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1/19
Luz (m) 25.000
Altura pilares 5.000
Pendiente 10%
I (cm4) A (cm2)
Pilar HEB-280 19270.00 131.00
Dintel IPE-450 33740.00 98.80
E 2100000Longitud (cm) a
Barra 1-2 500 90
Barra 2-3 1256.234453 5.710593137
Barra 3-4 1256.234453 354.2894069
Barra 4-5 500 270
0 -1 0 550200 0 0
1 0 0 0 3884.832 971208
0 0 1 0 971208 323736000
0 -3884.832 -971208 0 1 0 3884.832 0
550200 0 0 -1 0 0 0 550200
0 971208 323736000 0 0 1 -971208 0
0 -1 0 -550200 0 01 0 0 0 -3884.832 971208
0 0 1 0 -971208 161868000
0 3884.832 -971208 0 1 0 -3884.832 0
-550200 0 0 -1 0 0 0 -550200
0 -971208 161868000 0 0 1 971208 0
0 -1 0 -550200 0 0
1 0 0 0 -3884.832 -971208
0 0 1 0 971208 161868000
0 3884.832 971208 0 1 0 -3884.832 0
-550200 0 0 -1 0 0 0 -550200
0 971208 161868000 0 0 1 -971208 0
0 -1 0 550200 0 0
1 0 0 0 3884.832 -971208
0 0 1 0 -971208 323736000
0 -3884.832 971208 0 1 0 3884.832 0
550200 0 0 -1 0 0 0 5502000 -971208 323736000 0 0 1 971208 0
0.99503719 -0.09950372 0 165160.253 0 0
0.099503719 0.99503719 0 0 428.877753 269385.505
0 0 1 0 269385.505 225607568.2
164340.5941 -42.6749314 -26804.85956 0.99503719 0.09950372 0 163529.249 16310.03
16434.05939 426.7493148 268048.5959 -0.09950372 0.99503719 0 16310.0371 2059.881
0 269385.505 225607568.2 0 0 1 -26804.8596 268048.5
0.99503719 -0.09950372 0 -165160.253 0 0
0.099503719 0.99503719 0 0 -428.877753 269385.505
0 0 1 0 -269385.505 112803784.1
-164340.5941 42.67493143 -26804.85956 0.99503719 0.09950372 0 -163529.249 -16310.03
-16434.05939 -426.749315 268048.5959 -0.09950372 0.99503719 0 -16310.0371 -2059.8810 -269385.505 112803784.1 0 0 1 26804.8596 -268048.5
0.99503719 -0.09950372 0 -165160.253 0 0
0.099503719 0.99503719 0 0 -428.877753 -269385.505
0 0 1 0 269385.505 112803784.1
-164340.5941 42.67493143 26804.85956 0.99503719 0.09950372 0 -163529.249 -16310.03
-16434.05939 -426.749315 -268048.5959 -0.09950372 0.99503719 0 -16310.0371 -2059.881
0 269385.505 112803784.1 0 0 1 -26804.8596 268048.5
0.99503719 -0.09950372 0 165160.253 0 0
0.099503719 0.99503719 0 0 428.877753 -269385.505
0 0 1 0 -269385.505 225607568.2
164340.5941 -42.6749314 26804.85956 0.99503719 0.09950372 0 163529.249 16310.03
16434.05939 426.7493148 -268048.5959 -0.09950372 0.99503719 0 16310.0371 2059.881
0 -269385.505 225607568.2 0 0 1 26804.8596 -268048.5
K22
K23
K32
K33
BARRA 2-3
Prtico biempotrado a dos aguas simtrico
BARRA 1-2
D
A
TO
S
K22
K11
K12
K21
1
2
3
4
5
8/22/2019 Portico Biem Pot Rado Si Met Rico
2/19
0.99503719 0.099503726 0 165160.253 0 0
-0.099503726 0.99503719 0 0 428.877753 269385.505
0 0 1 0 269385.505 225607568.2
164340.5939 42.67493449 26804.86149 0.99503719 -0.09950373 0 163529.249 -16310.0
-16434.06057 426.7493145 268048.5957 0.09950373 0.99503719 0 -16310.0383 2059.88
0 269385.505 225607568.2 0 0 1 26804.8615 268048.0.99503719 0.099503726 0 -165160.253 0 0
-0.099503726 0.99503719 0 0 -428.877753 269385.505
0 0 1 0 -269385.505 112803784.1
-164340.5939 -42.6749345 26804.86149 0.99503719 -0.09950373 0 -163529.249 16310.0
16434.06057 -426.749314 268048.5957 0.09950373 0.99503719 0 16310.0383 -2059.8
0 -269385.505 112803784.1 0 0 1 -26804.8615 -268048
0.99503719 0.099503726 0 -165160.253 0 0
-0.099503726 0.99503719 0 0 -428.877753 -269385.505
0 0 1 0 269385.505 112803784.1
-164340.5939 -42.6749345 -26804.86149 0.99503719 -0.09950373 0 -163529.249 16310.0
16434.06057 -426.749314 -268048.5957 0.09950373 0.99503719 0 16310.0383 -2059.8
0 269385.505 112803784.1 0 0 1 26804.8615 268048.
0.99503719 0.099503726 0 165160.253 0 0
-0.099503726 0.99503719 0 0 428.877753 -269385.505
0 0 1 0 -269385.505 225607568.2
164340.5939 42.67493449 -26804.86149 0.99503719 -0.09950373 0 163529.249 -16310.0
-16434.06057 426.7493145 -268048.5957 0.09950373 0.99503719 0 -16310.0383 2059.88
0 -269385.505 225607568.2 0 0 1 -26804.8615 -268048
0 1 0 550200 0 0
-1 0 0 0 3884.832 971208
0 0 1 0 971208 323736000
0 3884.832 971208 0 -1 0 3884.832 0
-550200 0 0 1 0 0 0 55020
0 971208 323736000 0 0 1 971208 0
0 1 0 -550200 0 0
-1 0 0 0 -3884.832 971208
0 0 1 0 -971208 161868000
0 -3884.832 971208 0 -1 0 -3884.832 0 550200 0 0 1 0 0 0 -55020
0 -971208 161868000 0 0 1 -971208 0
0 1 0 -550200 0 0
-1 0 0 0 -3884.832 -971208
0 0 1 0 971208 161868000
0 -3884.832 -971208 0 -1 0 -3884.832 0
550200 0 0 1 0 0 0 -55020
0 971208 161868000 0 0 1 971208 0
0 1 0 550200 0 0
-1 0 0 0 3884.832 -971208
0 0 1 0 -971208 323736000
0 3884.832 -971208 0 -1 0 3884.832 0
-550200 0 0 1 0 0 0 55020
0 -971208 323736000 0 0 1 -971208 0
K34
K43
K54
K55
K44
BARRA 4-5
K44
K45
BARRA 3-4
K33
8/22/2019 Portico Biem Pot Rado Si Met Rico
3/19
3884.832 0 -971208 -3884.832 0 -971208
0 550200 0 0 -550200 0
-971208 0 323736000 971208 0 161868000
-3884.832 0 971208 3884.832 0 971208
0 -550200 0 0 550200 0
-971208 0 161868000 971208 0 323736000
163529.2493 16310.03713 -26804.8596 -163529.249 -16310.0371 -26804.8596
16310.03713 2059.881465 268048.5959 -16310.0371 -2059.88146 268048.5959
-26804.8596 268048.5959 225607568.2 26804.85956 -268048.596 112803784.1
-163529.249 -16310.0371 26804.85956 163529.2493 16310.03713 26804.85956
-16310.0371 -2059.88146 -268048.596 16310.03713 2059.881465 -268048.596
-26804.8596 268048.5959 112803784.1 26804.85956 -268048.596 225607568.2
163529.249 -16310.0383 26804.86149 -163529.249 16310.03829 26804.86149
-16310.0383 2059.881699 268048.5957 16310.03829 -2059.8817 268048.5957
26804.86149 268048.5957 225607568.2 -26804.8615 -268048.596 112803784.1
-163529.249 16310.03829 -26804.8615 163529.249 -16310.0383 -26804.8615
16310.03829 -2059.8817 -268048.596 -16310.0383 2059.881699 -268048.596
26804.86149 268048.5957 112803784.1 -26804.8615 -268048.596 225607568.2
3884.832 0 971208 -3884.832 0 971208
0 550200 0 0 -550200 0
971208 0 323736000 -971208 0 161868000
-3884.832 0 -971208 3884.832 0 -971208
0 -550200 0 0 550200 0971208 0 161868000 -971208 0 323736000
167414.0813 16310.03713 944403.1404 327058.4983 -0.00115928 53609.72105
16310.03713 552259.8815 268048.5959 -0.00115928 4119.763164 -0.00019245
944403.1404 268048.5959 549343568.2 53609.72105 -0.00019245 451215136.5
167414.081 -16310.0383 944403.1385
-16310.0383 552259.8817 -268048.596
944403.1385 -268048.596 549343568.2
Submatrices Kij en coordenadas globales
K11 K12
K21 K22
K22 K33
K22 K23
K32 K33
K44
Ensamblando Kii
K33 K34
K43 K44
K44 K45
K54 K55
8/22/2019 Portico Biem Pot Rado Si Met Rico
4/19
3884.832 0 -971208 -3884.832 0 -971208 0 0 0
0 550200 0 0 -550200 0 0 0 0
-971208 0 323736000 971208 0 161868000 0 0 0
-3884.832 0 971208 167414.0813 16310.03713 944403.1404 -163529.249 -16310.03713 -26804.85956
0 -550200 0 16310.03713 552259.8815 268048.5959 -16310.0371 -2059.881465 268048.5959
-971208 0 161868000 944403.1404 268048.5959 549343568.2 26804.85956 -268048.5959 112803784.1
0 0 0 -163529.249 -16310.0371 26804.85956 327058.4983 -0.001159283 53609.72105
0 0 0 -16310.0371 -2059.88146 -268048.5959 -0.00115928 4119.763164 -0.000192448
0 0 0 -26804.8596 268048.5959 112803784.1 53609.72105 -0.000192448 451215136.5
0 0 0 0 0 0 -163529.249 16310.03829 -26804.86149
0 0 0 0 0 0 16310.03829 -2059.881699 -268048.5957
0 0 0 0 0 0 26804.86149 268048.5957 112803784.1
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
3
Matriz K0
1 2 3
1 2
3
1
2
5
4
8/22/2019 Portico Biem Pot Rado Si Met Rico
5/19
Luz (m) 25
Altura pilares 5
Pendiente 10.00%
I (cm4) A (cm2)
Pilar HEB-280 19270 131
Dintel IPE-450 33740 98.8
E 2100000
0 Longitud (cm) a
Barra 1-2 500 90
Barra 2-3 1256.234453 5.710593137
Barra 3-4 1256.234453 354.2894069
Barra 4-5 500 270
Dintel 515
Peso propio 0.0776
0.062395 Viento Viento
Sobrecarga 0 Pilar 1-2 0 Pilar 4-5 0
Nieve 0.398 Dintel 2-3 0 Dintel 3-4 0
q (total) 0.537995
q (kg/cm) 5.37995
Barra 2-3qx 0.53266832 Ne2-3 334.578145 Ne3-2 334.578145
qy 5.32668317 Te2-3 3345.78146 Te3-2 3345.78146
Me2-3 700514.323 Me3-2 -700514.323
Barra 3-4qx 0.53266832 Ne3-4 -334.578145 Ne4-3 -334.578145
qy 5.32668317 Te3-4 3345.78146 Te4-3 3345.78146
Me3-4 700514.323 Me4-3 -700514.323
Barra 1-2Ne1-2 0 Ne2-1 0
Te1-2 0 Te2-1 0
Me1-2 0 Me2-1 0Barra 2-3
Ne2-3 0 Ne3-2 0
Te2-3 0 Te3-2 0
Me2-3 0 Me3-2 0
Barra 3-4Ne3-4 0 Ne4-3 0
Te3-4 0 Te4-3 0
Me3-4 0 Me4-3 0
Barra 4-5Ne4-5 0 Ne5-4 0
Te4-5 0 Te5-4 0
Me4-5 0 Me5-4 0
Barra 1-2Ne1-2 0 Ne2-1 0
Te1-2 0 Te2-1 0
Me1-2 0 Me2-1 0
Barra 2-3Ne2-3 334.5781453 Ne3-2 334.5781453
Te2-3 3345.781457 Te3-2 3345.781457
Me2-3 700514.3229 Me3-2 -700514.3229
Re1-2L Re2-1L
Re2-3L
eacc ones e empo ram en o en coor ena as oca es
Re1-2L Re2-1L
Re4-3L
Re4-5L Re5-4L
Re2-3L Re3-2L
Obtencin de cargas
Re3-2L
Re3-4L
Datos
Carga en nudo superior del pilar (peso propio)
Re por sobrecarga + nieve (coordenadas locales)
Re2-3L
Re3-4L
Datos
previos
e por cargas e v en o coor enas oca es
Re3-2L
1
2
3
4
5
8/22/2019 Portico Biem Pot Rado Si Met Rico
6/19
Barra 3-4Ne3-4 -334.5781453 Ne4-3 -334.5781453
Te3-4 3345.781457 Te4-3 3345.781457
Me3-4 700514.3229 Me4-3 -700514.3229
Barra 4-5Ne4-5 0 Ne5-4 0
Te4-5 0 Te5-4 0
Me4-5 0 Me5-4 0
0.99503719 -0.099503719 0 334.578145 5.68434E-14
0.09950372 0.99503719 0 3345.78146 3362.46875
0 0 1 700514.323 700514.3229
0.99503719 -0.099503719 0 334.578145 5.68434E-14
0.09950372 0.99503719 0 3345.78146 3362.46875
0 0 1 -700514.323 -700514.3229
0.99503719 0.099503726 0 -334.578145 2.41411E-05
-0.09950373 0.99503719 0 3345.78146 3362.46875
0 0 1 700514.323 700514.3229
0.99503719 0.099503726 0 -334.578145 2.41411E-05
-0.09950373 0.99503719 0 3345.78146 3362.468750 0 1 -700514.323 -700514.3229
0 -1 0 0 0
1 0 0 0 0
0 0 1 0 0
0 -1 0 0 0
1 0 0 0 0
0 0 1 0 0
0.99503719 -0.099503719 0 0 0
0.09950372 0.99503719 0 0 0
0 0 1 0 0
0.99503719 -0.099503719 0 0 0
0.09950372 0.99503719 0 0 0
0 0 1 0 0
0.99503719 0.099503726 0 0 0
-0.09950373 0.99503719 0 0 0
0 0 1 0 0
0.99503719 0.099503726 0 0 0
-0.09950373 0.99503719 0 0 0
0 0 1 0 0
0 1 0 0 0
-1 0 0 0 0
0 0 1 0 0
0 1 0 0 0
-1 0 0 0 0
0 0 1 0 0
Re4-3G
Re por cargas de viento (coordenadas globales)
Re1-2G
Re2-1G
Re2-3G
Re3-2G
Re3-4G
Re4-5G
Re3-4G
Re4-5L Re5-4L
Re por sobrecarga+nieve (coordenadas globales)
Re2-3G
Re3-2G
Re3-4L Re4-3L
Re4-3G
Re4-5G
8/22/2019 Portico Biem Pot Rado Si Met Rico
7/19
0
0
0
0 -1 0 -515 0
1 0 0 0 -515
0 0 1 0 0
00
0
0 1 0 515 0
-1 0 0 0 -515
0 0 1 0 0
0
0
0
0 0 0
0 0 0
0 0 0
0 5.68434E-14 0 0 -5.6843E-14
-515 3362.46875 0 0 -3877.46875
0 700514.3229 0 0 -700514.323
0 5.68434E-14 2.41411E-05 0 0 -2.4141E-05
0 3362.46875 3362.46875 0 0 -6724.9375
0 -700514.3229 700514.3229 0 0 0
0 2.41411E-05 0 0 -2.4141E-05
-515 3362.46875 0 0 -3877.46875
0 -700514.3229 0 0 700514.323
0 0 0
0 0 0
0 0 0
P4
P5
P1
P2
P3
Estado de carga 2
Pa2
Cargas (coordenadas globales)
Pa3
Pa1
Pa4
Pa5
8/22/2019 Portico Biem Pot Rado Si Met Rico
8/19
167414.0813 16310.03713 944403.1404 -163529.2493 -16310.03713 -26804.85956 0 0
16310.03713 552259.8815 268048.5959 -16310.03713 -2059.881465 268048.5959 0 0
944403.1404 268048.5959 549343568.2 26804.85956 -268048.5959 112803784.1 0 0
-163529.2493 -16310.03713 26804.85956 327058.4983 -0.001159283 53609.72105 -163529.249 16310.03829 2680
-16310.03713 -2059.881465 -268048.5959 -0.001159283 4119.763164 -0.000192448 16310.03829 -2059.881699 2680
-26804.85956 268048.5959 112803784.1 53609.72105 -0.000192448 451215136.5 -26804.86149 -268048.5957 11280 0 0 -163529.249 16310.03829 -26804.86149 167414.081 -16310.03829 9444
0 0 0 16310.03829 -2059.881699 -268048.5957 -16310.03829 552259.8817 -2680
0 0 0 26804.86149 268048.5957 112803784.1 944403.1385 -268048.5957 5493
-3884.832 0 -971208 0 0 0 0 0
0 -550200 0 0 0 0 0 0
971208 0 161868000 0 0 0 0 0
0 0 0 0 0 0 -3885 0 -9
0 0 0 0 0 0 0 -550200
0 0 0 0 0 0 971208 0 161
Matriz P Matriz K-1-5.68434E-14 0.000267708 1.22937E-07 -4.67607E-07 0.000253706 0.000115474 2.49742E-07 0.000239598 -1.
-3877.46875 1.22937E-07 1.81746E-06 -4.91749E-10 2.13788E-07 9.0876E-07 -8.44566E-10 1.22937E-07 5.
-700514.3229 -4.67607E-07 -4.91749E-10 3.04473E-09 -5.00003E-07 3.90877E-07 -9.98969E-10 -5.31972E-07 4.
-2.41411E-05 0.000253706 2.13788E-07 -5.00003E-07 0.000256826 4.42121E-12 2.49377E-07 0.000253706 -2.
-6724.9375 0.000115474 9.0876E-07 3.90877E-07 4.42121E-12 0.001208822 -3.78905E-16 -0.000115474 9
0 2.49742E-07 -8.44566E-10 -9.98969E-10 2.49377E-07 -3.78913E-16 2.71677E-09 2.49742E-07 8.4
-2.41411E-05 0.000239598 1.22937E-07 -5.31972E-07 0.000253706 -0.000115474 2.49742E-07 0.000267708 -1.
-3877.46875 -1.22937E-07 5.78687E-11 4.91749E-10 -2.13788E-07 9.0876E-07 8.44566E-10 -1.22937E-07 1.
700514.3229 -5.31972E-07 -4.91749E-10 9.53581E-10 -5.00003E-07 -3.90877E-07 -9.98969E-10 -4.67607E-07 4.
d2x -0.821643668 -0.822 Rx 7167.591289
d2y -0.013158738 -0.013 Ry 7239.937478
q2 -0.004093504 -0.004 M -1460594.183
d3x -4.40587E-08 0.000 Rx -7167.59124
d3y -8.683931795 -8.684 Ry 7239.937523
q3 -9.36039E-12 0.000 M 1460594.167
d4x 0.821643643 0.822
d4y -0.013158738 -0.013
q4 0.004093504 0.004
Matriz K
Matriz K1
d2
d3
d4
Reacciones (kg y cm)
R1
R7
Desplazamientos (cm y rad)
8/22/2019 Portico Biem Pot Rado Si Met Rico
9/19
550200 0 0 0 1 0 0 550200 0
0 3884.832 971208 -1 0 0 -3884.832 0 971208
0 971208 323736000 0 0 1 -971208 0 323736000
-550200 0 0 0 1 0 0 -550200 0
0 -3884.832 971208 -1 0 0 3884.832 0 971208
0 -971208 161868000 0 0 1 971208 0 161868000
-550200 0 0 0 1 0 0 -550200 0
0 -3884.832 -971208 -1 0 0 3884.832 0 -971208
0 971208 161868000 0 0 1 -971208 0 161868000
550200 0 0 0 1 0 0 550200 0
0 3884.832 -971208 -1 0 0 -3884.832 0 -971208
0 -971208 323736000 0 0 1 971208 0 323736000
165160.253 0 0 0.99503719 0.099503719 0 164340.5941 16434.05939 0
0 428.8777535 269385.505 -0.09950372 0.99503719 0 -42.6749314 426.7493148 269385.505
0 269385.505 225607568.2 0 0 1 -26804.8596 268048.5959 225607568.2
-165160.253 0 0 0.99503719 0.099503719 0 -164340.594 -16434.0594 0
0 -428.877753 269385.505 -0.09950372 0.99503719 0 42.67493143 -426.749315 269385.505
0 -269385.505 112803784.1 0 0 1 26804.85956 -268048.596 112803784.1
-165160.253 0 0 0.99503719 0.099503719 0 -164340.594 -16434.0594 0
0 -428.877753 -269385.505 -0.09950372 0.99503719 0 42.67493143 -426.749315 -269385.5050 269385.505 112803784.1 0 0 1 -26804.8596 268048.5959 112803784.1
165160.253 0 0 0.99503719 0.099503719 0 164340.5941 16434.05939 0
0 428.8777535 -269385.505 -0.09950372 0.99503719 0 -42.6749314 426.7493148 -269385.505
0 -269385.505 225607568.2 0 0 1 26804.85956 -268048.596 225607568.2
165160.253 0 0 0.99503719 -0.09950373 0 164340.5939 -16434.0606 0
0 428.8777535 269385.505 0.099503726 0.99503719 0 42.67493449 426.7493145 269385.505
0 269385.505 225607568.2 0 0 1 26804.86149 268048.5957 225607568.2
-165160.253 0 0 0.99503719 -0.09950373 0 -164340.594 16434.06057 0
0 -428.877753 269385.505 0.099503726 0.99503719 0 -42.6749345 -426.749314 269385.505
0 -269385.505 112803784.1 0 0 1 -26804.8615 -268048.596 112803784.1
-165160.253 0 0 0.99503719 -0.09950373 0 -164340.594 16434.06057 0
0 -428.877753 -269385.505 0.099503726 0.99503719 0 -42.6749345 -426.749314 -269385.505
0 269385.505 112803784.1 0 0 1 26804.86149 268048.5957 112803784.1
165160.253 0 0 0.99503719 -0.09950373 0 164340.5939 -16434.0606 0
0 428.8777535 -269385.505 0.099503726 0.99503719 0 42.67493449 426.7493145 -269385.505
0 -269385.505 225607568.2 0 0 1 -26804.8615 -268048.596 225607568.2
550200 0 0 0 -1 0 0 -550200 0
0 3884.832 971208 1 0 0 3884.832 0 971208
0 971208 323736000 0 0 1 971208 0 323736000
-550200 0 0 0 -1 0 0 550200 0
0 -3884.832 971208 1 0 0 -3884.832 0 971208
0 -971208 161868000 0 0 1 -971208 0 161868000
-550200 0 0 0 -1 0 0 550200 0
0 -3884.832 -971208 1 0 0 -3884.832 0 -971208
0 971208 161868000 0 0 1 971208 0 161868000
550200 0 0 0 -1 0 0 -550200 0
0 3884.832 -971208 1 0 0 3884.832 0 -9712080 -971208 323736000 0 0 1 -971208 0 323736000
C55
C44
BARRA 4-5
C44
C45
C32
BARRA 3-4
C33
C34
C43
C54
C21
C22
C33
Matrices Cij para la obtencin de los esfuerzos en las barras
BARRA 1-2
C11
C12
BARRA 2-3
C22
C23
8/22/2019 Portico Biem Pot Rado Si Met Rico
10/19
Nudo 2 Nudo 3 Nudo 4
dx -0.8216437 -4.406E-08 0.82164364
dy -0.0131587 -8.6839318 -0.0131587
q -0.0040935 -9.36E-12 0.0040935
N T M N T M
Re 1-2 0 0 0 Re 3-4 -334.57815 3345.78146 700514.323
Re 2-1 0 0 0 Re 4-3 -334.57815 3345.78146 -700514.32
Re 2-3 334.578145 3345.78146 700514.323 Re 4-5 0 0 0
Re 3-2 334.578145 3345.78146 -700514.32 Re 5-4 0 0 0
N12 7240 N23 7801 N34 7132 N45 7240
T12 -7168 T23 5978 T34 713 T45 7168
M12 -1460594 M23 2123201 M34 -1183936 M45 2123201
N21 -7240 N32 -7132 N43 -7801 N54 -7240
T21 7168 T32 713 T43 5978 T54 -7168
M21 -2123201 M32 1183936 M43 -2123201 M54 1460594
N12 0 0 550200 0 0 0 -550200 0 -0.8216437
T12 0 -3884.832 0 971208 0 3884.832 0 971208 -0.0131587M12 0 -971208 0 323736000 0 971208 0 161868000 -0.0040935
N21 0 0 -550200 0 0 0 550200 0 -0.8216437
T21 0 3884.832 0 -971208 0 -3884.832 0 -971208 -0.0131587
M21 0 -971208 0 161868000 0 971208 0 323736000 -0.0040935
N23 334.578145 164340.594 16434.0594 0 -0.8216437 -164340.59 -16434.059 0 -4.406E-08
T23 3345.78146 -42.674931 426.749315 269385.505 -0.0131587 42.6749314 -426.74931 269385.505 -8.6839318
M23 700514.323 -26804.86 268048.596 225607568 -0.0040935 26804.8596 -268048.6 112803784 -9.36E-12
N32 334.578145 -164340.59 -16434.059 0 -0.8216437 164340.594 16434.0594 0 -4.406E-08
T32 3345.78146 42.6749314 -426.74931 -269385.5 -0.0131587 -42.674931 426.749315 -269385.5 -8.6839318
M32 -700514.32 -26804.86 268048.596 112803784 -0.0040935 26804.8596 -268048.6 225607568 -9.36E-12
N34 -334.57815 164340.594 -16434.061 0 -4.406E-08 -164340.59 16434.0606 0 0.82164364
T34 3345.78146 42.6749345 426.749314 269385.505 -8.6839318 -42.674934 -426.74931 269385.505 -0.0131587
M34 700514.323 26804.8615 268048.596 225607568 -9.36E-12 -26804.861 -268048.6 112803784 0.0040935
N43 -334.57815 -164340.59 16434.0606 0 -4.406E-08 164340.594 -16434.061 0 0.82164364
T43 3345.78146 -42.674934 -426.74931 -269385.5 -8.6839318 42.6749345 426.749314 -269385.5 -0.0131587M43 -700514.32 26804.8615 268048.596 112803784 -9.36E-12 -26804.861 -268048.6 225607568 0.0040935
N45 0 0 -550200 0 0.82164364 0 550200 0 0
T45 0 3884.832 0 971208 -0.0131587 -3884.832 0 971208 0
M45 0 971208 0 323736000 0.0040935 -971208 0 161868000 0
N54 0 0 550200 0 0.82164364 0 -550200 0 0
T54 0 -3884.832 0 -971208 -0.0131587 3884.832 0 -971208 0
M54 0 971208 0 161868000 0.0040935 -971208 0 323736000 0
Barra 4-5
Desplazamientos (cm y rad)
Clculo de los esfuerzos en las barras
Barra 1-2 Barra 2-3 Barra 3-4
Resultados
Reacciones en coordenadas locales (kg y cm)
Clculosprevios
8/22/2019 Portico Biem Pot Rado Si Met Rico
11/19
Longitud (cm) a N (kg) x
Barra 1-2 500 90 7240 0.928057168
Barra 2-3 1256.234453 5.710593137 7801 1
Barra 3-4 1256.234453 354.2894069 7801 1
Barra 4-5 500 270 7240 0.928057174
N0 7801 Axil mx.
0 -1 0 0 0 0
1 0 0 0 36 1500
0 0 1 0 1500 1000000
0 -36 -1500 0 1 0 36
0 0 0 -1 0 0 0
0 1500 1000000 0 0 1 -1500
0 -1 0 0 0 0
1 0 0 0 -36 1500
0 0 1 0 -1500 -250000
0 36 -1500 0 1 0 -36
0 0 0 -1 0 0 0
0 -1500 -250000 0 0 1 1500
0 -1 0 0 0 01 0 0 0 -36 -1500
0 0 1 0 1500 -250000
0 36 1500 0 1 0 -36
0 0 0 -1 0 0 0
0 1500 -250000 0 0 1 -1500
0 -1 0 0 0 0
1 0 0 0 36 -1500
0 0 1 0 -1500 1000000
0 -36 1500 0 1 0 36
0 0 0 -1 0 0 0
0 -1500 1000000 0 0 1 1500
0.99503719 -0.099503719 0 0 0 0
0.099503719 0.99503719 0 0 36 3768.703358
0 0 1 0 3768.703358 63125000 -3.582133881 -374.9999996 0.99503719 0.099503719 0 0.356435643 -
0 35.82133885 3750 -0.099503719 0.99503719 0 -3.564356432 3
0 3768.703358 6312500 0 0 1 -374.9999996
0.99503719 -0.099503719 0 0 0 0
0.099503719 0.99503719 0 0 -36 3768.703358
0 0 1 0 -3768.703358 -1578125
0 3.582133881 -374.9999996 0.99503719 0.099503719 0 -0.356435643 3
0 -35.82133885 3750 -0.099503719 0.99503719 0 3.564356432 -
0 -3768.703358 -1578125 0 0 1 374.9999996
0.99503719 -0.099503719 0 0 0 0
0.099503719 0.99503719 0 0 -36 -3768.703358
0 0 1 0 3768.703358 -1578125
0 3.582133881 374.9999996 0.99503719 0.099503719 0 -0.356435643 3
0 -35.82133885 -3750 -0.099503719 0.99503719 0 3.564356432 -
0 3768.703358 -1578125 0 0 1 -374.9999996
0.99503719 -0.099503719 0 0 0 0
0.099503719 0.99503719 0 0 36 -3768.703358
0 0 1 0 -3768.703358 6312500
0 -3.582133881 374.9999996 0.99503719 0.099503719 0 0.356435643 -
0 35.82133885 -3750 -0.099503719 0.99503719 0 -3.564356432 3
0 -3768.703358 6312500 0 0 1 374.9999996
Kg32
Kg33
Obtencin de la matriz Kg
Barra 1-2
Kg11
Kg12
Kg21
Kg22
Barra 2-3
Kg22
Kg23
1
2
3
4
5
8/22/2019 Portico Biem Pot Rado Si Met Rico
12/19
0.99503719 0.099503726 0 0 0 0
-0.099503726 0.99503719 0 0 36 3768.703358
0 0 1 0 3768.703358 6312500
0 3.582134138 375.0000265 0.99503719 -0.099503726 0 0.356435694
0 35.82133882 3749.999997 0.099503726 0.99503719 0 3.564356685
0 3768.703358 6312500 0 0 1 375.0000265
0.99503719 0.099503726 0 0 0 0
-0.099503726 0.99503719 0 0 -36 3768.7033580 0 1 0 -3768.703358 -1578125
0 -3.582134138 375.0000265 0.99503719 -0.099503726 0 -0.356435694
0 -35.82133882 3749.999997 0.099503726 0.99503719 0 -3.564356685
0 -3768.703358 -1578125 0 0 1 -375.0000265
0.99503719 0.099503726 0 0 0 0
-0.099503726 0.99503719 0 0 -36 -3768.703358
0 0 1 0 3768.703358 -1578125
0 -3.582134138 -375.0000265 0.99503719 -0.099503726 0 -0.356435694
0 -35.82133882 -3749.999997 0.099503726 0.99503719 0 -3.564356685
0 3768.703358 -1578125 0 0 1 375.0000265
0.99503719 0.099503726 0 0 0 0
-0.099503726 0.99503719 0 0 36 -3768.703358
0 0 1 0 -3768.703358 6312500
0 3.582134138 -375.0000265 0 .99503719 -0.099503726 0 0.356435694
0 35.82133882 -3749.999997 0.099503726 0.99503719 0 3.564356685 0 -3768.703358 6312500 0 0 1 -375.0000265
0 1 0 0 0 0
-1 0 0 0 36 1500
0 0 1 0 1500 1000000
0 36 1500 0 -1 0 36
0 0 0 1 0 0 0
0 1500 1000000 0 0 1 1500
0 1 0 0 0 0
-1 0 0 0 -36 1500
0 0 1 0 -1500 -250000
0 -36 1500 0 -1 0 -36
0 0 0 1 0 0 0
0 -1500 -250000 0 0 1 -1500
0 1 0 0 0 0-1 0 0 0 -36 -1500
0 0 1 0 1500 -250000
0 -36 -1500 0 -1 0 -36
0 0 0 1 0 0 0
0 1500 -250000 0 0 1 1500
0 1 0 0 0 0
-1 0 0 0 36 -1500
0 0 1 0 -1500 1000000
0 36 -1500 0 -1 0 36
0 0 0 1 0 0 0
0 -1500 1000000 0 0 1 -1500
Kg44
Kg45
Kg54
Kg55
Kg44
Barra 4-5
Barra 3-4
Kg33
Kg34
Kg43
8/22/2019 Portico Biem Pot Rado Si Met Rico
13/19
36 0 -1500 0.002227337 0 -0.092805717
0 0 0 0 0 0
-1500 0 1000000 -0.092805717 0 61.87047787
-36 0 -1500 -0.002227337 0 -0.092805717
0 0 0 0 0 0
1500 0 -250000 0.092805717 0 -15.46761947
-36 0 1500 -0.002227337 0 0.0928057170 0 0 0 0 0
-1500 0 -250000 -0.092805717 0 -15.46761947
36 0 1500 0.002227337 0 0.092805717
0 0 0 0 0 0
1500 0 1000000 0.092805717 0 61.87047787
0.356435643 -3.564356432 -374.9999996 9.45778E-06 -9.45778E-05 -0.009950372
-3.564356432 35.64356436 3750 -9.45778E-05 0.000945778 0.099503719
-374.9999996 3750 6312500 -0.009950372 0.099503719 167.497927
-0.356435643 3.564356432 -374.9999996 -9.45778E-06 9.45778E-05 -0.009950372
3.564356432 -35.64356436 3750 9.45778E-05 -0.000945778 0.099503719
374.9999996 -3750 -1578125 0.009950372 -0.099503719 -41.87448175
-0.356435643 3.564356432 374.9999996 -9.45778E-06 9.45778E-05 0.009950372
3.564356432 -35.64356436 -3750 9.45778E-05 -0.000945778 -0.099503719
-374.9999996 3750 -1578125 -0.009950372 0.099503719 -41.874481750.356435643 -3.564356432 374.9999996 9.45778E-06 -9.45778E-05 0.009950372
-3.564356432 35.64356436 -3750 -9.45778E-05 0 .000945778 -0.099503719
374.9999996 -3750 6312500 0.009950372 -0.099503719 167.497927
0.356435694 3.564356685 375.0000265 9.45778E-06 9.45778E-05 0.009950373
3.564356685 35.64356431 3749.999997 9.45778E-05 0.000945778 0.099503719
375.0000265 3749.999997 6312500 0.009950373 0.099503719 167.497927
-0.356435694 -3.564356685 375.0000265 -9.45778E-06 -9.45778E-05 0.009950373
-3.564356685 -35.64356431 3749.999997 -9.45778E-05 -0.000945778 0.099503719
-375.0000265 -3749.999997 -1578125 -0.009950373 -0.099503719 -41.87448175
-0.356435694 -3.564356685 -375.0000265 -9.45778E-06 -9.45778E-05 -0.009950373
-3.564356685 -35.64356431 -3749.999997 -9.45778E-05 -0.000945778 -0.099503719
375.0000265 3749.999997 -1578125 0.009950373 0.099503719 -41.87448175
0.356435694 3.564356685 -375.0000265 9.45778E-06 9.45778E-05 -0.009950373
3.564356685 35.64356431 -3749.999997 9.45778E-05 0.000945778 -0.099503719
-375.0000265 -3749.999997 6312500 -0.009950373 -0.099503719 167.497927
36 0 1500 0.002227337 0 0.092805717
0 0 0 0 0 0
1500 0 1000000 0.092805717 0 61.87047825
-36 0 1500 -0.002227337 0 0.092805717
0 0 0 0 0 0
-1500 0 -250000 -0.092805717 0 -15.46761956
-36 0 -1500 -0.002227337 0 -0.092805717
0 0 0 0 0 0
1500 0 -250000 0.092805717 0 -15.46761956
36 0 -1500 0.002227337 0 -0.092805717
0 0 0 0 0 0
-1500 0 1000000 -0.092805717 0 61.87047825
0.002236795 -9.45778E-05 0.082855345 1.89156E-05 6.71476E-12
-9.45778E-05 0.000945778 0.099503719 6.71476E-12 0.001891556
0.082855345 0.099503719 229.3684049 0.019900744 -7.9469E-11
0.002236795 9.45778E-05 0.082855345
9.45778E-05 0.000945778 -0.099503719
0.082855345 -0.099503719 229.3684053
Kg43
Kg33
Kg44
Kg45
Kg54
Kg55
Kg22
Kg34
Kg44
Kg44
Kg32
Kg33
Kg12
Kg21
Kg22
Kg22
Kg23
Kg11
x.Kgij/30.L
Kg33
8/22/2019 Portico Biem Pot Rado Si Met Rico
14/19
-1500
0
1000000
-1500
0
-250000
1500
0
-250000
1500
0
1000000
-375
3750
6312500
-375
3750
-1578125
375
-3750
-1578125
375
-3750
6312500
8/22/2019 Portico Biem Pot Rado Si Met Rico
15/19
375.000026
3750
6312500
375.000026
3750
-1578125
-375.000026
-3750
-1578125
-375.000026
-37506312500
1500
0
1000000
1500
0
-250000
-1500
0
-250000
-1500
0
1000000
8/22/2019 Portico Biem Pot Rado Si Met Rico
16/19
0.002236795 -9.45778E-05 0.082855345 -9.45778E-06 9.45778E-05 -0.009950372 0 0
-9.45778E-05 0.000945778 0.099503719 9.45778E-05 -0.000945778 0.099503719 0 0
0.082855345 0.099503719 229.3684049 0.009950372 -0.099503719 -41.87448175 0 0
-9.45778E-06 9.45778E-05 0.009950372 1.89156E-05 6.71476E-12 0.019900744 -9.45778E-06 -9.45778E-05 0
9.45778E-05 -0.000945778 -0.099503719 6.71476E-12 0.001891556 -7.9469E-11 -9.45778E-05 -0.000945778 0
-0.009950372 0.099503719 -41.87448175 0.019900744 -7.9469E-11 334.995854 -0.009950373 -0.099503719 -4
0 0 0 -9.45778E-06 -9.45778E-05 -0.009950373 0.002236795 9.45778E-05 0
0 0 0 -9.45778E-05 -0.000945778 -0.099503719 9.45778E-05 0.000945778 -0
0 0 0 0.009950373 0.099503719 -41.87448175 0.082855345 -0.099503719 2
0.000267708 1.22937E-07 -4.67607E-07 0.000253706 0.000115474 2.49742E-07 0.000239598 -1.22937E-07
1.22937E-07 1.81746E-06 -4.91749E-10 2.13788E-07 9.0876E-07 -8.44566E-10 1.22937E-07 5.78687E-11
-4.67607E-07 -4.91749E-10 3.04473E-09 -5.00003E-07 3.90877E-07 -9.98969E-10 -5.31972E-07 4.91749E-10
0.000253706 2.13788E-07 -5.00003E-07 0.000256826 4.42121E-12 2.49377E-07 0.000253706 -2.13788E-07
0.000115474 9.0876E-07 3.90877E-07 4.42121E-12 0.001208822 -3.78905E-16 -0.000115474 9.0876E-07
2.49742E-07 -8.44566E-10 -9.98969E-10 2.49377E-07 -3.78913E-16 2.71677E-09 2.49742E-07 8.44566E-10
0.000239598 1.22937E-07 -5.31972E-07 0.000253706 -0.000115474 2.49742E-07 0.000267708 -1.22937E-07
-1.22937E-07 5.78687E-11 4.91749E-10 -2.13788E-07 9.0876E-07 8.44566E-10 -1.22937E-07 1.81746E-06
-5.31972E-07 -4.91749E-10 9.53581E-10 -5.00003E-07 -3.90877E-07 -9.98969E-10 -4.67607E-07 4.91749E-10
5.66089E-07 -1.32099E-07 -0.000104485 -4.95186E-09 2.1468E-07 0.000125545 4.76038E-07 -8.25805E-08
1.5468E-10 7.35055E-10 2.53067E-08 1.47011E-10 -9.48215E-18 -5.90963E-08 1.5468E-10 -7.35055E-10
-7.41985E-10 -1.6965E-10 6.57536E-07 1.98075E-11 5.37375E-10 -5.0218E-07 -1.13316E-09 -3.67725E-10
5.21131E-07 -2.44409E-08 -0.00010153 -4.88819E-09 8.19999E-15 0.000125519 5.21131E-07 2.44409E-08
4.0492E-07 -1.11445E-06 -2.09695E-05 8.05822E-15 2.22889E-06 -3.76244E-14 -4.0492E-07 -1.11445E-06
4.46541E-10 1.70094E-10 -3.19806E-07 3.40188E-11 -8.43845E-19 9.93594E-07 4.46541E-10 -1.70094E-10
4.76038E-07 8.25805E-08 -9.85966E-05 -4.95186E-09 -2.1468E-07 0.000125545 5.66089E-07 1.32099E-07 -
-1.5468E-10 -7.35055E-10 -2.53067E-08 -1.47011E-10 9.48215E-18 5.90963E-08 -1.5468E-10 7.35055E-10
-1.13316E-09 3.67725E-10 2.50346E-07 1.98075E-11 -5.37375E-10 -5.0218E-07 -7.41985E-10 1.6965E-10
Matriz K-1
Matriz D
Matriz Kg
8/22/2019 Portico Biem Pot Rado Si Met Rico
17/19
U1 U2 U2N U3 U3N U4 U4N U5
1 -7.64989E-05 -0.577334087 -8.81475E-07 -0.577323403 -9.15854E-07 -0.577331482 -1.03417E-06 -
1 -8.02641E-09 -6.0575E-05 -2.676E-10 -0.000175265 -1.87935E-10 -0.00011847 -1.29475E-10 -
1 4.03846E-07 0.003047809 2.4931E-09 0.001632859 2.49543E-09 0.001573058 2.96295E-09 0
1 -7.65023E-05 -0.577360324 -8.8159E-07 -0.577399316 -9.15935E-07 -0.577382794 -1.03422E-06 -
1 -2.38608E-13 -1.80077E-09 -3.79069E-15 -2.48272E-09 -5.02496E-15 -3.16761E-09 -6.57703E-15 -
1 3.5491E-07 0.002678491 1.76652E-10 0.000115698 -1.46474E-09 -0.000923334 -2.45885E-09 -01 -7.64989E-05 -0.577334087 -8.81475E-07 -0.577323403 -9.15854E-07 -0.577331481 -1.03417E-06 -
1 8.02641E-09 6.0575E-05 2.676E-10 0.000175265 1.87935E-10 0.00011847 1.29475E-10 7
1 4.03846E-07 0.003047809 2.4931E-09 0.001632859 2.49543E-09 0.001573058 2.96295E-09 0
LANDA 0.000132504 1.52683E-06 1.58636E-06 1.79127E-06
P 7546.962582 654951.844 630375.0375 558264.0168
U6 U6N U7 U7N U8 U8N U9
-1.10705E-06 -0.577340475 -1.13791E-06 -0.577341497 -1.14913E-06 -0.57734185 -1.15297E-06 -
-9.87502E-11 -5.14995E-05 -8.63145E-11 -4.37932E-05 -8.187E-11 -4.11329E-05 -8.03576E-11 -
3.26221E-09 0.001701285 3.39017E-09 0.001720066 3.43682E-09 0.001726718 3.45282E-09 0
-1.10709E-06 -0.577362781 -1.13795E-06 -0.577360465 -1.14916E-06 -0.577359666 -1.153E-06 -
-7.74425E-15 -4.03873E-09 -8.59218E-15 -4.3594E-09 -9.32998E-15 -4.68754E-09 -1.00835E-14 -
-2.95715E-09 -0.001542195 -3.15575E-09 -0.001601126 -3.22631E-09 -0.001620954 -3.25027E-09 -
-1.10705E-06 -0.577340474 -1.13791E-06 -0.577341497 -1.14913E-06 -0.577341849 -1.15297E-06 -
9.87502E-11 5.14995E-05 8.63145E-11 4.37932E-05 8.187E-11 4.11329E-05 8.03576E-11 43.26221E-09 0.001701285 3.39017E-09 0.001720066 3.43682E-09 0.001726718 3.45282E-09 0
LANDA 1.9175E-06 1.97096E-06 1.99038E-06 1.99703E-06
P 521513.2202 507368.1819 502417.2529 500743.6744
U10 U10N U11 U11N U12 U12N U13
-1.15426E-06 -0.577342008 -1.15468E-06 -0.577342021 -1.15483E-06 -0.577342026 -1.15487E-06 -
-7.98521E-11 -3.99408E-05 -7.96842E-11 -3.98421E-05 -7.96286E-11 -3.98094E-05 -7.96102E-11 -
3.45818E-09 0.001729732 3.45997E-09 0.001729983 3.46056E-09 0.001730066 3.46075E-09 0
-1.15429E-06 -0.577359307 -1.15472E-06 -0.577359277 -1.15486E-06 -0.577359268 -1.15491E-06 -
-1.09136E-14 -5.45882E-09 -1.18533E-14 -5.92666E-09 -1.29267E-14 -6.46257E-09 -1.41563E-14 -
-3.25827E-09 -0.001629737 -3.26092E-09 -0.00163046 -3.2618E-09 -0.0016307 -3.26209E-09 -
-1.15426E-06 -0.577342007 -1.15468E-06 -0.57734202 -1.15483E-06 -0.577342024 -1.15487E-06 -
7.98521E-11 3.99408E-05 7.96842E-11 3.98421E-05 7.96286E-11 3.98094E-05 7.96102E-11 3
3.45818E-09 0.001729732 3.45997E-09 0.001729983 3.46056E-09 0.001730066 3.46075E-09 0
LANDA 1.99926E-06 2E-06 2.00025E-06 2.00033E-06P 500185.3361 500000.0032 499938.6058 499918.2818
8/22/2019 Portico Biem Pot Rado Si Met Rico
18/19
U14 U14N U15 U15N U16 U16N U17
-1.15489E-06 -0.577342028 -1.15489E-06 -0.577342028 -1.1549E-06 -0.577342028 -1.1549E-06 -
-7.96041E-11 -3.9795E-05 -7.96021E-11 -3.97938E-05 -7.96014E-11 -3.97934E-05 -7.96012E-11 -
3.46082E-09 0.001730103 3.46084E-09 0.001730106 3.46085E-09 0.001730107 3.46085E-09 0
-1.15492E-06 -0.577359263 -1.15493E-06 -0.577359263 -1.15493E-06 -0.577359263 -1.15493E-06 -
-1.5566E-14 -7.7816E-09 -1.71826E-14 -8.58972E-09 -1.90367E-14 -9.51659E-09 -2.11632E-14 -
-3.26219E-09 -0.001630805 -3.26222E-09 -0.001630814 -3.26223E-09 -0.001630817 -3.26223E-09 -
-1.15489E-06 -0.577342026 -1.15489E-06 -0.577342026 -1.1549E-06 -0.577342026 -1.1549E-06 -7.96041E-11 3.9795E-05 7.96021E-11 3.97938E-05 7.96014E-11 3.97934E-05 7.96012E-11 3
3.46082E-09 0.001730103 3.46084E-09 0.001730106 3.46085E-09 0.001730107 3.46085E-09 0
LANDA 2.00035E-06 2.00036E-06 2.00037E-06 2.00037E-06
P 499911.5562 499909.3308 499908.5946 499908.351
8/22/2019 Portico Biem Pot Rado Si Met Rico
19/19
Longitud (cm) a N (kg)
Barra 1-2 500 90 7240
Barra 2-3 1256.23445 5.710593137 7801
Barra 3-4 1256.23445 354.2894069 7801
Barra 4-5 500 270 7240
7801
I (cm4) A (cm2)
Pilar HEB-280 19270 131 acrit 64.0811512Dintel IPE-450 33740 98.8
E 2100000
Peuler Pcrit b
Barra 1-2 1597573 463944 1.856
Barra 2-3 443121 499908 0.941
Barra 3-4 443121 499908 0.941
Barra 4-5 1597573 463944 1.856
Obtencin de acrit y b
Axil mximo (N0)
Resultados
1
2
3
4
5