ANALISIS Y DISEÑO DE VIGAS DE CONEXIÓN

T1=2S1-2.5S1 A

C1 VIGA DE C2

T2
CONEXIÓN

S1 S2
P1 P2

NPT=+0.15m CORTE A-A

hf

ZAPATA EXTERIOR 0.10 ZAPATA INTERIOR Æ PRINCIPAL

L1 T
DATOS
ZAPATA EXTERIOR ZAPATA INTERIOR
P1 = PD1+PL1 P2 = PD2+PL2

PD1 = 12.0 Tn PD2 = 24.47 Tn

PL1 = 4.3 Tn PL2 = 9.08 Tn

st = 2.00 kg/cm² S/C piso = 0.25 Tn/m²

hf = 1.50 m f'c = 210 kg/cm²
ɣm = 2.00 Tn/m³ fy = 4200 kg/cm²

DIMENSION DE COLUMNAS
C1: C2:
t1= 0.15 m t1= 0.25 m
t2= 0.40 m t2= 0.40 m
 0.15 0.25

LP

###

###
L= 4.93 m

C1 VIGA DE C2
T1

T2
CONEXIÓN

S1 S2

0.08 4.93
DIMENSIONANDO ZAPATAS 0.4
4.530
𝐴�=1.20𝑃1/
(s𝑛)

P1 = 16.3 Tn → Az = 1.264 m²
sn = 16.75 Tn/m²
Pz = 1.08 S = 0.80 m

VIGA DE CONEXIÓN

h = L = 0.704 m
7 h/2= 0.35214
b = P1 = 0.107 m
31*L

Usar: b x h = 0.70 x 0.35 m²

DIMENSION DE ZAPATA EXTERIOR

wv = 0.7 * 0.35 * 2.4 = 0.588 Tn/m

åM2= 0
RN*(4.605)=P1 * 4.93+0.588*5.005²/2
RN = 19.09249 Tn

P1 = 16.34 Tn
wv = 0.588 Tn/m
 2

0.80 RN = reaccion neta de la zapata exterior

S1 /2 S1 /2
RN

0.400 4.605

5.01

Az = Rn = 1.14 m²
sn
S1 = 0.80
1.14= T2 *0.8 = 1.425 m

Usar: T1 x S1 = 1.45 x 0.80 m²

DISEÑO DE LA VIGA DE CONEXIÓN

 P1U = 24.17 Tn
wvu = 0.8232 Tn/m
2

wnu
0.80 RN = reaccion neta de la zapata exterior

Rnu
0.400
4.605
0.075 4.93

P1U = 24.17 Tn
Wvu = 0.8232 Tn/m

åM2= 0
RNU *4.605=P1U * 4.93+0.8232*5.005²/2
RNU = 28.11695 Tn

WNU = RNU = 35.1462 Tn/m

S1

SECCION DE MOMENTO MAXIMO, Xo £ S

Vx=(Wnu-Wvu)Xo-P1U=0

Xo = 0.704 m< S = 0.80 m CONFORME

𝑀𝑢𝑚𝑎�=(𝑊𝑛𝑢−𝑊𝑣𝑢) 〖��〗 ^2/2−𝑃1𝑈(��−𝑡1/2)

Mumax = -6.6987 Tn-m

𝐴�=𝑀𝑢/
(∅𝑓𝑦(𝑑−𝑎/2) ) → As = 7.08798 cm²

𝑎=(𝐴�∗𝑓𝑦)/
(0.85∗𝑓^′ 𝑐∗𝑏) → a = 2.38 cm

As = 5.242 cm² → a = 1.762 cm

As = 5.194 cm² → a = 1.746 cm
As = 5.193 cm² → a = 1.746 cm
 As = 5.193 cm² → a = 1.746 cm CONFORME

USAR: 4.10 7 Æ 1/2 "

�=𝐴�/𝑏 → r = 0.00362
𝑑

�𝑚𝑖𝑛=14/𝑓 → rmin = 0.00333

𝑦

r > r min CONFORME

REFUERZO EN LA CARGA INFERIOR

〖𝐴�〗 ^+=[ 〖𝐴�〗 ^−/3,

〖𝐴�〗 ^−/2]≥𝐴�𝑚𝑖𝑛

As = 4.43369 cm²
Asmin = 6.41667 cm²

COMO As < Asmin Þ USAR: 5.07 4 Æ 1/2 "

ESQUEMA DE DISTRIBUCION DE ACERO

7Æ 1/2 "

4Æ 1/2 "

DISEÑO POR CORTE

P
d V2U
WVU

WNU

�1𝑈=(𝑊𝑁𝑈−𝑊�𝑈)(𝑡1+𝑑)−𝑃1𝑈
 V1U = -0.90788 Tn

�2𝑈=(𝑊𝑁𝑈−𝑊�𝑈)∗𝑆−𝑃1𝑈

V2U = 3.286389 Tn

Vu = 3.29 = 4.38185 Tn
Æ 0.75

�𝑐=0.53√(𝑓^′ 𝑐)∗𝑏∗𝑑

Vc = 14.93536 Tn Þ Vc < Vn
CONFORME

USAR :Estribo de montaje Þ S £ 36*f → S £ 68.76 cm

Estribo: f 3/8" @ 0.65 m
DISEÑO DE LA ZAPATA EXTERIOR
𝑊𝑁𝑈=𝑅𝑁𝑈/𝑇1

→ WNU = 19.391 Tn/m

〖𝑀𝑢〗 _𝑚𝑎�=(�_��∗�_�
^2 " " )/2
0.70
MUmax= 4.096349 Tn/m VC 0.375

𝑀𝑈=∅ 〖∗𝑓〗 ^′ 𝑐∗𝑏∗𝑑^2∗𝜔(1−0.59𝜔)

𝜔=� 𝑓𝑦/
r = 0.004 → (𝑓^′ 𝑐) WNU

Si: w = 0.08 T 1.45

b = 80
Despejando
𝑑=√(𝑀𝑈/(∅∗𝑓^′
𝑐∗𝑏∗𝜔(1−0.59𝜔) ))
→ d = 18.85 cm

USAR: h = 50 cm Þ d = 41.55 cm

DISEÑO POR CORTE

�_𝑢𝑑=𝑊_𝑁𝑢
(𝑙_𝑣−𝑑)
 �_𝑢𝑑=𝑊_𝑁𝑢
(𝑙_𝑣−𝑑)

Vud = -0.78437 Tn

Vn = Vud = -1.0458 Tn
Æ
�𝑐=0.53√(𝑓^′ 𝑐)∗𝑏∗𝑑

Vc = 25.52668 Tn Þ Vc < Vn
CONFORME

DISEÑO POR FLEXION

𝐴�=𝑀𝑢/ → As = 2.8983 cm²

(∅𝑓𝑦(𝑑−𝑎/2) )

𝑎=(𝐴�∗𝑓𝑦)/
(0.85∗𝑓^′ 𝑐∗𝑆) → a = 0.85 cm

As = 2.63551 cm² → a = 0.775 cm

As = 2.63304 cm² → a = 0.774 cm
As = 2.633 cm² → a = 0.774 cm
As = 2.633 cm² → a = 0.774 cm CONFORME

USAR: 2.08 5 Æ 1/2 " @ 0.16 m

REFUERZO TRANSAVERSAL

〖𝐴𝑆〗 _𝑇𝑒𝑚𝑝=0.0018∗𝑏∗𝑡 → ASTemp = 13.05 cm²

USAR: 10.3 9 Æ 1/2 " @ 0.16 m

DISEÑO DE LA ZAPATA INTERIOR

P1 P2
wv

RN = reaccion neta de la zapata exterior

RN

P2efectivo = -P 2-P 1-Wv*lv+RN

 P2efectivo = -33.740452 Tn

P2Uefectivo= -P 2U-P 1U-WVU*Lvu+Rnu

P2Uefectivo= -49.87 Tn

𝐴�=𝑃_2𝑒𝑓𝑒𝑐𝑡𝑖𝑣�/ → Az = 2.01 cm² 1

(s𝑛)
S2 = 1.344 m T2 = 1.494

Usar: T2 x S2 = 1.50 x 1.40 m²

Wnu = P2efectivo = 24.76 Tn/m²

Az
lV = T2 -t2 → lV = 0.55 m
2

〖𝑀𝑢〗 _𝑚𝑎�=(�_��∗�_�
^2 " " )/2

Mumax = 5.61672 Tn/m

USAR: hmin = 0.50 m Þ dpr = 0.4059

VERIFICANDO POR PUNZONAMIENTO

�_𝑈= 〖𝑃𝑈〗 _𝑍𝑒𝑓𝑒𝑐𝑡𝑖𝑣�−𝑊_𝑛𝑢 (𝑚)

(𝑛) S2

m = 1.00295 m m=(lv+t1+d/2)
n = 0.906 m
t1
Vu = 27.37574 Tn T2
t2
Vn = Vu = 32.20676 Tn
f

�_𝑐=1.06∗√(𝑓^′
𝑐)*bo*d
→ Vc = 181.55 Tn
bo=2*m+n = 2.9118
Þ Vc > Vn
CONFORME
VERIFICACION POR CORTE

�𝑢𝑑=(𝑊𝑛𝑢∗𝐿)(𝑙𝑣−𝑑)
 Vud = -0.2191 Tn

Vn= Vu = -0.2578 Tn
f
�𝑐=0.53√(𝑓^′ 𝑐)∗𝑏∗𝑑

Vc = 43.6448 Tn Þ Vc > Vn
CONFORME

DISEÑO POR FLEXION

𝐴�=𝑀𝑢/ → As = 4.06752 cm²

(∅𝑓𝑦(𝑑−𝑎/2) )

𝑎=(𝐴�∗𝑓𝑦)/ → a = 0.68 cm
(0.85∗𝑓^′ 𝑐∗𝑆)

As = 3.691854 cm² → a = 0.620 cm

As = 3.68896 cm² → a = 0.620 cm
As = 3.689 cm² → a = 0.620 cm
As = 3.689 cm² → a = 0.620 cm CONFORME

USAR: 2.91 10 Æ 1/2 " @ 0.14 m

REFUERZO TRANSVERSAL

𝐴�𝑡𝑟𝑎𝑛�=𝐴�∗𝑇/𝑆

Astrans = 3.9525 cm²

USAR: 3.12 10 Æ 1/2 " @ 0.15 m

ESQUEMA DE ARMADO
Æ 1/2 @0.16m

1/2 @0.15m

1.50
###

C1 VIGA DE C2
CONEXIÓN
10 Æ
5
 1.50
###
9Æ 1/2 @0.16m 10 Æ 1/2 @0.14m

1.45 2.16 1.40

0.08 4.93

@0.16m

@0.15m
7Æ 1/2 "
Æ 1/2

### Æ ###
5

9Æ 1/2 @0.16m 4Æ 1/2 " 10 Æ 1/2 @0.14m

XIÓN

ORTE A-A

Æ PRINCIPAL
a zapata exterior
apata exterior
CONFORME
cm
 CONFORME

apata exterior
n
CONFORME