Método de Rigidez NO Sistematizado
Método de Rigidez NO Sistematizado
Método de Rigidez NO Sistematizado
4 9
A B C
D E
a) CASO A:
W=10 ton/m
4 9
A B C
D E
D1 3 D2
4 D
9 E
A B C
D E
ii. Hallamos 𝑅1 , 𝑅2 y 𝑅3 :
∑ 𝑀𝐵 = 0
𝑅1 = −18
𝑀 = −3 ∗ 6 ∗ 15 → 𝑀 = −27𝑡𝑜𝑛
𝑅2 = 18 − 27
𝑅2 = −9𝑡𝑜𝑛
𝑅3 = 0𝑡𝑜𝑛
K12
2EI/8 2EI/8 4EI/8 4EI/8 K22
B C
K12
2EI/8 2EI/8 4EI/8 4EI/8 K22
B C
K12
2EI/8 2EI/8 4EI/8 4EI/8 K22
B C
iv. Calculamos 𝐷1 , 𝐷2 y 𝐷3 :
𝐷1
K12
2EI/8 2EI/8 4EI/8 4EI/8 K22
B C 4𝐸𝐼 6𝐸𝐼
𝐾11 = +
16EI/3
4 6
.𝐾11 = 1.667𝐸𝐼
16EI/3
2𝐸𝐼
𝐾21 =
6
. 𝐾21 = 0.333𝐸𝐼
E
6𝐸𝐼
𝐾31 =
42
. 𝐾31 = 0.375𝐸𝐼
𝐷2
2𝐸𝐼
𝐾11 =
K12 6
2EI/8 2EI/8 4EI/8 4EI/8
B C
K22
.𝐾12 = 0.333𝐸𝐼
16EI/3
4𝐸𝐼 3𝐸𝐼
𝐾21 = +
16EI/3 6 4
. 𝐾22 = 1.417𝐸𝐼
−3𝐸𝐼
𝐾31 = 42
E . 𝐾32 = −0.188𝐸𝐼
𝐷3
K12
2EI/8 2EI/8 4EI/8 4EI/8 K22 6𝐸𝐼
B C 𝐾13 = 42
16EI/3 .𝐾13 = 0.375𝐸𝐼
16EI/3
−3𝐸𝐼
𝐾23 = 42
. 𝐾23 = −0.188𝐸𝐼
12𝐸𝐼 3𝐸𝐼
E 𝐾33 = +
43 43
. 𝐾33 = 0.234𝐸𝐼
v. Calculo de 𝐾𝑇
−18
[𝑅] = [ −9 ] … (1)
0
→ 𝑆𝑎𝑏𝑖𝑒𝑛𝑑𝑜 𝑞𝑢𝑒:
{𝑄} = −{𝑅}
→ 𝐸𝑛𝑡𝑜𝑛𝑐𝑒𝑠:
18
{𝑄} = [ 9 ]
0
{𝐷} = [𝑘]−1 × {𝑄} … (𝑧)
→ 𝐸𝑛𝑡𝑜𝑛𝑐𝑒𝑠 𝑧 𝑒𝑠 𝑖𝑔𝑢𝑎𝑙 ∶
18 𝐷1
{𝐷} = [ −1.895 ] = [𝐷2 ]
−30.316 𝐷3
𝑀𝑇 = 𝑀𝑐 ∗ 𝐷1 + 𝑀𝑐 ∗ 𝐷2 + 𝑀𝑐 ∗ 𝐷3 + 𝑀𝑃
Siendo que:
𝑀𝑇 = 𝑀𝑜𝑚𝑒𝑛𝑡𝑜 𝑇𝑜𝑡𝑎𝑙
𝑀𝑐 = 𝑀𝑜𝑚𝑒𝑛𝑡𝑜 𝐶𝑜𝑚𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑖𝑜
𝑀𝑃 = 𝑀𝑜𝑚𝑒𝑛𝑡𝑜 𝑃𝑟𝑖𝑚𝑎𝑟𝑖𝑜
4𝐸𝐼 6𝐸𝐼
𝑀𝐵𝐴 = ∗ 18 + ∗ −30.316
4 16
4𝐸𝐼 2𝐸𝐼
𝑀𝐵𝐶 = ∗ 18 + ∗ −1.895 − 18
6 6
2𝐸𝐼 4𝐸𝐼
𝑀𝐶𝐵 = ∗ 18 + ∗ −1.895 + 18
6 6
3𝐸𝐼 3𝐸𝐼
𝑀𝐶𝐷 = ∗ −1.895 − ∗ −30.316
4 16
vi. Reacciones
31.87
23.69
23.69 31.87
D E
Dx=23.69 Ex=31.87
Dy=45.26 Ey=44.74
∑ 𝑀𝐵 = 0
Ax=2.48
1.65 45.09 44.91 64.22
58.45
∑ 𝑀𝐴Ay=1.65
=0 29.63 32.11
32.11
29.63
E
4𝑉𝐴𝐵 = 98.66 𝑡𝑜𝑛
Dx=29.63
→D 𝑉𝐴𝐵 = 24.67 𝑡𝑜𝑛 Ex=32.11
Dy=45.09 Ey=44.91
∑ 𝑀𝐶 = 0
∑ 𝐹𝐴 = 0
CASO A
66.05 63.75
18.66
A B C 63.75
47.39
D E
23.69 31.87
ANEXOS
CASO A
CASO B
CASO B CASO B
8.06 8.06
A B C 64.51
A B C 64.51
57.34 57.34
D E
D
28.67 32.26
E 28.67 32.26
CASO A CASO A
25.76 25.76
A B C 63.89
A B C 63.88
40.99 40.98
D E
D
20.49 31.95
E 20.49 31.94
METODO DE RIGIDEZ
MÉTODO DE FLEXIBILIDAD
CASO B
65.03 64.22
6.58
A B C 64.22
58.45
D E
29.23 32.11
CASO A CASO A
25.76 18.66
A B C 63.89
A B C 63.75
40.99 47.39
D E
D
20.49 31.95
E 23.69 31.87