examen final caii 2012 ii
TRANSCRIPT
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1. Disear la siguiente escalera
0.25
f'c = 210 kg/cm2
f'y = 4200 kg/cm2 0.170
2.38 m
0.2 m3.25 m
13 pasos
1 m
0.2 m
2.38 m
1
0.25
3.25 m
t = 13 cm
t = 10.83 cm t = 0.11
t = 11.375 cm
1 Idealizacin
Metrdo de cargas
25
= 34.22
17 x = 1.21
NOTA: Slo cambiar los
valores marcados con
rojo
Solucin
Ancho de escalera =
Datos
Altura de piso a techo =
Espesor de losa =Longitud de la escalera =
Nro de Pasos =
viga
losa
n.p.t.
m
m
m
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P losa = 319.25 kg/m
P escalon = 204.00 kg/m
P pt = 100 kg/m
Wd = 623.25 kg/mWl = 200 kg/m
Wu = 1294.88 kg/m
M(-) = 1139.77 kg.m
M(+) = 1367.72 kg,m
Mur = 34226.82 kg.m
Clculo de acero
W = 0.091061 W = 0.110617
= 0.004553 = 0.005531
Asmin = 2.02 cm2 4.63 cm2
As (-) = 3.81 cm2
ELEGIR EL TIPO DE ACERO
ACERO Asmin TOTAL(cm2)
Cantidad Diam. (pulg) Cantidad Diam. (pulg)
1 3/8 0 1/2 = 0.713
ACERO As (+)
Cantidad Diam. (pulg) Cantidad Diam. (pulg)
1 1/2 0 1 = 1.267
ACERO As (-)
Cantidad Diam. (pulg) Cantidad Diam. (pulg)
1 1/2 0 1 = 1.267
SEPARACIN DEL ACERO
Acero mnimo
As (+) =
+
+
+
1/10
1/121/12
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0.71 cm2
35 cm
Acero positivo
1.27 cm2
27 cm
Acero negativo
1.27 cm2
33 cm
LONGITUD DE ANCLAJE
Acero negativo
Lanclaje = Ln/3
Lanclaje = 1.10 m
Acero positivo
Lanclaje = Ln/7
Lanclaje = 0.50 m
S =
rea de la varilla =
S =
rea de la varilla =
S =
rea de la varilla =
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COLUMNA b t ZAPATA
Seccin= 40 40 cm Esf. Terreno = 1.8 Kg/cm2
f'c = 210 Kg/cm2 fy = 4200 Kg/cm2
fy = 4200 Kg/cm2
f'c = 210 Kg/cm2
CM = 75 Tn
CV = 50 Tn
ASUMIENDO EL PESO PROPIO DE LA ZAPATA Incremento 5.6 %
Ptotal = 132 Tn
DIMENSIONAMIENTO EN PLANTA
Az = 73333.3333 cm2
L = 270.8 cm L = 2.75 m
CARGA NETA O CARGA MXIMA DE ROTURA
FCM = 1.4
FCV = 1.7
P rotura = 190 Tn
W neta = 2.51 Kg/cm2
DIMENSIONAMIENTO EN ELEVACIN
a) Punzonamiento
d = 50 cm
Vuc = 13.06 Kg/cm2
b0 = 360 cm
Vu = 169669 Kg
Esf Corte = 9.43 Kg/cm2
Ok
b) Flexin
m = 117.5
Vu = 46591.88
Esf c.flex = 3.39 Kg/cm2
Vc = 6.53 Kg/cm2
Ok
DISEO DE ACERO POR FLEXION
M = 4764882.03 Kg.cm
P1.- Una columna de 40 x 40 cm, con concreto de f'c = 210 Kg/cm 2 y acero de fy = 4200 Kg/cm2. debe soportar una carga
muerta de 75 Tn. Y una carga viva de 50 Tn ; el esfuerzo permisisble del terreno en condiciones de servicio es de 1.8 Kg/cm2. Se
solicita disear la zapata, la misma que debera disearse con acero de fy = 4200 Kg/cm 2 y f'c = 210 Kg/cm2.
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As = 29.6600189 a = 2.54
As = 27.389085 a = 2.34
As = 27.3345897 a = 2.34
As = 27.335 cm2
Usar : = 3/4''
10 3/4''
COMPROBACION DE ADHERENCIA
u = 48.68 Kg/cm2 Ok
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f'c = 210 Kg/cm2 n Pisos = 5
fy = 4200 Kg/cm2
METRADOS DE CARGA (Axial)
l a b h n veces Peso
Plosa = 350 7 5.5 13475 Kg
Pacabados = 200 7 5.5 7700 Kg
PVP = 2400 3.5 0.5 0.75 2 6300 Kg
PVS = 2400 2.75 0.5 0.5 2 3300 Kg
P COLUMNA = 2400 3.2 0.5 0.5 1920 Kg
CM = 32695 Kg
S/C = 400 7.5 6 18000 Kg
CV = 18000 Kg
P TOTAL = 381865 Kg
METRADOS DE CARGA (Vigas)
EJE X
linfluencia b h Peso
Plosa = 350 5.5 1925 Kg/m
Pacabados = 200 5.5 1100 Kg/m
PVIGA = 2400 0.5 0.75 900 Kg/m
CM = 3925 Kg/m
S/C = 400 6 2400 Kg/m
CV = 2400 Kg/m
Wu = 9575.00
EJE Y
linfluencia b h Peso
Plosa = 350 2 700 Kg/m
Pacabados = 200 2 400 Kg/m
PVIGA = 2400 0.5 0.5 600 Kg/m
CM = 1700 Kg/m
S/C = 400 2.5 1000 Kg/m
CV = 1000 Kg/m
Wu = 4080.00
K L Momentos
1/9 7 MX = 52.131 Tn.m
1/9 5.5 MY = 13.713 Tn.m
P = 381.865 Tn
Cuantia Asumida = 2 %
Ag = 2886.357 cm2
Sec. Cuad = 53.725 cm
Seccin
b = 50 cmh = 90 cm
recub = 5 cm
P3.- Disear la columna que se muestra en el plano adjunto; considerar: f'c = 210 Kg/cm2 y acero de fy = 4200 Kg/cm2. Si el plano que se m
corresponde a una universidad de 5 pisos (altura piso techo es h = 3 m incluido losa).
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XX
h = 80 = 0.9
Kn = 0.62
Rn = 0.009 Cuantia x = 1
As = 45
As var = 25.3
YY
h = 40 = 0.8
Kn = 0.62
Rn = 0.004 Cuantia y = 1
As = 45
As var = 25.3
Cuantia T = 1.12 %
P0 = 812.616 Tn
XX
Kn x = 0.68 Pux = 417.69 Tn
YY
Kn y = 0.76 Puy = 466.83 Tn
1/P = 0.00330563
P = 302.51 Corregir
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Kg/cm2 Tn/m2
Admisible = 0.9 9
PD PL PT PT(Factorizada)P1 = 40 25 65 98.5 Tn
P2 =
40 25 65 98.5 Tn
130 197 Tn
Columna (Ext.) 0.4 0.4
Columna (Int.) 0.4 0.4 h = 1.500 m
L1 = 5 m f'c = 210 Kg/cm
L = 5.4 m
PT
Admisible
rea za ata = 14.444 m
DISEO DE ZAPATAS COMBINADAS
TOTAL
Secciones ( b * t )
Profundidad de cimentacin
rea(zapata) =
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R = 130.000 Tn
x0
=2.900 m
LZ = 2x0 LZ = 5.8 m
Lv = 0 m
B = 2.5 m
B = 2.5 mLZ = 5.8 m
Reaccin neta por unidad de longitud
WNU = 33.966 Tn/m
Reaccin neta por unidad de longitud
Wnu = 13.586 Tn/m
Wnu = 1.4 Kg/cm
Clculo de hz ( profundidad mnima 0,60 m)
hz = 0.6 m
hz = 0.64107937 m
2
tLP
2
tPRx 12
110
Z
F2F1
NUL
PTPT
W
B
WW NUnu
nu1z WL0.11h
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DISEO EN SENTIDO LONGITUDINAL
X0 = 2.9
Mmx = -123.125 Tn.m
0NUF1xWPT-0Vx
2
t
xPT2
x
WM
1
0F1
2
0
NUmx
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VERIFICACIN POR CORTANTE
= 1 '' Pulgadas
Recubrimiento = 7.5 cm
d1 = 55.34 cm
VP1(+) = 6.79 Tn VP2(+) = 91.71 Tn
VP1(-) = -91.71 Tn VP2(-) = -6.79 Tn
y1 = 0.753 m
Vd1 = -66.118 Tn
y2 = 0.753 m
Vd2 = 66.118 Tn
= 3/4'' Pulgadas
Recubrimiento = 7.5 cm
d2 = 55.66 cm
y2 = 0.757 m
Vd3 = -18.904 Tn
Vu = 66.118 Tn
Vn = 77.786 Tn
Vc = 106.255 Tn
Vn Vc OK.
DISEO POR PUNZAMIENTO
2
Recub.hd Z
d2
ty 11
1NUP1(-)d1yWVV
d2
ty 22
2NU)P2(d2 yWVV
2
Recub.hd Z
d2ty 23
)y-2
tLv(WV 3
2
NUd3
VuV
n
dBf0.53V
cc
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a).- Columna exterior
Vu = 89.735 Tn Vn = 105.571 Tn
b0 = 2.307 m
Vc = 203.483 Tn
Vn Vc OK.
b).- Columna interior
Vu = 86.151 Tn Vn = 101.354 Tn
b0 = 3.814 m
Vc = 336.396 Tn
Vn Vc OK.
DISEO POR FLEXIN
a).- Refuerzo superior
Mmx = Mu = 123.125 Tn.m
a = d/5 a = 11.068 cm
dbf1.1V0
cc
dbf1.1V0
cc
a
MAs mx
fAsa
'
y
2
db
2
dtWPTVu 11
1
1NUF1
222NUF2 dtWPTVu
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As = 65.402 cm2 As = 62.146 cm2
a = 6.2 cm a = 5.8 cm
As = 62.328 cm2 As = 62.146 cm2
a = 5.9 cm a = 5.8 cm
As = 62.156 cm2 As = 62.146 cm2
a = 5.8 cm
As (mnimo) = 0,0018*b*d As (mnimo) = 24.902 cm
As = 62.146 cm2
Usar : = 3/4'' s = 0.111 m
22 3/4'' @ 0.11 m
a).- Refuerzo inferior
Mu = 0.000 Tn.m
a = d/5 a = 11.131 cm
As = 0.000 cm2 As = 0.000 cm2
a = 0.0 cm a = 0.0 cm
As = 0.000 cm2 As = 0.000 cm2
a = 0.0 cm a = 0.0 cm
As = 0.000 cm2 As = 0.000 cm2
a = 0.0 cm
As (mnimo) = 0,0018*b*d As (mnimo) = 25.045 cm
As = 25.045 cm2
Usar : = 3/4'' s = 0.291 m
9 3/4'' @ 0.29 m
DISEO DE LA SECCIN TRANSVERSAL
)2
-d(fy
c
)2
a-d(f
MAs
y
mx
Bf
fAsa
'
c
y
2
LWM
2
VNU
u
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l1
=68
l1
=70
l2 = 96 l2 = 95
DISEO VIGA EXTERIOR
qNU = 39.400
Mu = 21.719 Tn.m
a = d/5 a = 11.068 cm
As = 11.537 cm2 As = 10.733 cm2
a = 3.9 cm a = 3.6 cm
As = 10.760 cm2 As = 10.733 cm2
a = 3.6 cm a = 3.6 cm
As = 10.734 cm2 As = 10.733 cm2
a = 3.6 cm
As (mnimo) = 0,0018*b*d As (mnimo) = 6.973 cm
)2
a-d(f
MAs
y
mx
Bf
fAsa
'
c
y
B
PTq F1NU
2
2
t-Bq
M
2
1
NU
u
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As = 10.733 cm2
Usar : = 3/4'' s = 0.177 m
4 3/4'' @ 0.18 m
Dieo por montaje :
Smx = 36 = 68.58 cm
= 3/8'' s = 1.145 m3 3/8'' @ 1.15 m
DISEO VIGA INTERIOR
qNU = 39.400
Mu = 21.719 Tn.m
a = d/5 a = 11.131 cm
As = 11.471 cm
2
As = 10.573 cm
2
a = 2.8 cm a = 2.6 cm
As = 10.594 cm2 As = 10.573 cm2
a = 2.6 cm a = 2.6 cm
As = 10.573 cm2 As = 10.573 cm2
)2
a-d(f
MAs
y
mx
Bf
fAsa
'
c
y
B
PT
qF2
NU 2
2
t-Bq
M
2
2NU
u
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a = 2.6 cm
As (mnimo) = 0,0018*b*d As (mnimo) = 9.517 cm
As = 10.573 cm2
Usar : = 1/2'' s = 0.112 m
8 1/2'' @ 0.11 m
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