 -3055.56 4583.33 0.00
0.00 -4583.33 4583.33 [λ2]T = 0
110000.00 0.00 0.00 0
0.00 3055.56 -4583.33 0
0.00 -4583.33 9166.67 0

kab
kbb

6𝐸𝐼/𝐿^2 = 4𝐸𝐼/𝐿= 2𝐸𝐼/𝐿=


1760.00 4693.33

-88000 0 0 0
0 -880.00 1760.00 1
0 -1760.00 2346.66666667 [λ3] = 0
88000 0 0 0
0 880.00 -1760.00 0
0 -1760.00 4693.33333333 0

-880.00 0.00 -1760.00 0


0.00 -88000.00 0.00 -1
1760.00 0.00 2346.67 [λ3]T = 0
880.00 0.00 1760.00 0
0.00 88000.00 0.00 0
1760.00 0.00 4693.33 0

kab
kbb

4
0
0
k3ab
k3bb

3 4 5 6 7
0 -110000 0 0 0
4583 0 -3056 4583 0
9166.67 0 -4583 4583.33 0
0 220000 0 0 -110000
-4583 0 6111.11 0.00 0
4583.33 0 0.00 18333.33 0
0.00 -110000.00 0.00 0.00 110880
0.00 0.00 -3055.56 -4583.33 0
0 0.00 4583.33 4583.33 -1760.00
0 0 0 0 -880
0 0 0 0 0
0 0 0 0 -1760

3 4 6 9 12
0.00 -110000.00 0.00 0.00 0.00
4583.33 0.00 4583.33 0.00 0.00
9166.67 0.00 4583.33 0.00 0.00
0.00 220000.00 0.00 0.00 0.00
4583.33 0.00 18333.33 4583.33 0.00
0.00 0.00 4583.33 13860.00 2346.67
0.00 0.00 0.00 2346.67 4693.33
-4583.33 0.00 0.00 4583.00 0.00
0.00 -110000.00 0.00 -1760.00 -1760.00
0.00 0.00 -4583.33 -4583.33 0.00
0.00 0.00 0.00 1760.00 1760.00
0.00 0.00 0.00 0.00 0.00
3 4 6 9 12
0.00000 0.0000 0.000000 0.00000 0.00000
-0.001054 0.000000 -0.00039942 0.000144 -0.000072
0.00057 0.00000 0.000133 -0.000048 0.000024
0.00000 0.0000 0.000000 0.000000 0.00000
0.000133 0.000000 0.000133 -0.000048 0.000024
-0.000048 0.00000 -0.000048 0.00010 -0.000048
0.00002 0.00000 0.000024 -0.000048 0.00024

0 1
{FL} = 2.31 2
1.15 3
0 4
0.00 6
-1.15 9
0 12
3 4 6 9 12
-4583.33 0.00 0.00 4583.00 0.00
0.00 -110000.00 0.00 -1760.00 -1760.00
0.00 0.00 -4583.33 -4583.33 0.00
0.00 0.00 0.00 1760.00 1760.00
0.00 0.00 0.00 0.00 0.00

5 0.00 5 -4.8086
7 0.00 7 -0.1468
{R} =
8 2.31 {RC} - 8 0.1915
10 0.00 {RP} = 10 0.1468
11 0.00 11 0.0000

4 0.00 4
5 0.00 5
6 {d1} = 0.00 6 {q1c} =
1 [λ1]T x {D1} = 0.0000000 1 [k1] x {d1} =
2 0.0044028 2
3 -0.0017193 3

1 0.0000000 1
2 0.0044028 2
3 {d2} = -0.0017193 3 {q2c} =
7 [λ2]T x {D2} = 0.0000000 7 [k2] x {d2} =
8 0.0000000 8
9 0.0001668 9

10 0.0000000 10
11 0.0000000 11
12 {d2} = -0.0000834 12 {q2c} =
1 [λ2]T x {D2} = 0 1 [k2] x {d2} =
2 0 2
3 -0.0017193 3
4583.33333333

0.00 0 0 0 0
1.00 0 0 0 0
0 1 0 0 0
0 0 1.00 0.00 0
0 0 0.00 1.00 0
0 0 0 0 1

0 0 0 0 0
1.00 0 0 0 0
0 1 0 0 0
0 0 1.00 0 0
0 0 0 1.00 0
0 0 0 0 1
4583.33

0.00 0 0 0 0
1.00 0 0 0 0
0 1 0 0 0
0 0 1.00 0.00 0
0 0 0.00 1.00 0
0 0 0 0 1

0.00 0 0 0 0
1.00 0 0 0 0
0 1 0 0 0
0 0 1.00 0.00 0
0 0 0.00 1.00 0
0 0 0 0 1

2346.67

-1 0 0 0 0
0 0 0 0 0
0 1 0 0 0
0 0 0 -1 0
0 0 1 0 0
0 0 0 0 1

1 0 0 0 0
0 0 0 0 0
0 1 0 0 0
0 0 0.00 1 0
0 0 -1 0.00 0
0 0 0 0 1

8 9 10 11 12
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
-3055.56 4583 0 0 0
-4583 4583.33 0 0 0
0 -1760 -880 0 -1760
91055.56 -4583.33 0 -88000 0
-4583.33 13860.00 1760 0 2346.67
0 1760 880 0 1760
-88000 0 0 88000 0
0 2346.67 1760 0 4693.33

5 7 8 10 11
0.0000 4 0.0000 4
-24.5989 5 -24.5989 5
{q1} =
-34.5913 6 -34.5913 6
0.0000 1 {q1c} - {q1p} = 0.0000 1
24.5989 2 24.5989 2
-39.2053 3 -39.2053 3

0.00000 1 0.0000 1
6.33741 2 4.0304 2
{q2} =
5.18391 3 4.0304 3
0.00000 7 {q2c} - {q2p} = 0.0000 7
-6.33741 8 -8.6444 8
13.82832 9 14.9818 9

-387.4447 10 -387.4447 10
-3.1727 11 -3.1727 11
{q2} =
-4.4259 12 -4.4259 12
387.4447 1 {q2c} - {q2p} = 387.4447 1
3.1727 2 3.1727 2
-8 3 -8 3

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