DISEÑO ESTRUCTURAL DE UNA ARMADURA TIPO PRATT

DISEÑAR EL TECHO METALICO DE 30 X 50 MTS PARA USO DE ALMACEN DATOS : PESO DE LA COBERTURA (CANALON DE 6.2 X0.96 ) = 83.8 kg

DISEÑO DE LA ARMADURA

long de vigeta = 5 mtconsiderando 10 el numero de vanos

long vanos long(mt)long horizontal de cada vano = = 30 10 3

peralte de la armadurat = L/10 = 3 mtt = L/5= 6 mt

tomaremos 4 metros

peso de cobertura = 15.63 16 kg/m2

30

50

log𝑡𝑜𝑡𝑎𝑙/(𝑛𝑢𝑚𝑒𝑟𝑜𝑑𝑒𝑣𝑎𝑛𝑜𝑠)

t

30 3

(𝑝𝑒𝑠𝑜𝑐𝑎𝑛𝑎𝑙𝑜𝑛)/(𝑎𝑟𝑒𝑎𝑢𝑡𝑖𝑙) ~

peso de vigeta= 10 kg/m (asumido)area tributaria del nudo interior= 15 m2area tributaria del nudo exterior= 7.5 m 2

CARGA MUERTA

peso de cobertura(canalon) = 16 kg/m2

peso de vigeta= = 3.33 kg/m2

peso de la armadura y arriostre = 20 kg/m2 (asumido)

carga muerta total = 39.33 kg/m2

-Carga muerta en cada nudo interior del techo:

pd = carga muerta total x area tributaria 39.33 15 590 kg

-Carga muerta de cada nudo externo del techo:

pd = carga muerta total x area tributaria 39.33 7.5 295 kg

CARGA VIVA

-Cobertura liviana = 30 K/m2

-carga viva en cada nudo interno del techo:

PI = carga viva x area tributaria del nudo 30 15 450 kg

-carga viva en cada nudo externo del techo:

PI = carga viva x area tributaria del nudo 30 7.5 225 kg

CARGA ULTIMA

3

5

(𝑝𝑒𝑠𝑜𝑥𝑙𝑜𝑛𝑔)/(𝑎𝑟𝑒𝑎𝑡𝑟𝑖𝑏𝑢𝑡𝑎𝑟𝑖𝑎)

× =

=

=

=

Para el nudo interior :

PU = 1428 KG = 1.43 TN

Para el nudo exterior :

PU = 714 KG = 0.71 TN

ESQUEMA DE FUERZAS EXTERNAS

Esquema de fuerzas internas

Por el método de las secciones :

Especificaciones AISC-LRFD : Pu = 1.2 Pd +1.6 PL

0.71 tn1.43 tn1.43 tn

1.43 tn1.43 tn

1.43 tn

RA=7.15 tn RB=7.15 tn

0.71 tn 1.43 tn1.43 tn

1.43 tn1.43 tn

4.0

0

3.6

0

3.03

3

0.71 tn1.43 tn1.43 tn

1.43 tn1.43 tn

3

RB=7.15 tn

33.75°

A

A

5 6 7 8 9 10

LK

JIH

G

Corte A :

14.31 TN(TENSION)

GH cos 33.75 (3.6)-1.43(3)-1.43(6)-1.43(9)-1.43(12)-0.71(15)+7.15(15)=0GH= 17.96 TN(COMPRESION)

∑ F Y= 0-1.43-(17.96)sen 33.75-H5cos39.80-1.43-1.43-1.43-0.71+7.15=0H5= 12.65 TN(TENSION)

Nudo G

∑ F Y= 0

-1.43+17.96(sen 33.75)x2-G5=0G5= 18.53 TN(TENSION)

DISEÑO DE LA BRIDA INFERIOR:

∑ M H = 0

-F5-6(3.6)-1.43(3)-1.43(6)-1.43(9)-0.71(12)+7.15(12)

F5-6 =

∑ M 5 = 0

0.71 tn1.43 tn1.43 tn

1.43 tn1.43 tn

3

RB=7.15 tn

33.75°

A

A

5 6 7 8 9 10

LK

JIH

G

Diseño por tracción:

PU = 14310 KGL= 300 cm

fy= 2500 kg/cm2 = 36 ksi

ø = 0.9 Por fluencia del acero:

Pu = ø*fy*Ag

Ag= pu/ ø*fy = 6.36 cm2

Por esbeltez:

L/r ≤ 300r ≥ L/300

r ≥ 1 cm

seleccionamos el perfil en tablas :Ag =6.36r = 1

usaremos :

nuevo Ag = 6.8 cm2nuevo r = 1.16

comprobación por esbeltez:L/r < 300

258.62 < 300 ok

DISEÑO DE LA BRIDA SUPERIOR:

2 ˃ 11/2” x 11/2” x 3/16”

diseño por compresión

Pu = 17960 kgL = 3.03 M

asumimos a criterio un angulo de : 3” x 3”

2.36 Cm

determinamos esbeltez

ε = ≤ 200

donde :K= 1L = 303r = 2.36

128.27 ≤ 200 ………ok

128

fy = 2500 kg/cm2

907 kg / cm2

Con los datos :

907 kg / cm2

Determinaremos rx

rx = 0.31 h

rx =

ε =

Determinación del esfuerzo critico a la compresión ( ø FCr )

=

Según tablas se sabe que : ø FCr =

ø FCr =

angulo de 3” x 3”

= 19.80 cm2

Teniendo los datos de :

Ag = 19.80 cm2r = 2.36 cm2

por tablas determinamos el espesor :

e = 5/16”nuevo Ag = 22.9nuevo r = 2.34

A ) Verificación por esbeltez

≤ 200

129 ≤ 200 ok

= 129

fy = 2500 kg/cm2 = 36 ksi

895

Entonces.

Pu= 20496 > 17960 ………ok

C ) comprobacion por pandeo

ksi

PU = ø FCr x Ag

Ag =

COMPROBACIÓN

B ) por carga admisible (øcpn )

Según tabla determinamos øcpn =

PU = øc FCr x Ag

≤

9.6 12.67 ok

Entonces usaremos 2 > 3” x 3” x 5/16”

DISEÑO DE LAS MONTANTES

4.00 mt

Diseño por tracción:

PU= 18.53 tn = 18530 kgL = 4.00 m= 400 cmfy = 2500

Ag = 8.24 cm2

en tablas elegimos Ag = 10.5 cm2r = 1.34

entonces :

L/r ≤ 300

298.5 300 ……ok

usaremos :

DISEÑO DE LAS DIAGONALES

Ag =PU/ (øt Fy )

2 < 1 3/4” x 13/4” x 1/4”.

≤≤

≤

Diseño por tracción:fy = 2500PU = 12650 kgL = 469 cm

Ag = 5.62 cm2

en tablas :

Ag = 6.2 cm2r = 1.59 cm2 entonces:

L/r ≤ 300294.97 300

usaremos : 2 < 2” x 2” x 1/8”.

ancho tributario vigeta= mtlong de vigeta = mt

35

h =L/20 = 0.25

Ag =PU/ (øt Fy )

v  Diseño de las vigetas de celosía :

     Altura de vigeta :

≤

mt

h = mt

tang = h/(L/2) 0.25

= 45

L = 50.00

numero de vanos = cm

Metrado de cargas:

10

Peso de la cobertura x ancho tributario de vigueta= 48 kg/mPeso propio de La vigueta asumimos = 10 kg/m

WD = 58 kg/m

según norma = 30WL = 90 kg/m

Carga factorizada según AISC-LRFDkg/m2

Wu= 1.4 WD = kg/mWu = 1.2 wd+1.6wl = kg/mtomamos eñl mayor

Momento máximo actuante 81.2213.6

kg x m

    numero de vanos :

Numero de vanos en la vigueta =long total / long de cada vano

    Carga muerta WD :

  Carga viva WL:

M max = WU x L2 /8 =

Fuerza de traccion T y compression C :

M = T x d→T = M/d 667.5M = C x d→C= M/dd = 95 % h

d = 0.24T = C = 2781.25

fy= 2500 mtL = 50 kgø = 0.9

kg/cm2CM

T T

por fluencia del acero el área requerida es :

Ag = t/ øfy

Ag = 1.24

Usaremos 1 varilla de ½”

cm2

c

Asumiendo una varilla de ½” tenemos :

d= ½” = 1.27

A = πd2 /4

K = 1 cm2radio de giro = r = d/4

r = 0.32

Esbeltez = <

v  Diseño de la brida inferior (tracción):

v  Diseño de La brida superior (compresión) :

cm157.48 200 …..…ok

200

øfcr = tn/cm2<

Área requerida de acero es :

0.62A = cm2

Usaremos 2 varillas de de ¾”

4.49

Veremos en tablas : øfcr

30.00 m

50.0

0 m

5.00

m5.

00 m

5.00

m5.

00 m

5.00

m5.

00 m

5.00

m5.

00 m

5.00

m5.

00 m

METRADO DE CARGASCARGA MUERTA N. INTERIOR1. COBERTURA 16.00 kg/m2 240.00 kg2. VIGUETA 3.33 kg/m2 50.00 kg3. ARMADURA 20.00 kg/m2 300.00 kgTOTAL 590.00 kgCARGA VIVA1. SOBRECARGA 30.00 kg/m2 450.00 kgTOTAL 450.00 kg

CARGA TOTAL (P)TOTAL 1591.00 kg

m2 kg / m2 cm2

TIPO DE COLUMNA A. TRIBUTARIA n PG A. COLUMNA

C4 ESQUINA 37.50 1.50 0.20 59662.50 2130.80C4 ESQUINA 37.50 1.50 0.20 59662.50 2130.80C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C2 LATERAL 75.00 1.25 0.25 119325.00 2841.07C4 ESQUINA 37.50 1.50 0.20 59662.50 2130.80C4 ESQUINA 37.50 1.50 0.20 59662.50 2130.80

ÁREAS TRIBUTARIAS

COLUMNA ÁREA TIPO

C-1 37.50 C4 ESQUINAC-2 37.50 C4 ESQUINAC-3 75.00 C2 LATERALC-4 75.00 C2 LATERALC-5 75.00 C2 LATERALC-6 75.00 C2 LATERALC-7 75.00 C2 LATERALC-8 75.00 C2 LATERALC-9 75.00 C2 LATERAL

C-10 75.00 C2 LATERALC-11 75.00 C2 LATERALC-12 75.00 C2 LATERALC-13 75.00 C2 LATERALC-14 75.00 C2 LATERALC-15 75.00 C2 LATERALC-16 75.00 C2 LATERALC-17 75.00 C2 LATERALC-18 75.00 C2 LATERALC-19 75.00 C2 LATERALC-20 75.00 C2 LATERALC-21 37.50 C4 ESQUINAC-22 37.50 C4 ESQUINA

TIPO nC1 INTERIOR 1.10 0.30C2 LATERAL 1.25 0.25C4 ESQUINA 1.50 0.20

f'c = 210.00 kg/cm2

𝑏∗𝐷=𝑃/(𝑛∗𝑓´𝑐)

cm

b = d b = d ACERO (1%)

46.16 55.00 30.25 30.40 6 Ø 1"46.16 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"53.30 55.00 30.25 30.40 6 Ø 1"46.16 55.00 30.25 30.40 6 Ø 1"46.16 55.00 30.25 30.40 6 Ø 1"

DISEÑO DE COLUMNA

SECCION DE COLUMNA

Longitud X 0.55 mLongitud Y 0.55 m

REFUERZO DE LA SECCION

Varillas Y 0Varillas X 3Recubrimiento 0.04 mDiámetro del refuerzo 1.00 ''Área del refuerzo 30.40 cm2Espaciamiento Horizaontal 0.48 mEspaciamiento Vertical 0.44 m

MATERIALESf'c 210.00 kg/cm2f'y 4200.00 kg/cm2

AREAS 5.07 cm2 d (cm)

As1 2 10.14 d1 6.54As2 2 10.14 d2 27.5As3 2 10.14 d3 48.46

1. CONDICIÓN DE CARGA CONCÉNTRICA

Ag = 3025.00 cm2

Pno = 667.73 ton

Ag = 3025.00 cm2Ast = 30.42 cm2

2. CONDICIÓN BALANCEADA

48.4

6 cm

Es = 2000000.00

0.0021

Cb = 28.51 cm

a = 24.23 cm

fsi = f'yfs1 4.62 ton/cm2fs2 0.21 ton/cm2fs3 4.20 ton/cm2

#VARILLAS Ø 1"

Ɛy =

0 0.1 0.2 0.3 0.4 0.5 0.6-0.06

-0.01

0.04

0.09

0.14

0.19

0.24

0.29

0.34

0.39

0.44

0.49

0.54

0.59

0.64

SECCION 0.55m x 0.55m

𝑨𝒈=𝒃𝒙𝒅𝑷𝒏𝒐=𝟎.𝟖𝟓∗𝒇^′𝒄∗𝑨𝒈+𝑨𝒔𝒕∗𝒇^′𝒚

Cb

d

0.003

?y

𝒚=(𝒇^′𝒚)/𝑬𝒔ɛ

𝑪𝒃=(𝟎.𝟎𝟎𝟑)/(𝟎.𝟎𝟎𝟑+ 𝒚)∗𝒅ɛ

𝒂=𝟎.𝟖𝟓∗𝑪𝒃𝒇𝒔𝒊=𝟔∗((𝑪−𝒅𝒊))/𝑪

Cc = 237.91 ton

Cs1 = 46.85 ton

Ts2 = 2.13 ton

Ts3 = 42.59 ton

Pnb = 240.04 ton

Yo= 27.23 ton Mnb = 36.60 ton-m

e = 0.15 cm

3. FALLA DUCTIL

Asumiendo:C = 20.00 cm → a = 17.00 cm

34.0

0 cm

Es = 2000000.00

0.0021

d = 34.00 cm

a = 17.00 cm

fsi = f'yfs1 4.04 ton/cm2fs2 4.20 ton/cm2fs3 4.20 ton/cm2

Ɛy =

𝑪𝒄=𝟎.𝟖𝟓∗𝒇^′𝒄∗𝒃∗𝐚𝑪𝒔𝟏=𝑨𝒔𝟏∗𝒇𝒔𝟏𝑻𝒔𝟐=𝑨𝒔𝟐∗𝒇𝒔𝟐𝑻𝒔𝟑=𝑨𝒔𝟑∗𝒇𝒔𝟑𝑷𝒏𝒃=𝑪𝒄+𝑪𝒔𝟏−𝑻𝒔𝟐−𝑻𝒔𝟑𝑴𝒏𝒃=𝑪𝒄∗(𝒀𝒐−𝒂/𝟐)+𝑪𝒔𝟏∗(𝒀𝒐−𝒅𝟏)−𝑻𝒔𝟐∗(𝒅𝟐−𝒀𝒐)−𝑻𝒔𝟑∗(𝒅𝟑−𝒀𝒐) 𝒀𝒐=(𝑪𝒄∗(𝒉/𝟐)+𝑪𝒔𝟏∗𝒅𝟏+𝑻𝒔𝟐∗𝒅𝟐+𝑻𝒔𝟑∗𝒅𝟑)/(𝑪𝒄+𝑪𝒔𝟏+𝑻𝒔𝟐+𝑻𝒔𝟑)

𝒆=𝑴𝒏𝒃/𝑷𝒏𝒃

Cb

d

0.003

?y

𝒚=(𝒇^′𝒚)/𝑬𝒔ɛ

𝒂=𝟎.𝟖𝟓∗𝑪𝒃𝒇𝒔𝒊=𝟔∗((𝑪−𝒅𝒊))/𝑪

𝒅=((𝟎.𝟎𝟎𝟑+𝒚)∗𝑪𝒃)/(𝟎.𝟎𝟎𝟑)ɛ

Cc = 166.90 ton

Cs1 = 40.97 ton

Ts2 = 42.59 ton

Ts3 = 42.59 ton

Pnb = 122.69 ton

Yo= 27.62 ton Mnb = 31.71 ton-m

e = 0.26 cm

*NOTA: Debido a que la excentricidad en la condicion balanceada es menor a al excentricidad calculada en la falla ductil se asumira un "C" mayor

Asumiendo:C = 30.00 cm → a = 25.50 cm

51.0

0 cm

Es = 2000000.00

0.0021

d = 51.00 cm

a = 25.50 cm

fsi = f'yfs1 4.69 ton/cm2fs2 0.50 ton/cm2fs3 4.20 ton/cm2

Ɛy =

𝑪𝒄=𝟎.𝟖𝟓∗𝒇^′𝒄∗𝒃∗𝒂𝑪𝒔𝟏=𝑨𝒔𝟏∗𝒇𝒔𝟏𝑻𝒔𝟐=𝑨𝒔𝟐∗𝒇𝒔𝟐𝑻𝒔𝟑=𝑨𝒔𝟑∗𝒇𝒔𝟑𝑷𝒏𝒃=𝑪𝒄+𝑪𝒔𝟏−𝑻𝒔𝟐−𝑻𝒔𝟑𝑴𝒏𝒃=𝑪𝒄∗(𝒀𝒐−𝒂/𝟐)+𝑪𝒔𝟏∗(𝒀𝒐−𝒅𝟏)−𝑻𝒔𝟐∗(𝒅𝟐−𝒀𝒐)−𝑻𝒔𝟑∗(𝒅𝟑−𝒀𝒐) 𝒀𝒐=(𝑪𝒄∗(𝒉/𝟐)+𝑪𝒔𝟏∗𝒅𝟏+𝑻𝒔𝟐∗𝒅𝟐+𝑻𝒔𝟑∗𝒅𝟑)/(𝑪𝒄+𝑪𝒔𝟏+𝑻𝒔𝟐+𝑻𝒔𝟑)

𝒆=𝑴𝒏𝒃/𝑷𝒏𝒃

Cb

d

0.003

?y

𝒚=(𝒇^′𝒚)/𝑬𝒔ɛ

𝒂=𝟎.𝟖𝟓∗𝑪𝒃𝒇𝒔𝒊=𝟔∗((𝑪−𝒅𝒊))/𝑪

𝒅=((𝟎.𝟎𝟎𝟑+𝒚)∗𝑪𝒃)/(𝟎.𝟎𝟎𝟑)ɛ

Cc = 250.35 ton

Cs1 = 47.56 ton

Ts2 = 5.07 ton

Ts3 = 42.59 ton

Pnb = 250.24 ton

Yo= 27.20 ton Mnb = 47.57 ton-m

e = 0.19 cm

ACERO EN LA COLUMNA

Pu = 250.24 tonMu = 47.57 ton-m

ACERO LONGITUDINALCONSIDERANDO ACERO EN LAS 4 CARAS

ɣ = 0.80

kn = 0.39

Rn = 0.14

As = 24.204Ø1" 20.27 cm2

4Ø5/8" 7.92 cm228.19 cm2

USAR 4Ø1", 4Ø5/8"

𝑪𝒄=𝟎.𝟖𝟓∗𝒇^′𝒄∗𝒃∗𝒂𝑪𝒔𝟏=𝑨𝒔𝟏∗𝒇𝒔𝟏𝑻𝒔𝟐=𝑨𝒔𝟐∗𝒇𝒔𝟐𝑻𝒔𝟑=𝑨𝒔𝟑∗𝒇𝒔𝟑𝑷𝒏𝒃=𝑪𝒄+𝑪𝒔𝟏+𝑪𝒔𝟐−𝑻𝒔𝟑𝑴𝒏𝒃=𝑪𝒄∗(𝒀𝒐−𝒂/𝟐)+𝑪𝒔𝟏∗(𝒀𝒐−𝒅𝟏)−𝑻𝒔𝟐∗(𝒅𝟐−𝒀𝒐)−𝑻𝒔𝟑∗(𝒅𝟑−𝒀𝒐) 𝒀𝒐=(𝑪𝒄∗(𝒉/𝟐)+𝑪𝒔𝟏∗𝒅𝟏+𝑻𝒔𝟐∗𝒅𝟐+𝑻𝒔𝟑∗𝒅𝟑)/(𝑪𝒄+𝑪𝒔𝟏+𝑻𝒔𝟐+𝑻𝒔𝟑)

𝒆=𝑴𝒏𝒃/𝑷𝒏𝒃

𝜸=(𝒕−𝟏𝟐)/𝒕𝒌𝒏=𝑷𝒖/𝑨𝒈∗𝒇^′𝒄𝑹𝒏=𝑴𝒖/(𝑨𝒈∗𝒇^′𝒄−𝒕)

𝑨𝒔=𝒇∗𝒃∗𝒕

ACERO TRANSVERSAL

Ln = 6

Lo = 100.00 cm Lo = 55.00 cm Lo = 100.00 cm Lo = 45.00 cm

So = 27.50 cm So = 10.00 cmSo = 10.00 cm

y el numero de estribos (zona de confinamiento) = 95/10 = 9.5 = 10 estribos

c) Espaciamiento fuera de la zona de confinamiento (espaciamiento maximo)

So = 40.64 cmSo = 55.00 cm So = 30.00 cmSo = 30.00 cm

USAR ESTRIBOS Ø 1/2": 1@0.05; 6@0.10; R@0.30 a/s

a) Longitud de la zona de confinamiento (Lo)

b) Espaciamiento dentro de Lo (So)

*NOTA: Como se coloca 1@ 0.05; sólo se dispondra de 100-5 = 95cm

d) Espaciamiento dentro del nudo (S)

𝑳𝒐≥𝑳𝒏/𝟔𝑳𝒐≥𝒃,𝒅𝑳𝒐=𝟒𝟓𝒄𝒎

𝑺𝒐≤(𝒂/𝟐;𝒃/𝟐)𝐒𝒐=𝟏𝟎𝒄𝒎

𝑺𝒐≤𝟏𝟔𝒅𝒃𝑺𝒐≤(𝒃;𝒅)𝑺𝒐=𝟑𝟎𝒄𝒎

𝑺′≤𝟏𝟓𝒄𝒎

DISEÑO DE ZAPATA

DATOSCarga Muerta : 44250.00 kg 44.25 ton

Carga Viva : 33750.00 kg 33.75 tonCarga Ultima : 119325.00 kg 119.33 ton

Columna : b = 55.00 cm d = 55.00 cm bxd = 3025.00 cm2σt : 3.50 kg/cm2 35.00 ton/m2f'c : 210.00 kg/cm2f'y : 4200.00 kg/cm2

S/C : 500.00 kg/m2 0.50 ton/m2df : 1.50 m

ɣm : 2.10 ton/m3

Esfuerzo neto del terreno

=𝝈𝒏 30.30 ton/m2

Az = 2.57 m2

Si se desea una zapata cuadrada Lado = 1.60 m

Az = 2.56 m2

LV1 = 0.525 OK LV2 = 0.525

Reacción neta del terreno

Wnu = 46.61 ton/m2

Dimensionamiento de la altura h2 de la zapata por punzonamiento

Condición de diseño Vu/f = Vc

…1βc = Dmayor / Dmenor βc = 1.00 < 2 OK

…2bo = 2*(0.55+d) + 2*(0.55+d) bo = 2.20 + 4d

Vu/φ = 1/φ * { Pu - Wu*(0.55+d)*(0.55+d)}

Vc =0.27*(2+4/β)*√f'c*bo*d ≤ 1.06 * √f'c*bo*d

𝝈𝒏=𝝈𝒕− 𝒑𝒓𝒐𝒎∗𝒉𝒇−𝑺/𝑪ɣ

𝑨𝒛=𝑷/𝝈𝒏

𝑾𝒏𝒖=𝑷𝒍/𝑨𝒛

Igualando 1 y 2

119.33 - 46.61*(0.55+d)*(0.55+d) = 1.06*(210^1/2)*(2.2+4d)*0.85

ResolviendoX (+) = 0.70 mX (-) = -1.51 m

Asumiendo h = 0.50 m dprom = 0.4059

rec = 0.075 m dprom = 0.4

Verificacion de cortante

Vdu = (Wu*S)*(Lv-d) 9.32 ton10.97 ton49.15 ton

Vc > Vn OK

Diseño por flexión

Mu = (Wu*s)*LV^2/2 10.28 ton-m

AceroK = 0.85*f'c*b*d 1142400.00

7.30 cm2

Verificación de As min

11.52 cm2

# Varillas = As/AØ 9.00

*NOTA: Debido a que la sección de la zapata es cuadrada el acero longitudinal y transversal será el mismo

USAR 9Ø1/2" @0.16m

Vn = Vdu/φVc = 0.53*√f'c*b*d

As = k/f'y *{1- [1 - (2*Mu/φk*d)^1/2]}

Asmin = ƿtemp * b * d

TABLA KU VS N°

DIÁMETRO Ø PERIMETRO PESO N° DE BARRAS CONOCIENDO EL ÁREA EN cm2f´c=280 f´c=210 f´c=175 pulg ó mm cm cm kg/ml kg 1 2 3 4 5 6 7 8 9 10 11 12fy=4200 fy=4200 fy=4200 6mm 0.6000 1.88 0.22 1.98 0.28 0.57 0.85 1.13 1.41 1.70 1.98 2.26 2.54 2.83 3.11 3.39

p*b=0.0289 p*b=0.0216 p*b=0.0180 2 1/4" 0.6350 1.99 0.25 2.25 0.32 0.63 0.95 1.27 1.58 1.90 2.22 2.53 2.85 3.17 3.48 3.80Ku Ku Ku 8mm 0.8000 2.51 0.40 3.60 0.50 1.01 1.51 2.01 2.51 3.02 3.52 4.02 4.52 5.03 5.53 6.03

0.0216 66.0402 0.0162 49.5301 0.0134 41.0411 3 3/8" 0.9525 2.99 0.58 5.22 0.71 1.43 2.14 2.85 3.56 4.28 4.99 5.70 6.41 7.13 7.84 8.550.0214 65.5719 0.0160 49.0614 0.0132 40.5698 12mm 1.2000 3.77 0.89 8.01 1.13 2.26 3.39 4.52 5.65 6.79 7.92 9.05 10.18 11.31 12.44 13.570.0212 65.1009 0.0158 48.5891 0.0130 40.0943 4 1/2" 1.2700 3.99 1.02 9.18 1.27 2.53 3.80 5.07 6.33 7.60 8.87 10.13 11.40 12.67 13.93 15.200.0210 64.6272 0.0156 48.1132 0.0128 39.6145 5 5/8" 1.5875 4.99 1.60 14.40 1.98 3.96 5.94 7.92 9.90 11.88 13.86 15.83 17.81 19.79 21.77 23.750.0208 64.1509 0.0154 47.6337 0.0126 39.1304 6 3/4" 1.9050 5.98 2.26 20.34 2.85 5.70 8.55 11.40 14.25 17.10 19.95 22.80 25.65 28.50 31.35 34.200.0206 63.6719 0.0152 47.1507 0.0124 38.6420 8 1" 2.5400 7.98 4.04 36.36 5.07 10.13 15.20 20.27 25.34 30.40 35.47 40.54 45.60 50.67 55.74 60.800.0204 63.1902 0.0150 46.6641 0.0122 38.14940.0202 62.7058 0.0148 46.1739 0.0120 37.65240.0200 62.2188 0.0146 45.6802 0.0118 37.15120.0198 61.7291 0.0144 45.1829 0.0116 36.64570.0196 61.2367 0.0142 44.6821 0.0114 36.13590.0194 60.7416 0.0140 44.1776 0.0112 35.62190.0192 60.2439 0.0138 43.6696 0.0110 35.1035 28.190.0190 59.7435 0.0136 43.1581 0.0108 34.58090.0188 59.2404 0.0134 42.6429 0.0106 34.05400.0186 58.7346 0.0132 42.1242 0.0104 33.52280.0184 58.2262 0.0130 41.6019 0.0102 32.98730.0182 57.7150 0.0128 41.0761 0.0100 32.44750.0180 57.2012 0.0126 40.5467 0.0098 31.90350.0178 56.6848 0.0124 40.0137 0.0096 31.35520.0176 56.1656 0.0122 39.4772 0.0094 30.82600.0174 55.6438 0.0120 38.9370 0.0092 30.24570.0172 55.1193 0.0118 38.3934 0.0090 29.68450.0170 54.3921 0.0116 37.8461 0.0088 29.11910.0168 54.0623 0.0114 37.2953 0.0086 28.54930.0166 53.3297 0.0112 36.7409 0.0084 27.97530.0164 52.9945 0.0110 36.1829 0.0082 27.39700.0162 52.4566 0.0108 35.6214 0.0080 26.81440.0160 51.9161 0.0106 35.0563 0.0078 26.22760.0158 51.3728 0.0104 34.4877 0.0076 25.63640.0156 50.8269 0.0102 33.9154 0.0074 25.04100.0154 50.2783 0.0100 33.3396 0.0072 24.44130.0152 49.7271 0.0098 32.7603 0.0070 23.83730.0150 49.1737 0.0096 32.1773 0.0068 23.22900.0148 48.6165 0.0094 31.5908 0.0066 22.61650.0146 48.0572 0.0092 31.0008 0.0064 21.99970.0144 47.4952 0.0090 30.4071 0.0062 21.37850.0142 46.9306 0.0088 29.8099 0.0060 20.75310.0140 46.3633 0.0086 29.2091 0.0058 20.12340.0138 45.7933 0.0084 28.6048 0.0056 19.48930.0136 45.2206 0.0082 27.9969 0.0054 18.85120.0134 44.6452 0.0080 27.3854 0.0052 18.20870.0132 44.0672 0.0078 26.7703 0.0050 17.56190.0130 43.4865 0.0076 26.1517 0.0048 16.91080.0128 42.9031 0.0074 25.5295 0.0046 16.25540.0126 42.3170 0.0072 24.9038 0.0044 15.59580.0124 41.7283 0.0070 24.2744 0.0042 14.93180.0122 41.1369 0.0068 23.6416 0.0040 14.26360.0120 40.5429 0.0066 23.0051 0.0038 13.59110.0118 39.9461 0.0064 22.3651 0.0036 12.91430.0116 39.3466 0.0062 21.7215 0.0034 12.23330.0114 38.7445 0.0060 21.0743 0.0032 11.54790.0112 38.1397 0.0058 20.4236 0.0030 10.85830.0110 37.5322 0.0056 19.7693 0.0028 10.16440.0108 36.9221 0.0054 19.1114 0.0026 9.46620.0106 36.3093 0.0052 18.4500 0.0024 8.76370.0104 35.3938 0.0050 17.7847 0.0022 8.05700.0102 35.0756 0.0048 17.1164 0.0020 7.34590.0100 34.4548 0.0046 16.4442 0.0018 6.63060.0098 33.8312 0.0044 15.7685 0.0016 5.91100.0096 33.2050 0.0042 15.0892 0.0014 5.18710.0094 32.5762 0.0040 14.4064 0.0012 4.45890.0092 31.9446 0.0038 13.7200 0.0010 3.72650.0090 31.3104 0.0036 13.0300 0.0008 2.98980.0088 30.6735 0.0034 12.3364 0.0006 2.24870.0086 30.0339 0.0032 11.6373 0.0004 1.50350.0084 29.3916 0.0030 10.9386 0.0002 0.75350.0082 28.7467 0.0028 10.2343 0.0000 0.00000.0080 28.0991 0.0026 9.52650.0078 27.4488 0.0024 8.81510.0076 26.7958 0.0022 8.10020.0074 26.1402 0.0020 7.38160.0072 25.4819 0.0018 6.65750.0070 24.8209 0.0016 5.93390.0068 24.1572 0.0014 5.20460.0066 23.4909 0.0012 4.47180.0064 22.8218 0.0010 3.73540.0062 22.1501 0.0008 2.99550.0060 21.4758 0.0006 2.25200.0058 20.7987 0.0004 1.50470.0056 20.1190 0.0002 0.75430.0054 19.4366 0.0000 0.00000.0052 18.75150.0050 18.06370.0048 17.37330.0046 16.68020.0044 15.98440.0042 15.28600.0040 14.58480.0038 13.88100.0036 13.17450.0034 12.46540.0032 11.75350.0030 11.03900.0028 10.32180.0026 9.60190.0024 8.87940.0022 8.15420.0020 7.42630.0018 6.69570.0016 5.96240.0014 5.22650.0012 4.48790.0010 3.74660.0008 3.00270.0006 2.25600.0004 1.50670.0002 0.75470.0000 0.0001

𝝆 𝝆 𝝆𝝆