memoria de calculo.xlsx
TRANSCRIPT
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": [email protected]; [email protected]; [email protected] 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