Examen Final CAII 2012 II

7/29/2019 Examen Final CAII 2012 II

1/17

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


2/17

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 (+)


1 1/2 0 1 = 1.267

ACERO As (-)


1 1/2 0 1 = 1.267

SEPARACIN DEL ACERO

Acero mnimo

As (+) =

+

+

+

1/10

1/121/12


3/17

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 =


4/17

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.


5/17

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


6/17

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).


7/17

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


8/17

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) =


9/17

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


10/17

DISEO EN SENTIDO LONGITUDINAL

X0 = 2.9

Mmx = -123.125 Tn.m

0NUF1xWPT-0Vx

2

t

xPT2

x

WM

1

0F1

2

0

NUmx


11/17

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


12/17

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


13/17

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 = 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


14/17

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


)2

a-d(f

MAs

y

mx

Bf

fAsa

'

c

y

B

PTq F1NU

2

2

t-Bq

M

2

1

NU

u


15/17

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


16/17

a = 2.6 cm


As = 10.573 cm2

Usar : = 1/2'' s = 0.112 m

8 1/2'' @ 0.11 m


17/17

Examen Final CAII 2012 II

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