Analicis Esructural
Páginas: 5 (1046 palabras)
Publicado: 7 de diciembre de 2012
isis estructuralCalcular las siguientes vigas por el método del principio del trabajo virtual proponiendo un
f´c= 250 kg/m2 con las dimensiones de .15 m x .20 m
las deflexiones según se pidan.
Nota: solo vigas de concreto .
1..Calcular deflexiones en c y en d
10 T
a b c d e f
2 2 2 2 2
∑MA = 0
10(5) – RF (10)
RF = 5010 = 5
MOMENTOS FLECTORES
MoA= 0
MoB = RA (2) = (5) (2) = 10
MoC = RA (4) = (5) (4) = 20
MoD = RA (6) - (10) (1) = 30 - 10 = 20
MoE = RA (8) = 10 (3) = 40 – 30= 10
MoF = 0
1T
a b c d e f
MoA = 0
MoB = RA (2) = (0.5) (2) = 1
MoC = RA(4) = (0.5) (4) = 2
MoD = RA (6) – 1(1) = 0.5 (6) - 1(1 ) = 2
MoE = RA (8) – 1(3) = 0.5 (8) – 1 (3)= 1
MoF = 0
0 0
1 1
2 2
0 T
0T
10 T
10 T
20 T
20 T
20 T
20 T
10 T
10 T
0 T
0 T
Tramo
AB
Tramo
AB
Tramo
DE
Tramo
DE
Tramo
CD
Tramo
CD
Tramo
BC
Tramo
BC
Tramo
AB
Tramo
AB
0 T
0 T
0 T
0 T
10 T
10 T
10 T
10 T
20 T
20 T
20 T
20 T
DAB= 1/3[(10) (2) ]=6.66
DBC=1/6[2(10) (1)+1(20)+10(2)+2(20)(2)]2=46.67
DCD=1/3[2(20)(20)] = 26.67
I=(b)(h³)12 = (0.15m)(0.25m)³/ 12 = .000195
DEFLXION EN C = 6.67 + 46.67 + 26.67= 80
CONCRETO
0.25
0.15
bh3 / 12 = (0.15) (0.25) / 12 = 0.0001953125
DT = 80 / (3000000) (0.0001953125) = (0.1365) (100 ) = 13.65
DAB = 1/3 [(10) (1) (2)] = 6.67
DBC = 1/6[(10) (1) (2) + (10) (2) + (1) (20) + (2) (20 )(2 )] 2 = 46.67
DCD = 1/6 [(20) (2) (2) + (20) (2) +(20) (2) + (20) (2) (2) ] 2 = 80
DD = 1/3 [(20) (2) (2)] = 26.67
DEFLEXION EN D = 6.67 + 46.67 + 80 + 26.67 = 160
DEFLEXION EN D = 160 / (3000000) (0.0001953125) = 27.30
2..Calcular deflexión en c
3 T
2 T/m
a b c d
1.5 1.5 3 3
∑A = 0
(3) (1.5) + (18) (4.5) – RD (9)
4.5 + 81 – RD(9)
RD = 85.5 / 9 = 9.5
RD =9.5 RA = 11.5
MoA = 0
MoB = RA (3) – (3) (15) = 30
MoC = RA (6) – (18 ) (1.5) – (3) (4.5) = 28.5
MoD = 0
MoA = 0
MoB = (3) (RA) = 1.5
MoC = RA (6) – (1) (1.5) = 1.5
MoD = 0
DBA = 1/3 [ (3) (30) (1.5) ] = 4.5
DBC = 1/6 [[ (2) (30) (1.5) ]+ (30) (1.5) + (28.5) (1.5) + 2 (28.5) (1.5)] 3 =
1/6 [ 90 + 45 + 42.75 + 85.5] 3 = 131.625
DCD =1/3 [ (28.15) (1.5) (3) ] = 42.75
CONCRETO
0.25
0.15
Bh3 / 12 = (0.15) (0.25)3 / 12 = 0.0001953125
DT= 131.625 + 42.75 + 45 = 219.375
DEFLEXION EN C = 219.375 / (3000000) (0.0001953125) = 37.44 CM
3..Calcular deflexión en el punto c
8 T
5 T/m
a b c d e2 1.5 1.5 2
∑MoA = 0
1(10) + 8(5) – RE(7)
10 + 40 – RE(7)
50 – RE(7)
RE = 50 / 7
RE = 7.14
RA = 10.86
MoA = 0
MoB = RA(2) – 10(1) = 11.72
MoC = RA(3.5) – 10 (2.5) = 13.01
MoD = RA (5) – 10 (9) = 14.3
MoE =0
R=.5 R=.5
MoA = 0
MoB = RA (2) = 1
MoC = RA (3.5) = 1.75
MoD = RA (5) – 1 (1.5) 1
MoE = 0
DBA =1/3 [ (2) (11.72) (1) ] = 7.81
DBC = 1/6 [ (2) (11.72) (1) + (11.72) (1.75) + (13.01) (1) + (13.01) (1.75) (2) ] 1.5 = 25.62
DCD = 1/3 [ (1.75 ) (13.01) (1.5) ] = 11.38
DEFLEXION = 11.38 + 25.52 + 7.81 = 44.81
CONCRETO
0.25
0.15
Bh3 / 12 = (0.15 ) (0.25) 3 / 12 = 0.0001953125
DEFLEXION EN C = 44.81 / (3000000 ) (0.0001953125) = 7.64 CM
4..Calcule la deflexión en los puntos b, c, d y e
12 T
a b c d e f
1.2 2 2 2 1.2
1 1
∑MA = 0
12 (3.4) + (15) (3.8) – RF( 7.6 )
40.8 + 72.2 – RF (7.6)
113 – RF (7.6)
RF = 113/ 7.6 = 14.87
RA = 16.13 RF = 14.87
MOMENTOS DEFLECTORES
MoA = 0
MoB = RA (1.2) = 19.356
MoC = RA...
f´c= 250 kg/m2 con las dimensiones de .15 m x .20 m
las deflexiones según se pidan.
Nota: solo vigas de concreto .
1..Calcular deflexiones en c y en d
10 T
a b c d e f
2 2 2 2 2
∑MA = 0
10(5) – RF (10)
RF = 5010 = 5
MOMENTOS FLECTORES
MoA= 0
MoB = RA (2) = (5) (2) = 10
MoC = RA (4) = (5) (4) = 20
MoD = RA (6) - (10) (1) = 30 - 10 = 20
MoE = RA (8) = 10 (3) = 40 – 30= 10
MoF = 0
1T
a b c d e f
MoA = 0
MoB = RA (2) = (0.5) (2) = 1
MoC = RA(4) = (0.5) (4) = 2
MoD = RA (6) – 1(1) = 0.5 (6) - 1(1 ) = 2
MoE = RA (8) – 1(3) = 0.5 (8) – 1 (3)= 1
MoF = 0
0 0
1 1
2 2
0 T
0T
10 T
10 T
20 T
20 T
20 T
20 T
10 T
10 T
0 T
0 T
Tramo
AB
Tramo
AB
Tramo
DE
Tramo
DE
Tramo
CD
Tramo
CD
Tramo
BC
Tramo
BC
Tramo
AB
Tramo
AB
0 T
0 T
0 T
0 T
10 T
10 T
10 T
10 T
20 T
20 T
20 T
20 T
DAB= 1/3[(10) (2) ]=6.66
DBC=1/6[2(10) (1)+1(20)+10(2)+2(20)(2)]2=46.67
DCD=1/3[2(20)(20)] = 26.67
I=(b)(h³)12 = (0.15m)(0.25m)³/ 12 = .000195
DEFLXION EN C = 6.67 + 46.67 + 26.67= 80
CONCRETO
0.25
0.15
bh3 / 12 = (0.15) (0.25) / 12 = 0.0001953125
DT = 80 / (3000000) (0.0001953125) = (0.1365) (100 ) = 13.65
DAB = 1/3 [(10) (1) (2)] = 6.67
DBC = 1/6[(10) (1) (2) + (10) (2) + (1) (20) + (2) (20 )(2 )] 2 = 46.67
DCD = 1/6 [(20) (2) (2) + (20) (2) +(20) (2) + (20) (2) (2) ] 2 = 80
DD = 1/3 [(20) (2) (2)] = 26.67
DEFLEXION EN D = 6.67 + 46.67 + 80 + 26.67 = 160
DEFLEXION EN D = 160 / (3000000) (0.0001953125) = 27.30
2..Calcular deflexión en c
3 T
2 T/m
a b c d
1.5 1.5 3 3
∑A = 0
(3) (1.5) + (18) (4.5) – RD (9)
4.5 + 81 – RD(9)
RD = 85.5 / 9 = 9.5
RD =9.5 RA = 11.5
MoA = 0
MoB = RA (3) – (3) (15) = 30
MoC = RA (6) – (18 ) (1.5) – (3) (4.5) = 28.5
MoD = 0
MoA = 0
MoB = (3) (RA) = 1.5
MoC = RA (6) – (1) (1.5) = 1.5
MoD = 0
DBA = 1/3 [ (3) (30) (1.5) ] = 4.5
DBC = 1/6 [[ (2) (30) (1.5) ]+ (30) (1.5) + (28.5) (1.5) + 2 (28.5) (1.5)] 3 =
1/6 [ 90 + 45 + 42.75 + 85.5] 3 = 131.625
DCD =1/3 [ (28.15) (1.5) (3) ] = 42.75
CONCRETO
0.25
0.15
Bh3 / 12 = (0.15) (0.25)3 / 12 = 0.0001953125
DT= 131.625 + 42.75 + 45 = 219.375
DEFLEXION EN C = 219.375 / (3000000) (0.0001953125) = 37.44 CM
3..Calcular deflexión en el punto c
8 T
5 T/m
a b c d e2 1.5 1.5 2
∑MoA = 0
1(10) + 8(5) – RE(7)
10 + 40 – RE(7)
50 – RE(7)
RE = 50 / 7
RE = 7.14
RA = 10.86
MoA = 0
MoB = RA(2) – 10(1) = 11.72
MoC = RA(3.5) – 10 (2.5) = 13.01
MoD = RA (5) – 10 (9) = 14.3
MoE =0
R=.5 R=.5
MoA = 0
MoB = RA (2) = 1
MoC = RA (3.5) = 1.75
MoD = RA (5) – 1 (1.5) 1
MoE = 0
DBA =1/3 [ (2) (11.72) (1) ] = 7.81
DBC = 1/6 [ (2) (11.72) (1) + (11.72) (1.75) + (13.01) (1) + (13.01) (1.75) (2) ] 1.5 = 25.62
DCD = 1/3 [ (1.75 ) (13.01) (1.5) ] = 11.38
DEFLEXION = 11.38 + 25.52 + 7.81 = 44.81
CONCRETO
0.25
0.15
Bh3 / 12 = (0.15 ) (0.25) 3 / 12 = 0.0001953125
DEFLEXION EN C = 44.81 / (3000000 ) (0.0001953125) = 7.64 CM
4..Calcule la deflexión en los puntos b, c, d y e
12 T
a b c d e f
1.2 2 2 2 1.2
1 1
∑MA = 0
12 (3.4) + (15) (3.8) – RF( 7.6 )
40.8 + 72.2 – RF (7.6)
113 – RF (7.6)
RF = 113/ 7.6 = 14.87
RA = 16.13 RF = 14.87
MOMENTOS DEFLECTORES
MoA = 0
MoB = RA (1.2) = 19.356
MoC = RA...
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