Zapata Combinada 2s.xlsx

ZAPATA COMBINADA RECTANGULAR (Z-16,Z-15) Columna Izquierda Cm = 24.37 Tn Cv = 15.99 Tn t1 = 0.40 m t2 = 0.40 m f'c = 280 Kg/cm2

Columna Derecha Cm = 28.15 Tn Cv = 17.65 Tn t1 = 0.40 m t2 = 0.70 m f'c = 280 Kg/cm2

hf df S/C hc ϒc ϒs σ ult f'c fy

l1 = 2.30 m

1°

Esfuerzo Neto del Terreno

σn = 7.21 Tn/m2 2°

Area de la Zapata Pt Azap Xo Lz lv b Azap

3°

= 86.16 Tn = 11.95 cm2 = 1.64 m = 3.28 m = 0.20 m = 3.62 m = 12.045 cm2

�_𝑧𝑎𝑝=�_ �/�_𝑛

Reacción Neta del Terreno ● Por Unidad de Longitud P1u = 61.301 Tn P2u = 69.415 Tn WNU = 39.61 Tn/m

Cimentación = 2.00 m = 1.85 m = 500 Kg/m2 = 0.15 m = 2.3 Tn/m3 = 1.95 Tn/m3 = 3.50 Kg/cm2 = 210 Kg/cm2 = 4200 Kg/cm2

�_𝑛=�_𝑎𝑑�−�_𝑝𝑜�∙ℎ_𝑓−ℎ_𝑐∙�_(𝑐−) 𝑆/�

3.30 m 3.65 m

�_𝑛𝑢=�_𝑁𝑈/�

�_𝑁𝑈=(�_1𝑈+�_ 2𝑈)/𝑙𝑧

● Por Unidad de Area

WNU = b = Wnu =

39.61 3.65 10.85

Tn/m m Tn/m2

3°

Dimensionamiento de la Altura hz de la Zapata Para una Cuantía ρ = 0.0024 ρmin = 0.0024

φ = 0.9

�_𝑧=−�_1𝑈+�_𝑁𝑈∙�_𝑂=0

w = 0.048479 Xo = 1.55 m Mmáx = -35.17 Tn-m d = 0.33 m hz = 0.41 cm

�_�á𝑥=�_𝑁𝑈∙(�_𝑂^2)/2−�_1𝑈∙( �_𝑂−�_1/2)

�_𝑈=∅∙𝑓^′ 𝑐 ∙�∙𝑑^2∙�∙(1−0.59∙�)

hz = 0.45 m d = 0.37 m

�= 𝜌∙ (𝑓^′ 𝑦)/(𝑓^′ 𝑐)

4°

Verificaciónes ● Por Cortante

φ = 0.85 53.571

7.92218 Vd2 Y3

Y1

0.00 Vd1

Vd3

Y2 -15.8444

-53.38

Y1 = Y2 = Y3 =

0.57 0.57 0.57

�_𝑛=�𝑢/ ∅

m m m

Vd1 = Vd2 = Vd3 = Vu = Vn =

30.99 36.46

Tn Tn

-30.80 30.99 6.73

= = =

�_�=0.53∙√(𝑓^′ 𝑐)∙�∙𝑑

Abs. 30.80 Tn 30.99 Tn 6.73 Tn

Vc = 103.72 Tn

Vn < Vc ……….(Conforme)

● Por Punzonamiento

φ = 0.85

�_𝑈1=�_1𝑈−�_𝑛𝑢∙(�1)∙(𝑛1)

Λ

�_𝑈2=�_𝑈2−�_𝑛𝑢∙(�2)∙(𝑛2)

�_1=�_1+𝑑/2 , 𝑛_1 = �_2+𝑑 �_2+𝑑 m1 = 0.59 n1 = 0.77

Λ

�_2= �_1+𝑑 , 𝑛_2= m2 = n2 =

0.77 1.07

0.27∙(2+4/�)∙√(𝑓^′ 𝑐)∙�_𝑜∙𝑑 �_�≤

0.27∙((�_𝑠∙𝑑)/�_𝑜 +2)∙√(𝑓^′ 𝑐)∙�_𝑜∙𝑑 1.06∙√(𝑓^′ 𝑐)∙�_𝑜∙𝑑

a) Columna Exterior Vu = Vc1 = Vc2 = Vc3 =

56.41

Tn

168.5109 Tn 100.7075 Tn 110.2602 Tn

Vn = 66.3677 Tn

Vc = 100.71 Tn

Vn < Vc ……….(Conforme) b) Columna Interior Vu = Vc1 = Vc2 = Vc3 =

60.47 Tn 102.2358 Tn 189.5394 Tn 209.1535 Tn

Vn < Vc ……….(Conforme)

Vn = 71.1456 Tn

Vc = 102.24 Tn

5°

Diseño por Flexión

φ = 0.9

𝑎=(2𝑑±√(4𝑑^2−8�𝑢/(0.85∙𝑓^′ 𝑐∙∅∙�)))/2

�_𝑆=�_𝑈/(∅∙𝑓^′ 𝑦∙(𝑑−𝑎/2)) ● Refuerzo Superior

Mu As ρ ρmin As

= = = = =

35.174 Tn-m 25.7259 cm2 0.0019 0.0024 32.7351 cm2

a = 0.723 a = 0.0166

Diámetro de Varilla φ: AØ = 1.98 cm2 # var = 16.53 Esp. S = 21.84

5/8" 17 21

Varillas cm

Usar 17 φ 5/8" @ 21 cm ● Refuerzo Inferior

�_𝑆=�_(𝑆 (𝑅𝑒𝑓𝑢𝑒𝑟𝑧𝑜 𝑆𝑢𝑝𝑒𝑟𝑖𝑜𝑟))/3

As = 10.9117 cm2

6°

Diámetro de Varilla φ: 3/8" AØ = 0.71 cm2 # var = 15.37 16 Esp. S = 23.34 23 Usar 16 φ 3/8" @ 23 cm

Varillas cm

Diseño en Dirección Transversal b1 = b2 =

59 77

cm cm

● Zapata Exterior

�_𝑆=�_𝑈/(∅∙𝑓^′ 𝑦∙(𝑑−𝑎/2)) qNU Mu As ρ ρmin As

= 16.7948 Tn/m = 22.1744 Tn-m = 17.5063 cm2 = 0.00802 = 0.0024 = 17.506 cm2

�_𝑁𝑈=�_𝑈 /�

�_𝑈=(�_𝑁𝑈∙((�−�_2) /2)^2)/2

𝑎=(2𝑑±√(4𝑑^2−8�𝑢/(0.85∙𝑓^′ 𝑐∙∅∙�)))/2

a = 0.6702 a = 0.070

Diámetro de Varilla φ: AØ = 2.85 cm2 # var = 6.14 Esp. S = 7.18

3/4" 7 7

Usar 7 φ 3/4" @ 7 cm

● Zapata Interior

�_𝑆=�_𝑈/(∅∙𝑓^′ 𝑦∙(𝑑−𝑎/2))

𝑎=(2𝑑±√(4𝑑^2−8�𝑢/(0.85∙𝑓^′ 𝑐∙∅∙�)))/2

a = 0.6916 a = 0.0484

Varillas cm

qNU Mu As ρ ρmin As

7°

= 19.0178 Tn/m = 20.6878 Tn-m = 15.8261 Tn/cm2 = 0.00555 = 0.0024 = 15.826 cm2

Diámetro de Varilla φ: AØ = 2.85 cm2 # var = 5.55 Esp. S = 12.22

3/4" 6 12

Varillas cm

Usar 6 φ 3/4" @ 12 cm

Planos ● Perfil Usar 17 φ 5/8" @ 21 cm Usar 16 φ 3/8" @ 23 cm

l1 = 2.3 m

lv = 0.2 m

hz = 0.45 m

b1 = 0.59 m

b2 = 0.77 m Lz = 3.3 m Usar 7 φ 3/4" @ 7 cm

Usar 6 φ 3/4" @ 12 cm

● Planta

Acero Superior Usar 17 φ 5/8" @ 21 cm B = 3.65 m Usar 6 φ 3/4" @ 12 cm Usar 7 φ 3/4" @ 7 cm

Lz = 3.3 m Acero Inferior Usar 16 φ 3/8" @ 23 cm

● Secion Trasversal ● Zapata Exterior ( t2 = 0.4 m )

● Zapata Interior ( t2 = 0.7 m )

Lv = 1.625 m Usar 7 φ 3/4" @ 7 cm

Lv = 1.625 m

Lv = 1.475 m

Lv = 1.475 m

Usar 16 φ 3/8" @ 23 cm Usar 6 φ 3/4" @ 12 cm

b = 3.65 m

Usar 16 φ 3/8" @ 23 cm

b = 3.65 m