Ejercicios Concreto Armado II (Zapatas Aisladas)
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Desarrollo de ejercicios de Zapatas Aisladas, incluye verificaciones por corte, punzonamiento, cortante, etc
Transcript of Ejercicios Concreto Armado II (Zapatas Aisladas)
UNIVERSIDAD ALAS PERUANAS - FILIAL AREQUIPATRABAJO 1 DE CONCRETO ARMADO 2 - CICLO 2015 1B
DISEÑAR LAS SIGUIENTES ZAPATAS AISLADAS CONSIDERANDO LAS PARTES QUE SE INDICA
1. Dimesionado 2. Peralte de zapata 4. AceroCM + CV Punzonamiento "d" Momento máximo MuCM + CV + CS Cortante "d" Acero por flexión AsCM + CV - CS mínimo "d" Acero mínimo AsmínSISMO DE NORMA Anclaje "d" 5. Dibujo
3. Aplastamiento Planta, Corte de detalles
ZAPATA Z-1 ZAPATA Z-2 ZAPATA Z-3DATOS: DATOS: DATOS:
PD (tnf) = 40.00 PD (tnf) = 50.00 PD (tnf) = 70.00PL (tnf) = 30.00 PL (tnf) = 40.00 PL (tnf) = 50.00PS (tnf) = 10.00 PS (tnf) = 15.00 PS (tnf) = 20.00b (cm) = 30.00 b (cm) = 30.00 b (cm) = 30.00t (cm) = 40.00 t (cm) = 40.00 t (cm) = 40.00f'c (kgf/cm2) = 210.00 f'c (kgf/cm2) = 210.00 f'c (kgf/cm2) = 210.00qadm (kgf/cm2) = 1.50 qadm (kgf/cm2) = 2.00 qadm (kgf/cm2) = 2.50Ø columna (pulg) = 5/8 Ø columna (pulg) = 3/4 Ø columna (pulg) = 1 L/B = 1.30 L/B = 1.30 L/B = 1.30
ZAPATA Z-4 ZAPATA Z-5 ZAPATA Z-6DATOS: DATOS: DATOS:
PD (tnf) = 100.00 PD (tnf) = 70.00 PD (tnf) = 80.00PL (tnf) = 70.00 PL (tnf) = 50.00 PL (tnf) = 60.00PS (tnf) = 20.00 PS (tnf) = 20.00 PS (tnf) = 25.00b (cm) = 50.00 b (cm) = 40.00 b (cm) = 40.00t (cm) = 80.00 t (cm) = 60.00 t (cm) = 60.00f'c (kgf/cm2) = 280.00 f'c (kgf/cm2) = 175.00 f'c (kgf/cm2) = 175.00qadm (kgf/cm2) = 2.00 qadm (kgf/cm2) = 2.00 qadm (kgf/cm2) = 1.50Ø columna (pulg) = 1 Ø columna (pulg) = 3/4 Ø columna (pulg) = 5/8L/B = 1.40 L/B = 1.40 L/B = 1.40
ZAPATA Z-7 ZAPATA Z-8 ZAPATA Z-9DATOS: DATOS: DATOS:
PD (tnf) = 70.00 PD (tnf) = 100.00 PD (tnf) = 80.00PL (tnf) = 50.00 PL (tnf) = 80.00 PL (tnf) = 80.00PS (tnf) = 60.00 PS (tnf) = 50.00 PS (tnf) = 60.00b (cm) = 40.00 b (cm) = 40.00 b (cm) = 40.00t (cm) = 70.00 t (cm) = 70.00 t (cm) = 70.00f'c (kgf/cm2) = 210.00 f'c (kgf/cm2) = 210.00 f'c (kgf/cm2) = 210.00qadm (kgf/cm2) = 3.00 qadm (kgf/cm2) = 2.50 qadm (kgf/cm2) = 2.00Ø columna (pulg) = 3/4 Ø columna (pulg) = 3/4 Ø columna (pulg) = 3/4L/B = 1.30 L/B = 1.30 L/B = 1.30
ZAPATA Z-10 ZAPATA Z-11 ZAPATA Z-12DATOS: DATOS: DATOS:
PD (tnf) = 140.00 PD (tnf) = 100.00 PD (tnf) = 80.00PL (tnf) = 100.00 PL (tnf) = 70.00 PL (tnf) = 60.00PS (tnf) = 40.00 PS (tnf) = 30.00 PS (tnf) = 40.00b (cm) = 60.00 b (cm) = 40.00 b (cm) = 40.00t (cm) = 120.00 t (cm) = 80.00 t (cm) = 80.00f'c (kgf/cm2) = 280.00 f'c (kgf/cm2) = 210.00 f'c (kgf/cm2) = 210.00qadm (kgf/cm2) = 3.00 qadm (kgf/cm2) = 3.00 qadm (kgf/cm2) = 3.00Ø columna (pulg) = 1 Ø columna (pulg) = 1 Ø columna (pulg) = 3/4L/B = 1.50 L/B = 1.50 L/B = 1.50
ZAPATA Z-1 2. Peralte de zapata ANCLAJE:DATOS:
PD (tnf) = 40.00 Pu=1.4(PD)+1.7(PL) = 116.80 tnf ldg = 34.59 cmPL (tnf) = 30.00 Pu=1.25(PD+PL)+PS = 106.25 tnf d1 = 30.31 cmPS (tnf) = 10.00 Pu=1.25(PD+PL)-PS = 88.56 tnf d2 = 32.29 cmb (cm) = 30.00 Pu=0.9(PD)+PS = 52.3 tnf d3 = 30.00 cmt (cm) = 40.00 Pu=0.9(PD)-PS = 32.3 tnf d4 = 34.59 cm
f'c (kgf/cm2) = 210.00 Pu = 116.80 tnf d = 34.59 cmqadm (kgf/cm2) = 1.50Ø columna (pulg) = 5/8 PUNZONAMIENTO: d h = 44.59 cmL/B = 1.30 h = 50.00 cm%P-> PP 10%PS servicio 8.00 3. Aplastamiento
Bc = 1.331. Dimesionado Vc = 19.64 kgf/cm2
- COMB. 1: CM + CV fa = 97.33 kgf/cm2PD 40.00 tnf Vc = 15.94 kgf/cm2PL 30.00 tnfPpzap. 7.00 tnf A2 = 40376 cm2P 77.00 tnf A1 = 1200 cm2qadm 15.00 tnf/m2 qu = 2.25 kgf/cm2
56.44 = 5.80Az= P/qadm 2054.15Az= 5.13 m2 -114104.62 f = 2
d = 30.31 cmL*B= 5.13 m2 d = -66.70 fa ≤ 249.9 kgf/cm2
B= 1.99 m OKL= 2.58 m CORTE:
B (m) L (m) Area (m2)2.00 2.60 5.20
Vc = 7.68 kgf/cm2- COMB. 2: CM + CV + CS
PD 40.00 tnfPL 30.00 tnfPpzap. 7.00 tnf d1 = 32.29 cmPS servicio 8.00 d2 = 24.95 cmP 85.00 tnf d = 32.29 cm
qadm = 19.5 tnf/m2 d minimo:qact = P/Az 16.56 tnf/m2
OK d = 30 cm19.5 ≥ 16.56
- COMB. 3: CM + CV - CS
P 69.00 tnf
qadm = 19.5 tnf/m2qact = P/Az 13.44 tnf/m2
OK19.5 ≥ 13.44
qadm ≥ qact
qadm ≥ qact
𝑉𝑐=(0.53+1.1/𝐵𝑐)∗√(𝑓^′ 𝑐); 𝐵𝑐= 𝑡/𝑏
𝑉𝑐=1.1∗√(𝑓^′ 𝑐)𝑞𝑢=(𝑃𝑢 )/(𝐵 𝑥 𝐿)
𝑑^2 (4Ø𝑉𝑐+𝑞𝑢)+𝑑(𝑏+𝑡)(2Ø𝑉𝑐+𝑞𝑢)−𝑞𝑢(𝐵×𝐿−𝑏×𝑡)=0 𝑎𝑏𝑐
𝑉𝑐=0.53∗√(𝑓^′ 𝑐)𝑑1=(𝑞𝑢(𝐿−𝑡) )/(2(0.85×𝑉𝑐+𝑞𝑢))𝑑2=(𝑞𝑢(𝐵−𝑏) )/(2(0.85×𝑉𝑐+𝑞𝑢))
𝑓𝑎=𝑃𝑢/𝐴1
√(𝐴2/𝐴1)≤2𝐴2=(𝑏+4×(ℎ−8.5))(𝑡+4×(ℎ−8.5))
𝑓𝑎≤0.7×0.85×𝑓^′ 𝑐×𝑓
ZAPATA Z-2 2. Peralte de zapata ANCLAJE:DATOS:
PD (tnf) = 50.00 Pu=1.4(PD)+1.7(PL) = 148.08 tnf ldg = 41.51 cmPL (tnf) = 40.00 Pu=1.25(PD+PL)+PS = 136.5 tnf d1 = 35.14 cmPS (tnf) = 15.00 Pu=1.25(PD+PL)-PS = 109.416 tnf d2 = 38.83 cmb (cm) = 30.00 Pu=0.9(PD)+PS = 66.48 tnf d3 = 30.00 cmt (cm) = 40.00 Pu=0.9(PD)-PS = 36.48 tnf d4 = 41.51 cm
f'c (kgf/cm2) = 210.00 Pu = 148.08 tnf d = 41.51 cmqadm (kgf/cm2) = 2.00Ø columna (pulg) = 3/4 PUNZONAMIENTO: d h = 51.51 cmL/B = 1.30 h = 55.00 cm%P-> PP 8%PS servicio 12.00 3. Aplastamiento
Bc = 1.331. Dimesionado Vc = 19.64 kgf/cm2
- COMB. 1: CM + CV fa = 123.40 kgf/cm2PD 50.00 tnf Vc = 15.94 kgf/cm2PL 40.00 tnfPpzap. 7.20 tnf A2 = 48816 cm2P 97.20 tnf A1 = 1200 cm2qadm 20.00 tnf/m2 qu = 2.96 kgf/cm2
57.16 = 6.38Az= P/qadm 2104.23Az= 4.86 m2 -144526.08 f = 2
d = 35.14 cmL*B= 4.86 m2 d = -71.95 fa ≤ 249.9 kgf/cm2
B= 1.93 m OKL= 2.51 m CORTE:
B (m) L (m) Area (m2)2.00 2.50 5.00
Vc = 7.68 kgf/cm2- COMB. 2: CM + CV + CS
PD 50.00 tnfPL 40.00 tnfPpzap. 7.20 tnf d1 = 38.83 cmPS servicio 12.00 d2 = 31.43 cmP 109.20 tnf d = 38.83 cm
qadm = 26 tnf/m2 d minimo:qact = P/Az 22.47 tnf/m2
OK d = 30 cm26 ≥ 22.47
- COMB. 3: CM + CV - CS
P 85.20 tnf
qadm = 26 tnf/m2qact = P/Az 17.53 tnf/m2
OK26 ≥ 17.53
qadm ≥ qact
qadm ≥ qact
𝑉𝑐=(0.53+1.1/𝐵𝑐)∗√(𝑓^′ 𝑐); 𝐵𝑐= 𝑡/𝑏
𝑉𝑐=1.1∗√(𝑓^′ 𝑐)𝑞𝑢=(𝑃𝑢 )/(𝐵 𝑥 𝐿)
𝑑^2 (4Ø𝑉𝑐+𝑞𝑢)+𝑑(𝑏+𝑡)(2Ø𝑉𝑐+𝑞𝑢)−𝑞𝑢(𝐵×𝐿−𝑏×𝑡)=0 𝑎𝑏𝑐
𝑉𝑐=0.53∗√(𝑓^′ 𝑐)𝑑1=(𝑞𝑢(𝐿−𝑡) )/(2(0.85×𝑉𝑐+𝑞𝑢))𝑑2=(𝑞𝑢(𝐵−𝑏) )/(2(0.85×𝑉𝑐+𝑞𝑢))
𝑓𝑎=𝑃𝑢/𝐴1
√(𝐴2/𝐴1)≤2𝐴2=(𝑏+4×(ℎ−8.5))(𝑡+4×(ℎ−8.5))
𝑓𝑎≤0.7×0.85×𝑓^′ 𝑐×𝑓
𝑉𝑐=(0.53+1.1/𝐵𝑐)∗√(𝑓^′ 𝑐); 𝐵𝑐= 𝑡/𝑏
𝑉𝑐=1.1∗√(𝑓^′ 𝑐)𝑞𝑢=(𝑃𝑢 )/(𝐵 𝑥 𝐿)
𝑑^2 (4Ø𝑉𝑐+𝑞𝑢)+𝑑(𝑏+𝑡)(2Ø𝑉𝑐+𝑞𝑢)−𝑞𝑢(𝐵×𝐿−𝑏×𝑡)=0 𝑎𝑏𝑐
𝑉𝑐=0.53∗√(𝑓^′ 𝑐)𝑑1=(𝑞𝑢(𝐿−𝑡) )/(2(0.85×𝑉𝑐+𝑞𝑢))𝑑2=(𝑞𝑢(𝐵−𝑏) )/(2(0.85×𝑉𝑐+𝑞𝑢))
𝑓𝑎=𝑃𝑢/𝐴1
√(𝐴2/𝐴1)≤2𝐴2=(𝑏+4×(ℎ−8.5))(𝑡+4×(ℎ−8.5))
𝑓𝑎≤0.7×0.85×𝑓^′ 𝑐×𝑓
ZAPATA Z-3 2. Peralte de zapata ANCLAJE:DATOS:
PD (tnf) = 70.00 Pu=1.4(PD)+1.7(PL) = 196.44 tnf ldg = 55.35 cmPL (tnf) = 50.00 Pu=1.25(PD+PL)+PS = 182 tnf d1 = 41.84 cmPS (tnf) = 20.00 Pu=1.25(PD+PL)-PS = 145.888 tnf d2 = 49.37 cmb (cm) = 30.00 Pu=0.9(PD)+PS = 91.64 tnf d3 = 30.00 cmt (cm) = 40.00 Pu=0.9(PD)-PS = 51.64 tnf d4 = 55.35 cm
f'c (kgf/cm2) = 210.00 Pu = 196.44 tnf d = 55.35 cmqadm (kgf/cm2) = 2.50Ø columna (pulg) = 1 PUNZONAMIENTO: d h = 65.35 cmL/B = 1.30 h = 70.00 cm%P-> PP 8%PS servicio 16.00 3. Aplastamiento
Bc = 1.331. Dimesionado Vc = 19.64 kgf/cm2
- COMB. 1: CM + CV fa = 163.70 kgf/cm2PD 70.00 tnf Vc = 15.94 kgf/cm2PL 50.00 tnfPpzap. 9.60 tnf A2 = 78936 cm2P 129.60 tnf A1 = 1200 cm2qadm 25.00 tnf/m2 qu = 3.78 kgf/cm2
57.98 = 8.11Az= P/qadm 2161.36Az= 5.18 m2 -191906.77 f = 2
d = 41.84 cmL*B= 5.18 m2 d = -79.12 fa ≤ 249.9 kgf/cm2
B= 2.00 m OKL= 2.60 m CORTE:
B (m) L (m) Area (m2)2.00 2.60 5.20
Vc = 7.68 kgf/cm2- COMB. 2: CM + CV + CS
PD 70.00 tnfPL 50.00 tnfPpzap. 9.60 tnf d1 = 49.37 cmPS servicio 16.00 d2 = 38.15 cmP 145.60 tnf d = 49.37 cm
qadm = 32.5 tnf/m2 d minimo:qact = P/Az 28.09 tnf/m2
OK d = 30 cm32.5 ≥ 28.09
- COMB. 3: CM + CV - CS
P 113.60 tnf
qadm = 32.5 tnf/m2qact = P/Az 21.91 tnf/m2
OK32.5 ≥ 21.91
qadm ≥ qact
qadm ≥ qact
𝑉𝑐=(0.53+1.1/𝐵𝑐)∗√(𝑓^′ 𝑐); 𝐵𝑐= 𝑡/𝑏
𝑉𝑐=1.1∗√(𝑓^′ 𝑐)𝑞𝑢=(𝑃𝑢 )/(𝐵 𝑥 𝐿)
𝑑^2 (4Ø𝑉𝑐+𝑞𝑢)+𝑑(𝑏+𝑡)(2Ø𝑉𝑐+𝑞𝑢)−𝑞𝑢(𝐵×𝐿−𝑏×𝑡)=0 𝑎𝑏𝑐
𝑉𝑐=0.53∗√(𝑓^′ 𝑐)𝑑1=(𝑞𝑢(𝐿−𝑡) )/(2(0.85×𝑉𝑐+𝑞𝑢))𝑑2=(𝑞𝑢(𝐵−𝑏) )/(2(0.85×𝑉𝑐+𝑞𝑢))
𝑓𝑎=𝑃𝑢/𝐴1
√(𝐴2/𝐴1)≤2𝐴2=(𝑏+4×(ℎ−8.5))(𝑡+4×(ℎ−8.5))
𝑓𝑎≤0.7×0.85×𝑓^′ 𝑐×𝑓
ZAPATA Z-4 2. Peralte de zapata ANCLAJE:DATOS:
PD (tnf) = 100.00 Pu=1.4(PD)+1.7(PL) = 278.04 tnf ldg = 47.93 cmPL (tnf) = 70.00 Pu=1.25(PD+PL)+PS = 249.5 tnf d1 = 38.24 cmPS (tnf) = 20.00 Pu=1.25(PD+PL)-PS = 215.008 tnf d2 = 46.09 cmb (cm) = 50.00 Pu=0.9(PD)+PS = 122.24 tnf d3 = 30.00 cmt (cm) = 80.00 Pu=0.9(PD)-PS = 82.24 tnf d4 = 47.93 cm
f'c (kgf/cm2) = 280.00 Pu = 278.04 tnf d = 47.93 cmqadm (kgf/cm2) = 2.00Ø columna (pulg) = 1 PUNZONAMIENTO: d h = 57.93 cmL/B = 1.40 h = 60.00 cm%P-> PP 8%PS servicio 16.00 3. Aplastamiento
Bc = 1.601. Dimesionado Vc = 20.37 kgf/cm2
- COMB. 1: CM + CV fa = 69.51 kgf/cm2PD 100.00 tnf Vc = 18.41 kgf/cm2PL 70.00 tnfPpzap. 13.60 tnf A2 = 73216 cm2P 183.60 tnf A1 = 4000 cm2qadm 20.00 tnf/m2 qu = 2.97 kgf/cm2
65.55 = 4.28Az= P/qadm 4454.01Az= 9.18 m2 -266157.95 f = 2
d = 38.24 cmL*B= 9.18 m2 d = -106.18 fa ≤ 333.2 kgf/cm2
B= 2.56 m OKL= 3.58 m CORTE:
B (m) L (m) Area (m2)2.60 3.60 9.36
Vc = 8.87 kgf/cm2- COMB. 2: CM + CV + CS
PD 100.00 tnfPL 70.00 tnfPpzap. 13.60 tnf d1 = 46.09 cmPS servicio 16.00 d2 = 34.57 cmP 199.60 tnf d = 46.09 cm
qadm = 26 tnf/m2 d minimo:qact = P/Az 21.74 tnf/m2
OK d = 30 cm26 ≥ 21.74
- COMB. 3: CM + CV - CS
P 167.60 tnf
qadm = 26 tnf/m2qact = P/Az 18.26 tnf/m2
OK26 ≥ 18.26
qadm ≥ qact
qadm ≥ qact
𝑉𝑐=(0.53+1.1/𝐵𝑐)∗√(𝑓^′ 𝑐); 𝐵𝑐= 𝑡/𝑏
𝑉𝑐=1.1∗√(𝑓^′ 𝑐)𝑞𝑢=(𝑃𝑢 )/(𝐵 𝑥 𝐿)
𝑑^2 (4Ø𝑉𝑐+𝑞𝑢)+𝑑(𝑏+𝑡)(2Ø𝑉𝑐+𝑞𝑢)−𝑞𝑢(𝐵×𝐿−𝑏×𝑡)=0 𝑎𝑏𝑐
𝑉𝑐=0.53∗√(𝑓^′ 𝑐)𝑑1=(𝑞𝑢(𝐿−𝑡) )/(2(0.85×𝑉𝑐+𝑞𝑢))𝑑2=(𝑞𝑢(𝐵−𝑏) )/(2(0.85×𝑉𝑐+𝑞𝑢))
𝑓𝑎=𝑃𝑢/𝐴1
√(𝐴2/𝐴1)≤2𝐴2=(𝑏+4×(ℎ−8.5))(𝑡+4×(ℎ−8.5))
𝑓𝑎≤0.7×0.85×𝑓^′ 𝑐×𝑓
ZAPATA Z-5 2. Peralte de zapata ANCLAJE:DATOS:
PD (tnf) = 70.00 Pu=1.4(PD)+1.7(PL) = 196.44 tnf ldg = 45.47 cmPL (tnf) = 50.00 Pu=1.25(PD+PL)+PS = 182 tnf d1 = 39.21 cmPS (tnf) = 20.00 Pu=1.25(PD+PL)-PS = 145.888 tnf d2 = 47.96 cmb (cm) = 40.00 Pu=0.9(PD)+PS = 91.64 tnf d3 = 30.00 cmt (cm) = 60.00 Pu=0.9(PD)-PS = 51.64 tnf d4 = 45.47 cm
f'c (kgf/cm2) = 175.00 Pu = 196.44 tnf d = 47.96 cmqadm (kgf/cm2) = 2.00Ø columna (pulg) = 3/4 PUNZONAMIENTO: d h = 57.96 cmL/B = 1.40 h = 60.00 cm%P-> PP 8%PS servicio 16.00 3. Aplastamiento
Bc = 1.501. Dimesionado Vc = 16.71 kgf/cm2
- COMB. 1: CM + CV fa = 81.85 kgf/cm2PD 70.00 tnf Vc = 14.55 kgf/cm2PL 50.00 tnfPpzap. 9.60 tnf A2 = 65436 cm2P 129.60 tnf A1 = 2400 cm2qadm 20.00 tnf/m2 qu = 2.98 kgf/cm2
52.45 = 5.22Az= P/qadm 2771.41Az= 6.48 m2 -189296.73 f = 2
d = 39.21 cmL*B= 6.48 m2 d = -92.05 fa ≤ 208.25 kgf/cm2
B= 2.15 m OKL= 3.01 m CORTE:
B (m) L (m) Area (m2)2.20 3.00 6.60
Vc = 7.01 kgf/cm2- COMB. 2: CM + CV + CS
PD 70.00 tnfPL 50.00 tnfPpzap. 9.60 tnf d1 = 47.96 cmPS servicio 16.00 d2 = 35.97 cmP 145.60 tnf d = 47.96 cm
qadm = 26 tnf/m2 d minimo:qact = P/Az 22.47 tnf/m2
OK d = 30 cm26 ≥ 22.47
- COMB. 3: CM + CV - CS
P 113.60 tnf
qadm = 26 tnf/m2qact = P/Az 17.53 tnf/m2
OK26 ≥ 17.53
qadm ≥ qact
qadm ≥ qact
𝑉𝑐=(0.53+1.1/𝐵𝑐)∗√(𝑓^′ 𝑐); 𝐵𝑐= 𝑡/𝑏
𝑉𝑐=1.1∗√(𝑓^′ 𝑐)𝑞𝑢=(𝑃𝑢 )/(𝐵 𝑥 𝐿)
𝑑^2 (4Ø𝑉𝑐+𝑞𝑢)+𝑑(𝑏+𝑡)(2Ø𝑉𝑐+𝑞𝑢)−𝑞𝑢(𝐵×𝐿−𝑏×𝑡)=0 𝑎𝑏𝑐
𝑉𝑐=0.53∗√(𝑓^′ 𝑐)𝑑1=(𝑞𝑢(𝐿−𝑡) )/(2(0.85×𝑉𝑐+𝑞𝑢))𝑑2=(𝑞𝑢(𝐵−𝑏) )/(2(0.85×𝑉𝑐+𝑞𝑢))
𝑓𝑎=𝑃𝑢/𝐴1
√(𝐴2/𝐴1)≤2𝐴2=(𝑏+4×(ℎ−8.5))(𝑡+4×(ℎ−8.5))
𝑓𝑎≤0.7×0.85×𝑓^′ 𝑐×𝑓
ZAPATA Z-6 2. Peralte de zapata ANCLAJE:DATOS:
PD (tnf) = 80.00 Pu=1.4(PD)+1.7(PL) = 233.60 tnf ldg = 37.89 cmPL (tnf) = 60.00 Pu=1.25(PD+PL)+PS = 217.5 tnf d1 = 45.28 cmPS (tnf) = 25.00 Pu=1.25(PD+PL)-PS = 172.12 tnf d2 = 51.56 cmb (cm) = 40.00 Pu=0.9(PD)+PS = 109.6 tnf d3 = 30.00 cmt (cm) = 60.00 Pu=0.9(PD)-PS = 59.6 tnf d4 = 37.89 cm
f'c (kgf/cm2) = 175.00 Pu = 233.60 tnf d = 51.56 cmqadm (kgf/cm2) = 1.50Ø columna (pulg) = 5/8 PUNZONAMIENTO: d h = 61.56 cmL/B = 1.40 h = 65.00 cm%P-> PP 10%PS servicio 20.00 3. Aplastamiento
Bc = 1.501. Dimesionado Vc = 16.71 kgf/cm2
- COMB. 1: CM + CV fa = 97.33 kgf/cm2PD 80.00 tnf Vc = 14.55 kgf/cm2PL 60.00 tnfPpzap. 14.00 tnf A2 = 76076 cm2P 154.00 tnf A1 = 2400 cm2qadm 15.00 tnf/m2 qu = 2.25 kgf/cm2
51.72 = 5.63Az= P/qadm 2698.50Az= 10.27 m2 -228206.64 f = 2
d = 45.28 cmL*B= 10.27 m2 d = -97.45 fa ≤ 208.25 kgf/cm2
B= 2.71 m OKL= 3.79 m CORTE:
B (m) L (m) Area (m2)2.70 3.85 10.40
Vc = 7.01 kgf/cm2- COMB. 2: CM + CV + CS
PD 80.00 tnfPL 60.00 tnfPpzap. 14.00 tnf d1 = 51.56 cmPS servicio 20.00 d2 = 36.49 cmP 174.00 tnf d = 51.56 cm
qadm = 19.5 tnf/m2 d minimo:qact = P/Az 16.95 tnf/m2
OK d = 30 cm19.5 ≥ 16.95
- COMB. 3: CM + CV - CS
P 134.00 tnf
qadm = 19.5 tnf/m2qact = P/Az 13.05 tnf/m2
OK19.5 ≥ 13.05
qadm ≥ qact
qadm ≥ qact
𝑉𝑐=(0.53+1.1/𝐵𝑐)∗√(𝑓^′ 𝑐); 𝐵𝑐= 𝑡/𝑏
𝑉𝑐=1.1∗√(𝑓^′ 𝑐)𝑞𝑢=(𝑃𝑢 )/(𝐵 𝑥 𝐿)
𝑑^2 (4Ø𝑉𝑐+𝑞𝑢)+𝑑(𝑏+𝑡)(2Ø𝑉𝑐+𝑞𝑢)−𝑞𝑢(𝐵×𝐿−𝑏×𝑡)=0 𝑎𝑏𝑐
𝑉𝑐=0.53∗√(𝑓^′ 𝑐)𝑑1=(𝑞𝑢(𝐿−𝑡) )/(2(0.85×𝑉𝑐+𝑞𝑢))𝑑2=(𝑞𝑢(𝐵−𝑏) )/(2(0.85×𝑉𝑐+𝑞𝑢))
𝑓𝑎=𝑃𝑢/𝐴1
√(𝐴2/𝐴1)≤2𝐴2=(𝑏+4×(ℎ−8.5))(𝑡+4×(ℎ−8.5))
𝑓𝑎≤0.7×0.85×𝑓^′ 𝑐×𝑓
ZAPATA Z-7 2. Peralte de zapata ANCLAJE:DATOS:
PD (tnf) = 70.00 Pu=1.4(PD)+1.7(PL) = 193.08 tnf ldg = 41.51 cmPL (tnf) = 50.00 Pu=1.25(PD+PL)+PS = 219 tnf d1 = 36.40 cmPS (tnf) = 60.00 Pu=1.25(PD+PL)-PS = 102.816 tnf d2 = 42.75 cmb (cm) = 40.00 Pu=0.9(PD)+PS = 129.48 tnf d3 = 30.00 cmt (cm) = 70.00 Pu=0.9(PD)-PS = 9.48 tnf d4 = 41.51 cm
f'c (kgf/cm2) = 210.00 Pu = 219.00 tnf d = 42.75 cmqadm (kgf/cm2) = 3.00Ø columna (pulg) = 3/4 PUNZONAMIENTO: d h = 52.75 cmL/B = 1.30 h = 55.00 cm%P-> PP 6%PS servicio 48.00 3. Aplastamiento
Bc = 1.751. Dimesionado Vc = 16.79 kgf/cm2
- COMB. 1: CM + CV fa = 78.21 kgf/cm2PD 70.00 tnf Vc = 15.94 kgf/cm2PL 50.00 tnfPpzap. 7.20 tnf A2 = 57856 cm2P 127.20 tnf A1 = 2800 cm2qadm 30.00 tnf/m2 qu = 4.76 kgf/cm2
58.96 = 4.55Az= P/qadm 3504.57Az= 4.24 m2 -205669.57 f = 2
d = 36.40 cmL*B= 4.24 m2 d = -95.84 fa ≤ 249.9 kgf/cm2
B= 1.81 m OKL= 2.35 m CORTE:
B (m) L (m) Area (m2)2.00 2.30 4.60
Vc = 7.68 kgf/cm2- COMB. 2: CM + CV + CS
PD 70.00 tnfPL 50.00 tnfPpzap. 7.20 tnf d1 = 42.75 cmPS servicio 48.00 d2 = 42.75 cmP 175.20 tnf d = 42.75 cm
qadm = 39 tnf/m2 d minimo:qact = P/Az 41.32 tnf/m2
REVISAR d = 30 cm39 ≤ 41.32
- COMB. 3: CM + CV - CS
P 79.20 tnf
qadm = 39 tnf/m2qact = P/Az 18.68 tnf/m2
OK39 ≥ 18.68
qadm ≥ qact
qadm ≥ qact
𝑉𝑐=(0.53+1.1/𝐵𝑐)∗√(𝑓^′ 𝑐); 𝐵𝑐= 𝑡/𝑏
𝑉𝑐=1.1∗√(𝑓^′ 𝑐)𝑞𝑢=(𝑃𝑢 )/(𝐵 𝑥 𝐿)
𝑑^2 (4Ø𝑉𝑐+𝑞𝑢)+𝑑(𝑏+𝑡)(2Ø𝑉𝑐+𝑞𝑢)−𝑞𝑢(𝐵×𝐿−𝑏×𝑡)=0 𝑎𝑏𝑐
𝑉𝑐=0.53∗√(𝑓^′ 𝑐)𝑑1=(𝑞𝑢(𝐿−𝑡) )/(2(0.85×𝑉𝑐+𝑞𝑢))𝑑2=(𝑞𝑢(𝐵−𝑏) )/(2(0.85×𝑉𝑐+𝑞𝑢))
𝑓𝑎=𝑃𝑢/𝐴1
√(𝐴2/𝐴1)≤2𝐴2=(𝑏+4×(ℎ−8.5))(𝑡+4×(ℎ−8.5))
𝑓𝑎≤0.7×0.85×𝑓^′ 𝑐×𝑓
ZAPATA Z-8 2. Peralte de zapata ANCLAJE:DATOS:
PD (tnf) = 100.00 Pu=1.4(PD)+1.7(PL) = 296.16 tnf ldg = 41.51 cmPL (tnf) = 80.00 Pu=1.25(PD+PL)+PS = 293 tnf d1 = 46.85 cmPS (tnf) = 50.00 Pu=1.25(PD+PL)-PS = 198.832 tnf d2 = 55.22 cmb (cm) = 40.00 Pu=0.9(PD)+PS = 152.96 tnf d3 = 30.00 cmt (cm) = 70.00 Pu=0.9(PD)-PS = 52.96 tnf d4 = 41.51 cm
f'c (kgf/cm2) = 210.00 Pu = 296.16 tnf d = 55.22 cmqadm (kgf/cm2) = 2.50Ø columna (pulg) = 3/4 PUNZONAMIENTO: d h = 65.22 cmL/B = 1.30 h = 70.00 cm%P-> PP 8%PS servicio 40.00 3. Aplastamiento
Bc = 1.751. Dimesionado Vc = 16.79 kgf/cm2
- COMB. 1: CM + CV fa = 105.77 kgf/cm2PD 100.00 tnf Vc = 15.94 kgf/cm2PL 80.00 tnfPpzap. 14.40 tnf A2 = 90376 cm2P 194.40 tnf A1 = 2800 cm2qadm 25.00 tnf/m2 qu = 3.70 kgf/cm2
57.90 = 5.68Az= P/qadm 3388.10Az= 7.78 m2 -285794.40 f = 2
d = 46.85 cmL*B= 7.78 m2 d = -105.36 fa ≤ 249.9 kgf/cm2
B= 2.45 m OKL= 3.18 m CORTE:
B (m) L (m) Area (m2)2.50 3.20 8.00
Vc = 7.68 kgf/cm2- COMB. 2: CM + CV + CS
PD 100.00 tnfPL 80.00 tnfPpzap. 14.40 tnf d1 = 55.22 cmPS servicio 40.00 d2 = 46.39 cmP 234.40 tnf d = 55.22 cm
qadm = 32.5 tnf/m2 d minimo:qact = P/Az 30.14 tnf/m2
OK d = 30 cm32.5 ≥ 30.14
- COMB. 3: CM + CV - CS
P 154.40 tnf
qadm = 32.5 tnf/m2qact = P/Az 19.86 tnf/m2
OK32.5 ≥ 19.86
qadm ≥ qact
qadm ≥ qact
𝑉𝑐=(0.53+1.1/𝐵𝑐)∗√(𝑓^′ 𝑐); 𝐵𝑐= 𝑡/𝑏
𝑉𝑐=1.1∗√(𝑓^′ 𝑐)𝑞𝑢=(𝑃𝑢 )/(𝐵 𝑥 𝐿)
𝑑^2 (4Ø𝑉𝑐+𝑞𝑢)+𝑑(𝑏+𝑡)(2Ø𝑉𝑐+𝑞𝑢)−𝑞𝑢(𝐵×𝐿−𝑏×𝑡)=0 𝑎𝑏𝑐
𝑉𝑐=0.53∗√(𝑓^′ 𝑐)𝑑1=(𝑞𝑢(𝐿−𝑡) )/(2(0.85×𝑉𝑐+𝑞𝑢))𝑑2=(𝑞𝑢(𝐵−𝑏) )/(2(0.85×𝑉𝑐+𝑞𝑢))
𝑓𝑎=𝑃𝑢/𝐴1
√(𝐴2/𝐴1)≤2𝐴2=(𝑏+4×(ℎ−8.5))(𝑡+4×(ℎ−8.5))
𝑓𝑎≤0.7×0.85×𝑓^′ 𝑐×𝑓
ZAPATA Z-9 2. Peralte de zapata ANCLAJE:DATOS:
PD (tnf) = 80.00 Pu=1.4(PD)+1.7(PL) = 265.92 tnf ldg = 41.51 cmPL (tnf) = 80.00 Pu=1.25(PD+PL)+PS = 276 tnf d1 = 45.19 cmPS (tnf) = 60.00 Pu=1.25(PD+PL)-PS = 161.184 tnf d2 = 52.10 cmb (cm) = 40.00 Pu=0.9(PD)+PS = 143.52 tnf d3 = 30.00 cmt (cm) = 70.00 Pu=0.9(PD)-PS = 23.52 tnf d4 = 41.51 cm
f'c (kgf/cm2) = 210.00 Pu = 276.00 tnf d = 52.10 cmqadm (kgf/cm2) = 2.00Ø columna (pulg) = 3/4 PUNZONAMIENTO: d h = 62.10 cmL/B = 1.30 h = 65.00 cm%P-> PP 8%PS servicio 48.00 3. Aplastamiento
Bc = 1.751. Dimesionado Vc = 16.79 kgf/cm2
- COMB. 1: CM + CV fa = 98.57 kgf/cm2PD 80.00 tnf Vc = 15.94 kgf/cm2PL 80.00 tnfPpzap. 12.80 tnf A2 = 78736 cm2P 172.80 tnf A1 = 2800 cm2qadm 20.00 tnf/m2 qu = 3.12 kgf/cm2
57.32 = 5.30Az= P/qadm 3324.32Az= 8.64 m2 -267257.92 f = 2
d = 45.19 cmL*B= 8.64 m2 d = -103.18 fa ≤ 249.9 kgf/cm2
B= 2.58 m OKL= 3.35 m CORTE:
B (m) L (m) Area (m2)2.60 3.40 8.84
Vc = 7.68 kgf/cm2- COMB. 2: CM + CV + CS
PD 80.00 tnfPL 80.00 tnfPpzap. 12.80 tnf d1 = 52.10 cmPS servicio 48.00 d2 = 42.46 cmP 220.80 tnf d = 52.10 cm
qadm = 26 tnf/m2 d minimo:qact = P/Az 25.56 tnf/m2
OK d = 30 cm26 ≥ 25.56
- COMB. 3: CM + CV - CS
P 124.80 tnf
qadm = 26 tnf/m2qact = P/Az 14.44 tnf/m2
OK26 ≥ 14.44
qadm ≥ qact
qadm ≥ qact
𝑉𝑐=(0.53+1.1/𝐵𝑐)∗√(𝑓^′ 𝑐); 𝐵𝑐= 𝑡/𝑏
𝑉𝑐=1.1∗√(𝑓^′ 𝑐)𝑞𝑢=(𝑃𝑢 )/(𝐵 𝑥 𝐿)
𝑑^2 (4Ø𝑉𝑐+𝑞𝑢)+𝑑(𝑏+𝑡)(2Ø𝑉𝑐+𝑞𝑢)−𝑞𝑢(𝐵×𝐿−𝑏×𝑡)=0 𝑎𝑏𝑐
𝑉𝑐=0.53∗√(𝑓^′ 𝑐)𝑑1=(𝑞𝑢(𝐿−𝑡) )/(2(0.85×𝑉𝑐+𝑞𝑢))𝑑2=(𝑞𝑢(𝐵−𝑏) )/(2(0.85×𝑉𝑐+𝑞𝑢))
𝑓𝑎=𝑃𝑢/𝐴1
√(𝐴2/𝐴1)≤2𝐴2=(𝑏+4×(ℎ−8.5))(𝑡+4×(ℎ−8.5))
𝑓𝑎≤0.7×0.85×𝑓^′ 𝑐×𝑓
ZAPATA Z-10 2. Peralte de zapata ANCLAJE:DATOS:
PD (tnf) = 140.00 Pu=1.4(PD)+1.7(PL) = 386.16 tnf ldg = 47.93 cmPL (tnf) = 100.00 Pu=1.25(PD+PL)+PS = 358 tnf d1 = 39.08 cmPS (tnf) = 40.00 Pu=1.25(PD+PL)-PS = 285.632 tnf d2 = 54.88 cmb (cm) = 60.00 Pu=0.9(PD)+PS = 178.96 tnf d3 = 30.00 cmt (cm) = 120.00 Pu=0.9(PD)-PS = 98.96 tnf d4 = 47.93 cm
f'c (kgf/cm2) = 280.00 Pu = 386.16 tnf d = 54.88 cmqadm (kgf/cm2) = 3.00Ø columna (pulg) = 1 PUNZONAMIENTO: d h = 64.88 cmL/B = 1.50 h = 65.00 cm%P-> PP 6%PS servicio 32.00 3. Aplastamiento
Bc = 2.001. Dimesionado Vc = 18.07 kgf/cm2
- COMB. 1: CM + CV fa = 53.63 kgf/cm2PD 140.00 tnf Vc = 18.41 kgf/cm2PL 100.00 tnfPpzap. 14.40 tnf A2 = 98956 cm2P 254.40 tnf A1 = 7200 cm2qadm 30.00 tnf/m2 qu = 4.47 kgf/cm2
67.05 = 3.71Az= P/qadm 6436.90Az= 8.48 m2 -353980.00 f = 2
d = 39.08 cmL*B= 8.48 m2 d = -135.08 fa ≤ 333.2 kgf/cm2
B= 2.38 m OKL= 3.57 m CORTE:
B (m) L (m) Area (m2)2.40 3.60 8.64
Vc = 8.87 kgf/cm2- COMB. 2: CM + CV + CS
PD 140.00 tnfPL 100.00 tnfPpzap. 14.40 tnf d1 = 54.88 cmPS servicio 32.00 d2 = 41.16 cmP 286.40 tnf d = 54.88 cm
qadm = 39 tnf/m2 d minimo:qact = P/Az 33.77 tnf/m2
OK d = 30 cm39 ≥ 33.77
- COMB. 3: CM + CV - CS
P 222.40 tnf
qadm = 39 tnf/m2qact = P/Az 26.23 tnf/m2
OK39 ≥ 26.23
qadm ≥ qact
qadm ≥ qact
𝑉𝑐=(0.53+1.1/𝐵𝑐)∗√(𝑓^′ 𝑐); 𝐵𝑐= 𝑡/𝑏
𝑉𝑐=1.1∗√(𝑓^′ 𝑐)𝑞𝑢=(𝑃𝑢 )/(𝐵 𝑥 𝐿)
𝑑^2 (4Ø𝑉𝑐+𝑞𝑢)+𝑑(𝑏+𝑡)(2Ø𝑉𝑐+𝑞𝑢)−𝑞𝑢(𝐵×𝐿−𝑏×𝑡)=0 𝑎𝑏𝑐
𝑉𝑐=0.53∗√(𝑓^′ 𝑐)𝑑1=(𝑞𝑢(𝐿−𝑡) )/(2(0.85×𝑉𝑐+𝑞𝑢))𝑑2=(𝑞𝑢(𝐵−𝑏) )/(2(0.85×𝑉𝑐+𝑞𝑢))
𝑓𝑎=𝑃𝑢/𝐴1
√(𝐴2/𝐴1)≤2𝐴2=(𝑏+4×(ℎ−8.5))(𝑡+4×(ℎ−8.5))
𝑓𝑎≤0.7×0.85×𝑓^′ 𝑐×𝑓
ZAPATA Z-11 2. Peralte de zapata ANCLAJE:DATOS:
PD (tnf) = 100.00 Pu=1.4(PD)+1.7(PL) = 273.28 tnf ldg = 55.35 cmPL (tnf) = 70.00 Pu=1.25(PD+PL)+PS = 255.25 tnf d1 = 41.65 cmPS (tnf) = 30.00 Pu=1.25(PD+PL)-PS = 200.656 tnf d2 = 58.05 cmb (cm) = 40.00 Pu=0.9(PD)+PS = 129.18 tnf d3 = 30.00 cmt (cm) = 80.00 Pu=0.9(PD)-PS = 69.18 tnf d4 = 55.35 cm
f'c (kgf/cm2) = 210.00 Pu = 273.28 tnf d = 58.05 cmqadm (kgf/cm2) = 3.00Ø columna (pulg) = 1 PUNZONAMIENTO: d h = 68.05 cmL/B = 1.50 h = 70.00 cm%P-> PP 6%PS servicio 24.00 3. Aplastamiento
Bc = 2.001. Dimesionado Vc = 15.65 kgf/cm2
- COMB. 1: CM + CV fa = 85.40 kgf/cm2PD 100.00 tnf Vc = 15.94 kgf/cm2PL 70.00 tnfPpzap. 10.20 tnf A2 = 93236 cm2P 180.20 tnf A1 = 3200 cm2qadm 30.00 tnf/m2 qu = 4.41 kgf/cm2
58.61 = 5.40Az= P/qadm 3780.79Az= 6.01 m2 -259175.23 f = 2
d = 41.65 cmL*B= 6.01 m2 d = -106.17 fa ≤ 249.9 kgf/cm2
B= 2.00 m OKL= 3.00 m CORTE:
B (m) L (m) Area (m2)2.00 3.10 6.20
Vc = 7.68 kgf/cm2- COMB. 2: CM + CV + CS
PD 100.00 tnfPL 70.00 tnfPpzap. 10.20 tnf d1 = 58.05 cmPS servicio 24.00 d2 = 40.38 cmP 204.20 tnf d = 58.05 cm
qadm = 39 tnf/m2 d minimo:qact = P/Az 34.00 tnf/m2
OK d = 30 cm39 ≥ 34.00
- COMB. 3: CM + CV - CS
P 156.20 tnf
qadm = 39 tnf/m2qact = P/Az 26.00 tnf/m2
OK39 ≥ 26.00
qadm ≥ qact
qadm ≥ qact
𝑉𝑐=(0.53+1.1/𝐵𝑐)∗√(𝑓^′ 𝑐); 𝐵𝑐= 𝑡/𝑏
𝑉𝑐=1.1∗√(𝑓^′ 𝑐)𝑞𝑢=(𝑃𝑢 )/(𝐵 𝑥 𝐿)
𝑑^2 (4Ø𝑉𝑐+𝑞𝑢)+𝑑(𝑏+𝑡)(2Ø𝑉𝑐+𝑞𝑢)−𝑞𝑢(𝐵×𝐿−𝑏×𝑡)=0 𝑎𝑏𝑐
𝑉𝑐=0.53∗√(𝑓^′ 𝑐)𝑑1=(𝑞𝑢(𝐿−𝑡) )/(2(0.85×𝑉𝑐+𝑞𝑢))𝑑2=(𝑞𝑢(𝐵−𝑏) )/(2(0.85×𝑉𝑐+𝑞𝑢))
𝑓𝑎=𝑃𝑢/𝐴1
√(𝐴2/𝐴1)≤2𝐴2=(𝑏+4×(ℎ−8.5))(𝑡+4×(ℎ−8.5))
𝑓𝑎≤0.7×0.85×𝑓^′ 𝑐×𝑓
ZAPATA Z-12 2. Peralte de zapata ANCLAJE:DATOS:
PD (tnf) = 80.00 Pu=1.4(PD)+1.7(PL) = 225.76 tnf ldg = 41.51 cmPL (tnf) = 60.00 Pu=1.25(PD+PL)+PS = 225.5 tnf d1 = 35.87 cmPS (tnf) = 40.00 Pu=1.25(PD+PL)-PS = 149.952 tnf d2 = 51.09 cmb (cm) = 40.00 Pu=0.9(PD)+PS = 119.56 tnf d3 = 30.00 cmt (cm) = 80.00 Pu=0.9(PD)-PS = 39.56 tnf d4 = 41.51 cm
f'c (kgf/cm2) = 210.00 Pu = 225.76 tnf d = 51.09 cmqadm (kgf/cm2) = 3.00Ø columna (pulg) = 3/4 PUNZONAMIENTO: d h = 61.09 cmL/B = 1.50 h = 65.00 cm%P-> PP 6%PS servicio 32.00 3. Aplastamiento
Bc = 2.001. Dimesionado Vc = 15.65 kgf/cm2
- COMB. 1: CM + CV fa = 70.55 kgf/cm2PD 80.00 tnf Vc = 15.94 kgf/cm2PL 60.00 tnfPpzap. 8.40 tnf A2 = 81396 cm2P 148.40 tnf A1 = 3200 cm2qadm 30.00 tnf/m2 qu = 4.48 kgf/cm2
58.68 = 5.04Az= P/qadm 3789.39Az= 4.95 m2 -211426.03 f = 2
d = 35.87 cmL*B= 4.95 m2 d = -100.45 fa ≤ 249.9 kgf/cm2
B= 1.82 m OKL= 2.72 m CORTE:
B (m) L (m) Area (m2)1.80 2.80 5.04
Vc = 7.68 kgf/cm2- COMB. 2: CM + CV + CS
PD 80.00 tnfPL 60.00 tnfPpzap. 8.40 tnf d1 = 51.09 cmPS servicio 32.00 d2 = 35.76 cmP 180.40 tnf d = 51.09 cm
qadm = 39 tnf/m2 d minimo:qact = P/Az 36.47 tnf/m2
OK d = 30 cm39 ≥ 36.47
- COMB. 3: CM + CV - CS
P 116.40 tnf
qadm = 39 tnf/m2qact = P/Az 23.53 tnf/m2
OK39 ≥ 23.53
qadm ≥ qact
qadm ≥ qact
𝑉𝑐=(0.53+1.1/𝐵𝑐)∗√(𝑓^′ 𝑐); 𝐵𝑐= 𝑡/𝑏
𝑉𝑐=1.1∗√(𝑓^′ 𝑐)𝑞𝑢=(𝑃𝑢 )/(𝐵 𝑥 𝐿)
𝑑^2 (4Ø𝑉𝑐+𝑞𝑢)+𝑑(𝑏+𝑡)(2Ø𝑉𝑐+𝑞𝑢)−𝑞𝑢(𝐵×𝐿−𝑏×𝑡)=0 𝑎𝑏𝑐
𝑉𝑐=0.53∗√(𝑓^′ 𝑐)𝑑1=(𝑞𝑢(𝐿−𝑡) )/(2(0.85×𝑉𝑐+𝑞𝑢))𝑑2=(𝑞𝑢(𝐵−𝑏) )/(2(0.85×𝑉𝑐+𝑞𝑢))
𝑓𝑎=𝑃𝑢/𝐴1
√(𝐴2/𝐴1)≤2𝐴2=(𝑏+4×(ℎ−8.5))(𝑡+4×(ℎ−8.5))
𝑓𝑎≤0.7×0.85×𝑓^′ 𝑐×𝑓
4. Acero 5. Dibujo
Para L: PLANTAL = 2.60 m f'c 210.00
fy 4200b 200.00 Ø 5/8 @ 0.2m
1.10 0.40 1.10 d 41.50ᶲ 0.9Mu ###
a As0 17.3255
2.03829 17.7617 2.00 m0.50 2.089606 17.7729
2.090932 17.7732qu = 22.46 tnf/m2
2.60
Ø 5/8 @ 0.2mR = 49.42 tnf d = 41.50 cm
brazo = 0.55 m b = 200.00 cmMu = 27.18 tnf.m 2.60 mAs = 17.77 cm2
As min = 18.00 cm2Ø varilla = 5/8 1.98 cm2 CORTE
S = 0.22 cmØ 5/8 @ 0.20 m
Para B:B = 2.00 m f'c 210.00
fy 4200b 260.00
0.85 0.30 0.85 d 41.50ᶲ 0.9Mu ###
a As0 13.4487
1.217078 13.64890.50 1.235191 13.6519
1.235464 13.6519qu = 22.46 tnf/m2
2.00 Ø 5/8 @ 0.2m Ø 5/8 @ 0.2m
R = 49.64 tnf d = 41.50 cm 2.60 mbrazo = 0.43 m b = 260.00 cm
Mu = 21.10 tnf.mAs = 13.65 cm2
As min = 23.40 cm2Ø varilla = 5/8 1.98 cm2
S = 0.22 cm
𝑅=𝑞𝑢×((𝐿−𝑡)/2)×𝐵
𝑅=𝑞𝑢×((𝐵−𝑡)/2)×L
Ø 5/8 @ 0.20 m
4. Acero 5. Dibujo
Para L: PLANTAL = 2.50 m f'c 210.00
fy 4200b 200.00 Ø 3/4 @ 0.25m
1.05 0.40 1.05 d 46.50ᶲ 0.9Mu ###
a As0 18.5763
2.185452 19.0234 2.00 m0.55 2.238045 19.0344
2.239342 19.0347qu = 29.62 tnf/m2
2.50
Ø 3/4 @ 0.25mR = 62.19 tnf d = 46.50 cm
brazo = 0.53 m b = 200.00 cmMu = 32.65 tnf.m 2.50 mAs = 19.03 cm2
As min = 19.80 cm2Ø varilla = 3/4 2.85 cm2 CORTE
S = 0.29 cmØ 3/4 @ 0.25 m
Para B:B = 2.00 m f'c 210.00
fy 4200b 250.00
0.85 0.30 0.85 d 46.50ᶲ 0.9Mu ###
a As0 15.217
1.43219 15.4550.55 1.45459 15.4588
1.454946 15.4589qu = 29.62 tnf/m2
2.00 Ø 3/4 @ 0.25m Ø 3/4 @ 0.25m
R = 62.93 tnf d = 46.50 cm 2.50 mbrazo = 0.43 m b = 250.00 cm
Mu = 26.75 tnf.mAs = 15.46 cm2
As min = 24.75 cm2Ø varilla = 3/4 2.85 cm2
S = 0.29 cm
𝑅=𝑞𝑢×((𝐿−𝑡)/2)×𝐵
𝑅=𝑞𝑢×((𝐵−𝑡)/2)×L
𝑅=𝑞𝑢×((𝐿−𝑡)/2)×𝐵
𝑅=𝑞𝑢×((𝐵−𝑡)/2)×L
Ø 3/4 @ 0.25 m
4. Acero 5. Dibujo
Para L: PLANTAL = 2.60 m f'c 210.00
fy 4200b 200.00 Ø 3/4 @ 0.2m
1.10 0.40 1.10 d 61.50ᶲ 0.9Mu ###
a As0 19.6628
2.313269 20.0397 2.00 m0.70 2.357609 20.047
2.358475 20.0472qu = 37.78 tnf/m2
2.60
Ø 3/4 @ 0.2mR = 83.11 tnf d = 61.50 cm
brazo = 0.55 m b = 200.00 cmMu = 45.71 tnf.m 2.60 mAs = 20.05 cm2
As min = 25.20 cm2Ø varilla = 3/4 2.85 cm2 CORTE
S = 0.23 cmØ 3/4 @ 0.20 m
Para B:B = 2.00 m f'c 210.00
fy 4200b 260.00
0.85 0.30 0.85 d 61.50ᶲ 0.9Mu ###
a As0 15.263
1.38127 15.43640.70 1.396958 15.4384
1.397138 15.4384qu = 37.78 tnf/m2
2.00 Ø 3/4 @ 0.2m Ø 3/4 @ 0.2m
R = 83.49 tnf d = 61.50 cm 2.60 mbrazo = 0.43 m b = 260.00 cm
Mu = 35.48 tnf.mAs = 15.44 cm2
As min = 32.76 cm2Ø varilla = 3/4 2.85 cm2
S = 0.23 cm
𝑅=𝑞𝑢×((𝐿−𝑡)/2)×𝐵
𝑅=𝑞𝑢×((𝐵−𝑡)/2)×L
Ø 3/4 @ 0.20 m
4. Acero 5. Dibujo
Para L: PLANTAL = 3.60 m f'c 280.00
fy 4200b 260.00 Ø 1/1 @ 0.3m
1.40 0.80 1.40 d 51.50ᶲ 0.9Mu ###
a As0 38.8805
2.638948 39.9028 2.60 m0.60 2.708338 39.9305
2.710212 39.9312qu = 29.71 tnf/m2
3.60
Ø 1/1 @ 0.45mR = 108.13 tnf d = 51.50 cm
brazo = 0.70 m b = 260.00 cmMu = 75.69 tnf.m 3.60 mAs = 39.93 cm2
As min = 28.08 cm2Ø varilla = 1 5.07 cm2 CORTE
S = 0.33 cmØ 1 @ 0.30 m
Para B:B = 2.60 m f'c 280.00
fy 4200b 360.00
1.05 0.50 1.05 d 51.50ᶲ 0.9Mu ###
a As0 30.2819
1.484408 30.72470.60 1.506114 30.7313
1.506436 30.7314qu = 29.71 tnf/m2
2.60 Ø 1/1 @ 0.45m Ø 1/1 @ 0.3m
R = 112.29 tnf d = 51.50 cm 3.60 mbrazo = 0.53 m b = 360.00 cm
Mu = 58.95 tnf.mAs = 30.73 cm2
As min = 38.88 cm2Ø varilla = 1 5.07 cm2
S = 0.47 cm
𝑅=𝑞𝑢×((𝐿−𝑡)/2)×𝐵
𝑅=𝑞𝑢×((𝐵−𝑡)/2)×L
Ø 1 @ 0.45 m
4. Acero 5. Dibujo
Para L: PLANTAL = 3.00 m f'c 175.00
fy 4200b 220.00 Ø 3/4 @ 0.25m
1.20 0.60 1.20 d 51.50ᶲ 0.9Mu ###
a As0 24.2182
3.10822 24.9718 2.20 m0.60 3.204935 24.996
3.208041 24.9968qu = 29.76 tnf/m2
3.00
Ø 3/4 @ 0.25mR = 78.58 tnf d = 51.50 cm
brazo = 0.60 m b = 220.00 cmMu = 47.15 tnf.m 3.00 mAs = 25.00 cm2
As min = 23.76 cm2Ø varilla = 3/4 2.85 cm2 CORTE
S = 0.25 cmØ 3/4 @ 0.25 m
Para B:B = 2.20 m f'c 175.00
fy 4200b 300.00
0.90 0.40 0.90 d 51.50ᶲ 0.9Mu ###
a As0 18.5765
1.748374 18.89720.60 1.778564 18.9029
1.779095 18.903qu = 29.76 tnf/m2
2.20 Ø 3/4 @ 0.25m Ø 3/4 @ 0.25m
R = 80.36 tnf d = 51.50 cm 3.00 mbrazo = 0.45 m b = 300.00 cm
Mu = 36.16 tnf.mAs = 18.90 cm2
As min = 32.40 cm2Ø varilla = 3/4 2.85 cm2
S = 0.26 cm
𝑅=𝑞𝑢×((𝐿−𝑡)/2)×𝐵
𝑅=𝑞𝑢×((𝐵−𝑡)/2)×L
Ø 3/4 @ 0.25 m
4. Acero 5. Dibujo
Para L: PLANTAL = 3.85 m f'c 175.00
fy 4200b 270.00 Ø 1/1 @ 0.35m
1.63 0.60 1.63 d 56.50ᶲ 0.9Mu ###
a As0 37.5101
3.922628 38.8591 2.70 m0.65 4.063693 38.9094
4.068956 38.9113qu = 22.47 tnf/m2
3.85
Ø 3/4 @ 0.2mR = 98.60 tnf d = 56.50 cm
brazo = 0.81 m b = 270.00 cmMu = 80.11 tnf.m 3.85 mAs = 38.91 cm2
As min = 31.59 cm2Ø varilla = 1 5.07 cm2 CORTE
S = 0.35 cmØ 1 @ 0.35 m
Para B:B = 2.70 m f'c 175.00
fy 4200b 385.00
1.15 0.40 1.15 d 56.50ᶲ 0.9Mu ###
a As0 26.7876
1.964564 27.26160.65 1.999323 27.2701
1.999949 27.2703qu = 22.47 tnf/m2
2.70 Ø 3/4 @ 0.2m Ø 1/1 @ 0.35m
R = 99.50 tnf d = 56.50 cm 3.85 mbrazo = 0.58 m b = 385.00 cm
Mu = 57.21 tnf.mAs = 27.27 cm2
As min = 45.04 cm2Ø varilla = 3/4 2.85 cm2
S = 0.24 cm
𝑅=𝑞𝑢×((𝐿−𝑡)/2)×𝐵
𝑅=𝑞𝑢×((𝐵−𝑡)/2)×L
Ø 3/4 @ 0.20 m
4. Acero 5. Dibujo
Para L: PLANTAL = 2.30 m f'c 210.00
fy 4200b 200.00 Ø 3/4 @ 0.25m
0.80 0.70 0.80 d 46.50ᶲ 0.9Mu ###
a As0 17.3349
2.039401 17.7236 2.00 m0.55 2.085126 17.7325
2.086174 17.7327qu = 47.61 tnf/m2
2.30
Ø 3/4 @ 0.25mR = 76.17 tnf d = 46.50 cm
brazo = 0.40 m b = 200.00 cmMu = 30.47 tnf.m 2.30 mAs = 17.73 cm2
As min = 19.80 cm2Ø varilla = 3/4 2.85 cm2 CORTE
S = 0.29 cmØ 3/4 @ 0.25 m
Para B:B = 2.00 m f'c 210.00
fy 4200b 230.00
0.80 0.40 0.80 d 46.50ᶲ 0.9Mu ###
a As0 19.9351
2.039401 20.38210.55 2.085126 20.3924
2.086174 20.3926qu = 47.61 tnf/m2
2.00 Ø 3/4 @ 0.25m Ø 3/4 @ 0.25m
R = 87.60 tnf d = 46.50 cm 2.30 mbrazo = 0.40 m b = 230.00 cm
Mu = 35.04 tnf.mAs = 20.39 cm2
As min = 22.77 cm2Ø varilla = 3/4 2.85 cm2
S = 0.29 cm
𝑅=𝑞𝑢×((𝐿−𝑡)/2)×𝐵
𝑅=𝑞𝑢×((𝐵−𝑡)/2)×L
Ø 3/4 @ 0.25 m
4. Acero 5. Dibujo
Para L: PLANTAL = 3.20 m f'c 210.00
fy 4200b 250.00 Ø 3/4 @ 0.2m
1.25 0.70 1.25 d 61.50ᶲ 0.9Mu ###
a As0 31.1028
2.927323 31.8611 2.50 m0.70 2.99869 31.88
3.000473 31.8805qu = 37.02 tnf/m2
3.20
Ø 3/4 @ 0.2mR = 115.69 tnf d = 61.50 cm
brazo = 0.63 m b = 250.00 cmMu = 72.30 tnf.m 3.20 mAs = 31.88 cm2
As min = 31.50 cm2Ø varilla = 3/4 2.85 cm2 CORTE
S = 0.22 cmØ 3/4 @ 0.20 m
Para B:B = 2.50 m f'c 210.00
fy 4200b 320.00
1.05 0.40 1.05 d 61.50ᶲ 0.9Mu ###
a As0 28.0911
2.065519 28.57080.70 2.100797 28.5792
2.10141 28.5793qu = 37.02 tnf/m2
2.50 Ø 3/4 @ 0.2m Ø 3/4 @ 0.2m
R = 124.39 tnf d = 61.50 cm 3.20 mbrazo = 0.53 m b = 320.00 cm
Mu = 65.30 tnf.mAs = 28.58 cm2
As min = 40.32 cm2Ø varilla = 3/4 2.85 cm2
S = 0.23 cm
𝑅=𝑞𝑢×((𝐿−𝑡)/2)×𝐵
𝑅=𝑞𝑢×((𝐵−𝑡)/2)×L
Ø 3/4 @ 0.20 m
4. Acero 5. Dibujo
Para L: PLANTAL = 3.40 m f'c 210.00
fy 4200b 260.00 Ø 3/4 @ 0.2m
1.35 0.70 1.35 d 56.50ᶲ 0.9Mu ###
a As0 34.636
3.134478 35.6241 2.60 m0.65 3.223905 35.6532
3.226531 35.654qu = 31.22 tnf/m2
3.40
Ø 3/4 @ 0.2mR = 109.59 tnf d = 56.50 cm
brazo = 0.67 m b = 260.00 cmMu = 73.97 tnf.m 3.40 mAs = 35.65 cm2
As min = 30.42 cm2Ø varilla = 3/4 2.85 cm2 CORTE
S = 0.21 cmØ 3/4 @ 0.20 m
Para B:B = 2.60 m f'c 210.00
fy 4200b 340.00
1.10 0.40 1.10 d 56.50ᶲ 0.9Mu ###
a As0 30.0712
2.081052 30.63540.65 2.120097 30.6462
2.120843 30.6464qu = 31.22 tnf/m2
2.60 Ø 3/4 @ 0.2m Ø 3/4 @ 0.2m
R = 116.77 tnf d = 56.50 cm 3.40 mbrazo = 0.55 m b = 340.00 cm
Mu = 64.22 tnf.mAs = 30.65 cm2
As min = 39.78 cm2Ø varilla = 3/4 2.85 cm2
S = 0.24 cm
𝑅=𝑞𝑢×((𝐿−𝑡)/2)×𝐵
𝑅=𝑞𝑢×((𝐵−𝑡)/2)×L
Ø 3/4 @ 0.20 m
4. Acero 5. Dibujo
Para L: PLANTAL = 3.60 m f'c 280.00
fy 4200b 240.00 Ø 1/1 @ 0.3m
1.20 1.20 1.20 d 56.50ᶲ 0.9Mu ###
a As0 36.1624
2.658999 37.0338 2.40 m0.65 2.723075 37.0553
2.724658 37.0559qu = 44.69 tnf/m2
3.60
Ø 3/4 @ 0.2mR = 128.72 tnf d = 56.50 cm
brazo = 0.60 m b = 240.00 cmMu = 77.23 tnf.m 3.60 mAs = 37.06 cm2
As min = 28.08 cm2Ø varilla = 1 5.07 cm2 CORTE
S = 0.33 cmØ 1 @ 0.30 m
Para B:B = 2.40 m f'c 280.00
fy 4200b 360.00
0.90 0.60 0.90 d 56.50ᶲ 0.9Mu ###
a As0 30.512
1.495687 30.92130.65 1.515749 30.9269
1.516022 30.9269qu = 44.69 tnf/m2
2.40 Ø 3/4 @ 0.2m Ø 1/1 @ 0.3m
R = 144.81 tnf d = 56.50 cm 3.60 mbrazo = 0.45 m b = 360.00 cm
Mu = 65.16 tnf.mAs = 30.93 cm2
As min = 42.12 cm2Ø varilla = 3/4 2.85 cm2
S = 0.24 cm
𝑅=𝑞𝑢×((𝐿−𝑡)/2)×𝐵
𝑅=𝑞𝑢×((𝐵−𝑡)/2)×L
Ø 3/4 @ 0.20 m
4. Acero 5. Dibujo
Para L: PLANTAL = 3.10 m f'c 210.00
fy 4200b 200.00 Ø 3/4 @ 0.2m
1.15 0.80 1.15 d 61.50ᶲ 0.9Mu ###
a As0 25.0752
2.950027 25.6914 2.00 m0.70 3.022519 25.7069
3.024345 25.7073qu = 44.08 tnf/m2
3.10
Ø 3/4 @ 0.2mR = 101.38 tnf d = 61.50 cm
brazo = 0.58 m b = 200.00 cmMu = 58.29 tnf.m 3.10 mAs = 25.71 cm2
As min = 25.20 cm2Ø varilla = 3/4 2.85 cm2 CORTE
S = 0.22 cmØ 3/4 @ 0.20 m
Para B:B = 2.00 m f'c 210.00
fy 4200b 310.00
0.80 0.40 0.80 d 61.50ᶲ 0.9Mu ###
a As0 18.8088
1.427612 19.02970.70 1.444377 19.0323
1.444576 19.0323qu = 44.08 tnf/m2
2.00 Ø 3/4 @ 0.2m Ø 3/4 @ 0.2m
R = 109.31 tnf d = 61.50 cm 3.10 mbrazo = 0.40 m b = 310.00 cm
Mu = 43.72 tnf.mAs = 19.03 cm2
As min = 39.06 cm2Ø varilla = 3/4 2.85 cm2
S = 0.23 cm
𝑅=𝑞𝑢×((𝐿−𝑡)/2)×𝐵
𝑅=𝑞𝑢×((𝐵−𝑡)/2)×L
Ø 3/4 @ 0.20 m
4. Acero 5. Dibujo
Para L: PLANTAL = 2.80 m f'c 210.00
fy 4200b 180.00 Ø 3/4 @ 0.2m
1.00 0.80 1.00 d 56.50ᶲ 0.9Mu ###
a As0 18.8764
2.467501 19.2978 1.80 m0.65 2.522585 19.3074
2.523842 19.3076qu = 44.79 tnf/m2
2.80
Ø 3/4 @ 0.2mR = 80.63 tnf d = 56.50 cm
brazo = 0.50 m b = 180.00 cmMu = 40.31 tnf.m 2.80 mAs = 19.31 cm2
As min = 21.06 cm2Ø varilla = 3/4 2.85 cm2 CORTE
S = 0.24 cmØ 3/4 @ 0.20 m
Para B:B = 1.80 m f'c 210.00
fy 4200b 280.00
0.70 0.40 0.70 d 56.50ᶲ 0.9Mu ###
a As0 14.388
1.209075 14.54360.65 1.222152 14.5453
1.222295 14.5453qu = 44.79 tnf/m2
1.80 Ø 3/4 @ 0.2m Ø 3/4 @ 0.2m
R = 87.80 tnf d = 56.50 cm 2.80 mbrazo = 0.35 m b = 280.00 cm
Mu = 30.73 tnf.mAs = 14.55 cm2
As min = 32.76 cm2Ø varilla = 3/4 2.85 cm2
S = 0.24 cm
𝑅=𝑞𝑢×((𝐿−𝑡)/2)×𝐵
𝑅=𝑞𝑢×((𝐵−𝑡)/2)×L
Ø 3/4 @ 0.20 m
1.
%P
4 4%3 6%2 8%1 10%
2. DETALLES DE REFUERZO LdgDATOS:f'c = 175 kgf/cm2 17.17 Mpafy = 4200 kgf/cm2 412.17 MpaFactor 1 = 99.46
db (cm) db (mm) Ldg 1 (cm) Ldg 2 (cm) Ldg 3 (cm) Ldg (cm)
1/4 0.6350 6.350 15.16 5.08 15.00 15.00 3/8 0.9525 9.525 22.74 7.62 15.00 22.74 1/2 1.2700 12.700 30.32 10.16 15.00 30.32 5/8 1.5875 15.875 37.89 12.70 15.00 37.89 3/4 1.9050 19.050 45.47 15.24 15.00 45.47
1 2.5400 25.400 60.63 20.32 15.00 60.63
DATOS:f'c = 210 kgf/cm2 20.61 Mpafy = 4200 kgf/cm2 412.17 MpaFactor 1 = 90.79
db (cm) db (mm) Ldg 1 (cm) Ldg 2 (cm) Ldg 3 (cm) Ldg (cm)
1/4 0.6350 6.350 13.84 5.08 15.00 15.00 3/8 0.9525 9.525 20.76 7.62 15.00 20.76 1/2 1.2700 12.700 27.67 10.16 15.00 27.67 5/8 1.5875 15.875 34.59 12.70 15.00 34.59 3/4 1.9050 19.050 41.51 15.24 15.00 41.51
1 2.5400 25.400 55.35 20.32 15.00 55.35
DATOS:f'c = 280 kgf/cm2 27.48 Mpafy = 4200 kgf/cm2 412.17 MpaFactor 1 = 78.63
db (cm) db (mm) Ldg 1 (cm) Ldg 2 (cm) Ldg 3 (cm) Ldg (cm)
1/4 0.6350 6.350 11.98 5.08 15.00 15.00 3/8 0.9525 9.525 17.97 7.62 15.00 17.97
qadm (kgf/cm2)
DIAMETRO pulgadas
DIAMETRO pulgadas
DIAMETRO pulgadas
1/2 1.2700 12.700 23.97 10.16 15.00 23.97 5/8 1.5875 15.875 29.96 12.70 15.00 29.96 3/4 1.9050 19.050 35.95 15.24 15.00 35.95
1 2.5400 25.400 47.93 20.32 15.00 47.93
2.CARACTERÍSTICAS DEL ACERO
N° (DE 1/8) ᶲ (pulg.) Peso (kgf/m)
2 1/4 0.320 0.253 3/8 0.710 0.564 1/2 1.270 15 5/8 1.980 1.556 3/4 2.850 2.248 1 5.07 4
11 1 - 3/8 9.58 7.52
Area (cm2)
![07. Zapatas Aisladas[1]](https://static.fdocuments.es/doc/165x107/5571fbf84979599169963552/07-zapatas-aisladas1.jpg?t=1685791979)
