Introduccion Al Analisis Estructural Con Matrices Kardestuncer Hayrettin
Analisis Matrices
44
L1= 5.25 L2= 6.25 L3= 5.25 W1= 550 1263.28125 W2= 550 1790.3645833333 Formula usada W3= 550 1263.28125 WL^2/12 Tramo 1 V 0 1443.75 M 1 1263.28125 V 0 1443.75 M 2 -1263.28125 Tramo 2 V 0 1718.75 M 2 1790.36458333 V 0 1718.75 M 3 -1790.36458333 Tramo 3 V 0 1443.75 M 3 1263.28125 V 0 1443.75 M 4 -1263.28125
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Transcript of Analisis Matrices
L1= 5.25L2= 6.25L3= 5.25
W1= 550 1263.28125W2= 550 1790.3645833333 Formula usadaW3= 550 1263.28125 WL^2/12
Tramo 1V 0 1443.75M 1 1263.28125V 0 1443.75M 2 -1263.28125
Tramo 2V 0 1718.75M 2 1790.36458333V 0 1718.75M 3 -1790.36458333
Tramo 3V 0 1443.75M 3 1263.28125V 0 1443.75M 4 -1263.28125
0 1 0 20.083 0.218 -0.083 0.218 0 1443.75
k1=0.218 0.762 -0.218 0.381 1
f1=1263.28125
-0.083 -0.218 0.083 -0.218 0 1443.750.218 0.381 -0.218 0.762 2 -1263.28125
0 2 0 30.049 0.154 -0.049 0.154 0 1718.75
k2=0.154 0.640 -0.154 0.320 2
f2=1790.364583
-0.049 -0.154 0.049 -0.154 0 1718.750.154 0.320 -0.154 0.640 3 -1790.36458
0 3 0 40.083 0.218 -0.083 0.218 0 1443.75
k3=0.218 0.762 -0.218 0.381 3
f3=1263.28125
-0.083 -0.218 0.083 -0.218 0 1443.750.218 0.381 -0.218 0.762 4 -1263.28125
0102
1 2 30 0.762 0.381 02
S=0.381 1.402 0.320
0 0 0.320 1.4023 0 0 0.381
Pf=0304 P-Pf=S*∆
P=0menosPf*S^-1=∆
1.534347493 -0.443694987 0.117202449
S^-1*Pf=-0.443694987 0.887389973 -0.2344048990.117202449 -0.234404899 0.887389973
-0.058601225 0.117202449 -0.443694987
40 10 2
0.381 30.762 4
1263.28125 1527.0833333 2
-527.0833333 3-1263.28125 4
-0.058601225 1263.28125 1716.70256 -1716.70256 10.117202449
X527.0833333
= --117.291834
=117.291834 2
= ∆-0.443694987 -527.0833333 117.291834 -117.291834 31.534347493 -1263.28125 -1716.70256 1716.70256 4
1 2 3 4 5 6 7 80.08293 0.21769 -0.08293 0.21769 0 0 0 00.21769 0.7619 -0.21769 0.38095 0 0 0 0-0.0829 -0.2177 0.132 -0.064 -0.04915 0.1536 0 00.21769 0.38095 -0.064 1.402 -0.1536 0.32 0 0
0 0 -0.04915 -0.1536 0.132 0.064 -0.08293 0.217690 0 0.1536 0.32 0.064 1.402 -0.21769 0.380950 0 0 0 -0.08293 -0.21769 0.08293 -0.217690 0 0 0 0.21769 0.38095 -0.21769 0.7619
2 4 6 8 1 3 5 70.7619 0.38095 0 0 0.21769 -0.21769 0 0
0.38095 1.402 0.32 0 0.21769 -0.06409 -0.1536 00 0.32 1.402 0.38095 0 0.1536 0.06409 -0.217690 0 0.38095 0.7619 0 0 0.21769 -0.21769
0.21769 0.21769 0 0 0.08293 -0.08293 0 0-0.2177 -0.0641 0.1536 0 -0.08293 0.13208 -0.04915 0
0 -0.1536 0.06409 0.21769 0 -0.04915 0.13208 -0.082930 0 -0.21769 -0.21769 0 0 -0.08293 0.08293
12345678
24681357
1 2 3 40.7619 0.38095 0 0 1
S= 0.38095 1.4019 0.32 0 2 Pf=0 0.32 1.4019 0.38095 30 0 0.38095 0.7619 4
MIEMBRO 1 1443.75 1W 1443.75 1 1263.28 2
550 P1= 1263.28 2 3162.5 3L 1443.75 3 Fs= 527.083 4
5.25 -1263.28 4 3162.5 5-527.083 6
MIEMBRO 2 1443.75 7W 1718.75 3 -1263.28 8
550 P2= 1790.36 4L 1718.75 5 -1263.28 2
6.25 -1790.36 6 -527.083 4527.083 6
MIEMBRO 3 Fe= 1263.28 8W 1443.75 5 -1443.75 1
550 P3= 1263.28 6 -3162.5 3L 1443.75 7 -3162.5 5
5.25 -1263.28 8 -1443.75 7
MIEMBRO 11443.75
+ K1
0 0
=
1095.58P1= 1263.28 -1716.7 1 0
1443.75 0 0 1791.92-1263.28 117.292 2 -1827.9
MIEMBRO 21718.75
+ K2
0 0
=
1718.75P2= 1790.36 117.292 2 1827.9
1718.75 0 0 1718.75-1790.36 -117.292 3 -1827.9
MIEMBRO 3
1443.75
+ K3
0 0
=
1791.92P3= 1263.28 -117.292 3 1827.9
1443.75 0 0 1095.58-1263.28 1716.7 4 0
-1263.28 1-527.083 2 k1=527.083 31263.28 4
k2=DESPLAZAMIENTO
X1.53435 -0.44369 0.1172 -0.0586 -1263.28-0.44369 0.88739 -0.2344 0.1172 -527.0830.1172 -0.2344 0.88739 -0.44369 527.083-0.0586 0.1172 -0.44369 1.53435 1263.28 k3=
∆
-1716.7 1117.292 2-117.292 31716.7 4
1 -348.1712 -1263.283 348.1714 -564.617 1 1095.58
2 03 3510.67
3 0 4 04 37.5334 5 3510.675 0 6 06 -37.5334 7 1095.58
8 0
5 348.1716 564.6177 -348.1718 1263.28
0.08293 0.21769 -0.08293 0.217690.21769 0.7619 -0.21769 0.38095-0.08293 -0.21769 0.08293 -0.217690.21769 0.38095 -0.21769 0.7619
0.04915 0.1536 -0.04915 0.15360.1536 0.64 -0.1536 0.32
-0.04915 -0.1536 0.04915 -0.15360.1536 0.32 -0.1536 0.64
0.08293 0.21769 -0.08293 0.217690.21769 0.7619 -0.21769 0.38095-0.08293 -0.21769 0.08293 -0.217690.21769 0.38095 -0.21769 0.7619
1 2 3 40.76190476 0.38095238 0 0 1
S= 0.38095238 1.40190476 0.32 0 20 0.32 1.40190476 0.38095238 30 0 0.38095238 0.76190476 4
MIEMBRO 1 0W 0 1 00 P1= 0 2 1093.75L 0 3 Fs= 1139.32292
5.25 0 4 1093.75-1139.3229
MIEMBRO 2 0W 1093.75 3 0
350 P2= 1139.32292 4L 1093.75 5 0
6.25 -1139.3229 6 -1139.32291139.32292
MIEMBRO 3 Fe= 0W 0 5 00 P3= 0 6 -1093.75L 0 7 -1093.75
5.25 0 8 0
MIEMBRO 10
+ K1
0 0P1= 0 639.043303 1
0 0 00 -1278.0866 2
MIEMBRO 21093.75
+ K2
0 0P2= 1139.32292 -1278.0866 2
1093.75 0 0-1139.3229 1278.08661 3
MIEMBRO 30
+ K3
0 0P3= 0 1278.08661 3
0 0 0
0
+ K3
-639.0433 4
0 1Pf= -1139.3229 2
1139.32292 30 4
1 DESPLAZAMIENTO2 X3 1.53434749 -0.443695 0.11720245 -0.0586012 04 -0.443695 0.88738997 -0.2344049 0.11720245 -1139.32295 0.11720245 -0.2344049 0.88738997 -0.443695 1139.322926 -0.0586012 0.11720245 -0.443695 1.53434749 078
∆
639.043303 1-1278.0866 2
2 1278.08661 34 -639.0433 4681357
=
-139.11147 1 -139.111470 2 0
139.111467 3 139.111467-730.3352 4 -730.3352
=
1093.75 3 0730.335203 4 -408.98771
1093.75 5 0-730.3352 6 408.987714
=
139.111467 5 139.111467730.335203 6 730.335203-139.11147 7 -139.11147
=
-1.137E-013 8 -1.137E-013
0.08292841 0.21768707k1= 0.21768707 0.76190476
-0.0829284 -0.21768710.21768707 0.38095238
0.049152 0.1536k2= 0.1536 0.64
-0.049152 -0.15360.1536 0.32
0.08292841 0.21768707k3= 0.21768707 0.76190476
-0.0829284 -0.21768710.21768707 0.38095238
1 -139.11146723652 03 1232.86146723654 05 1232.86146723656 07 -139.11146723658 -1.13686838E-013
-0.0829284 0.21768707-0.2176871 0.380952380.08292841 -0.2176871-0.2176871 0.76190476
-0.049152 0.1536-0.1536 0.32
0.049152 -0.1536-0.1536 0.64
-0.0829284 0.21768707-0.2176871 0.380952380.08292841 -0.2176871-0.2176871 0.76190476
1 2 3 40.761905 0.380952 0 0 1
S= 0.380952 1.401905 0.32 0 2 Pf=0 0.32 1.401905 0.380952 30 0 0.380952 0.761905 4
MIEMBRO 1 918.75 1W 918.75 1 803.9063 2
350 P1= 803.9063 2 918.75 3L 918.75 3 Fs= -803.906 4
5.25 -803.906 4 918.75 5803.9063 6
MIEMBRO 2 918.75 7W 0 3 -803.906 80 P2= 0 4L 0 5 -803.906 2
6.25 0 6 803.9063 4-803.906 6
MIEMBRO 3 Fe= 803.9063 8W 918.75 5 -918.75 1
350 P3= 803.9063 6 -918.75 3L 918.75 7 -918.75 5
5.25 -803.906 8 -918.75 7
MIEMBRO 1918.75
+ K1
0 0
=
836.2981P1= 803.9063 -1731.49 1 0
918.75 0 0 1001.202-803.906 1352.727 2 -432.873
MIEMBRO 20
+ K2
0 0
=
2.8E-014P2= 0 1352.727 2 432.8726
0 0 0 -3E-0140 -1352.73 3 -432.873
MIEMBRO 3
918.75
+ K3
0 0
=
1001.202P3= 803.9063 -1352.73 3 432.8726
918.75 0 0 836.2981-803.906 1731.49 4 0
-803.906 1803.9063 2 k1=-803.906 3803.9063 4
k2=DESPLAZAMIENTO
X1.534347 -0.44369 0.117202 -0.0586 -803.906-0.44369 0.88739 -0.2344 0.117202 803.90630.117202 -0.2344 0.88739 -0.44369 -803.906-0.0586 0.117202 -0.44369 1.534347 803.9063 k3=
∆
-1731.49 11352.727 2-1352.73 31731.49 4
1 -82.45192 -803.9063 82.451924 371.0337 1 836.2981
2 03 1001.202
3 2.8E-014 4 04 432.8726 5 1001.2025 -3E-014 6 06 -432.873 7 836.2981
8 0
5 82.451926 -371.0347 -82.45198 803.9063
0.082928 0.217687 -0.08293 0.2176870.217687 0.761905 -0.21769 0.380952-0.08293 -0.21769 0.082928 -0.217690.217687 0.380952 -0.21769 0.761905
0.049152 0.1536 -0.04915 0.15360.1536 0.64 -0.1536 0.32
-0.04915 -0.1536 0.049152 -0.15360.1536 0.32 -0.1536 0.64
0.082928 0.217687 -0.08293 0.2176870.217687 0.761905 -0.21769 0.380952-0.08293 -0.21769 0.082928 -0.217690.217687 0.380952 -0.21769 0.761905
1 2 3 40.761905 0.380952 0 0 1
S= 0.380952 1.401905 0.32 0 20 0.32 1.401905 0.380952 30 0 0.380952 0.761905 4
MIEMBRO 1 918.75 1W 918.75 1 803.9063 2
350 P1= 803.9063 2 2012.5 3L 918.75 3 Fs= 335.4167 4
5.25 -803.906 4 1093.75 5-1139.32 6
MIEMBRO 2 0 7W 1093.75 3 0 8
350 P2= 1139.323 4L 1093.75 5 -803.906 2
6.25 -1139.32 6 -335.417 41139.323 6
MIEMBRO 3 Fe= 0 8W 0 5 -918.75 10 P3= 0 6 -2012.5 3L 0 7 -1093.75 5
5.25 0 8 0 7
MIEMBRO 1918.75
+ K1
0 0
=P1= 803.9063 -951.117 1
918.75 0 0-803.906 -208.019 2
MIEMBRO 21093.75
+ K2
0 0
=P2= 1139.323 -208.019 2
1093.75 0 0-1139.32 995.4273 3
MIEMBRO 3
0
+ K3
0 0
=P3= 0 995.4273 3
0 0 00 -497.714 4
-803.906 1Pf= -335.417 2
1139.323 30 4
DESPLAZAMIENTOX
1.534347 -0.44369 0.117202 -0.0586 -803.906-0.44369 0.88739 -0.2344 0.117202 -335.4170.117202 -0.2344 0.88739 -0.44369 1139.323-0.0586 0.117202 -0.44369 1.534347 0
∆
-951.117 1-208.019 2995.4273 3-497.714 4
666.421 1 -252.3290 2 -803.906
1171.079 3 252.329-1324.73 4 -520.821 1 666.421
2 03 2385.775
1214.696 3 120.9459 4 01324.727 4 185.4045 5 1081.15972.8041 5 -120.946 6 0-568.816 6 570.5073 7 -108.346
8 0
108.3458 5 108.3458568.8156 6 568.8156-108.346 7 -108.346
0 8 0
0.082928 0.217687 -0.08293 0.217687k1= 0.217687 0.761905 -0.21769 0.380952
-0.08293 -0.21769 0.082928 -0.217690.217687 0.380952 -0.21769 0.761905
0.049152 0.1536 -0.04915 0.1536k2= 0.1536 0.64 -0.1536 0.32
-0.04915 -0.1536 0.049152 -0.15360.1536 0.32 -0.1536 0.64
0.082928 0.217687 -0.08293 0.217687k3= 0.217687 0.761905 -0.21769 0.380952
-0.08293 -0.21769 0.082928 -0.217690.217687 0.380952 -0.21769 0.761905
1 2 3 40.761905 0.380952 0 0 1
S= 0.380952 1.401905 0.32 0 20 0.32 1.401905 0.380952 30 0 0.380952 0.761905 4
MIEMBRO 1 0 1W 0 1 0 20 P1= 0 2 1093.75 3L 0 3 Fs= 1139.323 4
5.25 0 4 2012.5 5-335.417 6
MIEMBRO 2 918.75 7W 1093.75 3 -803.906 8
350 P2= 1139.323 4L 1093.75 5 0 2
6.25 -1139.32 6 -1139.32 4335.4167 6
MIEMBRO 3 Fe= 803.9063 8W 918.75 5 0 1
350 P3= 803.9063 6 -1093.75 3L 918.75 7 -2012.5 5
5.25 -803.906 8 -918.75 7
MIEMBRO 10
+ K1
0 0
=P1= 0 497.7136 1
0 0 00 -995.427 2
MIEMBRO 21093.75
+ K2
0 0
=P2= 1139.323 -995.427 2
1093.75 0 0-1139.32 208.0191 3
MIEMBRO 3
918.75
+ K3
0 0
=P3= 803.9063 208.0191 3
918.75 0 0-803.906 951.1174 4
0 1Pf= -1139.32 2
335.4167 3803.9063 4
DESPLAZAMIENTOX
1.534347 -0.44369 0.117202 -0.0586 0-0.44369 0.88739 -0.2344 0.117202 -1139.320.117202 -0.2344 0.88739 -0.44369 335.4167-0.0586 0.117202 -0.44369 1.534347 803.9063
∆
497.7136 1-995.427 2208.0191 3951.1174 4
-108.346 1 -108.3460 2 0
108.3458 3 108.3458-568.816 4 -568.816 1 -108.346
2 03 1081.15
972.8041 3 -120.946 4 0568.8156 4 -570.507 5 2385.7751214.696 5 120.9459 6 0-1324.73 6 -185.405 7 666.421
8 0
1171.079 5 252.3291324.727 6 520.8212666.421 7 -252.329
0 8 803.9063
0.082928 0.217687 -0.08293 0.217687k1= 0.217687 0.761905 -0.21769 0.380952
-0.08293 -0.21769 0.082928 -0.217690.217687 0.380952 -0.21769 0.761905
0.049152 0.1536 -0.04915 0.1536k2= 0.1536 0.64 -0.1536 0.32
-0.04915 -0.1536 0.049152 -0.15360.1536 0.32 -0.1536 0.64
0.082928 0.217687 -0.08293 0.217687k3= 0.217687 0.761905 -0.21769 0.380952
-0.08293 -0.21769 0.082928 -0.217690.217687 0.380952 -0.21769 0.761905
1 2 3 40.761905 0.380952 0 0 1
S= 0.380952 1.401905 0.32 0 20 0.32 1.401905 0.380952 30 0 0.380952 0.761905 4
MIEMBRO 1 918.75 1W 918.75 1 803.9063 2
350 P1= 803.9063 2 2012.5 3L 918.75 3 Fs= 335.4167 4
5.25 -803.906 4 2012.5 5-335.417 6
MIEMBRO 2 918.75 7W 1093.75 3 -803.906 8
350 P2= 1139.323 4L 1093.75 5 -803.906 2
6.25 -1139.32 6 -335.417 4335.4167 6
MIEMBRO 3 Fe= 803.9063 8W 918.75 5 -918.75 1
350 P3= 803.9063 6 -2012.5 3L 918.75 7 -2012.5 5
5.25 -803.906 8 -918.75 7
MIEMBRO 1918.75
+ K1
0 0
=P1= 803.9063 -1092.45 1
918.75 0 0-803.906 74.64026 2
MIEMBRO 21093.75
+ K2
0 0
=P2= 1139.323 74.64026 2
1093.75 0 0-1139.32 -74.6403 3
MIEMBRO 3
918.75
+ K3
0 0
=P3= 803.9063 -74.6403 3
918.75 0 0-803.906 1092.447 4
-803.906 1Pf= -335.417 2
335.4167 3803.9063 4
DESPLAZAMIENTOX
1.534347 -0.44369 0.117202 -0.0586 -803.906-0.44369 0.88739 -0.2344 0.117202 -335.4170.117202 -0.2344 0.88739 -0.44369 335.4167-0.0586 0.117202 -0.44369 1.534347 803.9063
∆
-1092.45 174.64026 2-74.6403 31092.447 4
697.1866 1 -221.5630 2 -803.906
1140.313 3 221.5634-1163.21 4 -359.302 1 697.1866
2 03 2234.063
1093.75 3 0 4 01163.208 4 23.88488 5 2234.0631093.75 5 0 6 0-1163.21 6 -23.8849 7 697.1866
8 0
1140.313 5 221.56341163.208 6 359.3015697.1866 7 -221.563
0 8 803.9063
0.082928 0.217687 -0.08293 0.217687k1= 0.217687 0.761905 -0.21769 0.380952
-0.08293 -0.21769 0.082928 -0.217690.217687 0.380952 -0.21769 0.761905
0.049152 0.1536 -0.04915 0.1536k2= 0.1536 0.64 -0.1536 0.32
-0.04915 -0.1536 0.049152 -0.15360.1536 0.32 -0.1536 0.64
0.082928 0.217687 -0.08293 0.217687k3= 0.217687 0.761905 -0.21769 0.380952
-0.08293 -0.21769 0.082928 -0.217690.217687 0.380952 -0.21769 0.761905
