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VIGA CONTINUA - V.2019-V.214-V.211-V.208-V.205-V.202 - DE HΒ° AΒ° Predimencionamiento Viga mΓ‘s solicitada: Viga voladizo m=8 h=
ππ.2,4 8
=
1,33π .2,4 22
h=42cm d=45m r=3cm
= 0,399m => Adopto h=0,43m
do= h+r = 0,43m+0,03m = 0,45m bo= 0,20m
ο·
AnΓ‘lisis de carga
P= RAV.220 = 2,21t Q= Rb L.201,L.202 + P.propio viga continua + Muro de 20cm de ladrillo comΓΊn hueco, cemento y arena P.propio Viga continua = 0,45m . 0,20m . 2,4t/m3 = 0,216t/m Rb L.201,L.202= 3,22 t/m Muro de 20cm de ladrillo comΓΊn hueco, cemento y arena = 0,28t/m 2 . 2,55m = 0,714t/m Q= 0,216t/m + 3,22t/m + 0,714T/m => Q = 4,15t/m
ο·
Calculo momentos de voladizo Apoyo V.219 y V.214 por izq. 2,21t q=4,15t/m
X= -
q.l2 2
+P.l =-(
4,15t/m.(1,33m)2 2
+2,12t . 1,33m) =-6,61tm
Apoyo V.219 y V.214 por derecha. q=4,15t/m
X= -
ο·
q.l2 2
= -(
4,15t/m.(1,05m)2 2
) =-2,288tm
Calculo de tΓ©rminos de carga
V.214 Estado 1 q=4,15t/m
L=R= -
q.l2 4
=
4,15t/m.(2,9m)2 4
=8,73tm
Estado 2 -6,61tm
L= 2 . Xizq = 2 . -6,61tm = -13,22tm R=Xizq = -6,61tm
TΓ©rminos de carga total Ltotal= 8,73tm -13,22tm = -4,49tm
Rtotal= 8,73tm -6,61tm = 2,21tm
V.211=V.208 Estado 1 q=4,15t/m
L=R= -
q.l2 4
=
4,15t/m.(2,9m)2 4
=8,73tm
TΓ©rminos de carga total Ltotal= 8,73tm
Rtotal= 8,73tm
V.205 Estado 1 q=4,15t/m
L=R= -
q.l2 4
=
4,15t/m.(2,9m)2 4
=8,73tm
Estado 2 -2,288tm
L= Xder. = -2,288tm R=2. Xder. = -4,576tm
TΓ©rminos de carga total Ltotal= 8,73tm -2,288tm = 6,442tm
ο·
X1= X2= X3=
Rtotal= 8,73tm -4,576tm = 4,154tm
Calculo de momento de apoyo
β15.(2,21tm+8,73tm)+4.(8,73tm+8,73tm)β(8,73tm+6,442) 56 4.(2,21tm+8,73tm)β16.(8,73tm+8,73tm)+4.(8,73tm+6,442) 56 β(2,21tm+8,73tm)+4.(8,73tm+8,73tm)β15.(8,73tm+6,442) 56
= -1,954tm = -3,123tm = -3,012tm
ο·
Calculo de reacciones de carga βRQβ
Reacciones Voladizo V.219 2,21t q=4,15t/m
RQ= RA=RB= q.l +P = 4,15t/m . 1,33m +2,21t =7,7295t
Reacciones Voladizo V.202
q=4,15t/m
RQ=RA=RB= q.l = 4,15t/m . 1,05m =4,3575t
V.214=V.211=V.208=V.205 q=4,15t/m
ο·
RQ=RA=RB=
q.l 2
=
4,15t/m.2,9m 2
=6,0175t
Calculo reacciones de momento βRMβ
V.214 Momento resultante=-6,61tm β (-1,954tm) =-4,656tm RM=4,656tm/2,9m=1,606t V.211 Momento resultante=-1,954tm β (-3,123tm) =1,169tm RM=1,169tm/2,9m=0,4031t V.208 Momento resultante=-3,012tm β (-3,123tm) =0,111tm RM=0,111tm/2,9m=0,0383t V.205 Momento resultante=-3,012tm β (-2,288tm) =-0,724tm RM=0,724tm/2,9m=0,2497t
ο·
Calculo de solicitaciones totales y momentos de tramos βMmΓ‘x.β
202 -6,61tm
-1,954tm
6,0175t
7,7295t
ο·
-3,123tm
6,0175t
6,0175t
+1,606t
-1,606t
-0,4031t
7,6235t
4,4115t
5,6144t
6,0175t +0,4031t 6,4206t
-3,012tm 6,0175t
6,0175t
6,0175t
+0,0383t
-0,0383t
+0,2497t
-0,2497t
6,0558t
5,9792t
6,2672t
5,7678t
Xm2izq.= Xm3izq.= Xm4izq.=
RM 4,3575t
RT
1,3529m | 1,5471m
1,4592m | 1,4408m
1,5102m | 1,3898m
Xm
0,3921tm|0,3907tm
1,8438tm|1,8438tm
1,2954tm|1,2953m
1,7203tm|1,7201tm
MmΓ‘x.
π π΄π.214 q π π΄π.211 q π π΄π.208 q π π΄π.205 q
X0 RQ
1,8398m | 1,0602m
Calculo distancia βXmβ
Xm1izq.=
-2,288tm
6,0175t
= = = =
7,635π‘
=1,8398m
4,15tm
5,6144π‘ 4,15tm 6,0558π‘ 4,15tm 6,2672π‘ 4,15tm
Xm1der.= 2,9m - 1,8398m=1,0602m
=1,3529m
Xm2der.= 2,9m β 1,3529m=1,5471m
=1,4592m
Xm3der.= 2,9m - 1,4592m=1,4408m
=1,5102m
Xm4der.= 2,9m - 1,5102m=1,3898m
Momento mΓ‘ximo V.214 Mmax.izq =7,6235t . 1,8398m - 4,15t/m. Mmax.der = 4,4115 . 1,0602m - 4,15t/m.
(1,8398π)2 2 (1,0602π)2 2
- 6,61tm =0,3921tm - 1,954= 0,3907tm
Momento mΓ‘ximo V.211 Mmax.izq =5,6144t . 1,3529m - 4,15t/m. Mmax.der = 6,4206t . 1,5471m- 4,15t/m.
(1,3529π)2 2
- 1,954tm =1,8438tm
(1,5471π)2
- 3,123tm= 1,8438tm
2
Momento mΓ‘ximo V.208 Mmax.izq =6,0558t . 1,4592m - 4,15t/m. Mmax.der = 5,9792 . 1,4408m - 4,15t/m.
(1,4592π)2 2 (1,4408π)2 2
- 3,123tm =1,2954tm - 3,012= 1,2953tm
Momento mΓ‘ximo V.205 Mmax.izq =6,2672t . 1,5102m - 4,15t/m. Mmax.der = 5,7678t . 1,3898m - 4,15t/m.
(1,5102π)2 2
- 3,012tm =1,7203tm
(1,3898π)2 2
- 2,288= 1,7201tm
ο·
Diagrama de corte y momento flector
202
ο·
Dimensionamiento- H-17
V.214 KH=
β(ππ) β
AS=
π(π‘π) π
42 ππ
= β
ππ .π(π‘π) β(π)
0,3921π‘π 0,20π
= 29,996 => Adopto por tabla 7,252
0,4876 .0,3921π‘π
=
0,30π
KS= 0,4876
= 0,64 cm2 Adopto 2 α΄ 12 (2,26cm2) se levanta 1 α΄ 12 (1,13cm2)
V.211 KH=
AS=
β(ππ) π(π‘π) β π
=
ππ .π(π‘π) β(π)
42ππ 1,8438π‘π β 0,20π
= 13,834 => Adopto por tabla KH= 7,252
0,4876.1,8438 π‘π
=
0,42π
KS= 0,4876
= 2,141 cm2 Adopto 2 α΄ 12 (2,26cm2) se levanta 1 α΄ 12 (1,13cm2)
V.208 KH=
β(ππ) βπ(π‘π)
β
π
AS=
42 ππ
=
ππ .π(π‘π) β(π)
1,2954π‘π 0,20π
= 16,503 => Adopto por tabla KH= 7,252
0,4876 . 1,2954π‘π
=
0,42π
KS= 0,4876
= 1,504 cm2 Adopto 2 α΄ 12 (2,26cm2) se levanta 1 α΄ 12 (1,13cm2)
V.205 KH=
β(ππ) βπ(π‘π)
β
π
AS=
42 ππ
=
ππ .π(π‘π) β(π)
1,7206π‘π 0,20π
= 14,32 => Adopto por tabla KH= 7,252
0,4876.1,7206π‘π
=
0,42π
KS= 0,4876
= 1,998 cm2 Adopto 2 α΄ 12 (2,26cm2) se levanta 1 α΄ 12 (1,13cm2)
V.219 KH=
AS=
β(ππ) βπ(π‘π) π
=
42 ππ β
ππ .π(π‘π) β(π)
6,61π‘π 0,20π
= 7,306 => Adopto por tabla 7,252
0,4876 .6,61π‘π
=
0,42π
KS= 0,4876
= 7,674cm2 => AS necesaria: 7,674cm2 ; As disponible : 1,13cm2
AS necesaria real:6,544cm2 => Adopto 6 α΄ 12 (6,78cm2)
V.202 KH=
β(ππ) βπ(π‘π) π
AS=
ππ .π(π‘π) β(π)
42 ππ
=
β
=
2,288π‘π 0,20π
= 12,418 => Adopto por tabla KH= 7,252
0,4876 . 2,288π‘π 0,42π
KS= 0,4876
= 2,63 cm2 => AS necesaria: 2,63cm2 ; As disponible : 1,13cm2
AS necesaria real: 1,5cm2 => Adopto 2 α΄ 12 (2,26cm2)
h=42cm d=45m r=3cm
ο· KH=
VerificaciΓ³n de apoyo X1 β(ππ) βπ(π‘π)
42 ππ
=
β
π
1,954π‘π 0,20π
= 13,437 => Adopto por tabla KH= 7,252
KS= 0,4876
Armadura principal: AS=
ο· KH=
ππ .πππππ¦π(π‘π) β(π)
=
0.4876 . 1,954π‘π 0,42π
= 2,269cm2 => AS necesaria: 2,269cm2 ; As disponible : 2,26cm2 *Diferencia < 2% Verifica
VerificaciΓ³n de apoyo X2 β(ππ) βπ(π‘π)
42 ππ
=
β
π
3,123π‘π 0,20π
= 10,629 => Adopto por tabla KH= 7,252
KS= 0,4876
Armadura principal: AS=
ππ .πππππ¦π(π‘π) β(π)
=
0.4876 . 3,123π‘π 0,42π
= 3,626cm2 => AS necesaria: 3,626cm2 ; As disponible : 2,26cm2
AS necesaria real: 1,366cm2 => Adopto 2 α΄ 12 (2,26cm2) ο·
KH=
VerificaciΓ³n de apoyo X3
β(ππ) βπ(π‘π) π
42 ππ
=
β
3,012π‘π 0,20π
= 10,823 => Adopto por tabla KH= 7,252
KS= 0,4876
Armadura principal: AS=
ππ .πππππ¦π(π‘π) β(π)
=
0.4876 . 3,012π‘π 0,42π
= 3,497cm2 => AS necesaria: 3,497cm2 ; As disponible : 2,26cm2
AS necesaria real: 1,237cm2 => Adopto 2 α΄ 12 (2,26cm2)
ο·
Esquema de armado
(FALTAN ESQUEMAS DE ARMADO SECCION DE VIGAS)
ππ.2,4 8
=
1,33π .2,4 22
h=42cm d=45m r=3cm
= 0,399m => Adopto h=0,43m
do= h+r = 0,43m+0,03m = 0,45m bo= 0,20m
ο·
AnΓ‘lisis de carga
P= RAV.220 = 2,21t Q= Rb L.201,L.202 + P.propio viga continua + Muro de 20cm de ladrillo comΓΊn hueco, cemento y arena P.propio Viga continua = 0,45m . 0,20m . 2,4t/m3 = 0,216t/m Rb L.201,L.202= 3,22 t/m Muro de 20cm de ladrillo comΓΊn hueco, cemento y arena = 0,28t/m 2 . 2,55m = 0,714t/m Q= 0,216t/m + 3,22t/m + 0,714T/m => Q = 4,15t/m
ο·
Calculo momentos de voladizo Apoyo V.219 y V.214 por izq. 2,21t q=4,15t/m
X= -
q.l2 2
+P.l =-(
4,15t/m.(1,33m)2 2
+2,12t . 1,33m) =-6,61tm
Apoyo V.219 y V.214 por derecha. q=4,15t/m
X= -
ο·
q.l2 2
= -(
4,15t/m.(1,05m)2 2
) =-2,288tm
Calculo de tΓ©rminos de carga
V.214 Estado 1 q=4,15t/m
L=R= -
q.l2 4
=
4,15t/m.(2,9m)2 4
=8,73tm
Estado 2 -6,61tm
L= 2 . Xizq = 2 . -6,61tm = -13,22tm R=Xizq = -6,61tm
TΓ©rminos de carga total Ltotal= 8,73tm -13,22tm = -4,49tm
Rtotal= 8,73tm -6,61tm = 2,21tm
V.211=V.208 Estado 1 q=4,15t/m
L=R= -
q.l2 4
=
4,15t/m.(2,9m)2 4
=8,73tm
TΓ©rminos de carga total Ltotal= 8,73tm
Rtotal= 8,73tm
V.205 Estado 1 q=4,15t/m
L=R= -
q.l2 4
=
4,15t/m.(2,9m)2 4
=8,73tm
Estado 2 -2,288tm
L= Xder. = -2,288tm R=2. Xder. = -4,576tm
TΓ©rminos de carga total Ltotal= 8,73tm -2,288tm = 6,442tm
ο·
X1= X2= X3=
Rtotal= 8,73tm -4,576tm = 4,154tm
Calculo de momento de apoyo
β15.(2,21tm+8,73tm)+4.(8,73tm+8,73tm)β(8,73tm+6,442) 56 4.(2,21tm+8,73tm)β16.(8,73tm+8,73tm)+4.(8,73tm+6,442) 56 β(2,21tm+8,73tm)+4.(8,73tm+8,73tm)β15.(8,73tm+6,442) 56
= -1,954tm = -3,123tm = -3,012tm
ο·
Calculo de reacciones de carga βRQβ
Reacciones Voladizo V.219 2,21t q=4,15t/m
RQ= RA=RB= q.l +P = 4,15t/m . 1,33m +2,21t =7,7295t
Reacciones Voladizo V.202
q=4,15t/m
RQ=RA=RB= q.l = 4,15t/m . 1,05m =4,3575t
V.214=V.211=V.208=V.205 q=4,15t/m
ο·
RQ=RA=RB=
q.l 2
=
4,15t/m.2,9m 2
=6,0175t
Calculo reacciones de momento βRMβ
V.214 Momento resultante=-6,61tm β (-1,954tm) =-4,656tm RM=4,656tm/2,9m=1,606t V.211 Momento resultante=-1,954tm β (-3,123tm) =1,169tm RM=1,169tm/2,9m=0,4031t V.208 Momento resultante=-3,012tm β (-3,123tm) =0,111tm RM=0,111tm/2,9m=0,0383t V.205 Momento resultante=-3,012tm β (-2,288tm) =-0,724tm RM=0,724tm/2,9m=0,2497t
ο·
Calculo de solicitaciones totales y momentos de tramos βMmΓ‘x.β
202 -6,61tm
-1,954tm
6,0175t
7,7295t
ο·
-3,123tm
6,0175t
6,0175t
+1,606t
-1,606t
-0,4031t
7,6235t
4,4115t
5,6144t
6,0175t +0,4031t 6,4206t
-3,012tm 6,0175t
6,0175t
6,0175t
+0,0383t
-0,0383t
+0,2497t
-0,2497t
6,0558t
5,9792t
6,2672t
5,7678t
Xm2izq.= Xm3izq.= Xm4izq.=
RM 4,3575t
RT
1,3529m | 1,5471m
1,4592m | 1,4408m
1,5102m | 1,3898m
Xm
0,3921tm|0,3907tm
1,8438tm|1,8438tm
1,2954tm|1,2953m
1,7203tm|1,7201tm
MmΓ‘x.
π π΄π.214 q π π΄π.211 q π π΄π.208 q π π΄π.205 q
X0 RQ
1,8398m | 1,0602m
Calculo distancia βXmβ
Xm1izq.=
-2,288tm
6,0175t
= = = =
7,635π‘
=1,8398m
4,15tm
5,6144π‘ 4,15tm 6,0558π‘ 4,15tm 6,2672π‘ 4,15tm
Xm1der.= 2,9m - 1,8398m=1,0602m
=1,3529m
Xm2der.= 2,9m β 1,3529m=1,5471m
=1,4592m
Xm3der.= 2,9m - 1,4592m=1,4408m
=1,5102m
Xm4der.= 2,9m - 1,5102m=1,3898m
Momento mΓ‘ximo V.214 Mmax.izq =7,6235t . 1,8398m - 4,15t/m. Mmax.der = 4,4115 . 1,0602m - 4,15t/m.
(1,8398π)2 2 (1,0602π)2 2
- 6,61tm =0,3921tm - 1,954= 0,3907tm
Momento mΓ‘ximo V.211 Mmax.izq =5,6144t . 1,3529m - 4,15t/m. Mmax.der = 6,4206t . 1,5471m- 4,15t/m.
(1,3529π)2 2
- 1,954tm =1,8438tm
(1,5471π)2
- 3,123tm= 1,8438tm
2
Momento mΓ‘ximo V.208 Mmax.izq =6,0558t . 1,4592m - 4,15t/m. Mmax.der = 5,9792 . 1,4408m - 4,15t/m.
(1,4592π)2 2 (1,4408π)2 2
- 3,123tm =1,2954tm - 3,012= 1,2953tm
Momento mΓ‘ximo V.205 Mmax.izq =6,2672t . 1,5102m - 4,15t/m. Mmax.der = 5,7678t . 1,3898m - 4,15t/m.
(1,5102π)2 2
- 3,012tm =1,7203tm
(1,3898π)2 2
- 2,288= 1,7201tm
ο·
Diagrama de corte y momento flector
202
ο·
Dimensionamiento- H-17
V.214 KH=
β(ππ) β
AS=
π(π‘π) π
42 ππ
= β
ππ .π(π‘π) β(π)
0,3921π‘π 0,20π
= 29,996 => Adopto por tabla 7,252
0,4876 .0,3921π‘π
=
0,30π
KS= 0,4876
= 0,64 cm2 Adopto 2 α΄ 12 (2,26cm2) se levanta 1 α΄ 12 (1,13cm2)
V.211 KH=
AS=
β(ππ) π(π‘π) β π
=
ππ .π(π‘π) β(π)
42ππ 1,8438π‘π β 0,20π
= 13,834 => Adopto por tabla KH= 7,252
0,4876.1,8438 π‘π
=
0,42π
KS= 0,4876
= 2,141 cm2 Adopto 2 α΄ 12 (2,26cm2) se levanta 1 α΄ 12 (1,13cm2)
V.208 KH=
β(ππ) βπ(π‘π)
β
π
AS=
42 ππ
=
ππ .π(π‘π) β(π)
1,2954π‘π 0,20π
= 16,503 => Adopto por tabla KH= 7,252
0,4876 . 1,2954π‘π
=
0,42π
KS= 0,4876
= 1,504 cm2 Adopto 2 α΄ 12 (2,26cm2) se levanta 1 α΄ 12 (1,13cm2)
V.205 KH=
β(ππ) βπ(π‘π)
β
π
AS=
42 ππ
=
ππ .π(π‘π) β(π)
1,7206π‘π 0,20π
= 14,32 => Adopto por tabla KH= 7,252
0,4876.1,7206π‘π
=
0,42π
KS= 0,4876
= 1,998 cm2 Adopto 2 α΄ 12 (2,26cm2) se levanta 1 α΄ 12 (1,13cm2)
V.219 KH=
AS=
β(ππ) βπ(π‘π) π
=
42 ππ β
ππ .π(π‘π) β(π)
6,61π‘π 0,20π
= 7,306 => Adopto por tabla 7,252
0,4876 .6,61π‘π
=
0,42π
KS= 0,4876
= 7,674cm2 => AS necesaria: 7,674cm2 ; As disponible : 1,13cm2
AS necesaria real:6,544cm2 => Adopto 6 α΄ 12 (6,78cm2)
V.202 KH=
β(ππ) βπ(π‘π) π
AS=
ππ .π(π‘π) β(π)
42 ππ
=
β
=
2,288π‘π 0,20π
= 12,418 => Adopto por tabla KH= 7,252
0,4876 . 2,288π‘π 0,42π
KS= 0,4876
= 2,63 cm2 => AS necesaria: 2,63cm2 ; As disponible : 1,13cm2
AS necesaria real: 1,5cm2 => Adopto 2 α΄ 12 (2,26cm2)
h=42cm d=45m r=3cm
ο· KH=
VerificaciΓ³n de apoyo X1 β(ππ) βπ(π‘π)
42 ππ
=
β
π
1,954π‘π 0,20π
= 13,437 => Adopto por tabla KH= 7,252
KS= 0,4876
Armadura principal: AS=
ο· KH=
ππ .πππππ¦π(π‘π) β(π)
=
0.4876 . 1,954π‘π 0,42π
= 2,269cm2 => AS necesaria: 2,269cm2 ; As disponible : 2,26cm2 *Diferencia < 2% Verifica
VerificaciΓ³n de apoyo X2 β(ππ) βπ(π‘π)
42 ππ
=
β
π
3,123π‘π 0,20π
= 10,629 => Adopto por tabla KH= 7,252
KS= 0,4876
Armadura principal: AS=
ππ .πππππ¦π(π‘π) β(π)
=
0.4876 . 3,123π‘π 0,42π
= 3,626cm2 => AS necesaria: 3,626cm2 ; As disponible : 2,26cm2
AS necesaria real: 1,366cm2 => Adopto 2 α΄ 12 (2,26cm2) ο·
KH=
VerificaciΓ³n de apoyo X3
β(ππ) βπ(π‘π) π
42 ππ
=
β
3,012π‘π 0,20π
= 10,823 => Adopto por tabla KH= 7,252
KS= 0,4876
Armadura principal: AS=
ππ .πππππ¦π(π‘π) β(π)
=
0.4876 . 3,012π‘π 0,42π
= 3,497cm2 => AS necesaria: 3,497cm2 ; As disponible : 2,26cm2
AS necesaria real: 1,237cm2 => Adopto 2 α΄ 12 (2,26cm2)
ο·
Esquema de armado
(FALTAN ESQUEMAS DE ARMADO SECCION DE VIGAS)
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