This document calculates the size of foundations (zapatas) for different structural loads. It analyzes isolated footings (zapatas aisladas) under several load cases (A1, A2, B1, etc.), providing the load values, maximum and minimum stresses, and resulting required sizes of the square footings. For example, a centered footing under load B2 requires a size of 1.00m to satisfy stresses of less than 12kg/cm^2. Corner and edge footings require larger sizes due to eccentric loads.

1. UNIVERSIDAD NORORIENTAL PRIVADA
“GRAN MARISCAL DE AYACUCHO”
FACULTAD DE INGENIERÍA
NÚCLEO CUMANÁ
ASIGNATURA: INGENIERIA DE FUNDACIONES
TAMAÑO DE LAS
ZAPATAS
PROFESOR: PARTICIPANTE:
Ing. Carlos Herrera. Acuña, Rosibert
18.211.076
Cumaná, Noviembre de 2011

2. CALCULAR LAS FUNDACIONES
Tipo: Zapatas Aisladas
F’c = 200 Kg/cm2
Fy = 4200 Kg/cm2
σ = 1.2 Kg/cm2
Dimensiones de Pedestales: 0.40 m x 0.40 m
Cargas Mayoradas Luces
A1, A2
C1, C3
B1
B3
A2
C2
B2 b1 b2 ℓ1 ℓ2 σs
14 TN 15 TN 16 TN 17 TN 4.0 5.0 5.0 6.0 1.2 Kg/cm2
1 2 3
A
B
C

3.  ZAPATA CENTRADA (B-2)
Datos
Pu = 17 TN
℮x = 0
℮y = 0
Bx = By = B Bx
P = 17 TN/1.47 = 11.56 TN
0 0
σMAX = 1 + 6℮x + 6℮y ≤ 12 TN/M2
Bx By
σMAX = 1 ≤ 12 TN/M2
= 12 TN/M2
B2 =
B = 0.96 M2 = 0.98 M ⋍ 1.00 M
By
11.56 TN
B2
P
B2
11.56 TN
B2
11.56 TN
12 TN/M2

4. 1.0 MTS
 ZAPATA CENTRADA (C-2)
Datos
Pu = 16 TN
℮x = 0
℮y = 0
Bx = By = B Bx
P = 16 TN/1.47 = 10.88 TN
0 0
σMAX = 1 + 6℮x + 6℮y ≤ 12 TN/M2
Bx By
σMAX = 1 ≤ 12 TN/M2
= 12 TN/M2
1.0 MTS
By
10.88 TN
B2
P
B2
10.88 TN
B2

5. B2 =
B = 0.91 M2 = 0.95 M ⋍ 1.00 M
1.0 MTS
10.88 TN
12 TN/M2
1.0 MTS

6.  ZAPATA LATERAL (A-2)
Datos
Pu = 16 TN ℮y
℮x = 0
℮y = 1.75 – 0.20 = 1.55 MTS
Bx = 1.00 MTS
By = 3.50 MTS Bx
P = 16 TN/1.47 = 10.88 TN
0
σMAX = 1 + 6℮x + 6℮y ≤ 12 TN/M2
Bx By
σMAX = 1 + 6 (1.55) ≤ 12 TN/M2
3.5
σMAX = 11.38 TN/M2 ≤ 12 TN/M2
0
σMIN = 1 - 6℮x - 6℮y ≤ 12 TN/M2
Bx By
By
P
Bx . By
P
Bx . By
10.88 TN
(1.00) (3.50)
By

7. σMIN = 1 - 6 (1.55) ≤ 12 TN/M2
3.5
σMIN = -5.15 TN/M2
B`x
B`x =
1.00
B`x = 1.83 MTS
1.83 MTS
10.88 TN
(1.00) (3.50)
By
11.38
-5.15
11.38
11.38 – 5.15
3.50 MTS

8. σMAX = 1 + 6 (1.55) ≤ 12 TN/M2
3.5
σMAX = 6,21 TN/M2 ≤ 12 TN/M2
 ZAPATA LATERAL (B-1 y B-3)
Datos
Pu = 15 TN
℮x = 0.50 – 0.20 = 0.30 MTS
℮y = 0
Bx = 1.00 MTS
By = 3.50 MTS Bx
P = 15 TN/1.47 = 10.20 TN
0
σMAX = 1 + 6℮x + 6℮y ≤ 12 TN/M2
Bx By
σMAX = 1 + 6 (0.30) ≤ 12 TN/M2
1.00
10.88 TN
(1.83) (3.50)
By
By
P
Bx . By
10.20 TN
(1.00) (3.50)
By
℮x

9. σMAX = 8.16 TN/M2 ≤ 12 TN/M2
0
σMIN = 1 - 6℮x - 6℮y ≤ 12 TN/M2
Bx By
σMIN = 1 - 6 (0.30) ≤ 12 TN/M2
1.00
σMIN = -2.33 TN/M2
B`x
B`x =
1.00
P
Bx . By
10.20 TN
(1.00) (3.50)
By
8.16
-2.33
8.16
8.16 – 2.33

10. B`x = 1.39 ⋍1.40 MTS
1.40 MTS
σMAX = 1 + 6 (0.50) ≤ 12 TN/M2
1.40
σMAX = 6,54 TN/M2 ≤ 12 TN/M2
 ZAPATA LATERAL (C-1 y C-3)
Datos
Pu = 14 TN
℮x = 0.50 – 0.20 = 0.30 MTS
℮y = 0
Bx = 1.00 MTS
By = 3.00 MTS Bx
3.50 MTS
10.20 TN
(1.40) (3.50)
By
By
℮x

11. P = 14 TN/1.47 = 9.52 TN
0
σMAX = 1 + 6℮x + 6℮y ≤ 12 TN/M2
Bx By
σMAX = 1 + 6 (0.30) ≤ 12 TN/M2
1.00
σMAX = 8.89 TN/M2 ≤ 12 TN/M2
0
σMIN = 1 - 6℮x - 6℮y ≤ 12 TN/M2
Bx By
σMIN = 1 - 6 (0.30) ≤ 12 TN/M2
1.00
σMIN = -2.54 TN/M2
P
Bx . By
P
Bx . By
9.52 TN
(1.00) (3.00)
By
9.52 TN
(1.00) (3.00)
By

12. B`x
B`x =
1.00
B`x = 1.40 MTS
1.40 MTS
σMAX = 1 + 6 (0.50) ≤ 12 TN/M2
1.40
σMAX = 7.12 TN/M2 ≤ 12 TN/M2
8.89
-2.54
8.89
8.89 – 2.54
3.00 MTS
9.52 TN
(1.40) (3.00)
By

13.  ZAPATA ESQUINERA (A-1 y A-3)
Datos
Pu = 14 TN
℮x = 0.50 – 0.20 = 0.30 MTS
℮y = 1.75 - 0.20 = 1.55 MTS
Bx = 1.00 MTS
By = 3.50 MTS Bx
P = 14 TN/1.47 = 9.52 TN
σMAX = 1 + 6℮x + 6℮y ≤ 12 TN/M2
Bx By
σMAX = 1 + 6 (0.30) + 6 (1.55) ≤ 12 TN/M2
1.0 3.55
σMAX = 14.74 TN/M2 ≥ 12 TN/M2
Se aumentan los valores de Bx y By
By
P
Bx . By
℮x
℮y
9.52 TN
(1.00) (3.50)
Bx = 2.00 MTS
By = 4.00 MTS
℮x = 1.00 – 0.20 = 0.80 MTS
℮y = 2.00 - 0.20 = 1.80 MTS

14. σMAX = 1 + 6 (0.80) + 6 (1.80) ≤ 12 TN/M2
2.0 4.0
σMAX = 1.19 ⦋ 1 + 2.4 +2.7⦌
σMAX = 7.26 TN/M2 ≤ 12 TN/M2
σMIN = 1 - 6℮x - 6℮y ≤ 12 TN/M2
Bx By
σMIN = 1 - 6 (0.80) - 6 (1.80) ≤ 12 TN/M2
2.0 4.0
σMIN = 1.19 ⦋ 1 - 2.4 - 2.7⦌
σMIN = -4.88 TN/M2
B`x
P
Bx . By
7.26
-4.88
9.52 TN
(2.0) (4.0)
9.52 TN
(2.0) (4.0)

15. B`x =
2.00
B`x = 6.10 MTS
6.10 MTS
σMAX = 1 + 6 (2.88) + 6 (1.80) ≤ 12 TN/M2
6.15 4.00
σMAX = 0.39 ⦋ 1 + 2.81 + 2.70⦌
σMAX = 2.54 TN/M2 ≤ 12 TN/M2
7.26
7.26 – 4.88
4.00 MTS
Bx = 6.10 MTS
By = 4.00 MTS
℮x = 3.08 – 0.20 = 2.88 MTS
℮y = 2.00 - 0.20 = 1.80 MTS
9.52 TN
(6.15) (4.0)