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7/16/2019 RESIS II
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METODO DE LAS FUERZAS
SOLUCION
1. Calculo de giros y fechas debido a las cargas externas
I 1.2 I 1.5 I
4.00m 6.00m 8.00m
W=4KN/m
W=4KN/m
648 KN-m
72KN
G1=-42.667/EI
D1=-4.667/EIH
G2=-520/EI
D2=-1140/EI
G3=-2147.556/EI
D3=-6997.33/EI
I1.2I
1.5I
32 KN /m200
164016 40 72
648
X1 X2 X3
1.2 II
1.5 I
4 KN/m 4 KN/m 4 KN/m
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/115.10183 I2147.556/Eθ
/451.25048 I2667.556/Eθ
/676.35846 I2710.223/Eθ
W
33
W
22
W
11
EI
EI
EI
−=∆=
−=∆=
−=∆=
Hallando giros y fechas debido a las cargas unitarias
EI
EI
EI
/114.327
/116.895
/117.1355
31
21
11
=
=
=
δ
δ
δ
EI
EI
EI
/775.241
/773.621
/105.895
32
22
12
=
=
=
δ
δ
δ
EI
EI
EI
/775.113/773.241
/773.327
33
23
13
=
=
=
δ δ
δ
1355.117 895.119 327.114 X1 -35846.718
1 1 1 1 1 1
18104
G1=8/EI
D1=10.667/EIG2=35/EI
D2=90/EI
G3=74.667/EI
D3=270.22/EI
1
1 11
6
14
11
8
G1=0
D1=0
G2=15/EI
D2=30/EIG3=53.333/EI
D3=184.889/EI
G1=0
D1=0
G2=0
D2=0G3=21.333/EI
D3=56.888/EI
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895.105 621.773 241.775 X2 = -15048.493
327.109 895.109 327.109 X3 -10183.115
X1 =5.785KN
X2 =20.853KN
X3 =28.558KN
DIAGRAMAS DE V y M EN KN y KN-M
I1.2I
1.5I
W=4KN/m
5.78520.8534
28.558 16.804
23.464
10.638
15.196
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METODO ITERATIVO
+
V-
-
M+
5.785
16.804
13.362
1.446m
2.554 m
2.6595m
3.3405m
3.799m
4.201m
8.862
17.03423.466
11.831
5.284
4.18
W=4KN/m
10.215
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I=1.00 f=L/I
4
METODO DE CROSS
4.00m 6.00m 8.00m
I1.2I
1.5I
X1 X2
X3
G
55.333
-10.667 +10.667 +30 -30 +56.889 -56.889
f
244.002
18
521.333
20.667
341.333
10.6675 5.333
13.556
7.460
8.557
8.772
8.815
8.823
8.825
8.825
8.825
21.946
17.995
17.220
17.068
17.038
17.032
17.031
17.030
17.030
21.027
23.002
23.390
23.466
23.481
23.483
23.484
23.485
23.485
X1=8.825 X2=17.030 X3=23.484
W=4KN/m
X1 X2 X3
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K=I/L I=24
K
F.D. 1 0.55 0.44 0.52 0.48 0
MEP 5.33 -5.33 12 -12 21.33 -21.33
-5.33 -3.67 -2.94 -4.85 -4.48
-1.83 -2.67 -2.43 -1.47 -2.24
1.83 2.81 2.24 0.76 0.71
1.4 0.92 0.38 1.12 0.35
-1.4 -0.72 -0.57 -0.58 -0.54
-0.36 -0.7 -0.29 -0.29 -0.29
0.36 0.54 0.44 0.15 0.14
0.27 0.18 0.07 0.22 0.07
-0.27 -0.14 -0.11 -0.11 -0.1
-0.07 -0.14 -0.06 -0.06 -0.05
0.07 0.11 0.09 0.031 0.03
0.05 0.04 0.16 0.04 0.01
-0.05 -0.11 -0.08 -0.02 -0.02
-0.05 -0.02 -0.01 -0.04 -0.01
0.05 0.02 0.01 0.02 0.02
0.01 0.02 0.01 0.01 0.01
-0.01 -0.02 -0.01 -0.01 0
-0.01 -0.01 0 -0.01 0
0.01 0 0 0 0
0 -8.89 8.9 -17.09 17.09 -23.48
6 4.8 4.5
METODO DE LAS FUERZAS
W=4KN/m
4.00m 6.00m 8.00m
I1.2I
1.5I
X1X2 X3
X1=8.89 X2=17.09 X3=23.48
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G
Calculo de giros y fechas debido a las cargas externas
718.740/EIθ
178.296/EIθ
/039.4157 I-561.704/Eθ
/815.2886 I-807.036/Eθ
4
3
W
22
W
11
=
=
−=∆=
−=∆=
EI
EI
4.00m 6.00m 8.00m
I1.2I
1.5I
I1.2I
1.5I
W=4KN/m
X1 X2
3636
36 2020
4 4
112 160
G1=245.333/EI
D1=341.333/EI
G2=740/EI
D2=2100/EI
G3=540.444/EI
D3=2730.667/EI
36
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-8.842/EIθ
-4.085/EIθ
/027.58 8.145/EIθ
/152.49 /EI369.14θ
4
3
212
111
=
=
==
==
EI
EI
δ
δ
-15.369/EIθ
-3.539/EIθ
/562.90 12.101/EIθ
/892.57 /EI657.15θ
4
3
222
121
=
=
==
==
EI
EI
δ
δ
I1.2I
1.5I
I1.2I
1.5I
1
0.778 0.222
0.7780.778 0.222 0.222
0.2220.222
3.112 1.78
0.4440.556
1
0.444 0.444 0.444 0.444 0.5560.556
1.776
4.44
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49.152 57.892 X1 2886.815
57.487 90.562 X2 = 4157.039
X1=18.986
X2=33.746
DIAGRAMAS DE V Y M EN KN Y KN-M
4.00m 6.00m 8.00m
I1.2I
1.5I
W=4KN/m
+
V-
6.235 18.986 33.74613.033
6.235
9.221
18.967
13.03314.779
9.765
1.559
2.441
2.305
3.695
4.742
3.258
7.058 23.735 21.236
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METODO DE TRES MOMENTOS
I1.2I
1.2I
Gf 4 5 5.3333-10.667 -30X1 X2 X3
W=4KN/m
-
M+
3.569
4.860
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18 5 0 244
20.667 5.333 521.333
10.667 341.33
X1= 8.824
X2=17.030
X3=23.485
METODO DE TRES MOMENTOS
4.00m 6.00m 8.00m
+10.667 +30 -56.889 +56.889
4.00m 6.00m 8.00m
I1.2I
1.5I
W=4KN/m
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18 5 244
20.667 521.333
X1= 7.02
X2= 23.527
METODO ITERATIVO
+10.667 +30 -56.889 +56.889-10.667 -30
X1 X2
4.00m 6.00m 8.00m
I1.2I
1.5I
W=4KN/m
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I=1.00 f=L/I
4
METODO DE CROSS
4.00m 6.00m 8.00m
I1.2I
1.5I
W=4KN/m
G
55.333
-10.667 +10.667 +30 -30 +56.889 -56.889
f
244.002
18
521.333
20.6675
13.556
7.460
7.050
7.022
7.020
7.020
X1=7.020 X2=23.527
21.946
23.421
23.520
23.527
23.527
23.527
X1=7.1
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K
F.D. 1 0.55 0.44 0.52 0.48 0
MEP 5.33 -5.33 12 -12 21.33 -21.33
-5.33 -3.67 -2.93 -4.85 -4.48 21.33
-1.83 -2.67 -2.43 -1.47 10.67 -2.24
1.83 2.81 2.24 -4.78 -4.42 2.24
1.4 0.92 -2.4 1.12 1.12 -2.21
-1.4 0.81 0.65 -1.16 -1.08 2.21
0.41 -0.7 -0.58 0.33 1.1 -0.54
-0.41 0.7 0.56 -0.74 -0.68 0.54
0.35 -0.2 -0.37 0.28 0.27 -0.34
-0.35 0.31 0.25 -0.29 -0.26 0.34
0.16 -0.17 -0.14 0.13 0.17 -0.13
-0.16 0.17 0.14 -0.16 -0.14 0.13
0.08 -0.08 -0.08 0.07 0.07 -0.07
-0.08 0.08 0.07 -0.07 -0.07 0.07
0.04 -0.04 -0.04 0.04 0.03 -0.03
-0.04 -0.04 0.04 -0.04 -0.03 0.03
0.02 -0.02 -0.02 0.02 0.02 -0.02
-0.02 0.02 0.02 -0.02 -0.02 0.02
0.01 -0.01 -0.01 0.01 0.01 -0.01
-0.01 0.01 0.01 -0.01 -0.01 0.01
0 -7.1 6.98 -23.59 23.6 0
6 4.8 4.5
X2=23.59