PREDIMENSIONAMIENTO
LOSA ALIGERADA h> L/25 = 3.58
= 0.1432
= 0.1 0.17 m
LOSA
= 0.17 m
= 0.3691
= 0.4 0.40 m
25
VIGA PRINCIPAL h> L/11 = 4.06 11
b> L' L'/2 /2+L +L''/ ''/2 2 = 4.06 20 2
+ 3.82 2
= 0.1970 m
20 = 0.2 0.20 m
VP =
0.20
x 0.0
VIGA SEC!NDARIA h> L/1 = 3.58
= 0.2557
= 0.3 0.30 m
14
b> L' L'/2 /2+L +L''/ ''/2 2 = 3.58 20 2
+ 3.11 2
= 0.1673 m
20 = 0.2 0.20 m
VS =
0.20
x 0."0
COL!MNA #+ CRITICA$ A = A% x * x At =
4.06
+ 3. 3.17
2
A% =
12.0&2 m2
Ac =
12.092
A =
1"".01 m2
Lc =
Ac
x
3 .5 8
+ 3.11
2
2
2
1 x
0.0011
=
= 133.01
0.0133014 0.0133014 m2
= 11.533 cm
L
= 1(.5"" m 25.533 cm
COL!MNA #TIPO $ )C) A = A% x * x At4 =
3 .8 2
x 3.58
2
2
A% = ".1(& m2 Ac4 Ac4 =
3.41 3.4189 89
x 10000
A = 71.7&7 m2 Lc4 Lc4 =
71.7 71.796 969 9
=
8.47331 cm 15.4733 cm
L
=
22.7" m
x
1
x
0.0021
METRADOS
, LOSA ALIGERADA DESCRIPCION PESO DE LOSA
1--2
2--"
"--
e = 0.17 0.17 m
280 ,*m2
(
1
)m
28 0
28 0
28 0
(
5
)
10 0
10 0
10 0
PESO DE PISO TERI!ADO 20 ,*m2
PESO DE "RO LO!#IT"DI!AL 290 ,*m2
e = 0.15 m
380
( 2.63 ) m
PESO DE "RO TRA!S$ERSAL 290 ,*m2
380
38 0 7 6 2 .7
e = 0.15 m
( 2.63 ) m
7 6 2 .7
PESO DE SO%RE&AR#A 200 ,*m2
(
1
)m
20 0
20 0
20 0
53 2
53 2
53 2
CARGA !LTIMA '1= 1.4 '1 '2= 1.4 '2
1067.78
P1= 1.4 P1
1067.78
L1= 1.4 L1
DESCRIPCION
34 0
34 0
34 0
1--2
2--"
"--
212.8
2 12 . 8
2 1 2 .8
&AR#AS "LTIAS POR $I#"ETA '1= '1*2.5 '2= '2*2.5
4 2 7 .1 1 2 21 2.8
6 39 . 9 12
P1= P1*2.5
427.112
4L1= L1*2.5
13 6
13 6
13 6
A-
-C
C-D
19 2
19 2
19 2
1271.1
12 71 . 1
12 71 . 1
METRADOS
, VIGA PRINCIPAL DESCRIPCION PESO DE $I#A 2400 -,*m3
( 0.20 0.40 ) m ( 0.20 0.40 ) m
PESO DE LOSA + A&A%ADO 380 ,*m2
e = 0.17 0.17 m ( 3.35 ) m
PESO DE "RO LO!#IT"DI!AL
e = 0.15 m
290 ,*m2
( 2.80 0.40 ) m
PESO DE "RO TRA!S$ERSAL 290 ,*m2
696
696
e = 0.15 m
( 2.63 1.43 ) m
348
669
669
669
268.8
268.8
268.8
1779.54
1779.54
1779.54
PESO DE SO%RE&AR#A 200 ,*m2
( 3.35 ) m
CARGA !LTIMA
974.4 3022.74
974.4 2048.34
3022.74 487.2
1137.3
1137.3
1137.3
A-
-C
C-D
192
192
192
( 3.35 ) m
1271.1
1271.1
1271.1
( 3.35 ) m
669
669
669
268.8
268.8
268.8
1779.54
1779.54
1779.54
SIG!IENTE NIVEL DESCRIPCION PESO DE $I#A 2400 -,*m3
( 0.20 0.40 ) m ( 0.20 0.40 ) m
PESO DE LOSA + A&A%ADO 380 ,*m2
e = 0.17 m
PESO DE SO%RE&AR#A 200 ,*m2
CARGA !LTIMA
2048.34
2048.34
2048.34
1137.3
1137.3
1137.3
1--2
2--"
"--
144
144
144
METRADOS
, VIGA SEC!NDARIA DESCRIPCION PESO DE $I#A 2400 -,*m3 PESO DE LOSA + A&A%ADO
( 0.20 0.30 ) m ( 0.20 0.30 ) m e = 0.17 m
380 ,*m2
( 1.00 ) m
PESO DE "RO LO!#IT"DI!AL 290 ,*m2
290 ,*m2
380
380
725
725
725
200
200
200
201.6
201.6
201.6
532
532
532
1015
1015
1015
e = 0.15 m
( 2.80 0.30 ) m
PESO DE "RO TRA!S$ERSAL
380
e = 0.15 m
( 2.63 0.38 ) m
286.01
PESO DE SO%RE&AR#A 200 ,*m2
( 1.00 ) m
CARGA !LTIMA
1748.6
1748.6
1748.6
400.418
340
340
340
1--2
2--"
"--
144
144
144
( 1.00 ) m
380
380
380
( 1.00 ) m
200
200
200
201.6
201.6
201.6
532
532
532
SIG!IENTE NIVEL.DESCRIPCION PESO DE $I#A 2400 -,*m3
( 0.20 0.30 ) m ( 0.20 0.30 ) m
PESO DE LOSA + A&A%ADO 380 ,*m2
e = 0.17 m
PESO DE SO%RE&AR#A 200 ,*m2
CARGA !LTIMA
733.6 340
COL!MNAS.- C1
METRADOS
733.6 340
733.6 340
CARGA PARCIAL
DESCRIPCION PESO DE &OL"!A 2400 -,*m3 PESO DE $I#A PRI!&IPAL 2400 -,*m3 PESO DE $I#A SE&"!D. 2400 -,*m3
CARGA !LTIMA
( 0.25 0.25 ) m ( 0.25 0.25 )
( 2.40 ) m
360
( 3.50 ) m
671.04
( 3.35 ) m
481.68
( 0.20 0.40 ) m ( 0.20 0.40 )
( 0.20 0.30 ) m ( 0.20 0.30 )
PESO DE LOSA + A&A%ADO 380 ,*m2
CARGA AC!M!LADA
e = 0.17 m ( 11.69 ) m
4442.4945 5955.2145
8337.3003
( 11.69 ) m
2338.155
2338.155
3974.8635
CARGA PARCIAL
CARGA AC!M!LADA
CARGA !LTIMA
6244.852
12200.05
170(0.0&"1
2338.155
7."1
7&&.727
CARGA PARCIAL
CARGA AC!M!LADA
CARGA !LTIMA
PESO DE SO%RE &AR#A 200 ,*m2
PARA EL SGTE NIVEL.-
DESCRIPCION PESO DE &OL"!A 2400 -,*m3 PESO DE $I#A PRI!&IPAL 2400 -,*m3 PESO DE $I#A SE&"!D. 2400 -,*m3
( 0.25 0.25 ) m ( 0.25 0.25 ) ( 0.20 0.40 )
360
( 3.50 ) m
671.04
( 3.35 ) m
481.68
( 0.20 0.30 ) m ( 0.20 0.30 )
e = 0.17 m ( 11.69 ) m
PESO DE "ROS 290 ,*m2
( 2.40 ) m
( 0.20 0.40 ) m
PESO DE LOSA + A&A%ADO 380 ,*m2
4442.4945 e = 0.15 m
( 0.43 2.35 ) m
289.64
PESO DE SO%RE &AR#A 200 ,*m2
( 11.69 ) m
METRADOS
COL!MNAS.- C2
DESCRIPCION PESO DE &OL"!A 2400 -,*m3 PESO DE $I#A PRI!&IPAL 2400 -,*m3 PESO DE $I#A SE&"!D. 2400 -,*m3
( 0.25 0.25 ) m ( 0.25 0.25 )
( 2.40 ) m
360
( 3.50 ) m
671.04
( 1.79 ) m
257.76
( 0.20 0.40 ) m ( 0.20 0.40 )
( 0.20 0.30 ) m ( 0.20 0.30 )
PESO DE LOSA + A&A%ADO 380 ,*m2
e = 0.17 m ( 6.26 ) m
2377.299
3666.099
5132.5386
( 6.26 ) m
1251.21
1251.21
2127.057
PESO DE SO%RE &AR#A 200 ,*m2
PARA EL SGTE NIVEL.CARGA PARCIAL
DESCRIPCION PESO DE &OL"!A 2400 -,*m3 PESO DE $I#A PRI!&IPAL 2400 -,*m3 PESO DE $I#A SE&"!D. 2400 -,*m3
CARGA !LTIMA
7418.9165
110(5.0155
1551&.0217
1251.21
2502.2
25.11
CARGA PARCIAL
CARGA AC!M!LADA
CARGA !LTIMA
( 0.25 0.25 ) m ( 0.25 0.25 )
( 2.40 ) m
360
( 3.50 ) m
671.04
( 1.79 ) m
257.76
( 0.20 0.40 ) m ( 0.20 0.40 )
( 0.20 0.30 ) m ( 0.20 0.30 )
PESO DE LOSA + A&A%ADO 380 ,*m2
CARGA AC!M!LADA
e = 0.17 m ( 6.26 ) m
PESO DE "ROS
2377.299 e = 0.15 m
290 ,*m2
( 1.73 2.40 ) m
1200.60
290 ,*m2
( 3.75 2.35 ) m
2552.22
PESO DE SO%RE &AR#A 200 ,*m2
( 6.26 ) m
METRADOS
COL!MNAS.- C"
DESCRIPCION PESO DE &OL"!A 2400 -,*m3 PESO DE $I#A PRI!&IPAL 2400 -,*m3 PESO DE $I#A SE&"!D. 2400 -,*m3
( 0.25 0.25 ) m ( 0.25 0.25 )
( 2.40 ) m
360
( 1.91 ) m
366.72
( 3.35 ) m
481.68
( 0.20 0.40 ) m ( 0.20 0.40 )
( 0.20 0.30 ) m ( 0.20 0.30 )
PESO DE LOSA + A&A%ADO 380 ,*m2
e = 0.17 m ( 6.39 ) m
2427.801
3636.201
5090.6814
( 6.39 ) m
1277.79
1277.79
2172.243
CARGA PARCIAL
CARGA AC!M!LADA
CARGA !LTIMA
PESO DE SO%RE &AR#A 200 ,*m2
PARA EL SGTE NIVEL.-
DESCRIPCION PESO DE &OL"!A 2400 -,*m3 PESO DE $I#A PRI!&IPAL 2400 -,*m3 PESO DE $I#A SE&"!D. 2400 -,*m3
( 0.25 0.25 ) m ( 0.25 0.25 )
( 2.40 ) m
360
( 1.91 ) m
366.72
( 3.35 ) m
481.68
( 0.20 0.40 ) m ( 0.20 0.40 )
( 0.20 0.30 ) m ( 0.20 0.30 )
PESO DE LOSA + A&A%ADO 380 ,*m2
e = 0.17 m ( 6.39 ) m
PESO DE "ROS
2427.801 e = 0.15 m
290 ,*m2
( 3.08 2.40 ) m
2142.29
290 ,*m2
( 2.05 2.35 ) m
1393.67 7172.1565
10(0(."575
151"1.7005
1277.79
2555.5(
".(
CARGA PARCIAL
CARGA AC!M!LADA
CARGA !LTIMA
PESO DE SO%RE &AR#A 200 ,*m2
( 6.39 ) m
METRADOS
COL!MNAS.- C
DESCRIPCION PESO DE &OL"!A 2400 -,*m3 PESO DE $I#A PRI!&IPAL 2400 -,*m3 PESO DE $I#A SE&"!D. 2400 -,*m3
( 0.25 0.25 ) m ( 0.25 0.25 )
( 2.40 ) m
360
( 1.91 ) m
366.72
( 1.79 ) m
257.76
( 0.20 0.40 ) m ( 0.20 0.40 )
( 0.20 0.30 ) m ( 0.20 0.30 )
PESO DE LOSA + A&A%ADO 380 ,*m2
e = 0.17 m ( 3.42 ) m
1299.182
2283.662
3197.1268
( 3.42 ) m
683.78
683.78
1162.426
CARGA PARCIAL
CARGA AC!M!LADA
CARGA !LTIMA
4877.9295
711.5&15
1002.22(1
683.78
1"7.5
2"2.(52
PESO DE SO%RE &AR#A 200 ,*m2
PARA EL SGTE NIVEL.-
DESCRIPCION PESO DE &OL"!A 2400 -,*m3 PESO DE $I#A PRI!&IPAL 2400 -,*m3 PESO DE $I#A SE&"!D. 2400 -,*m3
( 0.25 0.25 ) m ( 0.25 0.25 )
( 2.40 ) m
360
( 1.91 ) m
366.72
( 1.79 ) m
257.76
( 0.20 0.40 ) m ( 0.20 0.40 )
( 0.20 0.30 ) m ( 0.20 0.30 )
PESO DE LOSA + A&A%ADO 380 ,*m2
e = 0.17 m ( 3.42 ) m
PESO DE "ROS
1299.182 e = 0.15 m
290 ,*m2
( 1.73 2.40 ) m
1200.60
290 ,*m2
( 2.05 2.35 ) m
1393.67
PESO DE SO%RE &AR#A 200 ,*m2
( 3.42 ) m
IDEALIACION O ESTADOS DE SORECARGA #LOSA$
1" /m "&.&12 /m 212.( /m 1
2
3
4
1" /m "&.&12 /m 212.( /m 1
2
3
4
1" /m "&.&12 /m 212.( /m 1
2
3
4
1" /m "&.&12 /m 212.( /m 1
2
3
IDEALIACION O ESTADOS DE SORECARGA #VIGA PRINCIPAL$
11"7." /m 20(." /m
4
11"7." /m "022.7 /m
"022.7 /m 20(." /m
A
C
IDEALIACION O ESTADOS DE SORECARGA #VIGA SEC!NDARIA$
"0 /m 7"". /m
D
"0 /m 17(. /m
17(. /m
1
2
17(. /m
"
3.06 3.11 3.58 3.82
2= VP= VS=
At1=
3.17
4.06
2.(0 0.20 0.20
0.0 0."0
3.82
+
3.17
3.58
2
2
2
+ 3.11 2
At1=
11.690775
m2
/c1=
2.80
h1=
2.0
m
0.40
PREDIMENSIONAMIENTO DE APATA C1 =
P A
P=
17080.093
+ 7949.727
P=
2502&.(2
3
A=
Pt
AS!MIENDO A1=
S = 1.25 3/m2
25029.82
,
=
20023.8561 cm2
1.25 ,*cm2
A41=
2002".(5 m2
A1=
L x L
DESPEANDO L4 6 L=
A
=
L4=
11.505(
m
At2=
3.82
+
20023.86
2
A%2=
.2505
m2
/c2=
2.80
h2=
2.0
m
3.17
3.58
2
2
0.40
PREDIMENSIONAMIENTO DE APATA C1 =
P A
P=
15519.022
+ 4254.114
P=
1&77".1"
A=
Pt
3
AS!MIENDO A2=
S = 1.25 3/m2
19773.136
,
=
15818.5086 cm2
1.25 ,*cm2
A42=
15(1(.50& m2
A2=
L x L
DESPEANDO L4 6 L=
A
=
L4=
125.7715
m
At3=
3.58
+
15818.51
3.11
3.82
2
2
2
A%"=
."((&5
m2
/c3=
2.80
h"=
2.0
m
0.40
PREDIMENSIONAMIENTO DE APATA C1 =
P A
P=
15131.701
+ 4344.486
P=
1&7.1(7
3
A=
Pt
AS!MIENDO A3=
S = 1.25 3/m2
19476.187
,
1.25 ,*cm2
A4"=
155(0.&& m2
=
15580.9492 cm2
A3=
L x L
DESPEANDO L4 6 L=
A
=
L4=
12.(2"7
m
At4=
3.82
3.58
2
2
A%=
".1(&
m2
/c4=
2.80
h=
2.0
m
15580.95
0.40
PREDIMENSIONAMIENTO DE APATA C1 =
P A
P=
10026.228
+ 2324.852
P=
12"51.0(
3
A=
Pt
AS!MIENDO A4=
S = 1.25 3/m2
12351.08
,
=
1.25 ,*cm2
A4= A4=
&((0.(1 m2 L x L
DESPEANDO L4 6 L=
A
=
L4=
&&.025"
m
9880.864
9880.86408 cm2
DISEO APATA 1
1.5 m2
1.5 m2
DISEO APATA 2
1."0 m2
1."0 m2
DISEO APATA "
1.25 m2
1.25 m2
DISEO APATA
1.00 m2
1.00 m2
".- CALC!
METODO CROSS VIGAS
"022.7
20(."
".(2
"022.7 ".17
.0
1.- CALC!LO DE RIGIDES RELATIVO = 4EI*L 12 = 4E1I1*L1
23 = 4E2I1*L2
34 = 4E3I1*L3
, PARA SECCION CONSTANTE 39: = 1/L 12 =
1
=
0.2
=
0."2
=
0.25
3.82 23 =
1 3.17
34 =
1 4.06
2.- 8ACTOR DE DISTRI!CION DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO D = *-L D12=
0.26 0.00
D21=
D23=
D32=
D34=
D43=
0.55
=
0.5
=
0.
=
1
+ 0.25 0.25
0.25
=
+ 0.25 0.25
0.32
0.5
+ 0.32 0.32
0.32
=
+ 0.32 0.32
0.26
1
+ 0.26 0.26
0.26
=
+ 0.00
O DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO
"022.7 39: 8;9: ME
3.82
M12
M21
12= 21=
'L2
=
3022.7 x 3.82 2 =
12
"75.75
12
D T D T
20(." D 3.17
T
M2"
M"2 D T 23= 32=
'L2
=
2048.3 x 3.17 2 =
12
1715."0
12
D T D
"022.7
T
4.06
D
M"
M"
34= 43=
'L2 12
=
3022.7 x 4.06 2 = 12
152.1
V VI V R
"022.7
20(." ".(2
".17
0.2
.0
0."2
1.00 3675.75 3675.75
3675.75
0.25
0.5 0.55
0.5 0.
3675.75 1715.30
1715.30 4152.14
1960.46 1&0.
889.08 1071.38
444.54 444.54
"022.7
1837.88 684.20 2522.08 2522.0(
2436.84 -2".(
1.00 4152.14
4152.14
1368.40 1068.43
4152.14
535.69 2076.07
534.22
2611.76 -211.7
534.22
444.54
1143.78 1378.30
1466.63 1145.13
534.22
571.89
222.27 733.32
689.15 267.11
572.56
571.89
955.58 &55.5(
956.26 -&5.2
572.56
571.89
433.36 522.22
536.99 419.27
572.56
216.68
285.94 268.49
261.11 286.28
209.64
216.68
554.44 55.
547.39 -57."&
209.64
216.68
251.44 303.00
307.39 240.00
209.64
125.72
108.34 153.69
151.50 104.82
120.00
125.72
262.03 22.0"
256.32 -25."2
120.00
125.72
118.83 143.20
143.93 112.38
120.00
59.42
62.86 71.97
71.60 60.00
56.19
59.42
134.83 1".("
131.60 -1"1.0
59.42
61.14 73.68
73.90 57.70
30.57
29.71 36.95
36.84 28.10
30.57 30.57
0.00 -"2&.(&
66.66 . 30.23 36.43
-"2&.(& "2&.(& -0(.2"
64.94 -.&
56.19 56.19 28.85 DM8
36.47 28.47
-"&0".12 "&0".12 "&0".12
28.85 28.85
0.00
862.54
862.54 191.87
191.87 961.36
961.36
5773.43
5773.43 3246.62
3246.62 6136.16
6136.16
4910.90
6635.97 3054.75
3438.49 7097.52
4910.90
9690.72
10536.01
D8C
5174.80
5174.80
.- CALC!LO DE MOM "022.7
20(." 3.82
"022.7 3.17
4.06 4910.90 = 4910.90 x
3054.75 4910.90
7097.52
=
0
=
x x
+
+
-
+
mx = 4910.90
-
5174.80 6635.97
3438.49 3054.75 = 3054.75 x =
-
0
=
x
+
+
x
mx = 3054.75
3989.25
2277.82
8332.64
7097.52 = 7097.52 x =
0
=
x x
mx = 7097.52
ENTOS MA
M V
x
3022.74 x2 2 4910.90 3022.74 x = 0 =
x=
4910.90
1.2
3022.74 ( 1.62
) 3022.74 ( 1.62 )2
Mmx =
"&(&.25
Mmx =
2277.(2
Mmx =
(""2.
2 2048.34 -,*m
M V
x
2048.34 x2 2 3054.75 2048.34 x = 0 =
x=
3054.75
1.&
2048.34 ( 1.49
) 2048.34 ( 1.49 )2
3022.74 -,*m
M V
x
3022.74 x2 2 7097.52 3022.74 x = 0 =
7097.52
x=
2."5
3022.74 ( 2.35
) 3022.74 ( 2.35 )2
".- CALC!
METODO CROSS VIGAS
"022.7
"022.7
".(2
"022.7 ".17
.0
1.- CALC!LO DE RIGIDES RELATIVO = 4EI*L 12 = 4E1I1*L1
23 = 4E2I1*L2
34 = 4E3I1*L3
, PARA SECCION CONSTANTE 39: = 1/L 12 =
1
=
0.2
=
0."2
=
0.25
3.82 23 =
1 3.17
34 =
1 4.06
2.- 8ACTOR DE DISTRI!CION DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO D = *-L D12=
0.26 0.00
D21=
D23=
D32=
D34=
D43=
0.55
=
0.5
=
0.
=
1
+ 0.25 0.25
0.25
=
+ 0.25 0.25
0.32
0.5
+ 0.32 0.32
0.32
=
+ 0.32 0.32
0.26
1
+ 0.26 0.26
0.26
=
+ 0.00
O DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO
"022.7 39: 8;9: ME
3.82
M12
M21
12= 21=
'L2
=
3022.7 x 3.82 2 =
12
"75.75
12
D T D T
"022.7 D 3.17
T
M2"
M"2 D T 23= 32=
'L2
=
3022.7 x 3.17 2 =
12
25"1.27
12
D T D
"022.7
T
4.06
D
M"
M"
34= 43=
'L2 12
=
3022.7 x 4.06 2 = 12
152.1
V VI V R
"022.7
"022.7 ".(2
".17
0.2
.0
0."2
1.00 3675.75 3675.75
3675.75 259.51 259.51
"022.7
0.5 0.55
0.5 0.
3675.75 2531.27
2531.27 4152.14
1144.48 11.(
1620.87 -120.(7
1.00 4152.14
4152.14
519.03 625.46
910.20 710.67
4152.14
1837.88 455.10
312.73 2076.07
355.34
2292.97 22&2.&7
0.25
2388.80 -2"((.(0
355.34
259.51
1039.88 1253.10
1341.43 1047.37
355.34
519.94
129.76 670.71
626.55 177.67
523.68
519.94
800.47 (00.7
804.22 -(0.22
523.68
519.94
363.02 437.45
451.61 352.61
523.68
181.51
259.97 225.80
218.73 261.84
176.30
181.51
485.77 (5.77
480.57 -(0.57
176.30
181.51
220.30 265.47
269.86 210.71
176.30
110.15
90.75 134.93
132.74 88.15
105.35
110.15
225.69 225.&
220.89 -220.(&
105.35
110.15
102.35 123.34
124.04 96.85
105.35
51.17
55.08 62.02
61.67 52.68
48.42
51.17
117.10 117.10
114.34 -11."
51.17
53.10 63.99
64.21 50.13
26.55
25.59 32.11
32.00 24.21
26.55 26.55
0.00 -"750.&"
57.69 57.& 26.16 31.53
-"750.&" "750.&" -5((.(
56.21 -5.21
48.42 48.42 25.07 DM8
31.56 24.64
-""&.77 ""&.77 ""&.77
25.07 25.07
0.00
981.92
981.92 185.75
185.75 1068.91
1068.91
5773.43
5773.43 4791.04
4791.04 6136.16
6136.16
6755.35 4605.29
4976.80 7205.07
4791.51
4791.51
11360.64
12181.87
D8C
5067.25
5067.25
.- CALC!LO DE MOM "022.7
"022.7 3.82
"022.7 3.17
4.06 4791.51 = 4791.51 x
4605.29 4791.51
7205.07
=
0
=
x x
+
+
-
+
mx = 4791.51
-
5067.25 6755.35
4976.80 4605.29 = 4605.29 x =
-
0
=
x
+
+
x
mx = 4605.29
3797.65
3508.19
8587.09
7205.07 = 7205.07 x =
0
=
x x
mx = 7205.07
ENTOS MA
M V
x
3022.74 x2 2 4791.51 3022.74 x = 0 =
x=
4791.51
1.5&
3022.74 ( 1.59
) 3022.74 ( 1.59 )2
Mmx =
"7&7.5
Mmx =
"50(.1&
Mmx =
(5(7.0&
2 3022.74 -,*m
M V
x
3022.74 x2 2 4605.29 3022.74 x = 0 =
x=
4605.29
1.52
3022.74 ( 1.52
) 3022.74 ( 1.52 )2
3022.74 -,*m
M V
x
3022.74 x2 2 7205.07 3022.74 x = 0 =
7205.07
x=
2."(
3022.74 ( 2.38
) 3022.74 ( 2.38 )2
".- CALC!
METODO CROSS VIGAS
"022.7
20(."
".(2
20(." ".17
.0
1.- CALC!LO DE RIGIDES RELATIVO = 4EI*L 12 = 4E1I1*L1
23 = 4E2I1*L2
34 = 4E3I1*L3
, PARA SECCION CONSTANTE 39: = 1/L 12 =
1
=
0.2
=
0."2
=
0.25
3.82 23 =
1 3.17
34 =
1 4.06
2.- 8ACTOR DE DISTRI!CION DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO D = *-L D12=
0.26 0.00
D21=
D23=
D32=
D34=
D43=
0.55
=
0.5
=
0.
=
1
+ 0.25 0.25
0.25
=
+ 0.25 0.25
0.32
0.5
+ 0.32 0.32
0.32
=
+ 0.32 0.32
0.26
1
+ 0.26 0.26
0.26
=
+ 0.00
O DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO
"022.7 39: 8;9: ME
3.82
M12
M21
12= 21=
'L2
=
3022.7 x 3.82 2 =
12
"75.75
12
D T D T
20(." D 3.17
T
M2"
M"2 D T 23= 32=
'L2
=
2048.3 x 3.17 2 =
12
1715."0
12
D T D
20(."
T
4.06
D
M"
M"
34= 43=
'L2 12
=
2048.3 x 4.06 2 = 12
2(1".7
V VI V R
"022.7
20(." ".(2
".17
0.2
.0
0."2
1.00 3675.75 3675.75
3675.75 444.54 444.54
20(."
0.5 0.55
0.5 0.
3675.75 1715.30
1715.30 2813.67
1960.46 1&0.
1098.37 -10&(."7
1.00 2813.67
2813.67
889.08 1071.38
616.79 481.58
2813.67
1837.88 308.39
535.69 1406.83
240.79
2146.27 21.27
0.25
1942.52 -1&2.52
240.79
444.54
973.34 1172.93
1090.82 851.70
240.79
486.67
222.27 545.41
586.46 120.40
425.85
486.67
767.68 77.(
706.86 -70.(
425.85
486.67
348.15 419.53
396.94 309.92
425.85
174.07
243.34 198.47
209.77 212.93
154.96
174.07
441.80 1.(0
422.69 -22.&
154.96
174.07
200.36 241.44
237.36 185.33
154.96
100.18
87.04 118.68
120.72 77.48
92.66
100.18
100.18 46.65 46.65
205.72 205.72
198.20 -1&(.20
92.66
50.09 55.65
56.21 46.33
43.45
102.54 -102.5
47.95 57.79
57.58 44.96
23.98
23.32 28.79
28.89 21.73
23.98
0.00 -"5".(7
92.66
111.30 86.90
46.65 23.98
93.29 112.42 105.74 105.7
52.12 52.12 23.63 28.48
-"5".(7 "5".(7 (7.10
50.62 -50.2
43.45 43.45 22.48 DM8
28.42 22.19
-271.77 271.77 271.77
22.48 22.48
0.00
932.95
932.95 267.23
267.23 669.16
669.16
5773.43
5773.43 3246.62
3246.62 4158.13
4158.13
6706.38 3513.84
2979.39 4827.29
3488.98
7806.68
3488.98
4840.48
4840.48
10220.23
D8C
.- CALC!LO DE MOM "022.7
20(." 3.82
20(." 3.17
4.06 4840.48 = 4840.48 x
3513.84 4840.48
4827.29
=
0
=
x x
+
+
-
+
mx = 4840.48
-
3488.98 6706.38
2979.39 3513.84 = 3513.84 x =
-
0
=
x
+
+
x
mx = 3513.84
3875.67
3013.93
5688.19
4827.29 = 4827.29 x =
0
=
x x
mx = 4827.29
ENTOS MA
M V
x
3022.74 x2 2 4840.48 3022.74 x = 0 =
x=
4840.48
1.0
3022.74 ( 1.60
) 3022.74 ( 1.60 ) )2 2
Mmx =
"(75.7
Mmx =
"01".&"
Mmx =
5((.1&
2 2048.34 2048.34 -,*m
M V
x
2048.34 x2 2 3513.84 2048.34 x = 0 =
x=
3513.84
1.72
2048.34 ( 1.72
) 2048.34 ( 1.72 ) )2 2
2048.34 2048.34 -,*m
M V
x
2048.34 x2 2 4827.29 2048.34 x = 0 =
4827.29
x=
2."
2048.34 ( 2.36
) 2048.34 ( 2.36 ) )2 2
".- CALC!
METODO CROSS VIGAS
"022.7
"022.7
".(2
"022.7 ".17
.0
1.- CALC!LO DE RIGIDES RELATIVO = 4EI*L 12 = 4E1I1*L 4E1I1*L1 1
23 = 4E2I1* 4E2I1*L2 L2
34 = 4E3I1*L 4E3I1*L3 3
, PARA SECCION CONSTANTE 39: = 1/L 12 =
1
=
0.2
=
0."2
=
0.25
3.82 23 =
1 3.17
34 =
1 4.06
2.- 8ACTOR DE DISTRI!CION DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO D = *-L D12=
0.26 0.00
D21=
D23=
D32=
D34=
D43=
0.55
=
0.5
=
0.
=
1
+ 0.25 0.25
0.25
=
+ 0.25 0.25
0.32
0.5
+ 0.32 0.32
0.32
=
+ 0.32 0.32
0.26
1
+ 0.26 0.26
0.26
=
+ 0.00
O DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO
"022.7 39: 8;9: ME
3.82
M12
M21
12= 21=
'L2
=
3022 30 22.7 .7 x 3. 3.82 82 2 =
12
"75.75
12
D T D T
"022.7 D 3 .1 7
T
M2"
M"2 D T 23= 32=
'L2
=
3022 30 22.7 .7 x 3. 3.17 17 2 =
12
25"1.27
12
D T D
"022.7
T
4 .0 6
D
M"
M"
34= 43=
'L2 12
=
3022 30 22.7 .7 x 4. 4.06 06 2 = 12
152.1
V VI V R
"022.7
"022.7 ".(2
".17
0.2
.0
0."2
1.00 3675.75 3675.75
3675.75 259.51 259.51
"022.7
0.5 0.55
0.5 0.
3675.75 2531.27
2531.27 4152.14
1144.48 11.(
1620.87 -120.(7
1.00 4152.14
4152.14
519.03 625.46
910.20 710.67
4152.14
1837.88 455.10
312.73 2076.07
355.34
2292.97 22&2.&7
0.25
2388.80 -2"((.(0
355.34
259.51
1039.88 1253.10
1341.43 1047.37
355.34
519.94
129.76 670.71
626.55 177.67
523.68
519.94
800.47 (00.7
804.22 -(0.22
523.68
519.94
363.02 437.45
451.61 352.61
523.68
181.51
259.97 225.80
218.73 261.84
176.30
181.51
485.77 (5.77
480.57 -(0.57
176.30
181.51
220.30 265.47
269.86 210.71
176.30
110.15
90.75 134.93
132.74 88.15
105.35
110.15
225.69 225.&
220.89 -220.(&
105.35
110.15
102.35 123.34
124.04 96.85
105.35
51.17
55.08 62.02
61.67 52.68
48.42
51.17
117.10 117.10
114.34 -11."
51.17
53.10 63.99
64.21 50.13
26.55
25.59 32.11
32.00 24.21
26.55 26.55
0.00 -"750.&"
57.69 57.& 26.16 31.53
-"750.&" "750.&" -5((.(
56.21 -5.21
48.42 48.42 25.07 DM8
31.56 24.64
-""&.77 ""&.77 ""&.77
25.07 25.07
0.00
981.92
981.92 185.75
185.75 1068.91
1068.91
5773.43
5773.43 4791.04
4791.04 6136.16
6136.16
6755.35 4605.29
4976.80 7205.07
4791.51
4791.51
11360.64
12181.87
D8C
5067.25
5067.25
.- CALC!LO DE MOM "022.7
"022.7 3.82
"022.7 3.17
4.06 4791.51 = 4791.51 x
4605.29 4791.51
7205.07
=
0
=
x x
+
+
-
+
mx = 4791.51
-
5067.25 6755.35
4976.80 4605.29 = 4605.29 x =
-
0
=
x
+
+
x
mx = 4605.29
3797.65
3508.19
8587.09
7205.07 = 7205.07 x =
0
=
x x
mx = 7205.07
ENTOS MA
M V
x
3022.74 x2 2 4791.51 3022.74 x = 0 =
x=
4791.51
1.5&
3022.74 ( 1.59
) 3022.74 ( 1.59 )2
Mmx =
"7&7.5
Mmx =
"50(.1&
Mmx =
(5(7.0&
2 3022.74 -,*m
M V
x
3022.74 x2 2 4605.29 3022.74 x = 0 =
x=
4605.29
1.52
3022.74 ( 1.52
) 3022.74 ( 1.52 )2
3022.74 -,*m
M V
x
3022.74 x2 2 7205.07 3022.74 x = 0 =
7205.07
x=
2."(
3022.74 ( 2.38
) 3022.74 ( 2.38 )2
".- CALC!
METODO CROSS VIGAS
17(.
17(.
".5(
&&.2 ".11
".0
1.- CALC!LO DE RIGIDES RELATIVO = 4EI*L 12 = 4E1I1*L1
23 = 4E2I1*L2
34 = 4E3I1*L3
, PARA SECCION CONSTANTE 39: = 1/L 12 =
1
=
0.2(
=
0."2
=
0.""
3.58 23 =
1 3.11
34 =
1 3.06
2.- 8ACTOR DE DISTRI!CION DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO D = *-L D12=
0.28 0.00
D21=
D23=
D32=
D34=
D43=
0.5
=
0.50
=
0.50
=
1
+ 0.33 0.33
0.33
=
+ 0.33 0.33
0.32
0.
+ 0.32 0.32
0.32
=
+ 0.32 0.32
0.28
1
+ 0.28 0.28
0.28
=
+ 0.00
O DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO
17(. 39: 8;9: ME
3.58
M12
M21
12= 21=
'L2
=
1748.6 x 3.58 2 =
12
1(7.5
12
D T D T
17(. D 3.11
T
M2"
M"2 D T 23= 32=
'L2
=
1748.6 x 3.11 2 =
12
10&."&
12
D T D
&&.2
T
3.06
D
M"
M"
34= 43=
'L2 12
=
699.2 x 3.06 2 = 12
55.5&
V VI V R
17(.
17(.
&&.2
".5(
".11
0.2(
".0
0."2
1.00
0.""
0. 0.5
1867.56
0.50 0.50
1867.56 1409.39
1867.56
1867.56 106.50 106.50
458.18 5(.1(
1.00
1409.39 545.59
545.59
863.80 (".(0
545.59
212.99 245.18
428.40 435.40
545.59
933.78 214.20
122.59 272.79
217.70
719.58 71&.5(
395.38 -"&5."(
217.70
106.50
334.51 385.07
196.09 199.29
217.70
167.26
53.25 98.05
192.53 108.85
99.65
167.26
167.26 35.17 35.17
151.29 151.2&
99.65
70.33 80.96
41.50 42.18
99.65
83.63 20.75
40.48 49.82
21.09
104.38 10."(
83.68 -(".(
90.30 -&0."0
21.09
35.17
48.52 55.86
44.79 45.52
21.09
24.26
17.58 22.39
27.93 10.55
22.76
24.26
24.26 9.29 9.29
39.98 "&.&(
38.47 -"(.7
22.76
12.13 9.54
10.70 11.38
9.70
22.08 -22.0(
10.07 11.60
10.95 11.13
5.04
4.65 5.47
5.80 4.85
5.04
0.00 -2272.(
22.76
19.08 19.39
9.29 5.04
18.58 21.39 21.67 21.7
10.12 10.12 4.70 5.42
-2272.( 2272.( 1"7.21
D8C
9.70 9.70 5.56 DM8
10.65 -10.5
5.56
5.28 5.37
5.56
-(&(.5 (&(.5
0.00 (&(.5
634.88
634.88 441.87
441.87 293.68
293.68
3129.99
3129.99 2719.07
2719.07 1069.78
1069.78
2495.12
3764.87 3160.94
2277.21 1363.45
776.10
2495.12
6925.81
3640.66
776.10
.- CALC!LO DE MOM 17(.
17(. 3.58
&&.2 3.11
3.06 2495.12 = 2495.12 x
3160.94 2495.12
1363.45
=
0
=
x x
+
+
-
+
mx = 2495.12
-
776.10 3764.87
2277.21 3160.94 = 3160.94 x =
-
0
=
x
+
+
x
mx = 3160.94
1780.17
2857.01
1329.38
1363.45 = 1363.45 x =
0
=
x x
mx = 1363.45
ENTOS MA
M V
x
1748.6 x2 2 2495.12 1748.6 x = 0 =
x=
2495.12
1."
1748.6 ( 1.43
) 1748.6 ( 1.43 )2
Mmx =
17(0.17
Mmx =
2(57.01
Mmx =
1"2&."(
2 1748.6 -,*m
M V
x
1748.6 x2 2 3160.94 1748.6 x = 0 =
x=
3160.94
1.(1
1748.6 ( 1.81
) 1748.6 ( 1.81 )2
699.2 -,*m
M V
x
699.2
x2 2
1363.45 =
1363.45
699.2 x = 0
x=
1.&5
699.2 ( 1.95
) 699.2 ( 1.95 )2
".- CALC!
METODO CROSS VIGAS
17(.
17(.
".5(
17(. ".11
".0
1.- CALC!LO DE RIGIDES RELATIVO = 4EI*L 12 = 4E1I1*L1
23 = 4E2I1*L2
34 = 4E3I1*L3
, PARA SECCION CONSTANTE 39: = 1/L 12 =
1
=
0.2(
=
0."2
=
0.""
3.58 23 =
1 3.11
34 =
1 3.06
2.- 8ACTOR DE DISTRI!CION DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO D = *-L D12=
0.28 0.00
D21=
D23=
D32=
D34=
D43=
0.5
=
0.50
=
0.50
=
1
+ 0.33 0.33
0.33
=
+ 0.33 0.33
0.32
0.
+ 0.32 0.32
0.32
=
+ 0.32 0.32
0.28
1
+ 0.28 0.28
0.28
=
+ 0.00
O DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO
17(. 39: 8;9: ME
3.58
M12
M21
12= 21=
'L2
=
1748.6 x 3.58 2 =
12
1(7.5
12
D T D T
17(. D 3.11
T
M2"
M"2 D T 23= 32=
'L2
=
1748.6 x 3.11 2 =
12
10&."&
12
D T D
17(.
T
3.06
D
M"
M"
34= 43=
'L2 12
=
1748.6 x 3.06 2 = 12
1"."
V VI V R
17(.
17(. ".5(
".11
0.2(
".0
0."2
1.00 1867.56 1867.56
1867.56
0.""
0. 0.5
0.50 0.50
1867.56 1409.39
1409.39 1364.43
458.18 5(.1(
212.99 245.18
106.50
922.63 &22."
106.50
428.91 493.73
214.45
53.25 199.57
214.45
214.45 58.76
252.82 252.(2
1364.43
1364.43 1364.43
122.59 682.22
804.81 -(0.(1
11.33
399.14 405.66
11.33
246.86 5.66
241.20 -21.20
11.33 202.83
202.83
117.53 135.29
119.62 121.58
202.83
107.23 59.81
67.65 101.42
60.79
167.04 17.0
44.95 .&5
1.00
22.29 22.66
933.78 11.15
106.50
58.76
17(.
169.06 -1&.0
60.79
58.76
77.65 89.39
83.85 85.22
60.79
38.83
29.38 41.92
44.69 30.39
42.61
38.83
71.31 71."1
75.09 -75.0&
42.61
38.83
33.15 38.16
37.24 37.85
42.61
16.57
19.41 18.62
19.08 21.30
18.92
16.57
38.03 "(.0"
40.38 -0."(
16.57
17.68 20.35
20.03 20.35
8.84
8.29 10.01
10.18 9.46
8.84 8.84
0.00 -2122.(
18.30 1(."0 8.51 9.79
-2122.( 2122.( 57.(2
19.64 -1&.
D8C
18.92 18.92 10.18 DM8
9.74 9.90
-155. 155. 155.
10.18 10.18
0.00
592.87
592.87 185.47
185.47 505.12
505.12
3129.99
3129.99 2719.07
2719.07 2675.36
2675.36
2537.12
3722.87 2904.55
2533.60 3180.48
2170.24
2537.12
6627.41
5714.08
2170.24
.- CALC!LO DE MOM 17(.
17(. 3.58
17(. 3.11
3.06 2537.12 = 2537.12 x
2904.55 2537.12
3180.48
=
0
=
x x
+
+
-
+
mx = 2537.12
-
2170.24 3722.87
2533.60 2904.55 = 2904.55 x =
-
0
=
x
+
+
x
mx = 2904.55
1840.61
2412.33
2892.44
3180.48 = 3180.48 x =
0
=
x x
mx = 3180.48
ENTOS MA
M V
x
1748.6 x2 2 2537.12 1748.6 x = 0 =
x=
2537.12
1.5
1748.6 ( 1.45
) 1748.6 ( 1.45 ) )2 2
Mmx =
1(0.1
Mmx =
212.""
Mmx =
2(&2.
2 1748.6 1748.6 -,*m
M V
x
1748.6 x2 2 2904.55 1748.6 x = 0 =
x=
2904.55
1.
1748.6 ( 1.66
) 1748.6 ( 1.66 ) )2 2
1748.6 1748.6 -,*m
M V
x
1748.6 x2 2 3180.48 1748.6 x = 0 =
3180.48
x=
1.(2
1748.6 ( 1.82
) 1748.6 ( 1.82 ) )2 2
".- CALC!
METODO CROSS VIGAS
17(.
&&.2
".5(
&&.2 ".11
".0
1.- CALC!LO DE RIGIDES RELATIVO = 4EI*L 12 = 4E1I1*L 4E1I1*L1 1
23 = 4E2I1* 4E2I1*L2 L2
34 = 4E3I1*L 4E3I1*L3 3
, PARA SECCION CONSTANTE 39: = 1/L 12 =
1
=
0.2(
=
0."2
=
0.""
3.58 23 =
1 3.11
34 =
1 3.06
2.- 8ACTOR DE DISTRI!CION DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO D = *-L D12=
0.28 0.00
D21=
D23=
D32=
D34=
D43=
0.5
=
0.50
=
0.50
=
1
+ 0.33 0.33
0.33
=
+ 0.33 0.33
0.32
0.
+ 0.32 0.32
0.32
=
+ 0.32 0.32
0.28
1
+ 0.28 0.28
0.28
=
+ 0.00
O DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO
17(. 39: 8;9: ME
3.58
M12
M21
12= 21=
'L2
=
1748 17 48.6 .6 x 3. 3.58 58 2 =
12
1(7.5
12
D T D T
&&.2 D 3 .1 1
T
M2"
M"2 D T 23= 32=
'L2
=
12
699. 69 9.2 2 x 3. 3.11 11 2 =
5".5
12
D T D
&&.2
T
3 .0 6
D
M"
M"
34= 43=
'L2 12
=
699. 69 9.2 2 x 3. 3.06 06 2 = 12
55.5&
V VI V R
17(.
&&.2 ".5(
".11
0.2(
".0
0."2
1.00
0.""
0. 0.5
1867.56
0.50 0.50
1867.56 563.56
1867.56
1867.56
1304.00 1"0.00
929.32 &2&."2
303.10
432.02 497.31
216.01
151.55 154.16
216.01
216.01 71.06
305.71 "05.71
17.98 17.&(
545.59 545.59
348.90 272.79
4.53
621.70 -21.70
308.33 313.37
4.53
248.65 2.27
4.53 156.68
246.39 -2."&
156.68
142.12 163.60
122.20 124.19
156.68
108.00 61.10
81.80 78.34
62.10
169.10 1&.10
545.59
8.91 9.06
933.78 4.46
303.10
1.00
563.56 545.59
606.20 697.81
303.10
71.06
&&.2
160.14 -10.1
62.10
71.06
78.61 90.49
79.42 80.72
62.10
39.31
35.53 39.71
45.25 31.05
40.36
39.31
75.24 75.2
76.29 -7.2&
40.36
39.31
34.98 40.26
37.84 38.46
40.36
17.49
19.65 18.92
20.13 20.18
19.23
17.49
38.57 "(.57
40.31 -0."1
17.49
17.93 20.64
19.99 20.32
8.97
8.74 10.00
10.32 9.61
8.97 8.97
0.00 -1(0.2
18.74 1(.7 8.71 10.03
-1(0.2 1(0.2 127.01
19.23 19.23 10.16 DM8
19.93 -1&.&"
9.89 10.05
10.16 10.16
-"77.2 "77.2
0.00 "77.2
503.98
503.98 458.84
458.84 123.29
123.29
3129.99
3129.99 1087.26
1087.26 1069.78
1069.78
2626.01
3633.98 1546.10
628.41 1193.06
2626.01
5180.08
1821.47
D8C
946.49
946.49
.- CALC!LO DE MOM 17(.
&&.2 3.58
&&.2 3.11
3.06 2626.01 = 2626.01 x
1546.10 2626.01
1193.06
=
0
=
x x
+
+
-
+
mx = 2626.01
-
946.49 3633.98
628.41 1546.10 = 1546.10 x =
-
0
=
x
+
+
x
mx = 1546.10
1971.84
1709.40
1017.88
1193.06 = 1193.06 x =
0
=
x x
mx = 1193.06
ENTOS MA
M V
x
1748.6 x2 2 2626.01 1748.6 x = 0 =
x=
2626.01
1.50
1748.6 ( 1.50
) 1748.6 ( 1.50 )2
Mmx =
1&71.(
Mmx =
170&.0
Mmx =
1017.((
2 699.2 -,*m
M V
x
699.2
x2 2
1546.10 =
699.2 x = 0
x=
1546.10
2.21
699.2 ( 2.21
) 699.2 ( 2.21 )2
699.2 -,*m
M V
x
699.2
x2 2
1193.06 =
1193.06
699.2 x = 0
x=
1.71
699.2 ( 1.71
) 699.2 ( 1.71 )2
".- CALC!
METODO CROSS VIGAS
17(.
17(.
".5(
17(. ".11
".0
1.- CALC!LO DE RIGIDES RELATIVO = 4EI*L 12 = 4E1I1*L 4E1I1*L1 1
23 = 4E2I1* 4E2I1*L2 L2
34 = 4E3I1*L 4E3I1*L3 3
, PARA SECCION CONSTANTE 39: = 1/L 12 =
1
=
0.2(
=
0."2
=
0.""
3.58 23 =
1 3.11
34 =
1 3.06
2.- 8ACTOR DE DISTRI!CION DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO D = *-L D12=
0.28 0.00
D21=
D23=
D32=
D34=
D43=
0.5
=
0.50
=
0.50
=
1
+ 0.33 0.33
0.33
=
+ 0.33 0.33
0.32
0.
+ 0.32 0.32
0.32
=
+ 0.32 0.32
0.28
1
+ 0.28 0.28
0.28
=
+ 0.00
O DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO
17(. 39: 8;9: ME
3.58
M12
M21
12= 21=
'L2
=
1748 17 48.6 .6 x 3. 3.58 58 2 =
12
1(7.5
12
D T D T
17(. D 3 .1 1
T
M2"
M"2 D T 23= 32=
'L2
=
1748 17 48.6 .6 x 3. 3.11 11 2 =
12
10&."&
12
D T D
17(.
T
3 .0 6
D
M"
M"
34= 43=
'L2 12
=
1748 17 48.6 .6 x 3. 3.06 06 2 = 12
1"."
V VI V R
17(.
17(. ".5(
".11
0.2(
".0
0."2
1.00 1867.56 1867.56
1 8 6 7 .5 6
0.""
0. 0.5
0.50 0.50
1867.56 14 1 4 0 9 .3 9
1409.39 13 1364.43
458.18 5(.1(
212.99 245.18
1 0 6 .5 0
922.63 &22."
106.50
428.91 49 493.73
2 1 4 .4 5
53.25 199.57
214.45
214.45 58.76
252.82 252.(2
1 3 6 4 .4 3
1364.43 1 3 6 4 .4 3
1 2 2 .5 9 6 8 2 .2 2
804.81 -(0.(1
1 1 .3 3
399.14 4 405.66
11.33
2 4 6 .8 6 5 .6 6
241.20 -21.20
11.33 2 0 2 .8 3
202.83
117.53 13 135.29
119.62 1 121.58
2 0 2 .8 3
107.23 59.81
6 7 .6 5 1 0 1 .4 2
60.79
167.04 17.0
44.95 .&5
1.00
22.29 22.66
933.78 11.15
106.50
58.76
17(.
169.06 -1&.0
60.79
58.76
77.65 89.39
83.85 85.22
6 0 .7 9
38.83
29.38 41.92
44.69 30.39
42.61
38.83
71.31 71."1
75.09 -75.0&
42.61
38.83
33.15 38.16
37.24 37.85
4 2 .6 1
16.57
19.41 18.62
19.08 21.30
18.92
16.57
38.03 "(.0"
40.38 -0."(
16.57
17.68 20.35
20.03 20.35
8.84
8.29 10.01
10.18 9.46
8.84 8 .8 4
0.00 -2122.(
18.30 1(."0 8 . 5 1 9 .7 9
-2122.( 2122.( 57.(2
19.64 -1&.
D8C
18.92 1 8 .9 2 10.18 DM8
9.74 9.90
-155. 155. 155.
10.18 1 0 .1 8
0.00
592.87
592.87 18 185.47
185.47 50 505.12
5 0 5 .1 2
3129.99
3129.99 27 2719.07
2719.07 26 2675.36
2 6 7 5 .3 6
2537.12
3722.87 2904.55
2533.60 3180.48
2170.24
2537.12
6627.41
5714.08
2170.24
.- CALC!LO DE MOM 17(.
17(. 3.58
17(. 3.11
3.06 2537.12 = 2537.12 x
2904.55 2537.12
3180.48
=
0
=
x x
+
+
-
+
mx = 2537.12
-
2170.24 3722.87
2533.60 2904.55 = 2904.55 x =
-
0
=
x
+
+
x
mx = 2904.55
1840.61
2412.33
2892.44
3180.48 = 3180.48 x =
0
=
x x
mx = 3180.48
ENTOS MA
M V
x
1748.6 x2 2 2537.12 1748.6 x = 0 =
x=
2537.12
1.5
1748.6 ( 1.45
) 1748.6 ( 1.45 )2
Mmx =
1(0.1
Mmx =
212.""
Mmx =
2(&2.
2 1748.6 -,*m
M V
x
1748.6 x2 2 2904.55 1748.6 x = 0 =
x=
2904.55
1.
1748.6 ( 1.66
) 1748.6 ( 1.66 )2
1748.6 -,*m
M V
x
1748.6 x2 2 3180.48 1748.6 x = 0 =
3180.48
x=
1.(2
1748.6 ( 1.82
) 1748.6 ( 1.82 )2
11&. /m
11&. /m
11&. /m
2=
"022.7 /m
20(." /m
"022.7 /m
1=
".(2 m VIGAS6 COL!MNAS6
".17 m
0.20
0.40 m
0.25
0.25 m
.0 m
1.- CALC!LO DE RIGIDE RELATIVO =4EI*L E=15200*
:c
I=;/3*12 15=26=37=48=%<3*L=
59=610=711=812=%<3*L= 56=910=%<3*L=
0.25 ( 0.25 ) 3 .* 3.00 =
0.25 ( 0.25 ) 3 .* 2.80 = 0.20 ( 0.40 ) 3 .* 3.82 =
67=1011=%<3*L=
0.20 ( 0.40 ) 3 .* 3.17 =
78=1112=%<3*L=
0.20 ( 0.40 ) 3 .* 4.06 =
1.72 103 1.(5 103 .( 103 5.(5 103 .57 103
2.- CALC!LO DE 8ACTOR DE DISTRI!CION DE MOMENTOS =*L D15=
1.72
* I> + 1.72
=
I>
=
0.20
=
0.5(
=
0.22
2.(0 D51=
1.72 1.72
D56=
4.86 1.72
".00
+ 4.86 + 1.85
D59=
+ 4.86 + 1.85 1.85
1.72 D62=
1.72 1.72
D65=
D610=
D67=
D73=
D76=
D711=
D78=
=
0.1 1.00
=
0.12
=
0.2
=
0.""
=
0.1"
+ 5.85 + 4.57 + 1.85 1.85
1.72
0.1
+ 5.85 + 4.57 + 1.85 4.57
1.72
=
+ 5.85 + 4.57 + 1.85 5.85
1.72
0."
+ 4.86 + 5.85 + 1.85 1.72
1.72
=
+ 4.86 + 5.85 + 1.85 1.85
1.72
0.12
+ 4.86 + 5.85 + 1.85 5.85
1.72
=
+ 4.86 + 5.85 + 1.85 4.86
1.72
1.00
+ 4.86 + 1.85
+ 5.85 + 4.57 + 1.85
1.00
D84=
1.72
=
0.21
=
0.5
=
0.2"
1.72 + 4.57 + 1.85 D87=
4.57 1.72 + 4.57 + 1.85
D812=
1.85
1.00
1.72 + 4.57 + 1.85 D95=
1.85
=
0.2(
=
0.72
1.85 + 4.86 D910=
4.86
1.00
1.85 + 4.86 D106=
1.85
=
0.15
=
0."&
=
0.7
1.85 + 4.86 + 5.85 D109=
4.86 1.85 + 4.86 + 5.85
D1011=
5.85
1.00
1.85 + 4.86 + 5.85 D117=
1.85
=
0.1
=
0."
=
0.1
1.85 + 4.86 + 4.57 D1110=
4.86 1.85 + 4.86 + 4.57
D1112=
4.57
1.00
1.85 + 4.86 + 4.57 D128=
1.85 1.85 +
D1211=
0.2&
=
0.71
4.57 4.57
1.85 +
=
4.57
1.00
".- CALC!LO DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO "022.7 /m 3.82
M5
M5
56= 65=
'L2
= 3022.74
12
3.82 2 =
"75.75
3.17 2 =
1715."0
4.06 2 =
152.1
12
20(." /m 3.17
M7
M7(
67= 78=
'L2
= 2048.34
12
12
"022.7 /m 4.06
M7(
M(7
78= 87=
'L2 12
= 3022.74 12
11&. /m
0.2(
3.82
392.13
M&10
M10&
403.33 317.65 87.58
910= 109=
'L2
= 1169.6
12
3.82 2
122.27
=
12
15.09 33.01 9.10 33.49 105.09
11&. /m
28.98 736.59
3.17
0.00
M1011
M1110
1011= 1110=
'L2
= 1169.6
12
3.17 2
&7&."
=
12
11&. /m 4.06
M1112
M1211
0.20 749.98
1112= 1211=
'L2 12
= 1169.6 12
4.06 2
10.0
=
137.54 28.06 305.24 62.28 43.24 8.82 849.14 0.00
0.72 122.27 -122.27
0."& -122.27
1030.14
171.35
85.68
515.07
"17.5
230.07 48.10
0." -&7&." 0.1
442.84
0.7 &7&." 2.(
0.1 10.0 627.2 -27.17
0.71 -10.0 10.0
65.23
206.26
270.22 102.86 254.09
1143.64
462.96 471.83
0.15
401.56 135.11 248.61
2(.1
96.20
36.62
115.80
115.04
314.71
59.66
-"".01
23.91
143.20
71.60
11.95
105.0&
370.09 -"70.0& 54.51 172.37 57.52
57.63
103.13
571.82
127.05
276.94
-27.&
-".7& 344.79
45.42
112.2
245.43
99.35
57.90 202.71 122.72
56.10
46.67
119.32
267.53
27.5"
115.27
43.88
108.39
73.16
29.61
86.19
6.28
36.58
54.19
23.27
43.33
".""
-77. 77.46
7.11
17.55
55.14
22.32
691.7 1851.93
819.33
819.33
76.12
39.93
15.20
48.07
18.67
736.59
1749.84
805.93
943.91
1160.19
0.00
102.77 102.77
0.00
0.00
1070.15
1615.18
1272.97
1373.66
9.49
43.92
31.89
8.89
4.55
27.26
21.94
36.58
66.99
115.04
12.57
46.54
43.79
18.31
22.71
122.72
30.18
629.42
405.43
93.34
196.07
32.61
51.43
571.82
806.66
803.13
796.02
943.67
0.1
0.5( "75.75 -"75.75
0." -"75.75
2119.12
667.21
333.61
1059.56
-1"7.5
0.""
0.1 0.12 1715."0 1960.46 1&0.5 236.13
253.98 509.49
1536.43 15"."
79.29
522.90
261.45
39.65
-"05.2
175.98
95.58
47.79
87.99
-".2
24.93
36.48
1919.29
3540.77
185.06
199.05
0.1" 152.1 2436.8 -2".(
0.5 -152.1 152.1
0.21
1018.98 299.60 322.24
2331.11
877.36
126.99
518.98 152.59
280.83
2(0.("
33.83
36.38
16.09
8.04
18.19
12.91
13.89
467.93 1457.66 0.00
1165.56 1241.12 -121.1
99.52
107.20
0.2"
0.2 -1715."0 0.12
259.49
107.20
0.2&
398.0
103.20 -10".20
0.22
.- VERI8IC
161.12
-10.70 410.70
164.12
230.58
115.29
82.06
38.47
"(.7
4.73
5.09
114.97
57.48
2.54
86.78
20.7( 204.78 43.27
97.61
-&7.1
-"&.12 39.12
12.00
12.91
21.96
8.27
3033.3 459.46
4765.7
2199.23
825.58
40.82
0.00
0.00
0.00
0.00
0.00
0.00
374.99
118.07
149.80
438.68
14.03
92.53
76.29
43.39
31.14
16.91
2.37
21.63
4.41
6.46
6.00
4.13
424.57
233.97
229.73
412.79
CION DE MOMENTOS POR N!DOS 5=0 -(&.1
+ -1070.15 +
1&1&.2&
=
0.00
-"50.77 + 7.&" + 115.1( + 157. =
0.00
7".5&
=0 -7".5&
7=0 -"0"".2( + -5&. + -1272.&7 + 75.70 =
0.00 "0.70
(=0 -21&&.2" + 1"7". +
(25.5(
=
0.00 1&1&.2&
&=0 -7".5&
+ 7".5&
=
0.00 -(&.1
10=0
-1070.15
-17&.( + (05.&" +
&".&1
=
0.00
11=0
(27".
-110.1& + -&1.7 + 1(51.&"
=
0.00
=
0.00
12=0 -(1&.""
+ (1&.""
NOTA6 CAMIAR EL SIGNO DE )) POR EL SIGNO DE LA S!MATORIA? A TODOS
5.- CALC!LANDO EL M 11&. -17&.(
-110.1& &".&1
1(51.&"
-(1&.""
3.82 $I= $<=
(05.&" -&1.7
(1&.""
11&. 252".1&
"77".1&
736.59
x 2499.18
-"50.77
-"0"".2( 157.
7.&" 115.1(
75.70
-21&&.2"
-5&.
(25.5( -1272.&7
Mmx= 2499.18
1"7".
&17&.
11&. 3.17 $I= $<=
11&. 943.91
x 1922.04
Mmx= 1922.04
OMENTO MA
m
3.82
22"".&
=
4.06
2 $I=
22"".& -25.25
736.59
1749.84
-25.25
=
$<=
3.82
V= 2&&.1( 11&. /m = 2499.18 x
1169.6 x2
$
736.59
1851.93
x
2 =
0
2119.95
x 2499.18
1169.6 x
x = 2499.18
=
0
x=
2.1
1169.6
Mmx= 2119.95
2.14
1169.6 2.14 2
736.59
2
Mmx= "0.70 "022.7 /m 1169.6 m
3.17
1(5".(2
=
3.82
2 $I=
1(5".(2 -(.2"
943.91
1160.19
-(.2"
=
$<=
3.17
V= 1&22.0 "022.7 /m = 1922.04
x
1169.6 x2
$
943.91
1919.29
x
2 =
0
6197.91
x 1922.04
1169.6 x
x = 1922.04
=
0
x=
1.
1169.6
Mmx= 6197.91
1.64
1169.6 1.64 2 2
943.91
Mmx= 252".1&
/m
"022.7 1169.6
m
4.06
=
2"7.2&
2
2"7.2& 25.""
1851.93
819.33
=
4.06
25.""
$I=
4.06
$<=
V= 211&.&5 /m
"022.7 = 2119.95
x
1169.6 x2
$
1851.93
2 =
4765.70
x
0
x
5165.69 2119.95
1169.6 x
x = 2119.95
=
0
x=
1.(1
1169.6
1.81
1169.6 1.81 2
1851.93
2
Mmx= "77".1&
/m 3022.74 m
3.82
=
577"."
=
-2.7
2
577"." -2.7
1919.29
3540.77 3.82
V= 1&7.&1 /m = 6197.91
x 3022.74 x2
$
1919.29
2 =
0
x 6197.91
3022.74 x
x = 6197.91
=
0
x=
2.05
3022.74
2.05
3022.74 2.05 2 2
Mmx= (27".
1919.29
Mmx= 5165.69
/m 3022.74 m
4.06
=
1".1
=
&70.7
2
1".1 &70.7
4765.70
825.58 4.06
V= 515.& /m = 5165.69
x 3022.74 x2
$
4765.70
2 =
0
x 5165.69
3022.74 x
x = 5165.69
=
0
x=
1.71
3022.74
1.71
3022.74
1.71 2 2
Mmx= &17&.
4765.70
2.- CALC 11&. /m
11&. /m
11&. /m
2= 2.(0
"022.7 /m
20(." /m
20(." /m
1= ".00
".(2 m VIGAS6 COL!MNAS6
".17 m
0.20
0.40 m
0.25
0.25 m
.0 m
1.- CALC!LO DE RIGIDE RELATIVO =4EI*L E=15200*
:c
I=;/3*12 15=26=37=48=%<3*L= 0.25 ( 0.25 ) 3 .* 3.00 = 59=610=711=812=%<3*L 0.25 ( 0.25 ) 3 .* 2.80 = 56=910=%<3*L=
0.2 (
0.4
) 3 .* 3.82 =
67=1011=%<3*L=
0.2 (
0.4
) 3 .* 3.17 =
78=1112=%<3*L=
0.2 (
0.4
) 3 .* 4.06 =
1.72 102 1.(5 102 .( 102 5.(5 102 .57 102
LO DE 8ACTOR DE DISTRI!CION DE MOMENTOS =*L D15=
1.72
D51=
* I> + 1.72 1.72
1.72 D56=
D59=
D62=
D65=
D610=
D67=
D73=
D76=
D711=
D78=
0.12
=
0."
=
0.1
=
0.1 1.00
=
0.12
=
0.2
=
0.""
=
0.1"
+ 5.85 + 4.57 + 1.85 1.85
1.72
=
+ 5.85 + 4.57 + 1.85 4.57
1.72
1.00
+ 5.85 + 4.57 + 1.85 5.85
1.72
0.22
+ 4.86 + 5.85 + 1.85 1.72
1.72
=
+ 4.86 + 5.85 + 1.85 1.85
1.72
0.5(
+ 4.86 + 5.85 + 1.85 5.85
1.72
=
+ 4.86 + 5.85 + 1.85 4.86
1.72
0.20
+ 4.86 + 1.85 1.72
1.72
=
+ 4.86 + 1.85 1.85
1.72
I>
+ 4.86 + 1.85 4.86
1.72
=
+ 5.85 + 4.57 + 1.85
1.00
D84=
1.72
=
0.21
=
0.5
=
0.2"
1.72 + 4.57 + 1.85 D87=
4.57 1.72 + 4.57 + 1.85
D812=
1.85
1.00
1.72 + 4.57 + 1.85 D95=
1.85
=
0.2(
=
0.72
1.85 + 4.86 D910=
4.86
1.00
1.85 + 4.86 D106=
1.85
=
0.15
=
0."&
=
0.7
1.85 + 4.86 + 5.85 D109=
4.86 1.85 + 4.86 + 5.85
D1011=
5.85
1.00
1.85 + 4.86 + 5.85 D117=
1.85
=
0.1
=
0."
=
0.1
1.85 + 4.86 + 4.57 D1110=
4.86 1.85 + 4.86 + 4.57
D1112=
4.57
1.00
1.85 + 4.86 + 4.57 D128=
1.85 1.85 +
D1211=
0.2&
=
0.71
4.57 4.57
1.85 +
=
4.57
1.00
".- CALC!LO DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO "022.7 /m 3.82
M5
M5
56= 65=
'L2
= 3022.74
12
3.82 2 =
"75.75
3.17 2 =
1715."0
4.06 2 =
2(1".7
12
20(." /m 3.17
M7
M7(
67= 78=
'L2
= 2048.34
12
12
20(." /m 4.06
M7(
M(7
78= 87=
'L2 12
= 2048.34 12
11&. /m
0.2(
3.82
392.13
M&10
M10&
403.33 317.65 87.58
910= 109=
'L2
= 1169.6
12
3.82 2
122.27
=
12
15.09 33.01 9.10 28.27 79.67
11&. /m
21.97 738.38
3.17
0.00
M1011
M1110
1011= 1110=
'L2
= 1169.6
12
3.17 2
&7&."
=
12
11&. /m 4.06
M1112
M1211
0.20 749.98
1112= 1211=
'L2 12
= 1169.6 12
4.06 2
10.0
=
137.54 28.06 257.62 52.56 29.87 6.09 836.70 0.00
0.72 122.27 -122.27
0."& -122.27
1030.14
171.35
85.68
515.07
"17.5
230.07
96.20
48.10
115.04
-"".01
23.91
102.80
51.40
11.95
7&.7
0." -&7&." 0.1
442.84
0.7 &7&." 2.(
0.1 10.0 627.2 -27.17
0.71 -10.0 10.0
65.23
206.26
270.22 102.86 254.09
1143.64
462.96 319.74
0.15
401.56 135.11
571.82
127.05
495.55
-&5.
-1&2.& 192.69
81.27
200.8
137.16
55.53
257.39 106.75
57.90 141.35
68.58
100.38
56.73
265.67 -25.7
39.13 123.74
2(.1
36.62
115.80
213.51
152.03
152.0"
65.50
24.93
61.59
111.84
45.27
157.11 157.11
61.87
16.23
55.92
30.80
14.30
41.43
32.75
62.23
-2.2"
10.28
-10.2(
1.69
4.16
32.10
12.99
465.4 1768.33
717.02
717.02
57.70
24.08
9.17
28.98
4.43
738.38
1693.59
753.93
939.65
1302.93
0.00
-5.0& 45.09
0.00
0.00
1056.76
1462.05
708.51
1099.56
6.56
29.93
19.89
14.20
4.55
19.57
12.47
55.92
56.54
82.86
32.46
28.59
43.79
18.31
40.64
68.58
30.18
514.78
282.69
113.45
196.07
32.61
51.43
571.82
806.66
803.13
358.80
639.47
0.22
0.1
0.5( "75.75 -"75.75
0." -"75.75
2119.12
667.21
333.61
1059.56
-1"7.5
0.""
0.1 0.12 1715."0 1960.46 1&0.5 236.13
253.98 229.65
1256.59 125.5&
79.29
427.66
213.83
39.65
-257.2
148.52
68.84
34.42
74.26
-2&.(7
17.22
24.86
1893.46
3660.64
0.2&
179.4
248.61
103.13
.- VERI8IC
151.35
162.79
0.2 -1715."0 0.12
0.1" 2(1".7 1098.4 -10&(."7
0.5 -2(1".7 2(1".7
0.21
459.29 135.04 145.25
1579.66
594.53
126.99
72.62
-(5.
-&&.20 499.20
361.87 106.40
114.44
280.26 105.48
81.40
202.27
202.27
24.36
26.20
41.55
20.78
13.10
73.05
7".05
8.80
9.46
0.00
789.83 865.39
180.93
420.65 1777.94
0.2"
140.13
57.22
99.37
&&."7
125.(0 125.80
12.22
13.14
70.63
35.31
6.57
26.58
60.88
-0.((
7.49
8.05
35.08
13.20
2298.9 236.70
3244.1
1601.99
502.43
25.46
0.00
-2.& 62.49
0.00
0.00
0.00
0.00
0.00
374.99
118.07
67.52
297.27
14.03
75.68
53.20
52.74
26.28
12.18
6.11
13.29
3.05
4.40
3.74
6.60
418.35
210.32
118.35
251.22
CION DE MOMENTOS POR N!DOS 5=0 -(".70
+ -105.7 +
1(&".
=
0.00
-"0. + 20.5 + 12.05 + 1777.& =
0.00
7"(."(
=0 -7"(."(
7=0 -22&(.(7 + -2".70 +
-70(.51
+ "2.0& =
0.00 ""7.12
(=0 -101.&& + 10&&.5 +
502."
=
0.00 1(&".
&=0 -7"(."(
+ 7"(."(
=
0.00 -(".70
10=0
-105.7
-1&".5& + 75".&" +
&"&.5
=
0.00
11=0
("2.0(
-1"02.&" + -5.0 + 17(.""
=
0.00
=
0.00
12=0 -717.02
+ 717.02
NOTA6 CAMIAR EL SIGNO DE )) POR EL SIGNO DE LA S!MATORIA? A TODOS
5.- CALC!LANDO EL M 11&. -1&".5&
-1"02.&" &"&.5
17(.""
-717.02
3.82 $I= $<=
75".&" -5.0
717.02
11&. 25&.05
"(1.2
738.38
x 2483.99
-"0.
-22&(.(7 1777.&
20.5 12.05
"2.0&
-101.&&
-2".70
502." -70(.51
Mmx= 2483.99
10&&.5
205.07
11&. 3.17 $I= $<=
11&. 939.65
x 1968.41
Mmx= 1968.41
OMENTO MA
m
3.82
22"".&
=
4.06
2 $I=
22"".& -250.05
738.38
1693.59
-250.05
=
$<=
3.82
V= 2(".&& 11&. /m = 2483.99 x
1169.6 x2
$
738.38
1768.33
x
2 =
0
2115.35
x 2483.99
1169.6 x
x = 2483.99
=
0
x=
2.12
1169.6
Mmx= 2115.35
2.12
1169.6 2.12 2
738.38
2
Mmx= ""7.12 "022.7 /m 1169.6 m
3.17
1(5".(2
=
3.82
2 $I=
1(5".(2 -11.0
939.65
1302.93
-11.0
=
$<=
3.17
V= 1&(.1 "022.7 /m = 1968.41
x
1169.6 x2
$
939.65
1893.46
x
2 =
0
6236.05
x 1968.41
1169.6 x
x = 1968.41
=
0
x=
1.(
1169.6
Mmx= 6236.05
1.68
1169.6 1.68 2 2
939.65
Mmx= 25&.05
/m
20(." 1169.6
m
4.06
=
2"7.2&
2
2"7.2& 25(.&
1768.33
717.02
=
4.06
25(.&
$I=
4.06
$<=
V= 2115."5 /m
20(." = 2115.35
x
1169.6 x2
$
1768.33
2 =
3244.09
x
0
x
3482.84 2115.35
1169.6 x
x = 2115.35
=
0
x=
1.(1
1169.6
1.81
1169.6 1.81 2
1768.33
2
Mmx= "(1.2
/m 3022.74 m
3.82
=
577"."
=
-2.1
2
577"." -2.1
1893.46
3660.64 3.82
V= 2".05 /m = 6236.05
x 3022.74 x2
$
1893.46
2 =
0
x 6236.05
3022.74 x
x = 6236.05
=
0
x=
2.0
3022.74
2.06
3022.74 2.06 2 2
Mmx= ("2.0(
1893.46
Mmx= 3482.84
/m 2048.34 m
4.06
=
15(.1"
=
75.2&
2
15(.1" 75.2&
3244.09
502.43 4.06
V= "(2.( /m = 3482.84
x 2048.34 x2
$
3244.09
2 =
0
x 3482.84
2048.34 x
x = 3482.84
=
0
x=
1.70
2048.34
1.70
2048.34
1.70 2 2
Mmx= 205.07
3244.09
2.- CALC "0 /m
"0 /m
"0 /m
2= 2.(0
17(. /m
&&.2 /m
&&.2 /m
1= ".00
".5( m VIGAS6 COL!MNAS6
".11 m
0.20
0.30 m
0.25
0.25 m
".0 m
1.- CALC!LO DE RIGIDE RELATIVO =4EI*L E=15200*
:c
I=;/3*12 15=26=37=48=%<3*L= 0.25 ( 0.25 ) 3 .* 3.00 = 59=610=711=812=%<3*L 0.25 ( 0.25 ) 3 .* 2.80 = 56=910=%<3*L=
0.2 (
0.3
) 3 .* 3.58 =
67=1011=%<3*L=
0.2 (
0.3
) 3 .* 3.11 =
78=1112=%<3*L=
0.2 (
0.3
) 3 .* 3.06 =
1.72 103 1.(5 103 2.1& 103 2.52 103 2.5 103
LO DE 8ACTOR DE DISTRI!CION DE MOMENTOS =*L D15=
1.72
D51=
* I> + 1.72 1.72
1.72 D56=
D59=
D62=
D65=
D610=
D67=
D73=
D76=
D711=
D78=
0.21
=
0.2
=
0."0
=
0.2 1.00
=
0.20
=
0.2&
=
0."0
=
0.21
+ 2.52 + 2.56 + 1.85 1.85
1.72
=
+ 2.52 + 2.56 + 1.85 2.56
1.72
1.00
+ 2.52 + 2.56 + 1.85 2.52
1.72
0."2
+ 2.19 + 2.52 + 1.85 1.72
1.72
=
+ 2.19 + 2.52 + 1.85 1.85
1.72
0."(
+ 2.19 + 2.52 + 1.85 2.52
1.72
=
+ 2.19 + 2.52 + 1.85 2.19
1.72
0."0
+ 2.19 + 1.85 1.72
1.72
=
+ 2.19 + 1.85 1.85
1.72
I>
+ 2.19 + 1.85 2.19
1.72
=
+ 2.52 + 2.56 + 1.85
1.00
D84=
1.72
=
0.2(
=
0.2
=
0."0
1.72 + 2.56 + 1.85 D87=
2.56 1.72 + 2.56 + 1.85
D812=
1.85
1.00
1.72 + 2.56 + 1.85 D95=
1.85
=
0.
=
0.5
1.85 + 2.19 D910=
2.19
1.00
1.85 + 2.19 D106=
1.85
=
0.2(
=
0.""
=
0."(
1.85 + 2.19 + 2.52 D109=
2.19 1.85 + 2.19 + 2.52
D1011=
2.52
1.00
1.85 + 2.19 + 2.52 D117=
1.85
=
0.2(
=
0.""
=
0."&
1.85 + 2.19 + 2.56 D1110=
2.19 1.85 + 2.19 + 2.56
D1112=
2.56
1.00
1.85 + 2.19 + 2.56 D128=
1.85 1.85 +
D1211=
0.2
=
0.5(
2.56 2.56
1.85 +
=
2.56
1.00
".- CALC!LO DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO 17(. /m 3.58
M5
M5
56= 65=
'L2
= 1748.6
12
3.58 2 =
1(7.5
3.11 2 =
5".5
3.06 2 =
55.5&
12
&&.2 /m 3.11
M7
M7(
67= 78=
'L2
=
12
699.2 12
&&.2 /m 3.06
M7(
M(7
78= 87=
'L2 12
=
699.2 12
"0 /m
0.
3.58
166.29
M&10
M10&
299.91 285.04 130.53
910= 109=
'L2
=
12
340
3.58 2
"".1"
=
12
14.34 31.28 14.32 17.70 36.55
"0 /m
16.74 336.65
3.11
0.00
M1011
M1110
1011= 1110=
'L2
=
12
340
3.11 2
27.0
=
12
"0 /m 3.06
M1112
M1211
0."0 557.68
1112= 1211=
'L2 12
=
340 12
3.06 2
25."0
=
89.31 26.67 110.21 32.91 16.32 4.87 622.13 0.00
0.5 "".1" -"".1"
0."" -"".1"1
89.09
0."( 27.0 (&.0&
196.85
29.74
25.12
14.87
98.42
198.44
2(5.0
0.2(
0."" -27.0 0.2(
8.7
0."& 25."0 (.7
34.22
2.90
2.45
3.39
154.01
111.29
1.45
17.11
2.7
77.00
1.70
82.33
96.78
-&.(
-(.02 84.02
101.46 -101.
0.5( -25."0 25."0
.- VERI8IC 0.2
154.52
33.87
28.61
38.98
32.11
27.13
37.5
48.78
35.25
16.94
77.26
51.72
16.06
19.49
38.60
24.39
18.77
11.91
82.47
(2.7
"0.( 30.68
"1.2(
112.92 -112.&2
16.96
37.70
31.84
43.38
27.37
23.12
31.99
17.81
12.87
18.85
8.48
10.54
13.68
21.69
1.17
8.90
15.99
7.89
32.70
-"2.70
13.96
1".&
".55
-2".(( 23.88
19.81
10.92
9.22
12.56
4.63
3.91
5.41
13.86
10.02
336.65
428.56
216.14
212.43
295.32
34.8
330.08
157.20
157.20
0.00
0.00
0.00
679.87
515.29
83.94
215.70
5.24
11.57
8.94
2.43
7.16
15.92
11.56
8.90
35.40
21.08
2.34
15.78
65.26
14.31
13.56
24.39
28.68
103.43
77.19
23.82
83.14
12.56
1.23
77.00
599.82
396.87
5.32
164.65
0."2
0."0
0."( 1(7.5 -1(7.5
0.2 -1(7.5
710.06
344.90
172.45
355.03
-(&."1
33.96
89.89
44.94
16.98
-110.21
41.90
18.32
9.16
20.95
-1."2
0."0
1304.00
0.2 5".5 1"0.0
270.88
291.35
5.24
2.62
145.68
0.21
339.85
""&.(5
70.60
0.2& -5".5 0.20
0."0 0.2 -55. 55.5&
0.2(
18.0
0.21 55. 17.&(
3.57
3.84
227.85
153.08
113.92
1.92
260.82
-20.(
-7(.&" 78.93
75.93
75.99
51.86
55.78
32.96
37.99
37.97
16.48
27.89
22.15
69.28
&.2(
7.92
-7.&2
52.2( 52.28
14.39
15.48
2.31
1.58
1.69
21.83
1.15
7.74
10.92
0.85
38.03
"(.0"
30.21
-"0.21
14.67
-(.0 8.06
6.21
10.06
7.90
8.50
8.80
6.01
6.46
3.36
2.26
1301.99
1797.35
363.77
918.29
454.0
55.87
593.8
359.05
1 43.35
0.00
0.00
0.00
0.00
0.00
0.00
0.00
278.84
135.44
1.79
76.54
13.33
35.30
25.93
11.07
16.45
7.20
0.79
7.33
2.44
3.95
3.00
1.13
311.06
181.88
27.94
71.67
CION DE MOMENTOS POR N!DOS 5=0 -22.1"
+ -7&.(7 +
1"01.&&
-17&7."5 + "".77 +
515.2&
+
-(".&
+
=
0.00
&1(.2&
=
0.00
5&".(5
=
0.00
"".5
=0 -"".5
7=0 -5.0
+
-55.(7
+
&2(.27 (=0 -"5&.05
+ 215.70
+
1"."5
=
0.00 1"01.&&
&=0 -"".5
+ "".5
=
0.00 -22.1"
10=0 -2(.5
-7&.(7 + 21.1
+
212."
=
0.00
11=0 -2&5."2
"5.& +
-".7
+
""0.0(
=
0.00
=
0.00
12=0 -157.20
+ 157.20
NOTA6 CAMIAR EL SIGNO DE )) POR EL SIGNO DE LA S!MATORIA? A TODOS
5.- CALC!LANDO EL M "0 -2(.5
-2&5."2 212."
""0.0(
-157.20
3.58 $I= $<=
21.1 -".7
157.20
"0 5.&(
.2&
336.65
x 634.27
-17&7."5
-5.0 &1(.2&
"".77 515.2&
5&".(5
-"5&.05
-55.(7
1"."5 -(".&
Mmx= 634.27
215.70
1202.(
"0 3.11 $I= $<=
"0 212.43
x 555.35
Mmx= 555.35
OMENTO MA
m
3.58
0(.0
=
3.06
2 $I=
0(.0 -25.7
336.65
V=
428.56
-25.7
=
$<=
3.58
".27 "0
/m =
634.27 x
340 x2
$
336.65
330.08
x
2 =
0
463.71
x 634.27
340 x
x = 634.27
=
0
x=
1.(7
340
Mmx= 463.71
1.87
340
1.87 2
336.65
2
Mmx=
&2(.27 17(.
/m 340 m
3.11
52(.70
=
3.58
2 $I=
52(.70 -2.5
212.43
V=
295.32
-2.5
=
$<=
3.11
555."5 17(.
/m = 555.35
x
340 x2
$
212.43
1301.99
x
2 =
0
3268.36
x 555.35
x = 555.35
340 x
=
0
x=
1."
340
Mmx= 3268.36
1.63
340
1.63 2 2
212.43
Mmx=
5.&(
/m
&&.2 340
m
3.06
520.20
=
2
520.20 5.&
330.08
V=
157.20
3.06
5.&
=
$I=
3.06
$<=
".71
/m
&&.2 = 463.71
x
340 x2
$
330.08
2 =
593.85
x
0
x
922.55 463.71
340 x
x = 463.71
=
0
x=
1."
340
1.36
340
1.36 2
330.08
2
Mmx=
.2&
/m 1748.6 m
3.58
=
"12&.&&
=
-1"(."7
2
"12&.&& -1"(."7
1301.99
1797.35 3.58
V= "2(." /m = 3268.36
x
1748.6 x2
$
1301.99
2 =
0
x 3268.36
1748.6 x
x = 3268.36
=
0
x=
1.(7
1748.6
1.87
1748.6 1.87 2 2
Mmx= "5.&
1301.99
Mmx= 922.55
/m 699.2 m
3.06
=
10&.7(
=
17.22
2
10&.7( 17.22
593.85
V=
143.35 3.06
&22.55
/m =
922.55
x
699.2 x2
$
593.85
2 =
0
x 922.55
x = 922.55
699.2 x
=
0
x=
1."2
699.2
1.32
699.2
1.32 2 2
Mmx= 1202.(
593.85
2.- CALC "0 /m
"0 /m
"0 /m
2= 2.(0
17(. /m
17(. /m
17(. /m
1= ".00
".5( m VIGAS6 COL!MNAS6
".11 m
0.20
0.30 m
0.25
0.25 m
".0 m
1.- CALC!LO DE RIGIDE RELATIVO =4EI*L E=15200*
:c
I=;/3*12 15=26=37=48=%<3*L= 0.25 ( 0.25 ) 3 .* 3.00 = 59=610=711=812=%<3*L 0.25 ( 0.25 ) 3 .* 2.80 = 56=910=%<3*L=
0.2 (
0.3
) 3 .* 3.58 =
67=1011=%<3*L=
0.2 (
0.3
) 3 .* 3.11 =
78=1112=%<3*L=
0.2 (
0.3
) 3 .* 3.06 =
1.72 103 1.(5 103 2.1& 103 2.52 103 2.5 103
LO DE 8ACTOR DE DISTRI!CION DE MOMENTOS =*L D15=
1.72
D51=
* I> + 1.72 1.72
1.72 D56=
D59=
D62=
D65=
D610=
D67=
D73=
D76=
D711=
D78=
0.21
=
0.2
=
0."0
=
0.2 1.00
=
0.20
=
0.2&
=
0."0
=
0.21
+ 2.52 + 2.56 + 1.85 1.85
1.72
=
+ 2.52 + 2.56 + 1.85 2.56
1.72
1.00
+ 2.52 + 2.56 + 1.85 2.52
1.72
0."2
+ 2.19 + 2.52 + 1.85 1.72
1.72
=
+ 2.19 + 2.52 + 1.85 1.85
1.72
0."(
+ 2.19 + 2.52 + 1.85 2.52
1.72
=
+ 2.19 + 2.52 + 1.85 2.19
1.72
0."0
+ 2.19 + 1.85 1.72
1.72
=
+ 2.19 + 1.85 1.85
1.72
I>
+ 2.19 + 1.85 2.19
1.72
=
+ 2.52 + 2.56 + 1.85
1.00
D84=
1.72
=
0.2(
=
0.2
=
0."0
1.72 + 2.56 + 1.85 D87=
2.56 1.72 + 2.56 + 1.85
D812=
1.85
1.00
1.72 + 2.56 + 1.85 D95=
1.85
=
0.
=
0.5
1.85 + 2.19 D910=
2.19
1.00
1.85 + 2.19 D106=
1.85
=
0.2(
=
0.""
=
0."(
1.85 + 2.19 + 2.52 D109=
2.19 1.85 + 2.19 + 2.52
D1011=
2.52
1.00
1.85 + 2.19 + 2.52 D117=
1.85
=
0.2(
=
0.""
=
0."&
1.85 + 2.19 + 2.56 D1110=
2.19 1.85 + 2.19 + 2.56
D1112=
2.56
1.00
1.85 + 2.19 + 2.56 D128=
1.85 1.85 +
D1211=
0.2
=
0.5(
2.56 2.56
1.85 +
=
2.56
1.00
".- CALC!LO DE MOMENTOS DE EMPOTRAMIENTO PER8ECTO 17(. /m 3.58
M5
M5
56= 65=
'L2
= 1748.6
12
3.58 2 =
1(7.5
3.11 2 =
10&."&
3.06 2 =
1"."
12
17(. /m 3.11
M7
M7(
67= 78=
'L2
= 1748.6
12
12
17(. /m 3.06
M7(
M(7
78= 87=
'L2 12
= 1748.6 12
"0 /m
0.
3.58
166.29
M&10
M10&
299.91 285.04 130.53
910= 109=
'L2
=
12
340
3.58 2
"".1"
=
12
3.62 8.17 3.74 17.61 36.25
"0 /m
16.60 336.81
3.11
0.00
M1011
M1110
1011= 1110=
'L2
=
12
340
3.11 2
27.0
=
12
"0 /m 3.06
M1112
M1211
0."0 557.68
1112= 1211=
'L2 12
=
340 12
3.06 2
25."0
=
22.55 6.73 109.69 32.75 3.55 1.06 584.76 0.00
0.5 "".1" -"".1"
0."" -"".1"1
89.09
0."( 27.0 (&.0&
196.85
29.74
25.12
14.87
98.42
2(5.0
8.7
0."& 25."0 (.7
34.22
2.90
2.45
3.39
154.01
111.29
69.72
1.45
17.11
6.7
77.00
1.70
205.89
27.25
27.25
100.77
-100.(
0.2(
0."" -27.0 0.2(
0.5( -25."0 25."0
.- VERI8IC 0.2
-207.5( 207.58
154.52
9.10
7.68
10.47
33.44
28.25
39.1
120.50
87.08
4.55
77.26
51.12
16.72
5.23
49.92
60.25
19.54
12.35
104.93
10.&"
-(.17
111.66 -111.
"1.(& 31.89
4.43
37.28
31.49
42.89
34.82
29.41
40.70
18.51
13.38
18.64
2.21
6.24
17.41
21.45
0.94
9.26
20.35
14.53
13.13
1".1"
".25
21.43
-21."
19.65
7.16
6.04
8.23
4.36
3.68
5.09
20.25
14.63
336.81
392.10
122.36
269.75
264.51
36.9
301.41
231.03
231.03
0.00
-".(& 34.89
0.00
0.00
648.70
266.24
98.25
439.58
1.14
11.42
11.66
2.59
1.87
15.74
14.71
9.26
35.23
12.48
1.87
29.07
65.26
3.84
14.12
60.25
7.24
102.24
99.83
24.69
83.14
12.56
1.23
77.00
599.82
139.45
13.30
411.78
0."2
0."0
0."( 1(7.5 -1(7.5
0.2 -1(7.5
710.06
121.18
60.59
355.03
22.55
8.57
88.85
44.42
4.29
-10&.&
41.70
10.85
5.42
20.85
-".55
1.35
9.92
1233.46
2008.36
0."0
0.2 0.21 10&."& 458.18 5(.2 95.18
0.2& -10&."& 0.20
102.37
13.10
6.55
51.19
335.92
""5.&2
69.78
0."0
45.0
0.21 1". .&5
0.2 -1". 1"."
8.94
9.61
569.81
284.91
4.81
0.2( 382.84
337.32
-""7."
-(1.(1 81.81
75.05
98.27
67.07
72.14
34.17
49.14
37.53
17.08
36.07
41.01
1.01
8.52
9.16
1.84
0.92
4.58
37.52
"7.52
7.79
8.38
181.27 1560.85 0.00
22.96
6.32
-."2
&."2 96.32
1.26
1.35
40.23
20.11
0.68
27.03
39.40
-"&.0
11.48
7.83
8.43
3.58
2.41
1414.6
67.23
1580.1
824.08
384.51
0.00
-(.5( 8.58
0.00
0.00
0.00
0.00
0.00
278.84
47.59
4.47
191.42
3.37
34.89
33.54
11.48
16.38
4.26
0.63
13.51
0.53
3.90
3.92
1.20
292.38
90.63
33.61
192.25
CION DE MOMENTOS POR N!DOS 5=0 -5(.7
+ -(.70 +
12"".
=
0.00
-200(." + 1(1.27 +
2.2
+ 150.(5 =
0.00
-&(.25
+ 15(0.0 =
0.00
"".(1
=0 -"".(1
7=0 -11.5& +
-7.2"
+
&0&.50 (=0 -(2.0(
+ "&.5(
+
"(.51
=
0.00 12"".
&=0 -"".(1
+ "".(1
=
0.00 -5(.7
10=0 -"&2.10
-(.70 + 122."
+
2&.75
=
0.00
11=0 -2.51
"5.5 +
-".&0
+
"01.1
=
0.00
=
0.00
12=0 -2"1.0"
+ 2"1.0"
NOTA6 CAMIAR EL SIGNO DE )) POR EL SIGNO DE LA S!MATORIA? A TODOS
5.- CALC!LANDO EL M "0 -"&2.10
-2.51 2&.75
"01.1
-2"1.0"
3.58 $I= $<=
122." -".&0
2"1.0"
"0 7(.20
.&5
336.81
x 624.05
-200(."
-11.5& 150.(5
1(1.27 2.2
15(0.0
-(2.0(
-7.2"
"(.51 -&(.25
Mmx= 624.05
"&.5(
"072.5(
"0 3.11 $I= $<=
"0 269.75
x 527.01
Mmx= 527.01
OMENTO MA
m
3.58
0(.0
=
3.06
2 $I=
0(.0 -15.5
336.81
V=
392.10
-15.5
=
$<=
3.58
2.05 "0
/m =
624.05 x
340 x2
$
336.81
301.41
x
2 =
0
497.20
x 624.05
340 x
x = 624.05
=
0
x=
1.(
340
Mmx= 497.20
1.84
340
1.84 2
336.81
2
Mmx=
&0&.50 17(.
/m 340 m
3.11
52(.70
=
3.58
2 $I=
52(.70 1.&
269.75
V=
264.51
1.&
=
$<=
3.11
527.01 17(.
/m = 527.01
x
340 x2
$
269.75
1233.46
x
2 =
0
3346.45
x 527.01
x = 527.01
340 x
=
0
x=
1.55
340
Mmx= 3346.45
1.55
340
1.55 2 2
269.75
Mmx=
7(.20
/m
17(. 340
m
3.06
520.20
=
2
520.20 2".00
301.41
V=
231.03
3.06
2".00
=
$I=
3.06
$<=
&7.20
/m
17(. = 497.20
x
340 x2
$
301.41
2 =
1580.06
x
0
x
2284.65 497.20
340 x
x = 497.20
=
0
x=
1.
340
1.46
340
1.46 2
301.41
2
Mmx=
.&5
/m 1748.6 m
3.58
=
"12&.&&
=
-21.5
2
"12&.&& -21.5
1233.46
2008.36 3.58
V= "".5 /m = 3346.45
x
1748.6 x2
$
1233.46
2 =
0
x 3346.45
1748.6 x
x = 3346.45
=
0
x=
1.&1
1748.6
1.91
1748.6 1.91 2 2
Mmx= "5.5
1233.46
Mmx= 2284.65
/m 1748.6 m
3.06
=
275."
=
"&0.70
2
275." "&0.70
1580.06
384.51 3.06
V= 22(.5 /m = 2284.65
x
1748.6 x2
$
1580.06
2 =
0
x 2284.65
1748.6 x
x = 2284.65
=
0
x=
1."1
1748.6
1.31
1748.6
1.31 2 2
Mmx= "072.5(
1580.06
2.- C 11&. /m
11&. /m
11&. /m
2= 2.(0
"022.7 /m
20(." /m
"022.7 /m
1= ".00
".(2 m VIGAS6 COL!MNAS6
".17 m
0.20
0.40 m
0.25
0.25 m
.0 m
1.- CALC!LO DE RIGIDE RELATIVO =4EI*L E=15200*
:c
I=;/3*12 15=26=37=48=%<3*L= 0.25 ( 0.25 ) 3 .* 3.00 = 59=610=711=812=%<3*L 0.25 ( 0.25 ) 3 .* 2.80 = 56=910=%<3*L=
0.2 (
0.4
) 3 .* 3.82 =
67=1011=%<3*L=
0.2 (
0.4
) 3 .* 3.17 =
78=1112=%<3*L=
0.2 (
0.4
) 3 .* 4.06 =
1."0 1.0 "."5 .0 ".15
LC!LO DE COE8ICIENTES DE GIRO ?= 1*2 x *-
N!DO 5 ?15=
1
x
1.30
* I> + 1.30
=
0
=
-0.11
=
-0.2(
=
-0.12
2 ?51=
1
x
2 ?56=
1
1.30 x
2 ?59=
1
1.30
3.35 1.30
x
2
+ 3.35 + 1.40
+ 3.35 + 1.40 1.40
1.30
-0.50
+ 3.35 + 1.40
N!DO ?62=
1
x
2 ?65=
1
1.30 x
2 ?610=
1
x
1
x
2
=
-0.17
=
-0.20
=
-0.07
+ 3.35 + 4.04 + 1.40 1.40
1.30
-0.0
+ 3.35 + 4.04 + 1.40 4.04
1.30
=
+ 3.35 + 4.04 + 1.40 3.35
1.30
2 ?67=
1.30
-0.50
+ 3.35 + 4.04 + 1.40
N!DO 7 ?73=
1
x
2 ?76=
1
1.30 x
2 ?711=
1
x
1 2
x
=
-0.20
=
-0.1
=
-0.07
+ 4.04 + 3.15 + 1.40 1.40
1.30
-0.07
+ 4.04 + 3.15 + 1.40 3.15
1.30
=
+ 4.04 + 3.15 + 1.40 4.04
1.30
2 ?78=
1.30
+ 4.04 + 3.15 + 1.40
-0.50
".- CALC!LO DE M N!DO ( ?84=
1
x
2
1.30
=
-0.11
1.30 + 3.15 + 1.40
M5 ?87=
1
x
2 ?812=
1
3.15
=
-0.27
=
-0.12
1.30 + 3.15 + 1.40 x
2
1.40
-0.50
1.30 + 3.15 + 1.40
N!DO & ?95=
1
x
2 ?910=
1
1.40
=
-0.15
=
-0."5
1.40 + 3.35 x
2
3.35
-0.50
1.40 + 3.35
M5
N!DO 10 ?106=
1
x
2 ?109=
1
1
=
-0.0(
=
-0.1&
=
-0.2"
1.40 + 3.35 + 4.04 x
2 ?1011=
1.40
3.35 1.40 + 3.35 + 4.04
x
2
4.04
-0.50
1.40 + 3.35 + 4.04
N!DO 11 ?117=
1
x
2 ?1110=
1
1
=
-0.0&
=
-0.21
=
-0.20
M7(
1.40 + 3.35 + 3.15 x
2 ?1112=
1.40
3.35 1.40 + 3.35 + 3.15
x
2
3.15
-0.50
1.40 + 3.35 + 3.15
N!DO 12 ?128=
1
x
2 ?1211
1 2
1.40 1.40 +
x
-0.15
=
-0."5
3.15 3.15
1.40 +
=
3.15
-0.50
OMENTOS DE EMPOTRAMIENTO PER8ECTO "022.7 3.82
M5
56= 65=
'L2
=
12
M&10
3022.7 x 3.82 2 = "75.75 12
20(." 3.17
M5
56= 65=
'L2
=
12
M1011
2048.3 x 3.17 2 = 1715."0 12
"022.7 4.06
M(7
78= 87=
'L2 12
=
M1112
3022.7 x 4.06 2 = 152.1 12
.- GIROS RELATIV 11&.
@= 1*2
3.82
M10& @5= 910= 109=
'L2
=
1169.6 x
12
3.82 2 =
122.27
12
@6=
@7=
11&. 3.17
@8=
M1110 @9= 1011= 1110=
'L2
=
1169.6 x
12
&7&."
3.17 2 =
12 @10=
11&.
@11=
4.06
M1211
1112= 1211=
'L2 12
=
1169.6 x 12
4.06 2 =
@12=
10.0 NOTA6 CAMIAR E
5.- SEC!ENCIA DE I
S INICIALES
.- PROCESO DE ITER
m*-
-1&.( 1
"75.75
x
2
1.30
+
3.35
= -"0".(( +
123.02 119.07 -0."5
1.40
118.68 1
-"75.75 + 1715."0
x
2
1.30
+
3.35
+
4.04
=
&7.1& -0.15
+ 1.40
& 1
-1715."0 + 152.1
x
2
1.30
+
4.04
+
3.15
= -12".2" + 1.40
1.0 1 2 1
-152.1
x 1.30
+
+
1.40
+
"5.(&
1.40
122.27
x
2
3.15
=
= -1&.(
-0.12 -"0".((
3.35
313.52 1 2 1
1.40
+
1.40
+
3.35
-10.02
x
2
3.35
+
&7&."
1.40 +
+
=
25.21
4.04
-&7&." + 10.0
x
2 1
-122.27" +
x
332.01 -0.2( 332.64
=
-"&.70
-0.11 5
3.15 =
17. 1."0
3.15
L SIGNO DE POR ESTE SIGNO ---> A CADA !NO DE ELLOS 1
TERACION
5 6 7 8 9 10 11 12
ACION ITERACIONES .-
1@B ITERACION6
"."5
25.21
-"&.70
17.
54.56
56.11
132.04
-0.1& 51.06 -0.2"
-0.21 63.37 -0.20
.0
50.21
-0.0( 10
-0.0& 11
1.0
"."5
303.88
'5 =
-"1".52
@:6 =
97.19
' =
152.75
@:7 =
123.23
'7 =
-17".12
-0."5 136.94 ".15
63.21
@:5 =
139.57
-0.15 12
1.0
1.0
-0.20 &7.1&
-0.1 -12".2"
-0.12 "5.(&
@:8 =
354.89
152.75
173.12
380.48
'( =
"(0.(
-0.17 153.39 -0.07
-0.20 172.44 -0.07
384.86
@:12 =
176.64
-0.11
'12 =
1"2.0
@:11 =
39.70
'11 =
-5.11
@:10 =
25.21
'10 =
5.5
.0
154.15
-0.0
".15
171.80
-0.07 7
1."0
2
-0.27 385.61
(
1."0
"
1."0
@:9 =
149.84
'& =
-12".02
2;B ITERACION6
+ 0.28 x
97.19 + 0.12 x 149.84
@:5 =
303.88 +
'5 =
-""2.01
@:6 = + 0.17 x 313.52 + 0.20 x
+ 0.20x 152.746+ 0.16 x
+ 0.27x 173.12 + 0.12 x
+ 0.15 x
380.48 + 0.35 x
25.21 + 0.07 x 123.23
39.70+
+ 0.35 x
354.89
176.64
39.70
+ 0.20x 132.038+ 0.09 x 173.12+
+ 0.23x 56.111 + 0.08 x
0.07 x
152.75+
54.56 + 0.15 x 313.52
0.21 x
25.21
0.19 x 149.84
97.19 +
' =
15"."&
@:7 =
123.23 +
'7 =
-172.
@:8 =
354.89 +
'( =
"(5.1
@:12 =
176.64 +
'12 =
1".&
@:11 =
39.70 +
'11 =
-"."7
@:10 =
25.21 +
'10 =
51.0
@:9 =
149.84 +
'& =
-11&.07
"@B ITERACION6 0.28 x
0.17 x
152.75 +
332 +
0.20 x 153.392 +
0.27 x
0.15 x
172.44 +
385.61 +
0.20 x 136.939 +
0.23 x
0.35 x
63.374 +
51.06 +
0.12 x 123.02
0.20 x
0.16 x
0.12 x
0.35 x
54.56 +
56.11 +
0.07 x
173.12
380.48
132.04
56.11
0.09 x 172.44 +
0.08 x
0.07 x
153.39 +
0.15 x 332.01
0.21 x
0.19 x
54.56
123.02
@:5 =
303.88 +
'5 =
-""2.
@:6 =
97.19 +
' =
15.15
@:7 =
123.23 +
'7 =
-171.(0
@:8 =
354.89 +
'( =
"(.(
@:12 =
176.64 +
'12 =
1"&.57
@:11 =
39.70 +
'11 =
-".21
@:10 =
25.21 +
'10 =
50.21
@:9 =
149.84 +
'& =
-11(.(
0.28 x
0.17 x
0.20 x
0.27 x
0.15 x
0.20 x
0.23 x
0.35 x
7.- CALC!LO DE MOMENTOS 8INALES = 153.39 +
332.64 +
154.151 +
0.12 x
0.20 x
0.16 x
119.07
51.06 +
63.37 +
0.07 x
0.07 x
172.44
385.61
M15=
0
+
1.30
x
M2=
0
+
1.30
x
M"7=
0
+
1.30
x
M(=
0
+
1.30
x
0
+
1.30
x
499.59 +
3.35
x
N!DO 5 M51=
171.80 +
0.12 x
M5=
136.94
M5&= 384.86 +
0.35 x
0
+
1.40
x
0
+
1.30
x
M5=
499.59 +
3.35
x
M7=
381.57 +
4.04
x
N!DO
63.37
M2= 139.572 +
63.214 +
0.09 x
0.08 x
171.80 +
154.15 +
0.21 x
0.19 x
51.06
119.07
M10=
0
+
1.40
x
0
+
1.30
x
M7=
381.57 +
4.04
x
M7(=
646.88 +
3.15
x
N!DO 7 50.21 +
0.15 x
332.64
M7"=
M711=
0
+
3.35
x
0
+
1.30
x
373.89 +
3.15
x
3.35
x
N!DO ( M(= M(7= M(12=
0
+
N!DO & M&5= 2 2
x x
0 0
+ 332.64 = + 154.15 =
0
+
1.40
x
2
x
M&10= 523.86 +
3.35
x
2
x
+
1.40
x
2
x
M10&= 523.86 +
3.35
x
2
x
M1011= 571.46 +
4.04
x
2
x
+
1.40
x
2
x
M1110= 571.46 +
4.04
x
2
x
M1112= 542.12 +
3.15
x
2
x
+
1.40
x
2
x
M1211= 542.12 +
3.15
x
2
x
-"".1" 200.72 N!DO 10
2
x
0
+ 171.80 =
-22".70 M10=
2
2
x
0
+ 384.86 =
x 332.64 +
0
=
0
501.12
-(.2 N!DO 11
2
x 332.64 + 154.15 =
-121".12 M117=
2
2
x 332.64 + 118.68 =
x
154.15
+
0
0
-10&".70
= 01."5
N!DO 12 2
x
154.15
+ 332.64 =
-5(1.15 M12(=
2
x 171.80 + 154.15 =
-"(".0
2
x 171.80 + 50.207 =
-0&."1
2
x 171.80 +
=
-7."&(
2
x 171.80 + 154.15 =
-11.5
2
x
+ 63.214 =
2(7.27
2
x 171.80 + 63.214 =
-1"".15
2
x
384.86
+
2
x
384.86
+ 171.80 =
1511.15
2
x
384.86
+ 139.572 =
"0.(2
384.86
0
0
0
= 1002.2"1
118.676 + 332.64 = -7&5.1&" 118.676 + 119.07 = -70."
50.207 + 154.15 = "55.11 50.207 + 63.2142 = -"&&.21 50.207 + 63.21
= 721.7
63.21 + 171.80 = -1.0 63.21 + 50.20703 = -(7&.2" 63.21 + 139.57 = 5(".5
139.57 + 384.86 = &2."1 139.57 + 63.21
= 1"(.
2.- C "0 /m
"0 /m
"0 /m
2= 2.(0
17(. /m
&&.2 /m
&&.2 /m
1= ".00
".5( m VIGAS6 COL!MNAS6
".11 m
0.20
0.30 m
0.25
0.25 m
".0 m
1.- CALC!LO DE RIGIDE RELATIVO =4EI*L E=15200*
:c
I=;/3*12 15=26=37=48=%<3*L= 0.25 ( 0.25 ) 3 .* 3.00 = 59=610=711=812=%<3*L 0.25 ( 0.25 ) 3 .* 2.80 = 56=910=%<3*L=
0.2 (
0.3
) 3 .* 3.58 =
67=1011=%<3*L=
0.2 (
0.3
) 3 .* 3.11 =
78=1112=%<3*L=
0.2 (
0.3
) 3 .* 3.06 =
0.00130 0.00140 0.00151 0.00174 0.00176
1."0 1.0 1.51 1.7 1.7
1."0 103 1.0 103 1.51 103 1.7 103 1.7 103
LC!LO DE COE8ICIENTES DE GIRO ?= 1*2 x *-
N!DO 5 ?15=
1
x
1.30
* I> + 1.30
=
0
=
-0.15
=
-0.1(
=
-0.17
2 ?51=
1
x
2 ?56=
1
1.30 x
2 ?59=
1
1.30
1.51 1.30
x
2
+ 1.51 + 1.40
+ 1.51 + 1.40 1.40
1.30
-0.50
+ 1.51 + 1.40
N!DO ?62=
1
x
2 ?65=
1
1.30 x
2 ?610=
1
x
1
x
2
=
-0.1"
=
-0.15
=
-0.12
+ 1.51 + 1.74 + 1.40 1.40
1.30
-0.11
+ 1.51 + 1.74 + 1.40 1.74
1.30
=
+ 1.51 + 1.74 + 1.40 1.51
1.30
2 ?67=
1.30
-0.50
+ 1.51 + 1.74 + 1.40
N!DO 7 ?73=
1
x
2 ?76=
1
1.30 x
2 ?711=
1
x
1 2
x
=
-0.1
=
-0.1
=
-0.11
+ 1.74 + 1.76 + 1.40 1.40
1.30
-0.11
+ 1.74 + 1.76 + 1.40 1.76
1.30
=
+ 1.74 + 1.76 + 1.40 1.74
1.30
2 ?78=
1.30
+ 1.74 + 1.76 + 1.40
-0.50
".- CALC!LO DE M N!DO ( ?84=
1
x
2
1.30
=
-0.15
1.30 + 1.76 + 1.40
M5 ?87=
1
x
2 ?812=
1
1.76
=
-0.20
=
-0.1
1.30 + 1.76 + 1.40 x
2
1.40
-0.50
1.30 + 1.76 + 1.40
N!DO & ?95=
1
x
2 ?910=
1
1.40
=
-0.2
=
-0.2
1.40 + 1.51 x
2
1.51
-0.50
1.40 + 1.51
M5
N!DO 10 ?106=
1
x
2 ?109=
1
1
=
-0.15
=
-0.1
=
-0.1&
1.40 + 1.51 + 1.74 x
2 ?1011=
1.40
1.51 1.40 + 1.51 + 1.74
x
2
1.74
-0.50
1.40 + 1.51 + 1.74
N!DO 11 ?117=
1
x
2 ?1110=
1
1
=
-0.15
=
-0.1
=
-0.1&
M7(
1.40 + 1.51 + 1.76 x
2 ?1112=
1.40
1.51 1.40 + 1.51 + 1.76
x
2
1.76
-0.50
1.40 + 1.51 + 1.76
N!DO 12 ?128=
1
x
2 ?1211
1 2
1.40 1.40 +
x
-0.22
=
-0.2(
1.76 1.76
1.40 +
=
1.76
-0.50
OMENTOS DE EMPOTRAMIENTO PER8ECTO 17(. 3.58
M5
56= 65=
'L2
=
12
M&10
1748.6 x 3.58 2 = 1(7.5 12
&&.2 3.11
M5
56= 65=
'L2
=
12
M1011
699.2 x 3.11 2 =
5".5
12
&&.2 3.06
M(7
78= 87=
'L2 12
=
M1112
699.2 x 3.06 2 = 12
55.5&
.- GIROS RELATIV "0
@= 1*2
3.58
M10& @5= 910= 109=
'L2
=
12
340 x
"".1"
3.58 2 =
12
@6=
@7=
"0 3.11
@8=
M1110 @9= 1011= 1110=
'L2
=
12
340 x
27.0
3.11 2 =
12 @10=
"0
@11=
3.06
M1211
1112= 1211=
'L2 12
=
340 x 12
3.06 2 =
@12=
25."0 NOTA6 CAMIAR E
5.- SEC!ENCIA DE I
S INICIALES
.- PROCESO DE ITER
m*-
-2.5" 1
1(7.5
x
2
1.30
+
1.51
= -222.0 +
1.40
6.83
-0.2
0.74 0.20
1
-1(7.5 +
x
2
1.30
+
1.51
+
5".5 1.74
=
10&.7" -0.2
+ 1.40
& 1
x
2
1.30
+
-5".5 +
55.5&
1.74
1.76
+
=
1.5
+ 1.40
1.0 1 2 1
-55.5&
x 1.30
+
+
1.40
+
1.1
=
-2.5"
1.40
"".1"
x
2
1.76
=
-0.17 -222.0
1.51
231.34 1 2 1
1.40
+
x
2 1
-"".1"1" +
x
1.40
+
1.40 +
+
25."0
1.51
1.76
+
=
&.0
1.74
-27.0 +
-25."02
x
2
1.51
27.0
245.56 -0.1( 247.72
=
0.&
-0.15 5
=
1.&( 1."0
1.76
L SIGNO DE POR ESTE SIGNO ---> A CADA !NO DE ELLOS 1
TERACION
5 6 7 8 9 10 11 12
ACION ITERACIONES .-
1@B ITERACION6 &.0
0.&
1.&(
0.48
2.31
28.59
-0.1 10.78 -0.1& 1.51
-0.1 0.73 1.7
12.39
-0.15 10
-0.1&
-0.15 11
1.0
1.51
222.04
28.56
'5 =
-2"1."
-0.22 12
@:6 =
109.73
' =
1"7.52
@:7 =
1.45
'7 =
-2.("
-0.2( 29.02 1.7
1.13
@:5 =
1.0
1.0
-0.15 10&.7"
-0.1 1.5
-0.1 1.1
@:8 =
61.14
137.52
24.83
59.48
'( =
5&.(
-0.1" 143.88 -0.12
-0.1 25.07 -0.11
61.70
@:12 =
41.98
-0.15
'12 =
2(.5&
@:11 =
0.94
'11 =
-2."1
@:10 =
9.60
'10 =
-0.(
1.7
145.69
-0.11
1.7
25.79
-0.11 7
1."0
2
-0.20 61.63
(
1."0
"
1."0
@:9 =
62.53
'& =
-.("
2;B ITERACION6
+ 0.18 x
109.73 + 0.17 x
+ 0.13 x 231.34 + 0.15 x
62.53
9.60 + 0.12 x
1.45
@:5 =
222.04 +
'5 =
-25.5
@:6 =
109.73 +
' =
1".((
@:7 = + 0.14 x
+ 0.20 x
+ 0.22 x
137.52 + 0.14 x
24.83 + 0.16 x
59.48 + 0.28 x
0.94 + 0.11 x
61.14
41.98
0.94
'7 =
24.83 + 0.16 x
9.60
61.14 +
'( =
1."
@:12 =
41.98 +
'12 =
2&.02
'11 = @:10 =
+ 0.19 x 2.3087 + 0.15 x
+ 0.26 x
137.52 + 0.16 x
0.48 + 0.24 x 231.34
62.53
-25.07
@:8 =
@:11 = + 0.19 x 28.5878 + 0.15 x
1.45 +
0.94 +
-0.7" 9.60 +
'10 =
-10.7(
@:9 =
62.53 +
'& =
-0.7
"@B ITERACION6 0.18 x
0.13 x
137.52 +
245.56 +
0.14 x 143.883 +
0.17 x
0.15 x
0.14 x
6.83
0.48 +
2.31 +
0.12 x
0.11 x
24.83
59.48
@:5 =
222.04 +
'5 =
-27.72
@:6 =
109.73 +
' =
15.&
@:7 =
'7 = 0.20 x
0.22 x
25.07 +
61.63 +
0.19 x 29.0211 +
0.19 x
0.26 x
0.7261 +
10.78 +
0.16 x
0.28 x
0.15 x
0.15 x
28.59
2.31
25.07 +
143.88 +
0.24 x 245.56
0.16 x
0.16 x
0.48
6.83
1.45 +
0.18 x
0.13 x
0.14 x
-25.7&
@:8 =
61.14 +
'( =
1.70
@:12 =
41.98 +
'12 =
2(.5
@:11 =
0.94 +
'11 =
1.1"
@:10 =
9.60 +
'10 =
-12."&
@:9 =
62.53 +
'& =
0.20
0.20 x
0.22 x
0.19 x
0.19 x
0.26 x
7.- CALC!LO DE MOMENTOS 8INALES = 143.88 +
247.72 +
145.69 +
0.17 x
0.15 x
0.14 x
0.74
10.78 +
0.73 +
0.12 x
0.11 x
25.07
61.63
M15=
0
+
1.30
x
M2=
0
+
1.30
x
M"7=
0
+
1.30
x
M(=
0
+
1.30
x
0
+
1.30
x
499.59 +
1.51
x
N!DO 5 M51=
25.79 +
0.16 x
M5=
29.02
M5&= 61.70 +
0.28 x
0
+
1.40
x
0
+
1.30
x
M5=
499.59 +
1.51
x
M7=
381.57 +
1.74
x
N!DO
0.73
M2= 28.5627 +
1.13325 +
0.15 x
0.15 x
25.79 +
145.69 +
0.16 x
0.16 x
10.78
0.74
M10=
0
+
1.40
x
0
+
1.30
x
M7=
381.57 +
1.74
x
M7(=
646.88 +
1.76
x
N!DO 7 12.39 +
0.24 x
247.72
M7"=
M711=
0
+
1.51
x
0
+
1.30
x
373.89 +
1.76
x
1.51
x
N!DO ( M(= M(7= M(12=
0
+
N!DO & M&5= 2 2
x x
0 0
+ 247.72 = + 145.69 =
0
+
1.40
x
2
x
M&10= 523.86 +
1.51
x
2
x
+
1.40
x
2
x
M10&= 523.86 +
1.51
x
2
x
M1011= 571.46 +
1.74
x
2
x
+
1.40
x
2
x
M1110= 571.46 +
1.74
x
2
x
M1112= 542.12 +
1.76
x
2
x
+
1.40
x
2
x
M1211= 542.12 +
1.76
x
2
x
-"22.55 1(&.70 N!DO 10
2
x
0
+
25.79
=
-"".5( M10=
2
2
x
0
+
x 247.72 +
61.70
0
=
=
0
(0."
-5.0& N!DO 11
2
x 247.72 + 145.69 =
-27.&5 M117=
2
2
x 247.72 + 0.19812 =
x
145.69
+
0
0
-&0.&0
= "7&.01(
N!DO 12 2
x
145.69
+ 247.72 =
-"".7" M12(=
2
x
25.79
+ 145.69 =
5.&(
2
x
25.79
+ 12.395 =
-(&.25
2
x
25.79
+
=
-7.15(
2
x
25.79
+ 145.69 =
-21(.1
2
x
61.70
+ 1.13325 =
(.5
2
x
25.79
+ 1.13325 =
-7.0&
2
x
61.70
+
0
=
10.(1
2
x
61.70
+
25.79
=
-201."
2
x
61.70
+ 28.5627 =
22&.22
0
0
0.19812 + 247.72 = -"5.0"" 0.19812 +
0.74
= 52"."5
12.3947 + 145.69 = 1(.7 12.3947 + 1.133254 = -55&.5 12.3947 +
1.13
= 5"0."(
=
-"2.(2
1.13
+ 25.79
1.13
+ 12.3947 = -5(&.05
1.13
+
28.56
= 5&.52
28.56 +
61.70
= 15.77
28.56 +
1.13
= -"&."1
METODO MATRICIAL "022.7
20(."
".(2
".17
"022.7 .0
1.- CALC!LO DE LAS 8!ERAS E
M21
12
21
12= 21=
'L2 = 3022.74 12
B12=B21=
'L
x
3.82
2 =
"75.75
3.82
=
577"."
3.17
2 =
1715."0
3.17
=
"2.2
4.06
2 =
152.1
4.06
=
1".1
12
=
3022.74
2
x 2
20(." ".17 M2"
M"2
2"
"2
23= 32=
'L2 = 2048.34 12
B23=B32=
'L
x 12
=
2048.34
2
x 2
"022.7 .0 M"
M"
" 34= 43=
" 'L2 = 3022.74 12
B34=B43=
'L
x 12
=
3022.74
x
2
2
2.- CREACIO
B12 12
=
B21 21
B23 23
=
B32 32
B34 34
=
B43 43
' E
=
210 -,*cm2
0.20
= =
,
0.0
15200 :c B1
EI
2"&5"5.22
=
B2
L!
EI
EI/L
EI/L2
EI/L"
B3
".(2
2"&5"5.22
1501.57
11010.((
21&.5
".17
2"&5"5.22
7117(."0
2""(10.1&
7"757.1
B4
.0
2"&5"5.22
57(70".2
125"7.75
"5107.(2
14.5924
55.742968
10.0489
31.855013
16.4836
66.923416
DE MATRICES POR TRAMO V1 505793.35
O1 966065.30
966065.30 2460246.30 505793.35
V2 505793.35
O2
885085.89 1402861.14
O2
V1
966065.30
$1
966065.30 1230123.15
O1
+
5773.43
B1
505793.35
3675.75
1
966065.30
966065.30
$2
5773.43
B2
-505793.35
966065.30 2460246.30
O2
3675.75
2 =
966065.30
966065.30 505793.35
966065.30 1230123.15
V2
".- ENSAMLE D
V"
B3
0.00
3
0.00
3246.62
B4
0.00
1715.30
4
0.00
O"
885085.89 1402861.14
$2
1402861.14 2964713.21 1402861.14 1482356.60
O2
885085.89 1402861.14
885085.89 1402861.14
$3
3246.62
1402861.14 1482356.60 1402861.14 2964713.21
O3
1715.30
855226.49
$3
6136.16
0
855226.49 1157406.51
O3
4152.14
0 =
1230123.15
V" 421293.84
O"
855226.49 421293.84
855226.49 2314813.02 421293.84
V
855226.49
855226.49 1157406.51
+
O +
2460246.30
855226.49
$4
6136.16
0
0.00
855226.49 2314813.02
O4
4152.14
0
0.00
421293.84
=21+23=
577"." "75.75 &020.05 -1&0.
B32+B34=
&"(2.7(
O1
2460246.30
=32+34=
2".(
O2 =
1230123.15
B43=
1".1
O3
0.00
=43=
-152.1
O4
0.00
B12= =12= B21+B23=
0.0000005 -0.0000001 0.0000000 0.0000000
E MATRI O1
V2
V"
O"
V
O
966065.30
0.00
0.00
0.00
0.00
$1
5773.43
12
2460246.30 -966065.30 1230123.15
0.00
0.00
O1
3675.75
B21
0.00
$2
9020.05
21
0.00
O2
-1960.46
855226.49
$3
9382.78
B12
=
1402861.14 1482356.60 -547634.65 5279526.23 -855226.49 1157406.51
O3
2436.84
12
=
-855226.49
$4
6136.16
B21
=
855226.49 1157406.51 -855226.49 2314813.02
O4
-4152.14
21
=
966065.30
O2
-505793.35
-966065.30 1390879.24
0.00
0.00
-885085.89 1402861.14
0.00
1230123.15 436795.84 5424959.51 -1402861.14 1482356.60
0.00
-885085.89 -1402861.14 1306379.73
0.00 0.00
436795.84
0.00 0.00
0.00
0.00
-421293.84
0.00
0.00
-547634.65 -421293.84
-855226.49
421293.84
B12 =
B23 23 1230123.15
0.00
0.00
O1
3675.75
B32
5424959.51
1482356.60
0.00
O2
1960.46
32
1482356.60 5279526.23
1157406.51
O3
2436.84
0.00 1157406.51
2314813.02
O4
4152.14
=
B23
=
23
=
B32
=
32
=
B34 -1
34
-20.&5 x10F-
B43
12.02 x10F-
43
1230123.15
0.00
0.00
-3675.75
5424959.51
1482356.60
0.00
1960.46
1482356.60 5279526.23
1157406.51
-2436.84
-1"."& x10F-
1157406.51 2314813.02
4152.14
2." x10F-
0.00
=
=
B34
=
34
=
-1.15142E-07 3.630896E-08 -1.81545E-08
0.00210
B43
=
2.302846E-07 -7.26179E-08 3.630896E-08
0.00120
43
=
2.35628E-07 -1.17814E-07
0.00134
3.630896E-08 -1.17814E-07 4.909073E-07
0.00246
-7.26179E-08
V1
O1
505793.35
V2
O2
966065.30 505793.35
966065.30
$1
966065.30 2460246.30 966065.30 1230123.15
O1
505793.35 966065.30 505793.35 966065.30
$2
5773.43
966065.30 1230123.15 966065.30 2460246.30
O2
3675.75
"022.7
5773.43 +
2536141.36(9.86x104)+2536141.36(4.57x104)+7684.13 =
3675.75
&10.((
0.00 "5.&&
4910.88
-"2&.&5 V2
O2
V"
O"
885085.89 1402861.14 885085.89 1402861.14 1402861.14 2964713.21 885085.89
CCC
$2
CCC 1482356.60 885085.89
O2
3246.62 +
1715.30
CCC
$3
3246.62
CCC 2964713.21
O3
1715.30
855226.49
$3
6136.16
855226.49 2314813.02 855226.49 1157406.51
O3
1402861.14 1482356.60
D8C
+
"05.7 "2&.&5 ""(.50 -"&0".22 V"
O"
421293.84
V
855226.49 421293.84
421293.84 855226.49
O +
4152.14
421293.84 855226.49
$4
6136.16
855226.49 1157406.51 855226.49 2314813.02
O4
4152.14
DM8 +
70&7.55 "&0".22 517.7( 0.00
3989.22
.- CALC!LO DE MOMEN 20(." 3.82
"022.7 3.17
4.06
4910.88
3054.74
= 7097.55
x
+ -
5174.78
6635.99
3438.50
3054.74 = x
3294.95
3903.22
+ 7097.55 = x 2277.80
8332.70
OS MA
3022.74
M x
V
0 =
x = Mmx =
1.2 "&(&.22
2048.34
M x
V
0 =
x = Mmx =
1.& 2277.(0
3022.74
M x
V
0 =
x = Mmx =
2."5 (""2.70
METODO MATRICIAL 17(.
&&.2
&&.2
".5(
".11
".0
1.- CALC!LO DE LAS 8!ERAS E
M21
12
21
12= 21=
'L2 =
1748.6
12
B12=B21=
'L
x
3.58
2 =
1(7.5
3.58
=
"12&.&&
3.11
2 =
5".5
3.11
=
10(7.2
3.06
2 =
55.5&
3.06
=
10&.7(
12
=
1748.6
2
x 2
&&.2 ".11 M2"
M"2
2"
"2
23= 32=
'L2 =
699.2
12 B23=B32=
'L
x 12
=
699.2
2
x 2
&&.2 ".0 M"
M"
" 34= 43=
" 'L2 =
699.2
12 B34=B43=
'L
x 12
=
699.2
x
2
2
2.- CREACIO
B12 12
=
B21 21
B23 23
=
B32 32
B34 34
=
B43 43
' E
=
210 -,*cm2
0.20
= =
,
0."0
15200 :c B1
EI
&&1210.17
=
B2
L!
EI
EI/L
EI/L2
EI/L"
B3
".5(
&&1210.17
27(7."5
77""&.20
210".1"
".11
&&1210.17
"1(717.10
102(1."(
"2&52.21
B4
".0
&&1210.17
"2"&2.(&
105(57.(1
"5&.05
12.8164
45.882712
9.6721
30.080231
9.3636
28.652616
DE MATRICES POR TRAMO V1 259237.55
O1
".- ENSAMLE D V2
O2
V1 3129.99
B1
259237.55
1867.56
1
464035.22
$2
3129.99
B2
-259237.55
O2
1867.56
2 =
464035.22
464035.22
259237.55
464035.22
$1
464035.22 1107497.40
464035.22
553748.70
O1
464035.22 259237.55
464035.22
553748.70 464035.22 1107497.40
259237.55 464035.22
V2 395426.55
O2
614888.29 395426.55
614888.29
V" 415128.66
0.00
1087.26
B4
0.00
563.56
4
0.00
O2
614888.29 395426.55
614888.29
$3
1087.26
637434.19 614888.29 1274868.39
O3
563.56
635146.85
$3
1069.78
0
635146.85
647849.78
O3
545.59
0 =
415128.66
635146.85
$4
1069.78
0
0.00
635146.85 1295699.57
O4
545.59
0
0.00
O"
V
635146.85 415128.66
635146.85
647849.78
=21+23=
"12&.&& 1(7.5 217.25 -1"0.00
B32+B34=
2157.0"
=32+34=
3
O" 637434.19
635146.85
B21+B23=
0.00
614888.29
415128.66
=12=
$2
635146.85 1295699.57
B12=
B3
614888.29
614888.29 1274868.39 395426.55
V"
+
-17.&(
+
O +
1107497.40 553748.70
1107497.40
O2 =
553748.70
O1
B43=
10&.7(
O3
0.00
=43=
-55.5&
O4
0.00
0.0000010 -0.0000003 0.0000001 0.0000000
E MATRI O1
V2
V"
O"
V
O
464035.22
0.00
0.00
0.00
0.00
$1
3129.99
12
1107497.40 -464035.22 553748.70
0.00
0.00
O1
1867.56
B21
0.00
$2
4217.25
21
0.00
O2
-1304.00
635146.85
$3
2157.03
B12
=
614888.29 637434.19 20258.56 2570567.95 -635146.85 647849.78
O3
-17.98
12
=
464035.22
O2
-259237.55
-464035.22
150853.07
0.00 0.00
553748.70 150853.07 2382365.78 -614888.29 637434.19
0.00
-395426.55
0.00
0.00 0.00
0.00
0.00
-614888.29
0.00
810555.21
-415128.66
0.00
-395426.55
0.00 614888.29
0.00
654664.11
20258.56 -415128.66
-635146.85
415128.66
B12
=
-635146.85
$4
1069.78
B21
=
635146.85 647849.78 -635146.85 1295699.57
O4
-545.59
21
=
B23 23 553748.70
0.00
0.00
O1
1867.56
B32
2382365.78
637434.19
0.00
O2
1304.00
32
637434.19 2570567.95
647849.78
O3
17.98
1295699.57
O4
545.59
0.00
647849.78
=
B23
=
23
=
B32
=
32
=
B34 -1
34
-22.( x10F-
B43
12.00 x10F-
43
553748.70
0.00
0.00
-1867.56
2382365.78
637434.19
0.00
1304.00
637434.19
2570567.95
647849.78
17.98
-.5
x10F-
0.00
647849.78
1295699.57
545.59
.(
x10F-
=
=
B34
=
34
=
-2.5979E-07 7.370945E-08 -3.68547E-08
0.00229
B43
=
5.195793E-07 -1.47419E-07 7.370945E-08
0.00120
43
=
-1.47419E-07 4.869353E-07 -2.43468E-07
0.00045
7.370945E-08 -2.43468E-07 8.935177E-07
0.00065
V1
O1
259237.55
V2
O2
464035.22 259237.55
464035.22
$1
464035.22 1107497.40 464035.22
553748.70
O1
259237.55 464035.22 259237.55 464035.22
$2
3129.99
O2
1867.56
464035.22
553748.70 464035.22 1107497.40
17(.
3129.99 +
2536141.36(9.86x104)+2536141.36(4.57x104)+7684.13 =
1867.56
225.&(
0.00 "".01
2625.98
-1(0."7 V2
O2
395426.55
V"
O"
614888.29 395426.55
614888.29
$2
614888.29 1274868.39 614888.29
637434.19
O2
395426.55 614888.29 395426.55 614888.29
$3
1087.26
O3
563.56
1069.78
614888.29
637434.19 614888.29 1274868.39
1087.26 +
563.56
D8C
+
15.15 1(0."7 2(."7 -"77.22 V"
O"
415128.66
V
O
635146.85 415128.66
635146.85
$3
635146.85 1295699.57 635146.85
647849.78
O3
415128.66 635146.85
$4
1069.78
647849.78 635146.85 1295699.57
O4
545.59
415128.66 635146.85 635146.85
+
545.59
DM8 +
11&".05 "77.22 &.50 0.00
1971.80
.- CALC!LO DE MOMEN &&.2 3.58
&&.2 3.11
3.06
2625.98
1546.15
= 1193.05
x
+ -
946.50
3634.01
628.37
1546.15 = x
1804.37
377.22
+ 1193.05 = x 1709.50
1017.86
