Peralte efectivo cuantiad = 1.75b p = 0.50 pb

fy = 4200 kg/cm2f´c = 350 kg/cm2

CUANTIA BALANCEADA

B1= 0.8

Pb = 0.0333

CUANTIA

p = 0.0167

HALLANDO q

q = 0.20

HALLANDO K

0.20 0.200785817K = 0.177

HALLANDO LA BASE

𝜌=0.50𝜌_𝑏

13 tn.m 20 tn.m 18 tn.m 20 tn.m

13 tn.m 13 tn.m14 tn.m 14 tn.m

TRAMOS (APOYOS A Y E) TRAMOS (APOYOS B Y D) TRAMO (APOYO C)

b = 0.20 m b = 0.23 m b =b = 0.20 m b = 0.25 m b =

TRAMOS (A-B, D-E) TRAMOS (B-C, C-D)b = 0.20 m b = 0.20 mb = 0.20 m b = 0.20 m

HALLANDO EL PERALTE EFECTIVO b va a ser la base del momento mas altod = 1.75bd = 0.44 m

HALLANDO EL PERALTE peralte = d+6peralte = 50 cm

SOLUCION PARA HALLAR EL ACERO

13 tn.m 20 tn.m 18 tn.m 20 tn.m

13 tn.m 13 tn.m14 tn.m

A B C D

13 tn.m 20 tn.m 18 tn.m 20 tn.m

hallando K corregidod = 50 -6d = 44

TRAMOS (APOYOS A Y E) TRAMOS (APOYOS B Y D) TRAMO (APOYO C)k = 0.0853 k = 0.1312 k =

TRAMOS (A-B, D-E) TRAMOS (B-C, C-D)k = 0.0918 k = 0.0853

hallando q corregido

TRAMOS (APOYOS A Y E) TRAMOS (APOYOS B Y D) TRAMO (APOYO C)q = 0.0901 q = 0.1433 q =

TRAMOS (A-B, D-E) TRAMOS (B-C, C-D)q = 0.0974 q = 0.0901

hallando cuantia corregida

TRAMOS (APOYOS A Y E) TRAMOS (APOYOS B Y D) TRAMO (APOYO C)p = 0.0075 p = 0.0119 p =

TRAMOS (A-B, D-E) TRAMOS (B-C, C-D)p = 0.0081 p = 0.0075

cuantia minima

cuantia min = 0.0031

area de acero

13 tn.m 13 tn.m14 tn.m

A B C D

TRAMOS (APOYOS A Y E) TRAMOS (APOYOS B Y D) TRAMO (APOYO C)As = 9.38 cm2 As = 14.93 cm2 As =

TRAMOS (A-B, D-E) TRAMOS (B-C, C-D)As = 10.15 cm2 As = 9.38 cm2

area de acero minima area de acero maxima

As = 3.90 cm2 As = 20.83 cm2

area de acero corregida

TRAMOS (APOYOS A Y E) TRAMOS (APOYOS B Y D) TRAMO (APOYO C)As = 10.55 cm2 As = 16.10 cm2 As =

TRAMOS (A-B, D-E) TRAMOS (B-C, C-D)As = 11.32 cm2 As = 10.55 cm2

distribucion del acero

TRAMOS (APOYOS A Y E) TRAMOS (APOYOS B Y D) TRAMO (APOYO C)

varillas = varillas = varillas =

TRAMOS (A-B, D-E) TRAMOS (B-C, C-D)

varillas = varillas =

3 Ø 3/4"

2 Ø 3/4" 2 Ø 3/4" + 1 Ø 5/8"

2 Ø 5/8" 2 Ø 5/8"

3 Ø 3/4"

5 Ø 3/4" 5 Ø 3/4" + 1 Ø 5/8"

3 Ø 3/4" + 2 Ø 5/8" 3 Ø 3/4" + 2 Ø 5/8"

13 tn.m

14 tn.m

TRAMO (APOYO C)

0.22 m0.25 m

20 tn.m 13 tn.m

14 tn.m

E

20 tn.m 13 tn.m

0.50

0.25

TRAMO (APOYO C)0.1181

TRAMO (APOYO C)0.1277

TRAMO (APOYO C)0.0106

14 tn.m

D E

TRAMO (APOYO C)13.30 cm2

TRAMO (APOYO C)14.47 cm2

5 Ø 3/4"

3 Ø 3/4" + 2 Ø 5/8"

TRAMO (APOYO C) 5 Ø 3/4" + 1 Ø 5/8"

3 Ø 3/4" + 2 Ø 5/8"

3 Ø 3/4"

2 Ø 3/4" 2 Ø 3/4" + 1 Ø 5/8" 2 Ø 3/4"

2 Ø 5/8" 2 Ø 5/8"

3 Ø 3/4"

5 Ø 3/4"