Practica De Analisis De German.docx
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METODO DE ROTACIONES ANGULARES
1.4[tn ] 4[tn / m]
6[tn / m ] 65�
2
2
2
2[tn ]
4.5
[m ]
CALCULO DE GRADO DE DESPLASAMIENTO
1A
1A
GD = ND - A GD = 2 - 2 GD = 0 \ La estructura no tiene desplasamiento CONFIGURACION DE NUDOS qA = 0
qB = ?
A
C
B
MOMENTOS FIJOS EN LAS BARRAS 6[tn / m ] A
B MFBA
MFAB
2
2
qC = 0
[m ]
6� 42 =12
M AB
2 2 �2 �� �2 � �2 �� 6 - 8 � �+ 3 � �� � �� �4 �� �4 � �4 ��
M AB = - 5.5 6� 42 = 12
M BA
2 2 �2 ���2 � �2 �� 4 � �- 3 � �� � �� �4 ���4 � �4 ��
M BA = - 2.5 4[tn / m] C
B 2[tn ]
MFBC = -13.054
4.5
2
MFCB = 0
[m ]
ECUACION DE COMPATIBILIDAD ECUACION EN LOS NUDOS
qB = ? M BA B
�M
B
M BC
=0
M BA + M BC = 0 ECUACIÓN DE MOMENTOS EN LAS BARRAS BARRA A/B E/E BARRA
B/C E/A
0 M AB = MFAB + K AAq A + K ABq B 0 M BA = MFBA + K BAq A + K BBqB M BC = MFBC + K BBq B + K BCqC M CB = 0
0
REGIDEZ ROTACIONAL Y TRASLACIONAL DE LAS BARRAS BARRA
A/B E/E 4 gEI 4 g9000 � K AA = = 9000 L 4 2 gEI 2 g9000 K ij = K ji = � K AB = = 4500 L 4 B/C E/A 3 gEI 3 g9000 K ii = K JJ = � K BB = = 4153.846 L 6.5 K ij = K ji = 0 K ii = K jj =
BARRA
CALCULO DE LAS INCÓGNITAS M AB = -5.5 +4500 q B M BA = 2.5 + 9000 q B M BC = -13.045 + 4153.846 q B M BA + M BC = 0 2.5 + 9000 q B - 13.054 + 4153.846 q B = 0
[tn � m] [tn � m] [tn � m]
q B = 8.02351 �10 -4 M AB = -1.889 M BA = 9.721 M BC = -9.721 6[tn / m ] MFAB A
B 9.721
-1.889
2
2
VA = 7.042 [tn]
�M
B
=0
+
-9.721 + 1.889 + 12 ( 3) - VA ( 4 ) = 0
[tn]
VA = 7.042
[m ]
4[tn / m] C
B
MFBC = -13.054
2[tn ]
�M [tn]
B
=0
MFCB = 0
4.5
2
[m ]
+
-9.721 + 18 ( 4.25) + 2 ( 2 ) - VC ( 6.5 ) = 0 VC = 9.658
3.625 [ tn ]
6[tn / m]
4[tn / m]
1.690 [ tn ] CORTE 1-1' 0 ���2
1.889
2
2
2
2[tn ]
4.5
M Z = 7.042 x - 1889 - 3 ( x ) VA = 7.042 [tn] VB = 14.925 [tn] Mz Q� = dx Q� = 7.042 - 6 x + CORTE M A = 02-2' � ��� -01.889 +412 + 3.625 ( 4 ) - 2 ( 6 ) + 18 ( 8.25 ) - 9.658 ( 10.5 ) - VB ( 4 ) = 0 7.042 xtn- 1.889 - 12 ( x - 1) VM Z= =14.925
[m ]
2
B
3.625 [ tn ]
VC = 9.658 [tn]
[ ]
Mz Q� = dx 1 2 3 4 Q� = -4.958 6[tn / m ] 4[tn / m] CORTE 3-3' 0 ���6 M Z = -1.8891.889 + 7.042 x - 12 ( x - 1) - 3.625 ( x - 4 )2[ +tn 14].925 ( x - 4 )
2 2 Mz Q� = dx 1� 2� � Q =6.342 V = 7.042 A [tn] CORTE 4-4' 0 ���10.5
4.5
2
3� VB = 14.925 [tn]
4�
[m ] VC = 9.658 [tn]
M Z = -1.889 + 7.042 x - 12 ( x - 1) - 3.625 ( x - 4 ) + 14.925 ( x - 4 ) + 2 ( x - 6 ) - 2 ( x - 6 ) Mz Q� = dx Q� =8.342 - 4 ( x - 6 )
11.300
2[tn ]
2
TRAMO 1 0 ���2 Mz = -3 x 2 - 1.889 + 7.042 x Mz q = � dx + q EI q = - 1.111 �10-4 x 3 + 3.912 �10-4 x 2 - 2.099 �10-4 x
n = - 2.778 �10-5 x 4 + 1.304 �10-4 x3 - 1.049 �10-4 x 2 TRAMO 2 0 ���2 4[tn / m] 6[tn / m ] Mz = - 4.958 x + 0.195 2.962 0.195 Mz q = � dx + q 0.195 EI 1.889 2.962 -5 -4 -4 9.721 9.721 q = 2.167 �10 x - 2.7 54 � 10 x + 2.512 � 10 2 2 4.5 2 -3 -5 2 -4 4.958+ 1.083 �104.958 n7.042 = - 9.181 �10 x + 2.5026.392 �10-4 6.342 x + 1.790 �106.342 8.342 9.658 TRAMO 4 TRAMO 3 TRAMO TRAMO31 TRAMO 2 0 ���4.5 0 ���2 00� � � 22 � � � 0 ���2 Mz = 6.342 x - 9.721 Mz q = � dx + q EI q = 3.523 �10-4 x 2 - 1.080 �10-3 x - 8.022 �10-4
n = 1.174 �10-4 x3 - 5.401 �10-4 x 2 - 8.022 �10-4 x CALCULO DE FECHA Y ROTACIÓN TRAMO 4 0 ���4.5 Mz = 2.962 + 8.342 - 2 x 2 q X Mz q = � dx + q 0 0 EI -3 2 �102.562 q = - 7.407 �10-5 x 3 + 4.634 �10-4 x 2 + 3.294 �10-4 x - 1.353 �10-4
n 0 1.790 �10 -4
n = - 1.852 �10-5 x 4 + 1.545 �10-4 x3 + 1.647 �10-4 x 2 - 1.553 �10-3 x - 2.825 �10-3
X
q
n
0
2.562 �10-4
1.790 �10-4
2
-8.022 �10 -4
2.148 �10-7
X
q
n
0
-8.022 �10 -4
2.148 �10-7
2
X
q
n
0
-1.553 �10 -3
-2.825 �10-3
4.5
2.564 �10-3
5.500 �10-6
VALORES DE DESPLAZAMIENTO, MOMENTOS, CORTANTE Y ROTACIONAL [tn]
M
Q
0.0
-1.889
7.042
0.000E+00
0.000E+00
0.5
0.882
4.042
-2.104E-05
-1.166E-05
1.0
2.153
1.042
7.020E-05
-2.280E-06
1.5
1.924
-1.958
1.904E-04
6.344E-05
2.0
0.195
-4.958
2.562E-04
1.791E-04
2.5
-2.284
-4.958
1.982E-04
2.983E-04
3.0
-4.763
-4.958
2.470E-06
3.542E-04
3.5
-7.242
-4.958
-3.309E-04
2.778E-04
4.0
-9.721
-4.958
-8.021E-04
2.400E-07
4.5
-6.55
6.342
-1.254E-03
-5.215E-04
5.0
-3.379
6.342
-1.530E-03
-1.225E-03
5.5
-0.208
6.342
-1.630E-03
-2.022E-03
6.0
2.963
6.342
-1.553E-03
-2.826E-03
6.5
6.634
6.342
-1.282E-03
-3.542E-03
7.0
9.305
4.342
-8.343E-04
-4.077E-03
7.5
10.976
2.342
-2.662E-04
-4.356E-03
8.0
11.647
0.342
3.668E-04
-4.333E-03
8.5
11.318
-1.658
1.009E-03
-3.988E-03
9.0
9.989
-3.658
1.606E-03
-3.330E-03
9.5
7.66
-5.658
2.101E-03
-2.398E-03
10.0
4.331
-7.658
2.439E-03
-1.255E-03
10.5
0.002
-9.658
2.564E-03
6.130E-06
q
3.625 [ tn ] 6[tn / m]
1.690 [ tn ]
n
X
1.889 [ tn � m]
4[tn / m]
2[tn ]
2 VA = 7.042 [tn]
2
2 VB = 14.925 [tn]
4.5
[m ] VC = 9.658 [tn]
M=
Q=
q=
n =
1.4[tn ] 4[tn / m]
6[tn / m ] 65�
2
2
2
2[tn ]
4.5
[m ]
CALCULO DE GRADO DE DESPLASAMIENTO
1A
1A
GD = ND - A GD = 2 - 2 GD = 0 \ La estructura no tiene desplasamiento CONFIGURACION DE NUDOS qA = 0
qB = ?
A
C
B
MOMENTOS FIJOS EN LAS BARRAS 6[tn / m ] A
B MFBA
MFAB
2
2
qC = 0
[m ]
6� 42 =12
M AB
2 2 �2 �� �2 � �2 �� 6 - 8 � �+ 3 � �� � �� �4 �� �4 � �4 ��
M AB = - 5.5 6� 42 = 12
M BA
2 2 �2 ���2 � �2 �� 4 � �- 3 � �� � �� �4 ���4 � �4 ��
M BA = - 2.5 4[tn / m] C
B 2[tn ]
MFBC = -13.054
4.5
2
MFCB = 0
[m ]
ECUACION DE COMPATIBILIDAD ECUACION EN LOS NUDOS
qB = ? M BA B
�M
B
M BC
=0
M BA + M BC = 0 ECUACIÓN DE MOMENTOS EN LAS BARRAS BARRA A/B E/E BARRA
B/C E/A
0 M AB = MFAB + K AAq A + K ABq B 0 M BA = MFBA + K BAq A + K BBqB M BC = MFBC + K BBq B + K BCqC M CB = 0
0
REGIDEZ ROTACIONAL Y TRASLACIONAL DE LAS BARRAS BARRA
A/B E/E 4 gEI 4 g9000 � K AA = = 9000 L 4 2 gEI 2 g9000 K ij = K ji = � K AB = = 4500 L 4 B/C E/A 3 gEI 3 g9000 K ii = K JJ = � K BB = = 4153.846 L 6.5 K ij = K ji = 0 K ii = K jj =
BARRA
CALCULO DE LAS INCÓGNITAS M AB = -5.5 +4500 q B M BA = 2.5 + 9000 q B M BC = -13.045 + 4153.846 q B M BA + M BC = 0 2.5 + 9000 q B - 13.054 + 4153.846 q B = 0
[tn � m] [tn � m] [tn � m]
q B = 8.02351 �10 -4 M AB = -1.889 M BA = 9.721 M BC = -9.721 6[tn / m ] MFAB A
B 9.721
-1.889
2
2
VA = 7.042 [tn]
�M
B
=0
+
-9.721 + 1.889 + 12 ( 3) - VA ( 4 ) = 0
[tn]
VA = 7.042
[m ]
4[tn / m] C
B
MFBC = -13.054
2[tn ]
�M [tn]
B
=0
MFCB = 0
4.5
2
[m ]
+
-9.721 + 18 ( 4.25) + 2 ( 2 ) - VC ( 6.5 ) = 0 VC = 9.658
3.625 [ tn ]
6[tn / m]
4[tn / m]
1.690 [ tn ] CORTE 1-1' 0 ���2
1.889
2
2
2
2[tn ]
4.5
M Z = 7.042 x - 1889 - 3 ( x ) VA = 7.042 [tn] VB = 14.925 [tn] Mz Q� = dx Q� = 7.042 - 6 x + CORTE M A = 02-2' � ��� -01.889 +412 + 3.625 ( 4 ) - 2 ( 6 ) + 18 ( 8.25 ) - 9.658 ( 10.5 ) - VB ( 4 ) = 0 7.042 xtn- 1.889 - 12 ( x - 1) VM Z= =14.925
[m ]
2
B
3.625 [ tn ]
VC = 9.658 [tn]
[ ]
Mz Q� = dx 1 2 3 4 Q� = -4.958 6[tn / m ] 4[tn / m] CORTE 3-3' 0 ���6 M Z = -1.8891.889 + 7.042 x - 12 ( x - 1) - 3.625 ( x - 4 )2[ +tn 14].925 ( x - 4 )
2 2 Mz Q� = dx 1� 2� � Q =6.342 V = 7.042 A [tn] CORTE 4-4' 0 ���10.5
4.5
2
3� VB = 14.925 [tn]
4�
[m ] VC = 9.658 [tn]
M Z = -1.889 + 7.042 x - 12 ( x - 1) - 3.625 ( x - 4 ) + 14.925 ( x - 4 ) + 2 ( x - 6 ) - 2 ( x - 6 ) Mz Q� = dx Q� =8.342 - 4 ( x - 6 )
11.300
2[tn ]
2
TRAMO 1 0 ���2 Mz = -3 x 2 - 1.889 + 7.042 x Mz q = � dx + q EI q = - 1.111 �10-4 x 3 + 3.912 �10-4 x 2 - 2.099 �10-4 x
n = - 2.778 �10-5 x 4 + 1.304 �10-4 x3 - 1.049 �10-4 x 2 TRAMO 2 0 ���2 4[tn / m] 6[tn / m ] Mz = - 4.958 x + 0.195 2.962 0.195 Mz q = � dx + q 0.195 EI 1.889 2.962 -5 -4 -4 9.721 9.721 q = 2.167 �10 x - 2.7 54 � 10 x + 2.512 � 10 2 2 4.5 2 -3 -5 2 -4 4.958+ 1.083 �104.958 n7.042 = - 9.181 �10 x + 2.5026.392 �10-4 6.342 x + 1.790 �106.342 8.342 9.658 TRAMO 4 TRAMO 3 TRAMO TRAMO31 TRAMO 2 0 ���4.5 0 ���2 00� � � 22 � � � 0 ���2 Mz = 6.342 x - 9.721 Mz q = � dx + q EI q = 3.523 �10-4 x 2 - 1.080 �10-3 x - 8.022 �10-4
n = 1.174 �10-4 x3 - 5.401 �10-4 x 2 - 8.022 �10-4 x CALCULO DE FECHA Y ROTACIÓN TRAMO 4 0 ���4.5 Mz = 2.962 + 8.342 - 2 x 2 q X Mz q = � dx + q 0 0 EI -3 2 �102.562 q = - 7.407 �10-5 x 3 + 4.634 �10-4 x 2 + 3.294 �10-4 x - 1.353 �10-4
n 0 1.790 �10 -4
n = - 1.852 �10-5 x 4 + 1.545 �10-4 x3 + 1.647 �10-4 x 2 - 1.553 �10-3 x - 2.825 �10-3
X
q
n
0
2.562 �10-4
1.790 �10-4
2
-8.022 �10 -4
2.148 �10-7
X
q
n
0
-8.022 �10 -4
2.148 �10-7
2
X
q
n
0
-1.553 �10 -3
-2.825 �10-3
4.5
2.564 �10-3
5.500 �10-6
VALORES DE DESPLAZAMIENTO, MOMENTOS, CORTANTE Y ROTACIONAL [tn]
M
Q
0.0
-1.889
7.042
0.000E+00
0.000E+00
0.5
0.882
4.042
-2.104E-05
-1.166E-05
1.0
2.153
1.042
7.020E-05
-2.280E-06
1.5
1.924
-1.958
1.904E-04
6.344E-05
2.0
0.195
-4.958
2.562E-04
1.791E-04
2.5
-2.284
-4.958
1.982E-04
2.983E-04
3.0
-4.763
-4.958
2.470E-06
3.542E-04
3.5
-7.242
-4.958
-3.309E-04
2.778E-04
4.0
-9.721
-4.958
-8.021E-04
2.400E-07
4.5
-6.55
6.342
-1.254E-03
-5.215E-04
5.0
-3.379
6.342
-1.530E-03
-1.225E-03
5.5
-0.208
6.342
-1.630E-03
-2.022E-03
6.0
2.963
6.342
-1.553E-03
-2.826E-03
6.5
6.634
6.342
-1.282E-03
-3.542E-03
7.0
9.305
4.342
-8.343E-04
-4.077E-03
7.5
10.976
2.342
-2.662E-04
-4.356E-03
8.0
11.647
0.342
3.668E-04
-4.333E-03
8.5
11.318
-1.658
1.009E-03
-3.988E-03
9.0
9.989
-3.658
1.606E-03
-3.330E-03
9.5
7.66
-5.658
2.101E-03
-2.398E-03
10.0
4.331
-7.658
2.439E-03
-1.255E-03
10.5
0.002
-9.658
2.564E-03
6.130E-06
q
3.625 [ tn ] 6[tn / m]
1.690 [ tn ]
n
X
1.889 [ tn � m]
4[tn / m]
2[tn ]
2 VA = 7.042 [tn]
2
2 VB = 14.925 [tn]
4.5
[m ] VC = 9.658 [tn]
M=
Q=
q=
n =
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