xcvv copia-copia reytryut
TRANSCRIPT
7252019 xcvv copia-copia reytryut
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UNIVERSIDAD ANDINA NESTOR CACERES VELASQUEZ UNIVERSIDAD ANDINA NESTOR CACERES VELASQUEZ
ESCUELA PROFESIONAL INGENIERIA CIVILESCUELA PROFESIONAL INGENIERIA CIVIL
Guido F Rodriguez MolinaGuido F Rodriguez Molina
2016
guidormolinahotmailcom
rodriguezgfpucpedupe
CONCRETO ARMADO II
ZAPATA AISLADA BIAXIAL
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 217
Z A P A T A A I S L A D A B I A X I A L
Disentildear la zapata los datos son obtenidos de el anaacutelisis estructural realizado enetabs
P
983107983105983122983111983105983123 983108983109 983123983109983122983126983113983107983113983119
983124983150 (983124983150983085983149) (983124983150983085983149)
983120983149 12540 983117983149983160 165 983117983149983161 045
983120983158 4550 983117983158983160 225 983117983158983161 050983120983155983160 320 983117983155983160 02983097 983117983155983161 09830975
983120983155983161 021
GUIDO F RODRIGUEZ MOLINA - UANCV
My
B
ZAPATA
Mx My
B
LMx
b
h
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 317
Z A P A T A A I S L A D A B I A X I A L
1- DIMENSIONAMIENTO
983124983150451983095983097)504540125(051983120983155 =+=
983137
983155
983153983120983105 = 29831499830979830964
)40(98309700451983095983097983105 ==
9830969830974983106 = 983149232983106 =
400400302983116 +minus=
983149302983116 =
GUIDO F RODRIGUEZ MOLINA - UANCV
Asumimos B = 230 m
09qa debido a queno toma momentos
7252019 xcvv copia-copia reytryut
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Z A P A T A A I S L A D A B I A X I A L
Si se supone que el suelo trabaja con un comportamiento elaacutestico ydebido a que la carga se encuentra en el tercio medio de la cimentacioacutenpuede aplicarse la siguiente expresioacuten para calcular el esfuerzo maacuteximode reaccioacuten en el suelo la misma que es una variante en presentacioacuten delas ecuaciones tradicionales de la Resistencia de Materiales para carga
axial maacutes flexioacuten en dos direcciones ortogonales
22
983125
983116983106
9831176
983106983116
9831176
983105
983120983153 plusmnplusmn=
Y
P
My
1 4
B
LXey
ex P
2 3
14
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 517
Z A P A T A A I S L A D A B I A X I A L
983123
983123983128983129
983120
983117983141 =
983123
983123983129983160
983120983117983141 = 983139983149333983096
6302983141983160 =lt
983139983149333983096
6
302983141983161 =lt
983139983149530451983095983097
98309750983141983160 ==
983139983149160
451983095983097
29830970983141983161 ==
2- VERIFICACION DE PRESIONES
Y
2 3VERIFICACION MOMENTO EN X
2
983123
1 983116983106983105 +=σ
2
9831609831232
983116983106
9831176
983105
983120minus=σ
1 4
B
LXey
ex P
GUIDO F RODRIGUEZ MOLINA - UANCV
221 983149983124983150983096535
)302(302)252651(6
)302(302451983095983097 =++=σ
2
22 983149983124983150032)302(302
)252651(6
)302(302
451983095983097=
+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 617
Z A P A T A A I S L A D A B I A X I A L
221983116983106
)983117983158983161983117983149983161(6983116983106
)983117983158983160983117983149983160(6983105983120983155 +minus++=σ
VERIFICACION BIAXIAL
222983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 +minus
+minus=σ
223983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 ++
+minus=σ
224983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 ++
++=σ
My
1
2 3
4
230Mx
b
h
GUIDO F RODRIGUEZ MOLINA - UANCV
230
2
4 98314998312498315031364698309609830972319830972233 =++=σ
2
221 983149983124983150398309635)302(302
)500450(6
)302(302
)252651(6
)302(302
451983095983097=
+minus
++=σ
2
2 98314998312498315053314698309609830972319830972233 =minusminus=σ
2
3 9831499831249831504983095324698309609830972319830972233 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 717
Z A P A T A A I S L A D A B I A X I A L
Esfuerzo maacuteximo (3706 Tnm2) es menoral esfuerzo admisible del suelo (40Tnm2)
VERIFICACION SISMO EN X
221983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 +minus+++++=σ
222983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 +minus
++minus
++=σ
223983116983106
)983117983158983161983117983149983161(6983116983106
)983117983155983160983117983158983160983117983149983160(6983105
)983120983155983160983120983158983120983149(051 ++++minus++=σ
224983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 ++
+++
++=σ
GUIDO F RODRIGUEZ MOLINA - UANCV
2
4 9831499831249831500983097398309546983096006625634 =++=σ
2
221 9831499831249831501598309636)302(302
)500450(6
)302(302
)29830970252651(6
)302(302
9830960519830962=
+minus
+++=σ
2
2 9831499831249831500263246983096006625634 =minusminus=σ
2
3 98314998312498315098309763246983096006625634 =+minus=σ
7252019 xcvv copia-copia reytryut
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Z A P A T A A I S L A D A B I A X I A L
Esfuerzo maacuteximo (3682 Tnm2) es menoral esfuerzo admisible del suelo (40Tnm2)
VERIFICACION SISMO EN Y
221983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 ++minus++++=σ
222983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 ++minus
+minus
++=σ
223983116983106
)983117983155983161983117983158983161983117983149983161(6983116983106
)983117983158983160983117983149983160(6983105
)983120983155983161983120983158983120983149(051 ++++minus++=σ
224983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 +++
++
++=σ
GUIDO F RODRIGUEZ MOLINA - UANCV
2
4 983149983124983150983096236983097398309509830972319830976433 =++=σ
2
221 983149983124983150983097534)302(302
)98309750500450(6
)302(302
)252651(6
)302(302
69830951983095983097=
++minus
++=σ
2
2 98314998312498315010431983097398309509830972319830976433 =minusminus=σ
2
3 98314998312498315098309798309632983097398309509830972319830976433 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 917
Z A P A T A A I S L A D A B I A X I A L
Por lo tanto
COMO LAS PRESIONES EJERCIDAS POR EL SUELO SON MENORES AL ESFUERZO
ADMISIBLE DEL SUELO SE CONSIDERA QUE LAS DIMENSIONES SON CORRECTAS
La carga de disentildeo (qu) se debe amplificar seguacuten la combinacioacuten de cargas a usar sinembargo se puede amplificar directamente la presioacuten obtenida con cargas de servicio usandoun coeficiente intermedio aproximado
- Cuando no se considero sismo se obtuvo 3631 Tnm2
2
983149983124983150098309765983096619831603136 ==σ
GUIDO F RODRIGUEZ MOLINA - UANCV
- Cuando se considero sismo en X se obtuvo 3709 Tnm2
- Cuando se considero sismo en Y se obtuvo 3682 Tnm2
2983149983124983150364625198316009830973983095 ==σ
29831499831249831500346251983160983096236 ==σ
Entonces el disentildeo por cortante y flexioacuten se hace con σu = 5736 Tnm2
7252019 xcvv copia-copia reytryut
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Z A P A T A A I S L A D A B I A X I A L
3- DISENtildeO A CORTE
El peralte de la zapata estaacute definido por su capacidad resistente a cortante tipo viga y acortante por punzonamiento Para ambos casos se utilizan los estados de carga uacuteltimos
Se asume una altura tentativa de 65 cm para la zapata y una distancia desde la carainferior de concreto hasta la capa de refuerzo de 10 cm
P
Asumimos h = 65
d = 65 ndash 10 = 55 cm
My
230
Mx
065055
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1117
Z A P A T A A I S L A D A B I A X I A L
Pu
MyMx
2 3
230
055 040
598309610 9831249831509831492
1 4
230
)1()400(105983096983126983125 =
Cortante uacuteltimo Actuante9831249831502423983126983125 =
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1217
Z A P A T A A I S L A D A B I A X I A L
983140983138983139983142 530983126983107 φ=
Vu lt Vc
Cortante Admisible
100)55(210)530(98309650983126983107 =
983124983150036983126983107 =
Ok2324 lt 360
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1317
Z A P A T A A I S L A D A B I A X I A L
5- PUNZONAMIENTO
983140983138983139983142 )11
530(983126983139 983151β
+φ=
bo = 380 cm Periacutemetro
9831249831509830971254983126983125 = Cortante ultimo
)9830975098316098309750(105983096)302983160302(105983096983126983157 minus=
598309610 9831249831509831492
9831402 9831402
983140983138983139983142 11983126983139 983151φ=
Tomamos el menor valor
Vu lt Vc
9831249831506341983097)55(39830960210)1
11530(98309650983126983139 =+=
98312498315019830962983096355)39830960(210)11(98309650983126983139 ==
25491 lt 28318 OkGUIDO F RODRIGUEZ MOLINA - UANCV
1
2 3
4
230
230
055 040
9830975
9830975
Arsquo
A
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1417
Z A P A T A A I S L A D A B I A X I A L
6- FLEXION
Z A P A T A A I S L A D A B I A X I A L
9831249831502226983117983157 =598309610 9831249831509831492
9830975
9831162
983148983153983117983157
2
=
12
98309750105983096
983117983157
2
=
GUIDO F RODRIGUEZ MOLINA - UANCV
230
230
0952983138983140
983117983157983115983157=
698309598309655100
109831602226983115983157
2
5
==
230=ρ
983140983138983105983155 ρ=
7252019 xcvv copia-copia reytryut
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Z A P A T A A I S L A D A B I A X I A L
)55()100(00230983105983155 =
29831399831496512983105983155 =
983142983161
983139983142 9830950983149983145983150 =ρ
Verificacioacuten Cuantiacutea Miacutenima
983140983138983105983155 983149983145983150ρ=
GUIDO F RODRIGUEZ MOLINA - UANCV
4200
2109830950983149983145983150 =ρ 00240983149983145983150 =ρ
Cuantiacutea Miacutenima es mayor que cuantiacutea adoptada entonces asumimos cuantiacutea miacutenima
)55()100(00240983105983155 =
29831399831492013983105983155 =
7252019 xcvv copia-copia reytryut
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Z A P A T A A I S L A D A B I A X I A L
9830965φ as = 200 cm2 2013
)002(100
983155 =
43φ as = 285 cm2
s = 1515 cm
s = 2159 cm
2013
)98309652(100983155 =
Asumimos Oslash 34 020 m
2 3
Oslash 34 020
GUIDO F RODRIGUEZ MOLINA - UANCV
1 4
230
230
Oslash 34 020
DISENtildeO FINAL DE LA ZAPATA
7252019 xcvv copia-copia reytryut
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Z A P A T A A I S L A D A B I A X I A L
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 217
Z A P A T A A I S L A D A B I A X I A L
Disentildear la zapata los datos son obtenidos de el anaacutelisis estructural realizado enetabs
P
983107983105983122983111983105983123 983108983109 983123983109983122983126983113983107983113983119
983124983150 (983124983150983085983149) (983124983150983085983149)
983120983149 12540 983117983149983160 165 983117983149983161 045
983120983158 4550 983117983158983160 225 983117983158983161 050983120983155983160 320 983117983155983160 02983097 983117983155983161 09830975
983120983155983161 021
GUIDO F RODRIGUEZ MOLINA - UANCV
My
B
ZAPATA
Mx My
B
LMx
b
h
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 317
Z A P A T A A I S L A D A B I A X I A L
1- DIMENSIONAMIENTO
983124983150451983095983097)504540125(051983120983155 =+=
983137
983155
983153983120983105 = 29831499830979830964
)40(98309700451983095983097983105 ==
9830969830974983106 = 983149232983106 =
400400302983116 +minus=
983149302983116 =
GUIDO F RODRIGUEZ MOLINA - UANCV
Asumimos B = 230 m
09qa debido a queno toma momentos
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 417
Z A P A T A A I S L A D A B I A X I A L
Si se supone que el suelo trabaja con un comportamiento elaacutestico ydebido a que la carga se encuentra en el tercio medio de la cimentacioacutenpuede aplicarse la siguiente expresioacuten para calcular el esfuerzo maacuteximode reaccioacuten en el suelo la misma que es una variante en presentacioacuten delas ecuaciones tradicionales de la Resistencia de Materiales para carga
axial maacutes flexioacuten en dos direcciones ortogonales
22
983125
983116983106
9831176
983106983116
9831176
983105
983120983153 plusmnplusmn=
Y
P
My
1 4
B
LXey
ex P
2 3
14
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 517
Z A P A T A A I S L A D A B I A X I A L
983123
983123983128983129
983120
983117983141 =
983123
983123983129983160
983120983117983141 = 983139983149333983096
6302983141983160 =lt
983139983149333983096
6
302983141983161 =lt
983139983149530451983095983097
98309750983141983160 ==
983139983149160
451983095983097
29830970983141983161 ==
2- VERIFICACION DE PRESIONES
Y
2 3VERIFICACION MOMENTO EN X
2
983123
1 983116983106983105 +=σ
2
9831609831232
983116983106
9831176
983105
983120minus=σ
1 4
B
LXey
ex P
GUIDO F RODRIGUEZ MOLINA - UANCV
221 983149983124983150983096535
)302(302)252651(6
)302(302451983095983097 =++=σ
2
22 983149983124983150032)302(302
)252651(6
)302(302
451983095983097=
+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 617
Z A P A T A A I S L A D A B I A X I A L
221983116983106
)983117983158983161983117983149983161(6983116983106
)983117983158983160983117983149983160(6983105983120983155 +minus++=σ
VERIFICACION BIAXIAL
222983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 +minus
+minus=σ
223983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 ++
+minus=σ
224983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 ++
++=σ
My
1
2 3
4
230Mx
b
h
GUIDO F RODRIGUEZ MOLINA - UANCV
230
2
4 98314998312498315031364698309609830972319830972233 =++=σ
2
221 983149983124983150398309635)302(302
)500450(6
)302(302
)252651(6
)302(302
451983095983097=
+minus
++=σ
2
2 98314998312498315053314698309609830972319830972233 =minusminus=σ
2
3 9831499831249831504983095324698309609830972319830972233 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 717
Z A P A T A A I S L A D A B I A X I A L
Esfuerzo maacuteximo (3706 Tnm2) es menoral esfuerzo admisible del suelo (40Tnm2)
VERIFICACION SISMO EN X
221983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 +minus+++++=σ
222983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 +minus
++minus
++=σ
223983116983106
)983117983158983161983117983149983161(6983116983106
)983117983155983160983117983158983160983117983149983160(6983105
)983120983155983160983120983158983120983149(051 ++++minus++=σ
224983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 ++
+++
++=σ
GUIDO F RODRIGUEZ MOLINA - UANCV
2
4 9831499831249831500983097398309546983096006625634 =++=σ
2
221 9831499831249831501598309636)302(302
)500450(6
)302(302
)29830970252651(6
)302(302
9830960519830962=
+minus
+++=σ
2
2 9831499831249831500263246983096006625634 =minusminus=σ
2
3 98314998312498315098309763246983096006625634 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 817
Z A P A T A A I S L A D A B I A X I A L
Esfuerzo maacuteximo (3682 Tnm2) es menoral esfuerzo admisible del suelo (40Tnm2)
VERIFICACION SISMO EN Y
221983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 ++minus++++=σ
222983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 ++minus
+minus
++=σ
223983116983106
)983117983155983161983117983158983161983117983149983161(6983116983106
)983117983158983160983117983149983160(6983105
)983120983155983161983120983158983120983149(051 ++++minus++=σ
224983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 +++
++
++=σ
GUIDO F RODRIGUEZ MOLINA - UANCV
2
4 983149983124983150983096236983097398309509830972319830976433 =++=σ
2
221 983149983124983150983097534)302(302
)98309750500450(6
)302(302
)252651(6
)302(302
69830951983095983097=
++minus
++=σ
2
2 98314998312498315010431983097398309509830972319830976433 =minusminus=σ
2
3 98314998312498315098309798309632983097398309509830972319830976433 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 917
Z A P A T A A I S L A D A B I A X I A L
Por lo tanto
COMO LAS PRESIONES EJERCIDAS POR EL SUELO SON MENORES AL ESFUERZO
ADMISIBLE DEL SUELO SE CONSIDERA QUE LAS DIMENSIONES SON CORRECTAS
La carga de disentildeo (qu) se debe amplificar seguacuten la combinacioacuten de cargas a usar sinembargo se puede amplificar directamente la presioacuten obtenida con cargas de servicio usandoun coeficiente intermedio aproximado
- Cuando no se considero sismo se obtuvo 3631 Tnm2
2
983149983124983150098309765983096619831603136 ==σ
GUIDO F RODRIGUEZ MOLINA - UANCV
- Cuando se considero sismo en X se obtuvo 3709 Tnm2
- Cuando se considero sismo en Y se obtuvo 3682 Tnm2
2983149983124983150364625198316009830973983095 ==σ
29831499831249831500346251983160983096236 ==σ
Entonces el disentildeo por cortante y flexioacuten se hace con σu = 5736 Tnm2
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1017
Z A P A T A A I S L A D A B I A X I A L
3- DISENtildeO A CORTE
El peralte de la zapata estaacute definido por su capacidad resistente a cortante tipo viga y acortante por punzonamiento Para ambos casos se utilizan los estados de carga uacuteltimos
Se asume una altura tentativa de 65 cm para la zapata y una distancia desde la carainferior de concreto hasta la capa de refuerzo de 10 cm
P
Asumimos h = 65
d = 65 ndash 10 = 55 cm
My
230
Mx
065055
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1117
Z A P A T A A I S L A D A B I A X I A L
Pu
MyMx
2 3
230
055 040
598309610 9831249831509831492
1 4
230
)1()400(105983096983126983125 =
Cortante uacuteltimo Actuante9831249831502423983126983125 =
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1217
Z A P A T A A I S L A D A B I A X I A L
983140983138983139983142 530983126983107 φ=
Vu lt Vc
Cortante Admisible
100)55(210)530(98309650983126983107 =
983124983150036983126983107 =
Ok2324 lt 360
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1317
Z A P A T A A I S L A D A B I A X I A L
5- PUNZONAMIENTO
983140983138983139983142 )11
530(983126983139 983151β
+φ=
bo = 380 cm Periacutemetro
9831249831509830971254983126983125 = Cortante ultimo
)9830975098316098309750(105983096)302983160302(105983096983126983157 minus=
598309610 9831249831509831492
9831402 9831402
983140983138983139983142 11983126983139 983151φ=
Tomamos el menor valor
Vu lt Vc
9831249831506341983097)55(39830960210)1
11530(98309650983126983139 =+=
98312498315019830962983096355)39830960(210)11(98309650983126983139 ==
25491 lt 28318 OkGUIDO F RODRIGUEZ MOLINA - UANCV
1
2 3
4
230
230
055 040
9830975
9830975
Arsquo
A
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1417
Z A P A T A A I S L A D A B I A X I A L
6- FLEXION
Z A P A T A A I S L A D A B I A X I A L
9831249831502226983117983157 =598309610 9831249831509831492
9830975
9831162
983148983153983117983157
2
=
12
98309750105983096
983117983157
2
=
GUIDO F RODRIGUEZ MOLINA - UANCV
230
230
0952983138983140
983117983157983115983157=
698309598309655100
109831602226983115983157
2
5
==
230=ρ
983140983138983105983155 ρ=
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1517
Z A P A T A A I S L A D A B I A X I A L
)55()100(00230983105983155 =
29831399831496512983105983155 =
983142983161
983139983142 9830950983149983145983150 =ρ
Verificacioacuten Cuantiacutea Miacutenima
983140983138983105983155 983149983145983150ρ=
GUIDO F RODRIGUEZ MOLINA - UANCV
4200
2109830950983149983145983150 =ρ 00240983149983145983150 =ρ
Cuantiacutea Miacutenima es mayor que cuantiacutea adoptada entonces asumimos cuantiacutea miacutenima
)55()100(00240983105983155 =
29831399831492013983105983155 =
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1617
Z A P A T A A I S L A D A B I A X I A L
9830965φ as = 200 cm2 2013
)002(100
983155 =
43φ as = 285 cm2
s = 1515 cm
s = 2159 cm
2013
)98309652(100983155 =
Asumimos Oslash 34 020 m
2 3
Oslash 34 020
GUIDO F RODRIGUEZ MOLINA - UANCV
1 4
230
230
Oslash 34 020
DISENtildeO FINAL DE LA ZAPATA
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1717
Z A P A T A A I S L A D A B I A X I A L
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 317
Z A P A T A A I S L A D A B I A X I A L
1- DIMENSIONAMIENTO
983124983150451983095983097)504540125(051983120983155 =+=
983137
983155
983153983120983105 = 29831499830979830964
)40(98309700451983095983097983105 ==
9830969830974983106 = 983149232983106 =
400400302983116 +minus=
983149302983116 =
GUIDO F RODRIGUEZ MOLINA - UANCV
Asumimos B = 230 m
09qa debido a queno toma momentos
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 417
Z A P A T A A I S L A D A B I A X I A L
Si se supone que el suelo trabaja con un comportamiento elaacutestico ydebido a que la carga se encuentra en el tercio medio de la cimentacioacutenpuede aplicarse la siguiente expresioacuten para calcular el esfuerzo maacuteximode reaccioacuten en el suelo la misma que es una variante en presentacioacuten delas ecuaciones tradicionales de la Resistencia de Materiales para carga
axial maacutes flexioacuten en dos direcciones ortogonales
22
983125
983116983106
9831176
983106983116
9831176
983105
983120983153 plusmnplusmn=
Y
P
My
1 4
B
LXey
ex P
2 3
14
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 517
Z A P A T A A I S L A D A B I A X I A L
983123
983123983128983129
983120
983117983141 =
983123
983123983129983160
983120983117983141 = 983139983149333983096
6302983141983160 =lt
983139983149333983096
6
302983141983161 =lt
983139983149530451983095983097
98309750983141983160 ==
983139983149160
451983095983097
29830970983141983161 ==
2- VERIFICACION DE PRESIONES
Y
2 3VERIFICACION MOMENTO EN X
2
983123
1 983116983106983105 +=σ
2
9831609831232
983116983106
9831176
983105
983120minus=σ
1 4
B
LXey
ex P
GUIDO F RODRIGUEZ MOLINA - UANCV
221 983149983124983150983096535
)302(302)252651(6
)302(302451983095983097 =++=σ
2
22 983149983124983150032)302(302
)252651(6
)302(302
451983095983097=
+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 617
Z A P A T A A I S L A D A B I A X I A L
221983116983106
)983117983158983161983117983149983161(6983116983106
)983117983158983160983117983149983160(6983105983120983155 +minus++=σ
VERIFICACION BIAXIAL
222983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 +minus
+minus=σ
223983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 ++
+minus=σ
224983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 ++
++=σ
My
1
2 3
4
230Mx
b
h
GUIDO F RODRIGUEZ MOLINA - UANCV
230
2
4 98314998312498315031364698309609830972319830972233 =++=σ
2
221 983149983124983150398309635)302(302
)500450(6
)302(302
)252651(6
)302(302
451983095983097=
+minus
++=σ
2
2 98314998312498315053314698309609830972319830972233 =minusminus=σ
2
3 9831499831249831504983095324698309609830972319830972233 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 717
Z A P A T A A I S L A D A B I A X I A L
Esfuerzo maacuteximo (3706 Tnm2) es menoral esfuerzo admisible del suelo (40Tnm2)
VERIFICACION SISMO EN X
221983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 +minus+++++=σ
222983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 +minus
++minus
++=σ
223983116983106
)983117983158983161983117983149983161(6983116983106
)983117983155983160983117983158983160983117983149983160(6983105
)983120983155983160983120983158983120983149(051 ++++minus++=σ
224983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 ++
+++
++=σ
GUIDO F RODRIGUEZ MOLINA - UANCV
2
4 9831499831249831500983097398309546983096006625634 =++=σ
2
221 9831499831249831501598309636)302(302
)500450(6
)302(302
)29830970252651(6
)302(302
9830960519830962=
+minus
+++=σ
2
2 9831499831249831500263246983096006625634 =minusminus=σ
2
3 98314998312498315098309763246983096006625634 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 817
Z A P A T A A I S L A D A B I A X I A L
Esfuerzo maacuteximo (3682 Tnm2) es menoral esfuerzo admisible del suelo (40Tnm2)
VERIFICACION SISMO EN Y
221983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 ++minus++++=σ
222983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 ++minus
+minus
++=σ
223983116983106
)983117983155983161983117983158983161983117983149983161(6983116983106
)983117983158983160983117983149983160(6983105
)983120983155983161983120983158983120983149(051 ++++minus++=σ
224983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 +++
++
++=σ
GUIDO F RODRIGUEZ MOLINA - UANCV
2
4 983149983124983150983096236983097398309509830972319830976433 =++=σ
2
221 983149983124983150983097534)302(302
)98309750500450(6
)302(302
)252651(6
)302(302
69830951983095983097=
++minus
++=σ
2
2 98314998312498315010431983097398309509830972319830976433 =minusminus=σ
2
3 98314998312498315098309798309632983097398309509830972319830976433 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 917
Z A P A T A A I S L A D A B I A X I A L
Por lo tanto
COMO LAS PRESIONES EJERCIDAS POR EL SUELO SON MENORES AL ESFUERZO
ADMISIBLE DEL SUELO SE CONSIDERA QUE LAS DIMENSIONES SON CORRECTAS
La carga de disentildeo (qu) se debe amplificar seguacuten la combinacioacuten de cargas a usar sinembargo se puede amplificar directamente la presioacuten obtenida con cargas de servicio usandoun coeficiente intermedio aproximado
- Cuando no se considero sismo se obtuvo 3631 Tnm2
2
983149983124983150098309765983096619831603136 ==σ
GUIDO F RODRIGUEZ MOLINA - UANCV
- Cuando se considero sismo en X se obtuvo 3709 Tnm2
- Cuando se considero sismo en Y se obtuvo 3682 Tnm2
2983149983124983150364625198316009830973983095 ==σ
29831499831249831500346251983160983096236 ==σ
Entonces el disentildeo por cortante y flexioacuten se hace con σu = 5736 Tnm2
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1017
Z A P A T A A I S L A D A B I A X I A L
3- DISENtildeO A CORTE
El peralte de la zapata estaacute definido por su capacidad resistente a cortante tipo viga y acortante por punzonamiento Para ambos casos se utilizan los estados de carga uacuteltimos
Se asume una altura tentativa de 65 cm para la zapata y una distancia desde la carainferior de concreto hasta la capa de refuerzo de 10 cm
P
Asumimos h = 65
d = 65 ndash 10 = 55 cm
My
230
Mx
065055
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1117
Z A P A T A A I S L A D A B I A X I A L
Pu
MyMx
2 3
230
055 040
598309610 9831249831509831492
1 4
230
)1()400(105983096983126983125 =
Cortante uacuteltimo Actuante9831249831502423983126983125 =
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1217
Z A P A T A A I S L A D A B I A X I A L
983140983138983139983142 530983126983107 φ=
Vu lt Vc
Cortante Admisible
100)55(210)530(98309650983126983107 =
983124983150036983126983107 =
Ok2324 lt 360
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1317
Z A P A T A A I S L A D A B I A X I A L
5- PUNZONAMIENTO
983140983138983139983142 )11
530(983126983139 983151β
+φ=
bo = 380 cm Periacutemetro
9831249831509830971254983126983125 = Cortante ultimo
)9830975098316098309750(105983096)302983160302(105983096983126983157 minus=
598309610 9831249831509831492
9831402 9831402
983140983138983139983142 11983126983139 983151φ=
Tomamos el menor valor
Vu lt Vc
9831249831506341983097)55(39830960210)1
11530(98309650983126983139 =+=
98312498315019830962983096355)39830960(210)11(98309650983126983139 ==
25491 lt 28318 OkGUIDO F RODRIGUEZ MOLINA - UANCV
1
2 3
4
230
230
055 040
9830975
9830975
Arsquo
A
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1417
Z A P A T A A I S L A D A B I A X I A L
6- FLEXION
Z A P A T A A I S L A D A B I A X I A L
9831249831502226983117983157 =598309610 9831249831509831492
9830975
9831162
983148983153983117983157
2
=
12
98309750105983096
983117983157
2
=
GUIDO F RODRIGUEZ MOLINA - UANCV
230
230
0952983138983140
983117983157983115983157=
698309598309655100
109831602226983115983157
2
5
==
230=ρ
983140983138983105983155 ρ=
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1517
Z A P A T A A I S L A D A B I A X I A L
)55()100(00230983105983155 =
29831399831496512983105983155 =
983142983161
983139983142 9830950983149983145983150 =ρ
Verificacioacuten Cuantiacutea Miacutenima
983140983138983105983155 983149983145983150ρ=
GUIDO F RODRIGUEZ MOLINA - UANCV
4200
2109830950983149983145983150 =ρ 00240983149983145983150 =ρ
Cuantiacutea Miacutenima es mayor que cuantiacutea adoptada entonces asumimos cuantiacutea miacutenima
)55()100(00240983105983155 =
29831399831492013983105983155 =
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1617
Z A P A T A A I S L A D A B I A X I A L
9830965φ as = 200 cm2 2013
)002(100
983155 =
43φ as = 285 cm2
s = 1515 cm
s = 2159 cm
2013
)98309652(100983155 =
Asumimos Oslash 34 020 m
2 3
Oslash 34 020
GUIDO F RODRIGUEZ MOLINA - UANCV
1 4
230
230
Oslash 34 020
DISENtildeO FINAL DE LA ZAPATA
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1717
Z A P A T A A I S L A D A B I A X I A L
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 417
Z A P A T A A I S L A D A B I A X I A L
Si se supone que el suelo trabaja con un comportamiento elaacutestico ydebido a que la carga se encuentra en el tercio medio de la cimentacioacutenpuede aplicarse la siguiente expresioacuten para calcular el esfuerzo maacuteximode reaccioacuten en el suelo la misma que es una variante en presentacioacuten delas ecuaciones tradicionales de la Resistencia de Materiales para carga
axial maacutes flexioacuten en dos direcciones ortogonales
22
983125
983116983106
9831176
983106983116
9831176
983105
983120983153 plusmnplusmn=
Y
P
My
1 4
B
LXey
ex P
2 3
14
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 517
Z A P A T A A I S L A D A B I A X I A L
983123
983123983128983129
983120
983117983141 =
983123
983123983129983160
983120983117983141 = 983139983149333983096
6302983141983160 =lt
983139983149333983096
6
302983141983161 =lt
983139983149530451983095983097
98309750983141983160 ==
983139983149160
451983095983097
29830970983141983161 ==
2- VERIFICACION DE PRESIONES
Y
2 3VERIFICACION MOMENTO EN X
2
983123
1 983116983106983105 +=σ
2
9831609831232
983116983106
9831176
983105
983120minus=σ
1 4
B
LXey
ex P
GUIDO F RODRIGUEZ MOLINA - UANCV
221 983149983124983150983096535
)302(302)252651(6
)302(302451983095983097 =++=σ
2
22 983149983124983150032)302(302
)252651(6
)302(302
451983095983097=
+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 617
Z A P A T A A I S L A D A B I A X I A L
221983116983106
)983117983158983161983117983149983161(6983116983106
)983117983158983160983117983149983160(6983105983120983155 +minus++=σ
VERIFICACION BIAXIAL
222983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 +minus
+minus=σ
223983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 ++
+minus=σ
224983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 ++
++=σ
My
1
2 3
4
230Mx
b
h
GUIDO F RODRIGUEZ MOLINA - UANCV
230
2
4 98314998312498315031364698309609830972319830972233 =++=σ
2
221 983149983124983150398309635)302(302
)500450(6
)302(302
)252651(6
)302(302
451983095983097=
+minus
++=σ
2
2 98314998312498315053314698309609830972319830972233 =minusminus=σ
2
3 9831499831249831504983095324698309609830972319830972233 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 717
Z A P A T A A I S L A D A B I A X I A L
Esfuerzo maacuteximo (3706 Tnm2) es menoral esfuerzo admisible del suelo (40Tnm2)
VERIFICACION SISMO EN X
221983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 +minus+++++=σ
222983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 +minus
++minus
++=σ
223983116983106
)983117983158983161983117983149983161(6983116983106
)983117983155983160983117983158983160983117983149983160(6983105
)983120983155983160983120983158983120983149(051 ++++minus++=σ
224983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 ++
+++
++=σ
GUIDO F RODRIGUEZ MOLINA - UANCV
2
4 9831499831249831500983097398309546983096006625634 =++=σ
2
221 9831499831249831501598309636)302(302
)500450(6
)302(302
)29830970252651(6
)302(302
9830960519830962=
+minus
+++=σ
2
2 9831499831249831500263246983096006625634 =minusminus=σ
2
3 98314998312498315098309763246983096006625634 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 817
Z A P A T A A I S L A D A B I A X I A L
Esfuerzo maacuteximo (3682 Tnm2) es menoral esfuerzo admisible del suelo (40Tnm2)
VERIFICACION SISMO EN Y
221983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 ++minus++++=σ
222983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 ++minus
+minus
++=σ
223983116983106
)983117983155983161983117983158983161983117983149983161(6983116983106
)983117983158983160983117983149983160(6983105
)983120983155983161983120983158983120983149(051 ++++minus++=σ
224983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 +++
++
++=σ
GUIDO F RODRIGUEZ MOLINA - UANCV
2
4 983149983124983150983096236983097398309509830972319830976433 =++=σ
2
221 983149983124983150983097534)302(302
)98309750500450(6
)302(302
)252651(6
)302(302
69830951983095983097=
++minus
++=σ
2
2 98314998312498315010431983097398309509830972319830976433 =minusminus=σ
2
3 98314998312498315098309798309632983097398309509830972319830976433 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 917
Z A P A T A A I S L A D A B I A X I A L
Por lo tanto
COMO LAS PRESIONES EJERCIDAS POR EL SUELO SON MENORES AL ESFUERZO
ADMISIBLE DEL SUELO SE CONSIDERA QUE LAS DIMENSIONES SON CORRECTAS
La carga de disentildeo (qu) se debe amplificar seguacuten la combinacioacuten de cargas a usar sinembargo se puede amplificar directamente la presioacuten obtenida con cargas de servicio usandoun coeficiente intermedio aproximado
- Cuando no se considero sismo se obtuvo 3631 Tnm2
2
983149983124983150098309765983096619831603136 ==σ
GUIDO F RODRIGUEZ MOLINA - UANCV
- Cuando se considero sismo en X se obtuvo 3709 Tnm2
- Cuando se considero sismo en Y se obtuvo 3682 Tnm2
2983149983124983150364625198316009830973983095 ==σ
29831499831249831500346251983160983096236 ==σ
Entonces el disentildeo por cortante y flexioacuten se hace con σu = 5736 Tnm2
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1017
Z A P A T A A I S L A D A B I A X I A L
3- DISENtildeO A CORTE
El peralte de la zapata estaacute definido por su capacidad resistente a cortante tipo viga y acortante por punzonamiento Para ambos casos se utilizan los estados de carga uacuteltimos
Se asume una altura tentativa de 65 cm para la zapata y una distancia desde la carainferior de concreto hasta la capa de refuerzo de 10 cm
P
Asumimos h = 65
d = 65 ndash 10 = 55 cm
My
230
Mx
065055
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1117
Z A P A T A A I S L A D A B I A X I A L
Pu
MyMx
2 3
230
055 040
598309610 9831249831509831492
1 4
230
)1()400(105983096983126983125 =
Cortante uacuteltimo Actuante9831249831502423983126983125 =
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1217
Z A P A T A A I S L A D A B I A X I A L
983140983138983139983142 530983126983107 φ=
Vu lt Vc
Cortante Admisible
100)55(210)530(98309650983126983107 =
983124983150036983126983107 =
Ok2324 lt 360
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1317
Z A P A T A A I S L A D A B I A X I A L
5- PUNZONAMIENTO
983140983138983139983142 )11
530(983126983139 983151β
+φ=
bo = 380 cm Periacutemetro
9831249831509830971254983126983125 = Cortante ultimo
)9830975098316098309750(105983096)302983160302(105983096983126983157 minus=
598309610 9831249831509831492
9831402 9831402
983140983138983139983142 11983126983139 983151φ=
Tomamos el menor valor
Vu lt Vc
9831249831506341983097)55(39830960210)1
11530(98309650983126983139 =+=
98312498315019830962983096355)39830960(210)11(98309650983126983139 ==
25491 lt 28318 OkGUIDO F RODRIGUEZ MOLINA - UANCV
1
2 3
4
230
230
055 040
9830975
9830975
Arsquo
A
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1417
Z A P A T A A I S L A D A B I A X I A L
6- FLEXION
Z A P A T A A I S L A D A B I A X I A L
9831249831502226983117983157 =598309610 9831249831509831492
9830975
9831162
983148983153983117983157
2
=
12
98309750105983096
983117983157
2
=
GUIDO F RODRIGUEZ MOLINA - UANCV
230
230
0952983138983140
983117983157983115983157=
698309598309655100
109831602226983115983157
2
5
==
230=ρ
983140983138983105983155 ρ=
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1517
Z A P A T A A I S L A D A B I A X I A L
)55()100(00230983105983155 =
29831399831496512983105983155 =
983142983161
983139983142 9830950983149983145983150 =ρ
Verificacioacuten Cuantiacutea Miacutenima
983140983138983105983155 983149983145983150ρ=
GUIDO F RODRIGUEZ MOLINA - UANCV
4200
2109830950983149983145983150 =ρ 00240983149983145983150 =ρ
Cuantiacutea Miacutenima es mayor que cuantiacutea adoptada entonces asumimos cuantiacutea miacutenima
)55()100(00240983105983155 =
29831399831492013983105983155 =
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1617
Z A P A T A A I S L A D A B I A X I A L
9830965φ as = 200 cm2 2013
)002(100
983155 =
43φ as = 285 cm2
s = 1515 cm
s = 2159 cm
2013
)98309652(100983155 =
Asumimos Oslash 34 020 m
2 3
Oslash 34 020
GUIDO F RODRIGUEZ MOLINA - UANCV
1 4
230
230
Oslash 34 020
DISENtildeO FINAL DE LA ZAPATA
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1717
Z A P A T A A I S L A D A B I A X I A L
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 517
Z A P A T A A I S L A D A B I A X I A L
983123
983123983128983129
983120
983117983141 =
983123
983123983129983160
983120983117983141 = 983139983149333983096
6302983141983160 =lt
983139983149333983096
6
302983141983161 =lt
983139983149530451983095983097
98309750983141983160 ==
983139983149160
451983095983097
29830970983141983161 ==
2- VERIFICACION DE PRESIONES
Y
2 3VERIFICACION MOMENTO EN X
2
983123
1 983116983106983105 +=σ
2
9831609831232
983116983106
9831176
983105
983120minus=σ
1 4
B
LXey
ex P
GUIDO F RODRIGUEZ MOLINA - UANCV
221 983149983124983150983096535
)302(302)252651(6
)302(302451983095983097 =++=σ
2
22 983149983124983150032)302(302
)252651(6
)302(302
451983095983097=
+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 617
Z A P A T A A I S L A D A B I A X I A L
221983116983106
)983117983158983161983117983149983161(6983116983106
)983117983158983160983117983149983160(6983105983120983155 +minus++=σ
VERIFICACION BIAXIAL
222983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 +minus
+minus=σ
223983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 ++
+minus=σ
224983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 ++
++=σ
My
1
2 3
4
230Mx
b
h
GUIDO F RODRIGUEZ MOLINA - UANCV
230
2
4 98314998312498315031364698309609830972319830972233 =++=σ
2
221 983149983124983150398309635)302(302
)500450(6
)302(302
)252651(6
)302(302
451983095983097=
+minus
++=σ
2
2 98314998312498315053314698309609830972319830972233 =minusminus=σ
2
3 9831499831249831504983095324698309609830972319830972233 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 717
Z A P A T A A I S L A D A B I A X I A L
Esfuerzo maacuteximo (3706 Tnm2) es menoral esfuerzo admisible del suelo (40Tnm2)
VERIFICACION SISMO EN X
221983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 +minus+++++=σ
222983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 +minus
++minus
++=σ
223983116983106
)983117983158983161983117983149983161(6983116983106
)983117983155983160983117983158983160983117983149983160(6983105
)983120983155983160983120983158983120983149(051 ++++minus++=σ
224983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 ++
+++
++=σ
GUIDO F RODRIGUEZ MOLINA - UANCV
2
4 9831499831249831500983097398309546983096006625634 =++=σ
2
221 9831499831249831501598309636)302(302
)500450(6
)302(302
)29830970252651(6
)302(302
9830960519830962=
+minus
+++=σ
2
2 9831499831249831500263246983096006625634 =minusminus=σ
2
3 98314998312498315098309763246983096006625634 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 817
Z A P A T A A I S L A D A B I A X I A L
Esfuerzo maacuteximo (3682 Tnm2) es menoral esfuerzo admisible del suelo (40Tnm2)
VERIFICACION SISMO EN Y
221983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 ++minus++++=σ
222983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 ++minus
+minus
++=σ
223983116983106
)983117983155983161983117983158983161983117983149983161(6983116983106
)983117983158983160983117983149983160(6983105
)983120983155983161983120983158983120983149(051 ++++minus++=σ
224983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 +++
++
++=σ
GUIDO F RODRIGUEZ MOLINA - UANCV
2
4 983149983124983150983096236983097398309509830972319830976433 =++=σ
2
221 983149983124983150983097534)302(302
)98309750500450(6
)302(302
)252651(6
)302(302
69830951983095983097=
++minus
++=σ
2
2 98314998312498315010431983097398309509830972319830976433 =minusminus=σ
2
3 98314998312498315098309798309632983097398309509830972319830976433 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 917
Z A P A T A A I S L A D A B I A X I A L
Por lo tanto
COMO LAS PRESIONES EJERCIDAS POR EL SUELO SON MENORES AL ESFUERZO
ADMISIBLE DEL SUELO SE CONSIDERA QUE LAS DIMENSIONES SON CORRECTAS
La carga de disentildeo (qu) se debe amplificar seguacuten la combinacioacuten de cargas a usar sinembargo se puede amplificar directamente la presioacuten obtenida con cargas de servicio usandoun coeficiente intermedio aproximado
- Cuando no se considero sismo se obtuvo 3631 Tnm2
2
983149983124983150098309765983096619831603136 ==σ
GUIDO F RODRIGUEZ MOLINA - UANCV
- Cuando se considero sismo en X se obtuvo 3709 Tnm2
- Cuando se considero sismo en Y se obtuvo 3682 Tnm2
2983149983124983150364625198316009830973983095 ==σ
29831499831249831500346251983160983096236 ==σ
Entonces el disentildeo por cortante y flexioacuten se hace con σu = 5736 Tnm2
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1017
Z A P A T A A I S L A D A B I A X I A L
3- DISENtildeO A CORTE
El peralte de la zapata estaacute definido por su capacidad resistente a cortante tipo viga y acortante por punzonamiento Para ambos casos se utilizan los estados de carga uacuteltimos
Se asume una altura tentativa de 65 cm para la zapata y una distancia desde la carainferior de concreto hasta la capa de refuerzo de 10 cm
P
Asumimos h = 65
d = 65 ndash 10 = 55 cm
My
230
Mx
065055
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1117
Z A P A T A A I S L A D A B I A X I A L
Pu
MyMx
2 3
230
055 040
598309610 9831249831509831492
1 4
230
)1()400(105983096983126983125 =
Cortante uacuteltimo Actuante9831249831502423983126983125 =
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1217
Z A P A T A A I S L A D A B I A X I A L
983140983138983139983142 530983126983107 φ=
Vu lt Vc
Cortante Admisible
100)55(210)530(98309650983126983107 =
983124983150036983126983107 =
Ok2324 lt 360
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1317
Z A P A T A A I S L A D A B I A X I A L
5- PUNZONAMIENTO
983140983138983139983142 )11
530(983126983139 983151β
+φ=
bo = 380 cm Periacutemetro
9831249831509830971254983126983125 = Cortante ultimo
)9830975098316098309750(105983096)302983160302(105983096983126983157 minus=
598309610 9831249831509831492
9831402 9831402
983140983138983139983142 11983126983139 983151φ=
Tomamos el menor valor
Vu lt Vc
9831249831506341983097)55(39830960210)1
11530(98309650983126983139 =+=
98312498315019830962983096355)39830960(210)11(98309650983126983139 ==
25491 lt 28318 OkGUIDO F RODRIGUEZ MOLINA - UANCV
1
2 3
4
230
230
055 040
9830975
9830975
Arsquo
A
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1417
Z A P A T A A I S L A D A B I A X I A L
6- FLEXION
Z A P A T A A I S L A D A B I A X I A L
9831249831502226983117983157 =598309610 9831249831509831492
9830975
9831162
983148983153983117983157
2
=
12
98309750105983096
983117983157
2
=
GUIDO F RODRIGUEZ MOLINA - UANCV
230
230
0952983138983140
983117983157983115983157=
698309598309655100
109831602226983115983157
2
5
==
230=ρ
983140983138983105983155 ρ=
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1517
Z A P A T A A I S L A D A B I A X I A L
)55()100(00230983105983155 =
29831399831496512983105983155 =
983142983161
983139983142 9830950983149983145983150 =ρ
Verificacioacuten Cuantiacutea Miacutenima
983140983138983105983155 983149983145983150ρ=
GUIDO F RODRIGUEZ MOLINA - UANCV
4200
2109830950983149983145983150 =ρ 00240983149983145983150 =ρ
Cuantiacutea Miacutenima es mayor que cuantiacutea adoptada entonces asumimos cuantiacutea miacutenima
)55()100(00240983105983155 =
29831399831492013983105983155 =
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1617
Z A P A T A A I S L A D A B I A X I A L
9830965φ as = 200 cm2 2013
)002(100
983155 =
43φ as = 285 cm2
s = 1515 cm
s = 2159 cm
2013
)98309652(100983155 =
Asumimos Oslash 34 020 m
2 3
Oslash 34 020
GUIDO F RODRIGUEZ MOLINA - UANCV
1 4
230
230
Oslash 34 020
DISENtildeO FINAL DE LA ZAPATA
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1717
Z A P A T A A I S L A D A B I A X I A L
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 617
Z A P A T A A I S L A D A B I A X I A L
221983116983106
)983117983158983161983117983149983161(6983116983106
)983117983158983160983117983149983160(6983105983120983155 +minus++=σ
VERIFICACION BIAXIAL
222983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 +minus
+minus=σ
223983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 ++
+minus=σ
224983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
983120983155 ++
++=σ
My
1
2 3
4
230Mx
b
h
GUIDO F RODRIGUEZ MOLINA - UANCV
230
2
4 98314998312498315031364698309609830972319830972233 =++=σ
2
221 983149983124983150398309635)302(302
)500450(6
)302(302
)252651(6
)302(302
451983095983097=
+minus
++=σ
2
2 98314998312498315053314698309609830972319830972233 =minusminus=σ
2
3 9831499831249831504983095324698309609830972319830972233 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 717
Z A P A T A A I S L A D A B I A X I A L
Esfuerzo maacuteximo (3706 Tnm2) es menoral esfuerzo admisible del suelo (40Tnm2)
VERIFICACION SISMO EN X
221983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 +minus+++++=σ
222983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 +minus
++minus
++=σ
223983116983106
)983117983158983161983117983149983161(6983116983106
)983117983155983160983117983158983160983117983149983160(6983105
)983120983155983160983120983158983120983149(051 ++++minus++=σ
224983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 ++
+++
++=σ
GUIDO F RODRIGUEZ MOLINA - UANCV
2
4 9831499831249831500983097398309546983096006625634 =++=σ
2
221 9831499831249831501598309636)302(302
)500450(6
)302(302
)29830970252651(6
)302(302
9830960519830962=
+minus
+++=σ
2
2 9831499831249831500263246983096006625634 =minusminus=σ
2
3 98314998312498315098309763246983096006625634 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 817
Z A P A T A A I S L A D A B I A X I A L
Esfuerzo maacuteximo (3682 Tnm2) es menoral esfuerzo admisible del suelo (40Tnm2)
VERIFICACION SISMO EN Y
221983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 ++minus++++=σ
222983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 ++minus
+minus
++=σ
223983116983106
)983117983155983161983117983158983161983117983149983161(6983116983106
)983117983158983160983117983149983160(6983105
)983120983155983161983120983158983120983149(051 ++++minus++=σ
224983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 +++
++
++=σ
GUIDO F RODRIGUEZ MOLINA - UANCV
2
4 983149983124983150983096236983097398309509830972319830976433 =++=σ
2
221 983149983124983150983097534)302(302
)98309750500450(6
)302(302
)252651(6
)302(302
69830951983095983097=
++minus
++=σ
2
2 98314998312498315010431983097398309509830972319830976433 =minusminus=σ
2
3 98314998312498315098309798309632983097398309509830972319830976433 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 917
Z A P A T A A I S L A D A B I A X I A L
Por lo tanto
COMO LAS PRESIONES EJERCIDAS POR EL SUELO SON MENORES AL ESFUERZO
ADMISIBLE DEL SUELO SE CONSIDERA QUE LAS DIMENSIONES SON CORRECTAS
La carga de disentildeo (qu) se debe amplificar seguacuten la combinacioacuten de cargas a usar sinembargo se puede amplificar directamente la presioacuten obtenida con cargas de servicio usandoun coeficiente intermedio aproximado
- Cuando no se considero sismo se obtuvo 3631 Tnm2
2
983149983124983150098309765983096619831603136 ==σ
GUIDO F RODRIGUEZ MOLINA - UANCV
- Cuando se considero sismo en X se obtuvo 3709 Tnm2
- Cuando se considero sismo en Y se obtuvo 3682 Tnm2
2983149983124983150364625198316009830973983095 ==σ
29831499831249831500346251983160983096236 ==σ
Entonces el disentildeo por cortante y flexioacuten se hace con σu = 5736 Tnm2
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1017
Z A P A T A A I S L A D A B I A X I A L
3- DISENtildeO A CORTE
El peralte de la zapata estaacute definido por su capacidad resistente a cortante tipo viga y acortante por punzonamiento Para ambos casos se utilizan los estados de carga uacuteltimos
Se asume una altura tentativa de 65 cm para la zapata y una distancia desde la carainferior de concreto hasta la capa de refuerzo de 10 cm
P
Asumimos h = 65
d = 65 ndash 10 = 55 cm
My
230
Mx
065055
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1117
Z A P A T A A I S L A D A B I A X I A L
Pu
MyMx
2 3
230
055 040
598309610 9831249831509831492
1 4
230
)1()400(105983096983126983125 =
Cortante uacuteltimo Actuante9831249831502423983126983125 =
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1217
Z A P A T A A I S L A D A B I A X I A L
983140983138983139983142 530983126983107 φ=
Vu lt Vc
Cortante Admisible
100)55(210)530(98309650983126983107 =
983124983150036983126983107 =
Ok2324 lt 360
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1317
Z A P A T A A I S L A D A B I A X I A L
5- PUNZONAMIENTO
983140983138983139983142 )11
530(983126983139 983151β
+φ=
bo = 380 cm Periacutemetro
9831249831509830971254983126983125 = Cortante ultimo
)9830975098316098309750(105983096)302983160302(105983096983126983157 minus=
598309610 9831249831509831492
9831402 9831402
983140983138983139983142 11983126983139 983151φ=
Tomamos el menor valor
Vu lt Vc
9831249831506341983097)55(39830960210)1
11530(98309650983126983139 =+=
98312498315019830962983096355)39830960(210)11(98309650983126983139 ==
25491 lt 28318 OkGUIDO F RODRIGUEZ MOLINA - UANCV
1
2 3
4
230
230
055 040
9830975
9830975
Arsquo
A
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1417
Z A P A T A A I S L A D A B I A X I A L
6- FLEXION
Z A P A T A A I S L A D A B I A X I A L
9831249831502226983117983157 =598309610 9831249831509831492
9830975
9831162
983148983153983117983157
2
=
12
98309750105983096
983117983157
2
=
GUIDO F RODRIGUEZ MOLINA - UANCV
230
230
0952983138983140
983117983157983115983157=
698309598309655100
109831602226983115983157
2
5
==
230=ρ
983140983138983105983155 ρ=
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1517
Z A P A T A A I S L A D A B I A X I A L
)55()100(00230983105983155 =
29831399831496512983105983155 =
983142983161
983139983142 9830950983149983145983150 =ρ
Verificacioacuten Cuantiacutea Miacutenima
983140983138983105983155 983149983145983150ρ=
GUIDO F RODRIGUEZ MOLINA - UANCV
4200
2109830950983149983145983150 =ρ 00240983149983145983150 =ρ
Cuantiacutea Miacutenima es mayor que cuantiacutea adoptada entonces asumimos cuantiacutea miacutenima
)55()100(00240983105983155 =
29831399831492013983105983155 =
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1617
Z A P A T A A I S L A D A B I A X I A L
9830965φ as = 200 cm2 2013
)002(100
983155 =
43φ as = 285 cm2
s = 1515 cm
s = 2159 cm
2013
)98309652(100983155 =
Asumimos Oslash 34 020 m
2 3
Oslash 34 020
GUIDO F RODRIGUEZ MOLINA - UANCV
1 4
230
230
Oslash 34 020
DISENtildeO FINAL DE LA ZAPATA
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1717
Z A P A T A A I S L A D A B I A X I A L
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 717
Z A P A T A A I S L A D A B I A X I A L
Esfuerzo maacuteximo (3706 Tnm2) es menoral esfuerzo admisible del suelo (40Tnm2)
VERIFICACION SISMO EN X
221983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 +minus+++++=σ
222983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 +minus
++minus
++=σ
223983116983106
)983117983158983161983117983149983161(6983116983106
)983117983155983160983117983158983160983117983149983160(6983105
)983120983155983160983120983158983120983149(051 ++++minus++=σ
224983116983106
)983117983158983161983117983149983161(6
983116983106
)983117983155983160983117983158983160983117983149983160(6
983105
)983120983155983160983120983158983120983149(051 ++
+++
++=σ
GUIDO F RODRIGUEZ MOLINA - UANCV
2
4 9831499831249831500983097398309546983096006625634 =++=σ
2
221 9831499831249831501598309636)302(302
)500450(6
)302(302
)29830970252651(6
)302(302
9830960519830962=
+minus
+++=σ
2
2 9831499831249831500263246983096006625634 =minusminus=σ
2
3 98314998312498315098309763246983096006625634 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 817
Z A P A T A A I S L A D A B I A X I A L
Esfuerzo maacuteximo (3682 Tnm2) es menoral esfuerzo admisible del suelo (40Tnm2)
VERIFICACION SISMO EN Y
221983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 ++minus++++=σ
222983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 ++minus
+minus
++=σ
223983116983106
)983117983155983161983117983158983161983117983149983161(6983116983106
)983117983158983160983117983149983160(6983105
)983120983155983161983120983158983120983149(051 ++++minus++=σ
224983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 +++
++
++=σ
GUIDO F RODRIGUEZ MOLINA - UANCV
2
4 983149983124983150983096236983097398309509830972319830976433 =++=σ
2
221 983149983124983150983097534)302(302
)98309750500450(6
)302(302
)252651(6
)302(302
69830951983095983097=
++minus
++=σ
2
2 98314998312498315010431983097398309509830972319830976433 =minusminus=σ
2
3 98314998312498315098309798309632983097398309509830972319830976433 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 917
Z A P A T A A I S L A D A B I A X I A L
Por lo tanto
COMO LAS PRESIONES EJERCIDAS POR EL SUELO SON MENORES AL ESFUERZO
ADMISIBLE DEL SUELO SE CONSIDERA QUE LAS DIMENSIONES SON CORRECTAS
La carga de disentildeo (qu) se debe amplificar seguacuten la combinacioacuten de cargas a usar sinembargo se puede amplificar directamente la presioacuten obtenida con cargas de servicio usandoun coeficiente intermedio aproximado
- Cuando no se considero sismo se obtuvo 3631 Tnm2
2
983149983124983150098309765983096619831603136 ==σ
GUIDO F RODRIGUEZ MOLINA - UANCV
- Cuando se considero sismo en X se obtuvo 3709 Tnm2
- Cuando se considero sismo en Y se obtuvo 3682 Tnm2
2983149983124983150364625198316009830973983095 ==σ
29831499831249831500346251983160983096236 ==σ
Entonces el disentildeo por cortante y flexioacuten se hace con σu = 5736 Tnm2
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1017
Z A P A T A A I S L A D A B I A X I A L
3- DISENtildeO A CORTE
El peralte de la zapata estaacute definido por su capacidad resistente a cortante tipo viga y acortante por punzonamiento Para ambos casos se utilizan los estados de carga uacuteltimos
Se asume una altura tentativa de 65 cm para la zapata y una distancia desde la carainferior de concreto hasta la capa de refuerzo de 10 cm
P
Asumimos h = 65
d = 65 ndash 10 = 55 cm
My
230
Mx
065055
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1117
Z A P A T A A I S L A D A B I A X I A L
Pu
MyMx
2 3
230
055 040
598309610 9831249831509831492
1 4
230
)1()400(105983096983126983125 =
Cortante uacuteltimo Actuante9831249831502423983126983125 =
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1217
Z A P A T A A I S L A D A B I A X I A L
983140983138983139983142 530983126983107 φ=
Vu lt Vc
Cortante Admisible
100)55(210)530(98309650983126983107 =
983124983150036983126983107 =
Ok2324 lt 360
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1317
Z A P A T A A I S L A D A B I A X I A L
5- PUNZONAMIENTO
983140983138983139983142 )11
530(983126983139 983151β
+φ=
bo = 380 cm Periacutemetro
9831249831509830971254983126983125 = Cortante ultimo
)9830975098316098309750(105983096)302983160302(105983096983126983157 minus=
598309610 9831249831509831492
9831402 9831402
983140983138983139983142 11983126983139 983151φ=
Tomamos el menor valor
Vu lt Vc
9831249831506341983097)55(39830960210)1
11530(98309650983126983139 =+=
98312498315019830962983096355)39830960(210)11(98309650983126983139 ==
25491 lt 28318 OkGUIDO F RODRIGUEZ MOLINA - UANCV
1
2 3
4
230
230
055 040
9830975
9830975
Arsquo
A
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1417
Z A P A T A A I S L A D A B I A X I A L
6- FLEXION
Z A P A T A A I S L A D A B I A X I A L
9831249831502226983117983157 =598309610 9831249831509831492
9830975
9831162
983148983153983117983157
2
=
12
98309750105983096
983117983157
2
=
GUIDO F RODRIGUEZ MOLINA - UANCV
230
230
0952983138983140
983117983157983115983157=
698309598309655100
109831602226983115983157
2
5
==
230=ρ
983140983138983105983155 ρ=
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1517
Z A P A T A A I S L A D A B I A X I A L
)55()100(00230983105983155 =
29831399831496512983105983155 =
983142983161
983139983142 9830950983149983145983150 =ρ
Verificacioacuten Cuantiacutea Miacutenima
983140983138983105983155 983149983145983150ρ=
GUIDO F RODRIGUEZ MOLINA - UANCV
4200
2109830950983149983145983150 =ρ 00240983149983145983150 =ρ
Cuantiacutea Miacutenima es mayor que cuantiacutea adoptada entonces asumimos cuantiacutea miacutenima
)55()100(00240983105983155 =
29831399831492013983105983155 =
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1617
Z A P A T A A I S L A D A B I A X I A L
9830965φ as = 200 cm2 2013
)002(100
983155 =
43φ as = 285 cm2
s = 1515 cm
s = 2159 cm
2013
)98309652(100983155 =
Asumimos Oslash 34 020 m
2 3
Oslash 34 020
GUIDO F RODRIGUEZ MOLINA - UANCV
1 4
230
230
Oslash 34 020
DISENtildeO FINAL DE LA ZAPATA
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1717
Z A P A T A A I S L A D A B I A X I A L
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 817
Z A P A T A A I S L A D A B I A X I A L
Esfuerzo maacuteximo (3682 Tnm2) es menoral esfuerzo admisible del suelo (40Tnm2)
VERIFICACION SISMO EN Y
221983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 ++minus++++=σ
222983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 ++minus
+minus
++=σ
223983116983106
)983117983155983161983117983158983161983117983149983161(6983116983106
)983117983158983160983117983149983160(6983105
)983120983155983161983120983158983120983149(051 ++++minus++=σ
224983116983106
)983117983155983161983117983158983161983117983149983161(6
983116983106
)983117983158983160983117983149983160(6
983105
)983120983155983161983120983158983120983149(051 +++
++
++=σ
GUIDO F RODRIGUEZ MOLINA - UANCV
2
4 983149983124983150983096236983097398309509830972319830976433 =++=σ
2
221 983149983124983150983097534)302(302
)98309750500450(6
)302(302
)252651(6
)302(302
69830951983095983097=
++minus
++=σ
2
2 98314998312498315010431983097398309509830972319830976433 =minusminus=σ
2
3 98314998312498315098309798309632983097398309509830972319830976433 =+minus=σ
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 917
Z A P A T A A I S L A D A B I A X I A L
Por lo tanto
COMO LAS PRESIONES EJERCIDAS POR EL SUELO SON MENORES AL ESFUERZO
ADMISIBLE DEL SUELO SE CONSIDERA QUE LAS DIMENSIONES SON CORRECTAS
La carga de disentildeo (qu) se debe amplificar seguacuten la combinacioacuten de cargas a usar sinembargo se puede amplificar directamente la presioacuten obtenida con cargas de servicio usandoun coeficiente intermedio aproximado
- Cuando no se considero sismo se obtuvo 3631 Tnm2
2
983149983124983150098309765983096619831603136 ==σ
GUIDO F RODRIGUEZ MOLINA - UANCV
- Cuando se considero sismo en X se obtuvo 3709 Tnm2
- Cuando se considero sismo en Y se obtuvo 3682 Tnm2
2983149983124983150364625198316009830973983095 ==σ
29831499831249831500346251983160983096236 ==σ
Entonces el disentildeo por cortante y flexioacuten se hace con σu = 5736 Tnm2
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1017
Z A P A T A A I S L A D A B I A X I A L
3- DISENtildeO A CORTE
El peralte de la zapata estaacute definido por su capacidad resistente a cortante tipo viga y acortante por punzonamiento Para ambos casos se utilizan los estados de carga uacuteltimos
Se asume una altura tentativa de 65 cm para la zapata y una distancia desde la carainferior de concreto hasta la capa de refuerzo de 10 cm
P
Asumimos h = 65
d = 65 ndash 10 = 55 cm
My
230
Mx
065055
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1117
Z A P A T A A I S L A D A B I A X I A L
Pu
MyMx
2 3
230
055 040
598309610 9831249831509831492
1 4
230
)1()400(105983096983126983125 =
Cortante uacuteltimo Actuante9831249831502423983126983125 =
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1217
Z A P A T A A I S L A D A B I A X I A L
983140983138983139983142 530983126983107 φ=
Vu lt Vc
Cortante Admisible
100)55(210)530(98309650983126983107 =
983124983150036983126983107 =
Ok2324 lt 360
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1317
Z A P A T A A I S L A D A B I A X I A L
5- PUNZONAMIENTO
983140983138983139983142 )11
530(983126983139 983151β
+φ=
bo = 380 cm Periacutemetro
9831249831509830971254983126983125 = Cortante ultimo
)9830975098316098309750(105983096)302983160302(105983096983126983157 minus=
598309610 9831249831509831492
9831402 9831402
983140983138983139983142 11983126983139 983151φ=
Tomamos el menor valor
Vu lt Vc
9831249831506341983097)55(39830960210)1
11530(98309650983126983139 =+=
98312498315019830962983096355)39830960(210)11(98309650983126983139 ==
25491 lt 28318 OkGUIDO F RODRIGUEZ MOLINA - UANCV
1
2 3
4
230
230
055 040
9830975
9830975
Arsquo
A
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1417
Z A P A T A A I S L A D A B I A X I A L
6- FLEXION
Z A P A T A A I S L A D A B I A X I A L
9831249831502226983117983157 =598309610 9831249831509831492
9830975
9831162
983148983153983117983157
2
=
12
98309750105983096
983117983157
2
=
GUIDO F RODRIGUEZ MOLINA - UANCV
230
230
0952983138983140
983117983157983115983157=
698309598309655100
109831602226983115983157
2
5
==
230=ρ
983140983138983105983155 ρ=
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1517
Z A P A T A A I S L A D A B I A X I A L
)55()100(00230983105983155 =
29831399831496512983105983155 =
983142983161
983139983142 9830950983149983145983150 =ρ
Verificacioacuten Cuantiacutea Miacutenima
983140983138983105983155 983149983145983150ρ=
GUIDO F RODRIGUEZ MOLINA - UANCV
4200
2109830950983149983145983150 =ρ 00240983149983145983150 =ρ
Cuantiacutea Miacutenima es mayor que cuantiacutea adoptada entonces asumimos cuantiacutea miacutenima
)55()100(00240983105983155 =
29831399831492013983105983155 =
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1617
Z A P A T A A I S L A D A B I A X I A L
9830965φ as = 200 cm2 2013
)002(100
983155 =
43φ as = 285 cm2
s = 1515 cm
s = 2159 cm
2013
)98309652(100983155 =
Asumimos Oslash 34 020 m
2 3
Oslash 34 020
GUIDO F RODRIGUEZ MOLINA - UANCV
1 4
230
230
Oslash 34 020
DISENtildeO FINAL DE LA ZAPATA
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1717
Z A P A T A A I S L A D A B I A X I A L
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 917
Z A P A T A A I S L A D A B I A X I A L
Por lo tanto
COMO LAS PRESIONES EJERCIDAS POR EL SUELO SON MENORES AL ESFUERZO
ADMISIBLE DEL SUELO SE CONSIDERA QUE LAS DIMENSIONES SON CORRECTAS
La carga de disentildeo (qu) se debe amplificar seguacuten la combinacioacuten de cargas a usar sinembargo se puede amplificar directamente la presioacuten obtenida con cargas de servicio usandoun coeficiente intermedio aproximado
- Cuando no se considero sismo se obtuvo 3631 Tnm2
2
983149983124983150098309765983096619831603136 ==σ
GUIDO F RODRIGUEZ MOLINA - UANCV
- Cuando se considero sismo en X se obtuvo 3709 Tnm2
- Cuando se considero sismo en Y se obtuvo 3682 Tnm2
2983149983124983150364625198316009830973983095 ==σ
29831499831249831500346251983160983096236 ==σ
Entonces el disentildeo por cortante y flexioacuten se hace con σu = 5736 Tnm2
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1017
Z A P A T A A I S L A D A B I A X I A L
3- DISENtildeO A CORTE
El peralte de la zapata estaacute definido por su capacidad resistente a cortante tipo viga y acortante por punzonamiento Para ambos casos se utilizan los estados de carga uacuteltimos
Se asume una altura tentativa de 65 cm para la zapata y una distancia desde la carainferior de concreto hasta la capa de refuerzo de 10 cm
P
Asumimos h = 65
d = 65 ndash 10 = 55 cm
My
230
Mx
065055
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1117
Z A P A T A A I S L A D A B I A X I A L
Pu
MyMx
2 3
230
055 040
598309610 9831249831509831492
1 4
230
)1()400(105983096983126983125 =
Cortante uacuteltimo Actuante9831249831502423983126983125 =
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1217
Z A P A T A A I S L A D A B I A X I A L
983140983138983139983142 530983126983107 φ=
Vu lt Vc
Cortante Admisible
100)55(210)530(98309650983126983107 =
983124983150036983126983107 =
Ok2324 lt 360
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1317
Z A P A T A A I S L A D A B I A X I A L
5- PUNZONAMIENTO
983140983138983139983142 )11
530(983126983139 983151β
+φ=
bo = 380 cm Periacutemetro
9831249831509830971254983126983125 = Cortante ultimo
)9830975098316098309750(105983096)302983160302(105983096983126983157 minus=
598309610 9831249831509831492
9831402 9831402
983140983138983139983142 11983126983139 983151φ=
Tomamos el menor valor
Vu lt Vc
9831249831506341983097)55(39830960210)1
11530(98309650983126983139 =+=
98312498315019830962983096355)39830960(210)11(98309650983126983139 ==
25491 lt 28318 OkGUIDO F RODRIGUEZ MOLINA - UANCV
1
2 3
4
230
230
055 040
9830975
9830975
Arsquo
A
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1417
Z A P A T A A I S L A D A B I A X I A L
6- FLEXION
Z A P A T A A I S L A D A B I A X I A L
9831249831502226983117983157 =598309610 9831249831509831492
9830975
9831162
983148983153983117983157
2
=
12
98309750105983096
983117983157
2
=
GUIDO F RODRIGUEZ MOLINA - UANCV
230
230
0952983138983140
983117983157983115983157=
698309598309655100
109831602226983115983157
2
5
==
230=ρ
983140983138983105983155 ρ=
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1517
Z A P A T A A I S L A D A B I A X I A L
)55()100(00230983105983155 =
29831399831496512983105983155 =
983142983161
983139983142 9830950983149983145983150 =ρ
Verificacioacuten Cuantiacutea Miacutenima
983140983138983105983155 983149983145983150ρ=
GUIDO F RODRIGUEZ MOLINA - UANCV
4200
2109830950983149983145983150 =ρ 00240983149983145983150 =ρ
Cuantiacutea Miacutenima es mayor que cuantiacutea adoptada entonces asumimos cuantiacutea miacutenima
)55()100(00240983105983155 =
29831399831492013983105983155 =
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1617
Z A P A T A A I S L A D A B I A X I A L
9830965φ as = 200 cm2 2013
)002(100
983155 =
43φ as = 285 cm2
s = 1515 cm
s = 2159 cm
2013
)98309652(100983155 =
Asumimos Oslash 34 020 m
2 3
Oslash 34 020
GUIDO F RODRIGUEZ MOLINA - UANCV
1 4
230
230
Oslash 34 020
DISENtildeO FINAL DE LA ZAPATA
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1717
Z A P A T A A I S L A D A B I A X I A L
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1017
Z A P A T A A I S L A D A B I A X I A L
3- DISENtildeO A CORTE
El peralte de la zapata estaacute definido por su capacidad resistente a cortante tipo viga y acortante por punzonamiento Para ambos casos se utilizan los estados de carga uacuteltimos
Se asume una altura tentativa de 65 cm para la zapata y una distancia desde la carainferior de concreto hasta la capa de refuerzo de 10 cm
P
Asumimos h = 65
d = 65 ndash 10 = 55 cm
My
230
Mx
065055
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1117
Z A P A T A A I S L A D A B I A X I A L
Pu
MyMx
2 3
230
055 040
598309610 9831249831509831492
1 4
230
)1()400(105983096983126983125 =
Cortante uacuteltimo Actuante9831249831502423983126983125 =
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1217
Z A P A T A A I S L A D A B I A X I A L
983140983138983139983142 530983126983107 φ=
Vu lt Vc
Cortante Admisible
100)55(210)530(98309650983126983107 =
983124983150036983126983107 =
Ok2324 lt 360
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1317
Z A P A T A A I S L A D A B I A X I A L
5- PUNZONAMIENTO
983140983138983139983142 )11
530(983126983139 983151β
+φ=
bo = 380 cm Periacutemetro
9831249831509830971254983126983125 = Cortante ultimo
)9830975098316098309750(105983096)302983160302(105983096983126983157 minus=
598309610 9831249831509831492
9831402 9831402
983140983138983139983142 11983126983139 983151φ=
Tomamos el menor valor
Vu lt Vc
9831249831506341983097)55(39830960210)1
11530(98309650983126983139 =+=
98312498315019830962983096355)39830960(210)11(98309650983126983139 ==
25491 lt 28318 OkGUIDO F RODRIGUEZ MOLINA - UANCV
1
2 3
4
230
230
055 040
9830975
9830975
Arsquo
A
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1417
Z A P A T A A I S L A D A B I A X I A L
6- FLEXION
Z A P A T A A I S L A D A B I A X I A L
9831249831502226983117983157 =598309610 9831249831509831492
9830975
9831162
983148983153983117983157
2
=
12
98309750105983096
983117983157
2
=
GUIDO F RODRIGUEZ MOLINA - UANCV
230
230
0952983138983140
983117983157983115983157=
698309598309655100
109831602226983115983157
2
5
==
230=ρ
983140983138983105983155 ρ=
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1517
Z A P A T A A I S L A D A B I A X I A L
)55()100(00230983105983155 =
29831399831496512983105983155 =
983142983161
983139983142 9830950983149983145983150 =ρ
Verificacioacuten Cuantiacutea Miacutenima
983140983138983105983155 983149983145983150ρ=
GUIDO F RODRIGUEZ MOLINA - UANCV
4200
2109830950983149983145983150 =ρ 00240983149983145983150 =ρ
Cuantiacutea Miacutenima es mayor que cuantiacutea adoptada entonces asumimos cuantiacutea miacutenima
)55()100(00240983105983155 =
29831399831492013983105983155 =
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1617
Z A P A T A A I S L A D A B I A X I A L
9830965φ as = 200 cm2 2013
)002(100
983155 =
43φ as = 285 cm2
s = 1515 cm
s = 2159 cm
2013
)98309652(100983155 =
Asumimos Oslash 34 020 m
2 3
Oslash 34 020
GUIDO F RODRIGUEZ MOLINA - UANCV
1 4
230
230
Oslash 34 020
DISENtildeO FINAL DE LA ZAPATA
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1717
Z A P A T A A I S L A D A B I A X I A L
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1117
Z A P A T A A I S L A D A B I A X I A L
Pu
MyMx
2 3
230
055 040
598309610 9831249831509831492
1 4
230
)1()400(105983096983126983125 =
Cortante uacuteltimo Actuante9831249831502423983126983125 =
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1217
Z A P A T A A I S L A D A B I A X I A L
983140983138983139983142 530983126983107 φ=
Vu lt Vc
Cortante Admisible
100)55(210)530(98309650983126983107 =
983124983150036983126983107 =
Ok2324 lt 360
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1317
Z A P A T A A I S L A D A B I A X I A L
5- PUNZONAMIENTO
983140983138983139983142 )11
530(983126983139 983151β
+φ=
bo = 380 cm Periacutemetro
9831249831509830971254983126983125 = Cortante ultimo
)9830975098316098309750(105983096)302983160302(105983096983126983157 minus=
598309610 9831249831509831492
9831402 9831402
983140983138983139983142 11983126983139 983151φ=
Tomamos el menor valor
Vu lt Vc
9831249831506341983097)55(39830960210)1
11530(98309650983126983139 =+=
98312498315019830962983096355)39830960(210)11(98309650983126983139 ==
25491 lt 28318 OkGUIDO F RODRIGUEZ MOLINA - UANCV
1
2 3
4
230
230
055 040
9830975
9830975
Arsquo
A
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1417
Z A P A T A A I S L A D A B I A X I A L
6- FLEXION
Z A P A T A A I S L A D A B I A X I A L
9831249831502226983117983157 =598309610 9831249831509831492
9830975
9831162
983148983153983117983157
2
=
12
98309750105983096
983117983157
2
=
GUIDO F RODRIGUEZ MOLINA - UANCV
230
230
0952983138983140
983117983157983115983157=
698309598309655100
109831602226983115983157
2
5
==
230=ρ
983140983138983105983155 ρ=
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1517
Z A P A T A A I S L A D A B I A X I A L
)55()100(00230983105983155 =
29831399831496512983105983155 =
983142983161
983139983142 9830950983149983145983150 =ρ
Verificacioacuten Cuantiacutea Miacutenima
983140983138983105983155 983149983145983150ρ=
GUIDO F RODRIGUEZ MOLINA - UANCV
4200
2109830950983149983145983150 =ρ 00240983149983145983150 =ρ
Cuantiacutea Miacutenima es mayor que cuantiacutea adoptada entonces asumimos cuantiacutea miacutenima
)55()100(00240983105983155 =
29831399831492013983105983155 =
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1617
Z A P A T A A I S L A D A B I A X I A L
9830965φ as = 200 cm2 2013
)002(100
983155 =
43φ as = 285 cm2
s = 1515 cm
s = 2159 cm
2013
)98309652(100983155 =
Asumimos Oslash 34 020 m
2 3
Oslash 34 020
GUIDO F RODRIGUEZ MOLINA - UANCV
1 4
230
230
Oslash 34 020
DISENtildeO FINAL DE LA ZAPATA
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1717
Z A P A T A A I S L A D A B I A X I A L
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1217
Z A P A T A A I S L A D A B I A X I A L
983140983138983139983142 530983126983107 φ=
Vu lt Vc
Cortante Admisible
100)55(210)530(98309650983126983107 =
983124983150036983126983107 =
Ok2324 lt 360
GUIDO F RODRIGUEZ MOLINA - UANCV
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1317
Z A P A T A A I S L A D A B I A X I A L
5- PUNZONAMIENTO
983140983138983139983142 )11
530(983126983139 983151β
+φ=
bo = 380 cm Periacutemetro
9831249831509830971254983126983125 = Cortante ultimo
)9830975098316098309750(105983096)302983160302(105983096983126983157 minus=
598309610 9831249831509831492
9831402 9831402
983140983138983139983142 11983126983139 983151φ=
Tomamos el menor valor
Vu lt Vc
9831249831506341983097)55(39830960210)1
11530(98309650983126983139 =+=
98312498315019830962983096355)39830960(210)11(98309650983126983139 ==
25491 lt 28318 OkGUIDO F RODRIGUEZ MOLINA - UANCV
1
2 3
4
230
230
055 040
9830975
9830975
Arsquo
A
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1417
Z A P A T A A I S L A D A B I A X I A L
6- FLEXION
Z A P A T A A I S L A D A B I A X I A L
9831249831502226983117983157 =598309610 9831249831509831492
9830975
9831162
983148983153983117983157
2
=
12
98309750105983096
983117983157
2
=
GUIDO F RODRIGUEZ MOLINA - UANCV
230
230
0952983138983140
983117983157983115983157=
698309598309655100
109831602226983115983157
2
5
==
230=ρ
983140983138983105983155 ρ=
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1517
Z A P A T A A I S L A D A B I A X I A L
)55()100(00230983105983155 =
29831399831496512983105983155 =
983142983161
983139983142 9830950983149983145983150 =ρ
Verificacioacuten Cuantiacutea Miacutenima
983140983138983105983155 983149983145983150ρ=
GUIDO F RODRIGUEZ MOLINA - UANCV
4200
2109830950983149983145983150 =ρ 00240983149983145983150 =ρ
Cuantiacutea Miacutenima es mayor que cuantiacutea adoptada entonces asumimos cuantiacutea miacutenima
)55()100(00240983105983155 =
29831399831492013983105983155 =
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1617
Z A P A T A A I S L A D A B I A X I A L
9830965φ as = 200 cm2 2013
)002(100
983155 =
43φ as = 285 cm2
s = 1515 cm
s = 2159 cm
2013
)98309652(100983155 =
Asumimos Oslash 34 020 m
2 3
Oslash 34 020
GUIDO F RODRIGUEZ MOLINA - UANCV
1 4
230
230
Oslash 34 020
DISENtildeO FINAL DE LA ZAPATA
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1717
Z A P A T A A I S L A D A B I A X I A L
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1317
Z A P A T A A I S L A D A B I A X I A L
5- PUNZONAMIENTO
983140983138983139983142 )11
530(983126983139 983151β
+φ=
bo = 380 cm Periacutemetro
9831249831509830971254983126983125 = Cortante ultimo
)9830975098316098309750(105983096)302983160302(105983096983126983157 minus=
598309610 9831249831509831492
9831402 9831402
983140983138983139983142 11983126983139 983151φ=
Tomamos el menor valor
Vu lt Vc
9831249831506341983097)55(39830960210)1
11530(98309650983126983139 =+=
98312498315019830962983096355)39830960(210)11(98309650983126983139 ==
25491 lt 28318 OkGUIDO F RODRIGUEZ MOLINA - UANCV
1
2 3
4
230
230
055 040
9830975
9830975
Arsquo
A
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1417
Z A P A T A A I S L A D A B I A X I A L
6- FLEXION
Z A P A T A A I S L A D A B I A X I A L
9831249831502226983117983157 =598309610 9831249831509831492
9830975
9831162
983148983153983117983157
2
=
12
98309750105983096
983117983157
2
=
GUIDO F RODRIGUEZ MOLINA - UANCV
230
230
0952983138983140
983117983157983115983157=
698309598309655100
109831602226983115983157
2
5
==
230=ρ
983140983138983105983155 ρ=
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1517
Z A P A T A A I S L A D A B I A X I A L
)55()100(00230983105983155 =
29831399831496512983105983155 =
983142983161
983139983142 9830950983149983145983150 =ρ
Verificacioacuten Cuantiacutea Miacutenima
983140983138983105983155 983149983145983150ρ=
GUIDO F RODRIGUEZ MOLINA - UANCV
4200
2109830950983149983145983150 =ρ 00240983149983145983150 =ρ
Cuantiacutea Miacutenima es mayor que cuantiacutea adoptada entonces asumimos cuantiacutea miacutenima
)55()100(00240983105983155 =
29831399831492013983105983155 =
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1617
Z A P A T A A I S L A D A B I A X I A L
9830965φ as = 200 cm2 2013
)002(100
983155 =
43φ as = 285 cm2
s = 1515 cm
s = 2159 cm
2013
)98309652(100983155 =
Asumimos Oslash 34 020 m
2 3
Oslash 34 020
GUIDO F RODRIGUEZ MOLINA - UANCV
1 4
230
230
Oslash 34 020
DISENtildeO FINAL DE LA ZAPATA
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1717
Z A P A T A A I S L A D A B I A X I A L
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1417
Z A P A T A A I S L A D A B I A X I A L
6- FLEXION
Z A P A T A A I S L A D A B I A X I A L
9831249831502226983117983157 =598309610 9831249831509831492
9830975
9831162
983148983153983117983157
2
=
12
98309750105983096
983117983157
2
=
GUIDO F RODRIGUEZ MOLINA - UANCV
230
230
0952983138983140
983117983157983115983157=
698309598309655100
109831602226983115983157
2
5
==
230=ρ
983140983138983105983155 ρ=
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1517
Z A P A T A A I S L A D A B I A X I A L
)55()100(00230983105983155 =
29831399831496512983105983155 =
983142983161
983139983142 9830950983149983145983150 =ρ
Verificacioacuten Cuantiacutea Miacutenima
983140983138983105983155 983149983145983150ρ=
GUIDO F RODRIGUEZ MOLINA - UANCV
4200
2109830950983149983145983150 =ρ 00240983149983145983150 =ρ
Cuantiacutea Miacutenima es mayor que cuantiacutea adoptada entonces asumimos cuantiacutea miacutenima
)55()100(00240983105983155 =
29831399831492013983105983155 =
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1617
Z A P A T A A I S L A D A B I A X I A L
9830965φ as = 200 cm2 2013
)002(100
983155 =
43φ as = 285 cm2
s = 1515 cm
s = 2159 cm
2013
)98309652(100983155 =
Asumimos Oslash 34 020 m
2 3
Oslash 34 020
GUIDO F RODRIGUEZ MOLINA - UANCV
1 4
230
230
Oslash 34 020
DISENtildeO FINAL DE LA ZAPATA
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1717
Z A P A T A A I S L A D A B I A X I A L
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1517
Z A P A T A A I S L A D A B I A X I A L
)55()100(00230983105983155 =
29831399831496512983105983155 =
983142983161
983139983142 9830950983149983145983150 =ρ
Verificacioacuten Cuantiacutea Miacutenima
983140983138983105983155 983149983145983150ρ=
GUIDO F RODRIGUEZ MOLINA - UANCV
4200
2109830950983149983145983150 =ρ 00240983149983145983150 =ρ
Cuantiacutea Miacutenima es mayor que cuantiacutea adoptada entonces asumimos cuantiacutea miacutenima
)55()100(00240983105983155 =
29831399831492013983105983155 =
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1617
Z A P A T A A I S L A D A B I A X I A L
9830965φ as = 200 cm2 2013
)002(100
983155 =
43φ as = 285 cm2
s = 1515 cm
s = 2159 cm
2013
)98309652(100983155 =
Asumimos Oslash 34 020 m
2 3
Oslash 34 020
GUIDO F RODRIGUEZ MOLINA - UANCV
1 4
230
230
Oslash 34 020
DISENtildeO FINAL DE LA ZAPATA
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1717
Z A P A T A A I S L A D A B I A X I A L
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1617
Z A P A T A A I S L A D A B I A X I A L
9830965φ as = 200 cm2 2013
)002(100
983155 =
43φ as = 285 cm2
s = 1515 cm
s = 2159 cm
2013
)98309652(100983155 =
Asumimos Oslash 34 020 m
2 3
Oslash 34 020
GUIDO F RODRIGUEZ MOLINA - UANCV
1 4
230
230
Oslash 34 020
DISENtildeO FINAL DE LA ZAPATA
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1717
Z A P A T A A I S L A D A B I A X I A L
7252019 xcvv copia-copia reytryut
httpslidepdfcomreaderfullxcvv-copia-copia-reytryut 1717
Z A P A T A A I S L A D A B I A X I A L