zapatas de cimentacion

P1 P2 P3

M1 M2 M3 M4

d1 d2 d3 d4

CARGA VIVA CARGA MUERTAP1 14.45 90.31

[T]

qa= 20 ton/m2P2 33.04 166.68 f'c= 210 kg/cm2P3 37.29 184.05 Fy= 4200 kg/cm2P4 31.61 160.77P5 13.9 88.07M1 0.2 0.88

[T.M]M2 0.25 1.03M3 0.05 0.23M4 0.23 0.98M5 0.18 0.82

d1 100

[cm]

d2 450d3 600d4 575d5 430d6 100

2055

A= 1.14 M2Ix= 0.06928224 M^4

P ESP. HORM 2.4 TON/M3PP= 2.736 Tr= 7 cm

P1 P2 P3

M1 M2 M3 M4

d1 d2 d3 d4

CARGA DE SERV CARGA ULTP1 104.76 131.492P2 199.72 252.88P3 221.34 280.524P4 192.38 243.5P5 101.97 127.924M1 1.08 1.376M2 1.28 1.636M3 0.28 0.356M4 1.21 1.544M5 1 1.272

β1 para f'c entre 170 kg/cm2 y 280 kg/cm2

β1= 0.85Ec= 2188197.888675 T/m2 fi= 0.9

r= 7 cm

β= 2400 T/m3

Presion. Max= T/m2 < 20

DISEÑO A FLEXION LONGITUDINAL

Cuantía mínima 0.00333333 0.002760262237

Mayor valor= 0.003333333333ro bal= 0.021422965116ro max= 0.016067223837 normal

0.65

𝐸𝑐=15100√𝑓^′ 𝑐𝛽=120∗𝑞𝑎

0.90.35

2.50

DISEÑO MOMENTO MAX NEGATIVO

DISEÑO EN EL PUNTO 1

M= 68.91 T.m 6891000RO= 0.004287446847

0.00333333 < 0.00428745 < 0.01606722

As= 23.13077573946 cm2Asmin= 17.98333333333 cm2

DISEÑO EN EL VOLADO

M= 9.61 T.m 961000RO= 0.000571600256

0.00333333 < 0.0005716 < 0.01606722

As= 17.98333333333 cm2 Ver tabla de hierrosAsmin= 17.98333333333 cm2


M= 71.52 T.m 7152000RO= 0.004459332608

0.00333333 < 0.00445933 < 0.01606722


Ver tabla de ACEROS


M= 93.12 T.m 9312000RO= 0.005912817105

0.00333333 < 0.00591282 < 0.01606722



M= 63.82 T.m 6382000RO= 0.003954441593

0.00333333 < 0.00395444 < 0.01606722


P4 P5

M5

d5 d6

R= 820.17 kg

AF= 47.159775 cm2

AF=BxL

B= 2.29487956 m

ASUMIMOS :

0.65

0.9 0.3

2.50 base (B=) aprox a multiplos d 5

P4 P5

M5

d5 d6

β1 para f'c entre 170 kg/cm2 y 280 kg/cm2

ho sumado 0.05

DISEÑO A CORTANTE LONGITUDINAL

f'c= 210 kg/cm2 cortante del estribobw= 65 cmd= 83 cmVi= 82.66 TVd= 80.83 Tλ= 1 f'c normφ= 0.75 compresionFy= 4200 kg/cm2

Vu= 82660 kgVc= 41435.9181 kgVs= 68777.4152 kgVn= 110213.333 kg

82660 >= 82660

S= 11.4548649 cmasumo= 10 cm

Se trabajara con varilla de 12 mm a cada 10 cm

𝑉𝑐=0.53√(𝑓^′ 𝑐)∗𝑏𝑤∗𝑑∗"λ"𝑉𝑢=∅∗(𝑉𝑐+𝑉𝑠)𝑉𝑠=𝑉𝑢/∅−Vc

𝑉𝑛=𝑉𝑐+𝑉𝑠

𝑉𝑛∗∅>𝑉𝑢

𝑉𝑠=(𝐴𝑣∗𝐹𝑦∗𝑑)/𝑆𝑆=(𝐴𝑣∗𝐹𝑦∗𝑑)/𝑉𝑠

DISEÑO DE LA ZAPATA

CORTANTE COMO VIGA DISEÑO A FLEXION TRANSVERSAL

Diseño por un metro de longitud

qmax= 2.124 kg/cm2f´c= 210 kg/cm2bw= 100 cm por un metror= 6 cmd= 29 cm Mu=B= 250.00 cm ro.cal=b= 65 cm As=λ= 1 f'c normφ= 0.75 compresiónφ= 0.9 flexión ro.retraccion=Fy= 4200

0.65

AsDist=As=

0.90.35

2.50

Vu= 13487.4 kgVc= 22273.2461 kg

φ*Vc= 16704.9345 kg

13487.4 <= 16704.9345

𝑉𝑢=𝑞𝑚𝑎𝑥(𝐵/2−𝑏/2−𝑑)𝑉𝑐=0.53∗λ∗√(𝑓^′ 𝑐)∗𝑏𝑤∗𝑑

𝑉𝑢≤∅∗𝑉𝑐

𝑀𝑢=𝑞𝑚𝑎𝑥(𝐵/2−𝑏/2)∗( /2− /𝐵 𝑏2)∗1/2∗100

𝐴𝑠=𝑟𝑜.𝑐𝑎𝑙∗𝑑∗100

𝐴𝑠𝐷𝑖𝑠𝑡=𝑟𝑜.𝑟𝑒𝑡𝑟𝑎𝑐𝑐𝑖ó𝑛∗( /2− /𝐵 𝑏2)∗ℎ

DISEÑO A FLEXION TRANSVERSAL

908673.75 kg/cm0.002961578.58854827 cm2

0.0018

5.8275 cm28.58854827 cm2

VER TABLA DE ACERO

𝑀𝑢=𝑞𝑚𝑎𝑥(𝐵/2−𝑏/2)∗( /2− /𝐵 𝑏2)∗1/2∗100

𝐴𝑠=𝑟𝑜.𝑐𝑎𝑙∗𝑑∗100

𝐴𝑠𝐷𝑖𝑠𝑡=𝑟𝑜.𝑟𝑒𝑡𝑟𝑎𝑐𝑐𝑖ó𝑛∗( /2− /𝐵 𝑏2)∗ℎ

COLUMNA A COLUMNA B

d1 d2 d3

DISEÑO A FLEXIÓN LONGITUDINALE= 218819.788867 kg/cm2

f'c= 210 kg/cm2β1= 0.85Fy= 4200 kg/cm2ϒc= 2.4 T/m3qa= 18 T/m2β= 2160 T/m3 z. no sismica

z.sismicaCOLUMNA BASE ALTURA

A 0.35 0.35B 0.45 0.45

CARGA VIVA CARGA MUERTA CARGA DE SERV.PA 2.787 14.074 16.861PB 9.348 38.074 47.422 M(-)MA 0.014 0.048 0.062 M(+)MB 0.15 0.502 0.652

d1= 0.175d2= 2.15 3.3d3= 0.975

R= 64.283 T

X= 1.59717654745 m DISEÑO A CORTANTE TRANSVERSAL

emax= 0.55e= 0.12217654745

𝑒𝑚𝑎𝑥=𝐿/6𝑒=𝐿/2−𝑥−0.175

∑▒〖𝑓𝑌 =0〗∑▒〖𝑀𝑎 =0〗

ex ≤ e0.122 0.55 PASA

DIMENSIONAMIENTO DE LA ZAPATA

AF= 4.11 m2B= 1.24 m

ASUMIR B= 1.5 md= 0.35 mr= 0.08 m

0.35

1.5

A= 0.525 m2

I= 0.005359375 m4 DISEÑO A CORTANTE LONGITUDINAL

PESO PROPIO:

Pp= 1.26 T/m

PESO PROPIO MAYORADO:Ppu=1.2*Pp

Presión max ≤ qa≤

Pp=A*γc

𝐴𝐹=(𝑅+𝑆𝑜𝑏𝑟𝑒𝑐𝑎𝑟𝑔𝑎)/𝑞𝑎 𝐴𝐹=𝐵∗𝐿𝐵=𝐴𝐹/𝐿𝑉𝑐=0.53√(𝑓^′ 𝑐)∗𝑑∗100𝑐𝑚𝑉𝑢≤ØVc

𝑉𝑐=0,53∗𝜆∗√(𝑓^′ 𝑐)*bw*d

𝜙𝑉𝑐≥𝑉𝑢

DISEÑO A FLEXIÓN

DISEÑO A FLEXIÓN LONGITUDINAL

Mu(-)= 729928.475 kg.cmMu(+)= 8229984.47 kg.cm

14/Fy

0.00333333ρbal= 0.02142297

0.01606722ρcal= 0.00180421ρcal= 0.03183074

CALCULO DEL As:

As= 13.5 cm2

12

DISEÑO A CORTANTE TRANSVERSAL

f'c= 210 kg/cm2b= 35 cm b= 45d= 27 cmB= 150 cm

qmax= 2.1065 kg/cm2λ= 1 f'c normφ= 0.75 compresion

ρmin=ρmax= 0.75*ρbalρmax= 0.5*ρbal

ρmin=

ρmax=

VER TABLA DE ACERO

12Ø12

ρ𝑐𝑎𝑙=(0,85𝑓^′ 𝑐)/𝑓𝑦 (1−√(1−2𝑀𝑢/(0,85∗∅∗𝑓^′ 𝑐∗𝑏∗𝑑^2 )))ρ𝑏𝑎𝑙=(0,85𝐵1𝑓^′ 𝑐)/𝑓𝑦 (6120/(6120+𝑓𝑦))

𝑀𝑢=𝑞𝑚𝑎𝑥/2 ((𝐵−𝑏)/2)^2∗𝑙

Fy= 4200 kg/cm2

Analizamos en un metro de long:

EJE A EJE BVu= 6424.825 kg Vu= 5371.575Vc= 20737.1601 kg Vc= 20737.1601

6424.825 ≤ 15552.8701 5371.575 ≤ 15552.8701ok ok

Mu= 215903.084 kg.m

ρcal= 0.00128308As= 3.02


Vu= 14177.52 KgVc= 31105.7402 Kg

23329.3051 ≥ 14177.52

𝑉𝑐=0.53√(𝑓^′ 𝑐)∗𝑑∗100𝑐𝑚 𝑉𝑢=𝑞𝑚𝑎𝑥∗𝑙∗1𝑚𝑉𝑢≤ØVc 𝑉𝑢=𝑞𝑚𝑎𝑥((𝐵−𝑏)/2−𝑑)∗100

𝑀𝑢=𝑞𝑚𝑎𝑥((𝐵−𝑏)/2)^2∗𝑙

𝑉𝑐=0,53∗𝜆∗√(𝑓^′ 𝑐)*bw*d

𝜙𝑉𝑐≥𝑉𝑢

𝑉𝑢=𝑃𝑢−𝑞∗(𝑐𝑥+𝑑/2)∗(𝑐𝑦+𝑑)

𝑉𝑐=0,53∗(1+2/𝛽)𝜆∗√(𝑓^′ 𝑐)*bo*d

𝑉𝑐=𝜆∗√(𝑓^′ 𝑐)*bo*d

DISEÑO A FLEXIÓN

DISEÑO A FLEXIÓN TRANSVERSAL

EJE A EJE BCOL 35*35 cm COL 45*45 cmL= 62 cm L= 99r= 7 cm Asumimos r= 7 cm

Mu= 215903.084 kg.m Mu= 287399.011

0.0018 0.0018ρbal= 0.02142297 ρbal= 0.02142297ρmax= 0.01606722 ρmax= 0.01606722ρcal= 0.00128308 ρcal= 0.00171686

As= 3.0132 As= 4.8114

DISEÑO A PUNZONAMIENTO

EJE A EJE BCX CY CX

COL = 35 35 COL = 45

as40 col. Int30 col. Borde

ρ retraccion= ρ retraccion=

VER TABLA DE ACERO

VER TABLA DE ACERO

𝑀𝑢=𝑞𝑚𝑎𝑥/2 ((𝐵−𝑏)/2)^2∗𝑙

𝑏𝑜=2(𝑐𝑥+𝑑/2)+(𝑐𝑦+𝑑) 𝑏𝑜=2(𝑐𝑥+𝑑/2)+(𝑐𝑦+𝑑)

bo= 159 20 col. Esquin bo= 288

Pu= 21348 kg Pu= 60645.6q= 1.4579 kg/cm2 q= 1.9667

Vu= En un area a una dist. d/2 alrededor de las columnas Vu= En un area a una dist. d/2 alrededor de las columnas

Vu= 16964.0947 kg Vu= 50450.2272

β= 1 β= 1Vc= 98916.2538 Vc= 179169.063

Vc= 119164.33 Vc= 174943.378

Vc= 62211.4804 Chequeo con el menor valor Vc= 112684.946

16964.095 ≤ 46658.610 50450.227 ≤ok ok


𝑉𝑐=0,53∗(1+2/𝛽)𝜆∗√(𝑓^′ 𝑐)*bo*d

𝑉𝑐=0,27∗((𝑎𝑠∗𝑑)/𝑏𝑜+2)𝜆∗√(𝑓^′ 𝑐)*bo*d


𝑽𝒖≤Ø𝐕𝐜


𝑉𝑐=0,53∗(1+2/𝛽)𝜆∗√(𝑓^′ 𝑐)*bo*d

𝑉𝑐=0,27∗((𝑎𝑠∗𝑑)/𝑏𝑜+2)𝜆∗√(𝑓^′ 𝑐)*bo*d


𝑽𝒖≤Ø𝐕𝐜

CY45

𝑏𝑜=2(𝑐𝑥+𝑑/2)+(𝑐𝑦+𝑑)

kgkg/cm2

En un area a una dist. d/2 alrededor de las columnas

kg

Chequeo con el menor valor

84513.709


𝑉𝑐=0,53∗(1+2/𝛽)𝜆∗√(𝑓^′ 𝑐)*bo*d

𝑉𝑐=0,27∗((𝑎𝑠∗𝑑)/𝑏𝑜+2)𝜆∗√(𝑓^′ 𝑐)*bo*d

TABLAS DE HIERROSSECCIONES (cm2)

1 2 3 4 5 66 0.222 0.283 Err:522 Err:522 Err:522 Err:522 Err:5228 0.392 0.000 Err:522 Err:522 Err:522 Err:522 Err:522

10 0.617 0.001 Err:522 Err:522 Err:522 Err:522 Err:52212 0.888 0.002 Err:522 Err:522 Err:522 Err:522 Err:52214 1.208 0.003 Err:522 Err:522 Err:522 Err:522 Err:52216 1.578 0.006 Err:522 Err:522 Err:522 Err:522 Err:52218 1.998 0.009 Err:522 Err:522 Err:522 Err:522 Err:52220 2.466 0.014 Err:522 Err:522 Err:522 Err:522 Err:52222 2.984 0.020 Err:522 Err:522 Err:522 Err:522 Err:52225 3.853 0.033 Err:522 Err:522 Err:522 Err:522 Err:52228 4.834 0.052 Err:522 Err:522 Err:522 Err:522 Err:52232 6.313 0.089 Err:522 Err:522 Err:522 Err:522 Err:522

f'c (kg/cm2) β1210 0.85280 0.85350 0.8420 0.75490 0.7

0.65

D (mm)

PESO (Kg/m)

≥560

TABLAS DE HIERROSSECCIONES (cm2)

7 8 9 10Err:522 Err:522 Err:522 Err:522 1.332 34.05Err:522 Err:522 Err:522 Err:522 4.704 9.57Err:522 Err:522 Err:522 Err:522 7.404 6.13Err:522 Err:522 Err:522 Err:522 10.656 4.26Err:522 Err:522 Err:522 Err:522 14.496 3.13Err:522 Err:522 Err:522 Err:522 18.936 2.39Err:522 Err:522 Err:522 Err:522 23.976 1.82Err:522 Err:522 Err:522 29.592 1.53Err:522 Err:522 Err:522 Err:522 35.808 1.27Err:522 Err:522 Err:522 Err:522 46.236 0.98Err:522 Err:522 Err:522 Err:522 58.008 0.78Err:522 Err:522 Err:522 Err:522 75.756 0.6

PESO X VAR (Kg)

PESO X qq

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