Torsion

SEXTO PISO:
1.- Valores D por eje:
| Direccion X | Direccion Y |
Eje | 1 | 2 | 3 | 4 | A | B | C | D |
Suma D | 2.59 | 3.75 | 3.75 | 2.59 | 1.948 | 1.948 | 1.948 | 0.941 |
| Sum Dx | 12.68 | | | | Suma Dy | 6.785 | |

2.-Centro de masa:
Xc.m=7.5*240+(18.25*29.25) 269.25 = 8.668
Yc.m=8*240+(7.75*29.25) 269.25 = 8.
3.-Centro de rigidez:Xc.r=1.948*9+(1.948*15)+(0.941*21.5) 6.785 =  9.872
Yc.r=3.75*5.5+(3.75*10)+(2.59*16) 12.68 =  7.852

4.- Excentricidad teórica:
ex=9.872-8.668=1.204
ey=8-7.852=0.148
5.-Por reglamento de amplificación de norma E030:
* Analisis del sismo X-X :
e1y =0.148 + 0.05*16 = 0.948 Mtxx1=125.76*0.948=119.22
e2y= 0.148-0.05*16=-0.652 Mtxx2=125.76*0.652=81.995

Eje | Di | ri | Di*ri^2| Di*ri/Ip |
1 | 2.59 | 7.852 | 159.68361 | 0.0275019 |
2 | 3.75 | 2.352 | 20.74464 | 0.0119275 |
3 | 3.75 | 2.148 | 17.30214 | 0.010893 |
4 | 2.59 | 8.148 | 171.94985 | 0.0285386 |
A | 1.948 | 9.872 | 189.84504 | |
B | 1.948 | 0.872 | 1.481228 | |
C | 1.948 | 5.128 | 51.225356 | |
D | 0.941 | 11.628 | 127.23297 | |
| | Ip= | 739.46483 | |

se corrige los ejes 1,2,3,4:Vij=MTij*Dij*riIp
Torsión | | eje | Traslación |
V1= | 2.2550 | 1 | 9.918 |
V2= | 0.9780 | 2 | 37.192 |
V3= | 1.2987 | 3 | 37.192 |
V4= | 3.4024 | 4 | 25.688 |

* Analisis del sismo Y-Y:
e1x =1.204 + 0.05*21.5 = 2.279 Mtyy1=125.76*2.279=286.607
e2x= 1.204-0.05*21.5=0.129

eje | Di | ri | Di*ri^2 | Di*ri/Ip |
1 | 2.59 | 7.852 | 159.6836114 | |
2 |3.75 | 2.352 | 20.74464 | |
3 | 3.75 | 2.148 | 17.30214 | |
4 | 2.59 | 8.148 | 171.9498514 | |
A | 1.948 | 9.872 | 189.845036 | |
B | 1.948 | 0.872 | 1.481228032 | |
C | 1.948 | 5.128 | 51.22535603 | 0.01350888 |
D | 0.941 | 11.628 | 127.2329713 | 0.01479712 |
| | Ip= | 739.4648342 | |
| | | | |
Torsión | | eje | Traslación |
Vc= | 3.8717 | A | 36.1062 |
Vd= |4.2410 | B | 36.1062 |
| | C | 36.1062 |
| | D | 17.4414 |

5.- Cortantes Totales:
* Por reglamento 0.3*125.76=37.728

* Si en algún eje o elemento, el cortante total excede el 30% del cortante de entrepiso esto deberá incrementarse en 25%

eje | Traslacion(Tn) | Torsion(Tn) | Total | Diseño (Tn) |
1 | 25.688 | 2.255 | 27.943 | 27.943 |
2 | 37.192 | 0.978 | 38.170 | 47.713|
3 | 37.192 | 1.299 | 38.491 | 48.114 |
4 | 25.688 | 3.402 | 29.090 | 29.090 |
A | 36.106 | | 36.106 | 36.106 |
B | 36.106 | | 36.106 | 36.106 |
C | 36.106 | 3.872 | 39.978 | 49.972 |
D | 17.441 | 4.241 | 21.682 | 21.682 |

QUINTO PISO:
1.- Valores D por eje:
| Direccion X | Direccion Y |
Eje | 1 | 2 | 3 | 4 | A | B | C | D |
Suma D | 2.95 | 4.41 | 4.41 | 2.95 | 2.168 |2.168 | 2.168 | 1.041 |
| Sum Dx | 14.72 | | | | Suma Dy | 7.545 | |

2.-Centro de masa:
Xc.m=7.5*240+(18.25*29.25) 269.25 = 8.668

Yc.m=8*240+(7.75*29.25) 269.25 = 8.

3.-Centro de rigidez:
Xc.r=2.168*9+(2.168*15)+(1.041*21.5) 7.545 =  9.862
Yc.r=4.41*5.5+(4.41*10)+(2.95*16) 14.72 =  7.85
4.- Excentricidad teórica:
ex=9.862-8.668=1.194
ey=8-7.85=0.15
5.-Por reglamento deamplificación de norma E030:
* Analisis del sismo X-X :
e1y =0.15 + 0.05*16 = 0.95 Mtxx1=174.64*0.95=165.908
e2y= 0.15-0.05*16=-0.65 Mtxx2=174.64*0.65=113.516

Eje | Di | ri | Di*ri^2 | Di*ri/Ip |
1 | 2.95 | 7.852 | 181.87902 | 0.03132455 |
2 | 4.41 | 2.352 | 24.395697 | 0.01402679 |
3 | 4.41 | 2.148 | 20.347317 | 0.01281018 |
4 | 2.95 |8.148 | 195.85022 | 0.0325054 |
A | 2.168 | 9.872 | 211.28544 | |
B | 2.168 | 0.872 | 1.6485125 | |
C | 2.168 | 5.128 | 57.010561 | |
D | 1.041 | 11.628 | 140.75401 | |
| | Ip= | 833.17077 | |

se corrige los ejes 1,2,3,4:
Vij=MTij*Dij*riIp
torsión | | eje | Traslación |
V1= | 3.5558 | 1 | 34.999 |
V2= | 1.5923 | 2 | 52.321 |
V3= | 2.1253 | 3 | 52.321 |
V4= |...