I.S.T.P "JOSÉ CARLOS MARIATEGUI" CONCRETO ARMADO VI SEMESTRE
DOCENTE : ING. JUAN LAJO RODRIGUEZ ALUMNO :ROBERTO FLORES RAMIREZ
DISEÑOS DE :
• VS EN EL SEGUNDO NIVEL • COLUMNA DEL CUARTO PISO
• VP EN ELQUINTO PISO • COLUMNA Y ZAPATA EN EL SEGUNDO PISO
• LOSA EN EL PRIMER PISO • COLUMNA Y ZAPATA EN EL TERCER PISO
DATOS GENERALES
1 er piso = 4.00
2 er piso = 3.80
3 er piso = 3.60
4 er piso = 3.40
5 er piso = 3.20
PLANO A DESARROLLAR
Ancho Tributario
5.90
H VS VS VS VS VS
###
VP
SENTID O DEL ALIGERADO
COL. EN EL 2º PISO
G VS
###
ZAPATA
VP
F VS
LO
SA
EN
EL
1º
PIS
O
###
VP
E VS
VP
EN
EL
5º
PIS
O
### V
P
VP
VP
VP
VP
COLUMNA EN EL 3º PISO
D VS
###
VP
ZAPATA
C VS
PLA
CA
PLA
CA
###
VP
###B VS EN 2º PISO
###
VP
COLUM 4º PISO
UBICACIÓN :ANCASH
USO : OFICINAS
Nº DE PISO : 5
I.S.T.P "JOSÉ CARLOS MARIATEGUI" CONCRETO ARMADO VI SEMESTRE
DOCENTE : ING. JUAN LAJO RODRIGUEZ ALUMNO :ROBERTO FLORES RAMIREZ
A VS7.30 4.50 5.60 5.30 5.60
1 2 3 4 5 6
DISEÑO DE VS EN EL SEGUNDO NIVEL
DATOS :
S/C = 500 salas de archivo OFICINAS
###
PISO T = 100
###F'c = 210 h d
Fy = 4200
ESPESOR DE LOSA = 20 cm
VIGA SECUNDARIA = 0.5 x 0.3 m b
RECUBRIMIENTO = 6 cm 30
Pp de losa de 20cm = 300
γ del concreto = 2400 = 2.4 ton/m3
28.30
C VS
PLA
CA
PLA
CA
###
VP
Anch
o tr
ibut
ario
###B VS EN 2º PISO
###
VP
A VS7.30 4.50 5.60 5.30 5.60
1 2 3 4 5 6
METRADO DE CARGAS
Se realiza por ancho tributario AT = 4.60 - 0.30
AT = 4.30
CARGA MUERTA : CM
Pp losa = 0.300 ton/m2 x 4.30 = 1.29 ton/m
Pp viga = 0.30 x 0.50 x 2.4 = 0.36 ton/m
Pp piso T = 0.10 x 4.30 = 0.43 ton/m
CM = 2.08 ton/m
CARGA VIVA : CV Se realiza con el ancho tributario sin descontar la viga
CV = S/C x AT
0.50 x 4.60 = 2.30 ton/m
CV = 2.30 ton/m
CALCULO DEL WURNC
Wu= 1.5 (CM)+1.8(CV)Wu= 7.26 ton/m
PARA EL CALCULO DE " q "
KU = Ø q F'c ( 1-0.59 q )
KU = 0.9 q 210 ( 1-0.59 q )
KU = 189 q - 111.5
111.5 - 189 q + KU = 0
111.5-
189 q+
KU= 0
111.51 111.5 111.5
q2 - 1.695 q +KU
= 0
Kg/m2
Kg/m2
Kg/m2
Kg/m2
Kg/m2
Kg/m3
q2
q2
q2
I.S.T.P "JOSÉ CARLOS MARIATEGUI" CONCRETO ARMADO VI SEMESTRE
DOCENTE : ING. JUAN LAJO RODRIGUEZ ALUMNO :ROBERTO FLORES RAMIREZ
q2 - 1.695 q +111.5
= 0
q =1.695 - 1.695 4
KU
111.5
2
para tomar el menor
DIAGRAMA A ANALIZAR
7.26
7.3 m 4.50 m 5.6 m 5.30 m 5.60 m
1/16 1/10 1/11 1/11 1/10 1/16
1/14 1/16 1/16 1/16 1/14
Luces 7.30 5.90 5.05 5.45 5.45 5.60
Promedio 7.30 4.500 5.60 5.30 5.60
Mu = 24.18 25.27 16.83 19.60 21.56 14.23
27.63 9.19 14.23 12.75 16.26
41.63 43.51 28.98 33.75 37.13 24.50
47.58 15.82 24.50 21.95 28.00
q = 0.260 0.275 0.170 0.203 0.227 0.141
0.308 0.088 0.141 0.125 0.164
ρ = (q x f`c ) 0.01301 0.01374 0.00852 0.01014 0.01134 0.00707fy 0.01538 0.00442 0.00707 0.00627 0.00820
AS= ρ x b x d 17.18 18.13 11.25 13.39 14.97 9.33
20.30 5.83 9.33 8.28 10.83
7 Ø de 3/4 4 Ø de 3/4 5 Ø de 3/4 5 Ø de 3/4 4 Ø de 3/4
4 Ø de 1'' 2 Ø de 3/4 2 Ø de 1'' 3 Ø de 3/4 2 Ø de 1''
uniformizando
2 Ø de 3/4 3 Ø de 3/4 4 Ø de 3/4 1 Ø de 3/4 1 Ø de 3/4
4 Ø de 1''
2 -
KU = Mu/bd2
6 Ø de 3/4
I.S.T.P "JOSÉ CARLOS MARIATEGUI"CONCRETO ARMADO VI SEMESTRE
DOCENTE : ING. JUAN LAJO RODRIGUEZ ALUMNO :ROBERTO FLORES RAMIREZ
DISEÑO DE VP EN EL QUINTO NIVEL
DATOS :
S/C = 500 salas de archivo OFICINAS
64
PISO T = 100
70F'c = 210 h d
Fy = 4200
ESPESOR DE LOSA = 20 cm
VIGA PRINCIPAL = 0.7 x 0.35 m b
RECUBRIMIENTO = 6 cm 35
Pp de losa de 20cm = 300
γ del concreto = 2400 = 2.4 ton/m3
A 4.50 B 4.70 C 5.20 D 7.60 E 6.50 F 5.50 G 7.50 H4
5.30
5.45
Anch
o tr
ibut
ario
5 PLACA VP EN EL 5º PISO
5.60
6
METRADO DE CARGAS
Se realiza por ancho tributario AT = 5.45 - 0.35
AT = 5.10 CARGA VIVA : CV
CARGA MUERTA : CM Se realiza con el ancho tributario sin descontar la viga
Pp losa = 0.300 ton/m2 x 5.10 = 1.53 ton/m CV = S/C x AT
Pp viga = 0.35 x 0.70 x 2.4 = 0.588 ton/m
Pp piso T = 0.10 x 5.10 = 0.51 ton/m 0.50 x 5.45 = 2.72 ton/m
CM = 2.63 ton/m CV = 2.72 ton/m
Kg/m2
Kg/m2
Kg/m2
Kg/m2
Kg/m2
Kg/m3
I.S.T.P "JOSÉ CARLOS MARIATEGUI"CONCRETO ARMADO VI SEMESTRE
DOCENTE : ING. JUAN LAJO RODRIGUEZ ALUMNO :ROBERTO FLORES RAMIREZ
CALCULO DEL WU PARA EL CALCULO DE " q "
RNCWu= 1.5 (CM)+1.8(CV) KU = Ø q F'c ( 1-0.59 q )
q2 - 1.695 q +KU
= 0Wu= 8.847 ton/m KU = 0.9 q 210 ( 1-0.59 q ) 111.51
KU = 189 q - 111.51
q =1.695 - 1.695 4
KU
111.51 - 189 q + KU = 0 111.51
111.51-
189 q+
KU= 0
2
111.51 111.51 111.51
para tomar el menor
DIAGRAMA A ANALIZAR
8.847
4.5 m 4.70 m 5.2 m 7.60 m 6.50 m 5.50 m 7.50 m
1/16 1/10 1/10 1/11 1/11 1/10 1/10 1/16
1/14 1/16 1/16 1/16 1/16 1/16 1/14
Luces 4.50 4.60 4.95 6.40 7.05 6.00 6.50 7.50
Promedio 4.50 4.700 5.20 7.60 6.50 5.50 7.50
Mu = 11.20 18.72 21.68 32.94 39.97 31.85 37.38 31.10
12.80 12.21 14.95 31.94 23.36 16.73 35.55
7.81 13.06 15.12 22.98 27.88 22.22 26.07 21.70
8.93 8.52 10.43 22.28 16.30 11.67 24.79
q = 0.042 0.072 0.084 0.132 0.163 0.127 0.151 0.124
0.049 0.046 0.057 0.127 0.091 0.064 0.143
ρ = (q x f`c ) 0.0021 0.0036 0.0042 0.0066 0.0082 0.0064 0.0076 0.0062
fy 0.0024 0.0023 0.0029 0.0064 0.0046 0.0032 0.0072
AS= ρ x b x d 4.75 8.08 9.43 14.77 18.29 14.23 16.97 13.87
5.45 5.19 6.40 14.28 10.21 7.19 16.05
q2
2 -q2
q2
KU = Mu/bd2
I.S.T.P "JOSÉ CARLOS MARIATEGUI"CONCRETO ARMADO VI SEMESTRE
DOCENTE : ING. JUAN LAJO RODRIGUEZ ALUMNO :ROBERTO FLORES RAMIREZ
4 Ø de 5/8 5 Ø de 5/8 5 Ø de 3/4 7 Ø de 3/4 5 Ø de 3/4 6 Ø de 3/4 5 Ø de 3/4
2 Ø de 3/4 2 Ø de 3/4 1 Ø de 3/4 + 2 Ø de 5/8 5 Ø de 3/4 2 Ø de 1'' 3 Ø de 3/4 6 Ø de 3/4
4 Ø de 1/2
I.S.T.P "JOSÉ CARLOS MARIATEGUI"CONCRETO ARMADO VI SEMESTRE
DOCENTE : ING. JUAN LAJO RODRIGUEZ ALUMNO :ROBERTO FLORES RAMIREZ
ANALISIS DE DISEÑO DE COLUMNAS - ESQUINERA
3.65 3.65
COLUMNA ESQUINERA : del 4º PISO BNº PISOS
DATOS Nº h
2.25VP = 35 x 70 I 4.00
VS = 30 x 50 II 3.80
VP
C4 = 40 x 40 III 3.60
###
fy = 4200 IV 3.40
f'c = 210 V 3.20
2.25γ c = 2.4 Ton/m3
losa = 20 cm
PISO T = 100
s/c = 300 Pp de losa de 20cm A VS
s/c = 500 kg/cm2 salas de archivo OFICINAS 1 7.30 2# de veces = 5 pisos - 4 pisos
# de pisos = 1 pisos
METRADOS
= ( - ) A vp AT y b col x b vp = ( - ) A vs ATx b col xb vp = A col L X A
AREA VP = 2.25 - 0.40 ) X 0.35 = 0.65
AREA VS = 3.65 - 0.40 ) X 0.3 = 0.98
AREA COL. = 0.40 X 0.40 0.160
1.78
AREA TOTAL = 3.65 X 2.25 = AT = 8.21
AREA LOSA. = 8.21 - 1.78 = A LOSA = 6.430
CALCULO DE CARGAS
a) CARGAS VIVAS CV
cv = S/C x ( AreaT - Area COL ) X # pisocv = 0.5 X ( 8.21 - 0.16 ) X 1
cv = 4.026 ton
b) CARGAS MUERTAS CM
PPpt = S/C x (AreaT - AreaCol) x # de piso = 0.10 X ( 8.21 - 0.16 ) X 1 PP pt = 0.805 ton
PP loza = A losa x S/C x # = 6.430 x 0.300 x 1 PP L = 1.929 ton
PP vp = Area vp x hvp x γ c' x # de piso = 0.65 x 0.70 x 2.40 x 1 PP vs = 1.088 ton
PP vs = Area vs x hvs x γc' # de piso = 0.98 x 0.50 x 2.40 x 1 PP vp = 1.17 ton
PP col = b x t x h piso x γc' 5º piso = 0.40 x 0.40 x 3.20 x 2.40 PP col = 1.229 ton
CM = 6.221 ton
CARGAS ULTIMA
PU = 1.5 CM + 1.8 CV
PU =( 1.5 x 6.221 ) + 1.8 X 4.026 )
PU = 16.579 ton
Kg/m2
Kg/m2
Kg/m2
Kg/m2
m2
m2
m2
m2
I.S.T.P "JOSÉ CARLOS MARIATEGUI"CONCRETO ARMADO VI SEMESTRE
DOCENTE : ING. JUAN LAJO RODRIGUEZ ALUMNO :ROBERTO FLORES RAMIREZ
PARA UNA COLUMNA CON ESTRIBOS
REFUERZO LONGITUDINAL
PU = Ø x 0.80 x ( 0.85 x f'c ( Ag - As ) + As x fy )
### = 0.70 x 0.80 x ( 0.85 X 0.210 x ( 0.16 - As ) + As x 4.200
16.58 = 0.56 x ( 0.179 x ( 0.16 - As ) + 4.200 As )
16.58 = 0.56 x ( 0.029 - 0.179 As + 4.200 As )
16.58 = 0.56 x ( 0.029 + 4.022 As )
16.58 = 0.016 + 2.252 As
-0.016 + 16.58 = 2.252 As
-0.016 + 16.58 = As
2.252
7.354 = As
As = 7.35 cm2
ADOPTAMOS = 4 Ø 5/8"
REFUERZO TRANSVERSAL
* POR CONFINAMIENTO ( NORMA 2.4.6 )
t = 0.40 m
LONGITUD = h/6 = 0.53 m @ 0.10 m
si h = 3.20 m Ø 3/8"
* ZONAS NO CONFINADAS ( R.C.N.)
16 Ø L = 16 x 0.953 = 15.25 cm
Ø 3/8" 48 Ø e = 48 x 0.953 = 45.74 cm Para diseño tomamos el menor
0.953 b = 40 cm
1 @ 0.05
2 @ 0.10
0.40 2 @ 0.15
resto @ 0.20
0.4
0 4 Ø 5/8"
Ø 3/8"
I.S.T.P "JOSÉ CARLOS MARIATEGUI"CONCRETO ARMADO VI SEMESTRE
DOCENTE : ING. JUAN LAJO RODRIGUEZ ALUMNO :ROBERTO FLORES RAMIREZ
ANALISIS DE DISEÑO DE COLUMNA PERIMETRAL
2.80 2.80
COLUMNA ESQUINERA : del 3º PISO ENº PISOS
DATOS Nº h
7.6
VP
VP = 35 x 70 I 4.00
3.80
6.40
VS = 30 x 50 II 3.80
C4 = 40 x 40 III 3.60 Dfy = 4200 IV 3.40
2.60f'c = 210 V 3.20
γ c = 2.4 Ton/m3
5.2
losa = 20 cm
PISO T = 100
s/c = 300 Pp de losa de 20cm C VS
s/c = 500 kg/cm2 salas de archivo OFICINAS 5 5.60 6# de veces = 5 pisos - 3 pisos
# de pisos = 2 pisos
METRADOS
A vp = (AT y - b col ) x b vp A vs = (ATx - b col)xb vp A col = L X A
AREA VP = 6.40 - 0.40 ) X 0.35 = 2.10
AREA VS = 2.80 - 0.40 ) X 0.3 = 0.72
AREA COL. = 0.40 X 0.40 0.160
2.98
AREA TOTAL = 6.40 X 2.80 = AT = 17.92
AREA LOSA. = 17.92 - 2.98 = A LOSA = 14.940
CALCULO DE CARGAS
a) CARGAS VIVAS CV
cv = S/C x ( AreaT - Area COL ) X # pisocv = 0.5 X ( 17.92 - 0.16 ) X 2
cv = 17.8 ton
b) CARGAS MUERTAS CM
PPpt = S/C x (AreaT - AreaCol) x # de piso = 0.10 X ( 17.92 - 0.16 ) X 2 PP pt = 3.552 ton
PP loza = A losa x S/C x # = ### x 0.300 x 2 PP L = 8.964 ton
PP vp = Area vp x hvp x γ c' x # de piso = 2.10 x 0.70 x 2.40 x 2 PP vs = 7.056 ton
PP vs = Area vs x hvs x γc' # de piso = 0.72 x 0.50 x 2.40 x 2 PP vp = 1.728 ton
PP col = b x t x h piso x γc' 4º piso = 0.40 x 0.40 x 3.40 x 2.40 PP col = 1.306 ton
5º piso = 0.40 x 0.40 x 3.20 x 2.40 PP col = 1.229 ton
CM = 23.83 ton
CARGAS ULTIMA
PU = 1.5 CM + 1.8 CV
PU =( 1.5 x 23.83 ) + 1.8 X 17.76 )
Kg/m2
Kg/m2
Kg/m2
Kg/m2
m2
m2
m2
m2
I.S.T.P "JOSÉ CARLOS MARIATEGUI"CONCRETO ARMADO VI SEMESTRE
DOCENTE : ING. JUAN LAJO RODRIGUEZ ALUMNO :ROBERTO FLORES RAMIREZ
PU = 67.720 ton
PARA UNA COLUMNA CON ESTRIBOS
REFUERZO LONGITUDINAL
PU = Ø x 0.80 x ( 0.85 x f'c ( Ag - As ) + As x fy )
### = 0.70 x 0.80 x ( 0.85 X 0.210 x ( 0.16 - As ) + As x 4.200
67.72 = 0.56 x ( 0.179 x ( 0.16 - As ) + 4.200 As )
67.72 = 0.56 x ( 0.029 - 0.179 As + 4.200 As )
67.72 = 0.56 x ( 0.029 + 4.022 As )
67.72 = 0.016 + 2.252 As
-0.016 + 67.72 = 2.252 As
-0.016 + 67.72 = As
2.252
30.06 = As
As = 30.06 cm2
ADOPTAMOS = 6 Ø DE 1"
REFUERZO TRANSVERSAL
* POR CONFINAMIENTO ( NORMA 2.4.6 )
t = 0.40 m
LONGITUD = h/6 = 0.53 m @ 0.10 m
si h = 3.20 m Ø 3/8"
* ZONAS NO CONFINADAS ( R.C.N.)
16 Ø L = 16 x 0.953 = 15.25 cm
Ø 3/8" 48 Ø e = 48 x 0.953 = 45.74 cm Para diseño tomamos el menor
0.953 b = 40 cm
1 @ 0.05
2 @ 0.10
0.40 2 @ 0.15
resto @ 0.20
0.4
0 6 Ø DE 1"
Ø 3/8"
I.S.T.P "JOSÉ CARLOS MARIATEGUI"CONCRETO ARMADO VI SEMESTRE
DOCENTE : ING. JUAN LAJO RODRIGUEZ ALUMNO :ROBERTO FLORES RAMIREZ
ANALISIS DE DISEÑO DE COLUMNA CENTRICA
5.05
COLUMNA ESQUINERA : del 2º PISO HNº PISOS
VP
DATOS Nº h 2.25 2.80
7.5VP = 35 x 70 I 4.00
6.50
3.75
VS = 30 x 50 II 3.80
C4 = 40 x 40 III 3.60 G
2.75fy = 4200 IV 3.40
f'c = 210 V 3.20
5.5γ c = 2.4 Ton/m3
losa = 20 cm
PISO T = 100 F VS
s/c = 300 Pp de losa de 20cm OFICINAS 2 4.5 3 5.6 4s/c = 500 kg/cm2 salas de archivo
# de veces = 5 pisos - 2 pisos
# de pisos = 3 pisos
METRADOS
= ( - ) A vp AT y b col x b vp = ( - ) A vs ATx b col xb vp = A col L X A
AREA VP = 6.50 - 0.40 ) X 0.35 = 2.14
AREA VS = 5.05 - 0.40 ) X 0.3 = 1.39
AREA COL. = 0.40 X 0.40 0.160
3.69
AREA TOTAL = 6.50 X 5.05 = AT = 32.82
AREA LOSA. = 32.82 - 3.69 = A LOSA = 29.135
CALCULO DE CARGAS
a) CARGAS VIVAS CV
cv = S/C x ( AreaT - Area COL ) X # pisocv = 0.5 X ( 32.82 - 0.16 ) X 3
cv = 49.0 ton
b) CARGAS MUERTAS CM
PPpt = S/C x (AreaT - AreaCol) x # de piso = 0.10 X ( 32.82 - 0.16 ) X 3 PP pt = 9.7995 ton
PP loza = A losa x S/C x # = 29.135 x 0.300 x 3 PP L = 26.222 ton
PP vp = Area vp x hvp x γ c' x # de piso = 2.14 x 0.70 x 2.40 x 3 PP vs = 10.76 ton
PP vs = Area vs x hvs x γc' # de piso = 1.39 x 0.50 x 2.40 x 3 PP vp = 5.022 ton
PP col = b x t x h piso x γc' 3º piso = 0.40 x 0.40 x 3.60 x 2.40 PP col = 1.3824 ton
4º piso = 0.40 x 0.40 x 3.40 x 2.40 PP col = 1.3056 ton
5º piso = 0.40 x 0.40 x 3.20 x 2.40 PP col = 1.2288 ton
CM = 55.72 ton
CARGAS ULTIMA
PU = 1.5 CM + 1.8 CV
Kg/m2
Kg/m2
Kg/m2
Kg/m2
m2
m2
m2
m2
m2
m2
PU =( 1.5 x 55.72 ) + 1.8 X 49 )
PU = 171.776 ton
PARA UNA COLUMNA CON ESTRIBOS
REFUERZO LONGITUDINAL
PU = Ø x 0.80 x ( 0.85 x f'c ( Ag - As ) + As x fy )
### = 0.70 x 0.80 x ( 0.85 X 0.210 x ( 0.16 - As ) + As x ###
171.78 = 0.56 x ( 0.179 x ( 0.16 - As ) + 4.200 As )
171.78 = 0.56 x ( 0.0286 - 0.179 As + 4.200 As )
171.78 = 0.56 x ( 0.0286 + 4.022 As )
171.78 = 0.016 + 2.252 As
-0.016 + 171.78 = 2.252 As
-0.016 + 171.78 = As
2.252
76.269 = As
As = 76.27 cm2
ADOPTAMOS = 4 Ø 1 1/4" + 8 Ø 1''
REFUERZO TRANSVERSAL
* POR CONFINAMIENTO ( NORMA 2.4.6 )
t = 0.40 m
LONGITUD = h/6 = 0.53 m @ 0.10 m
si h = 3.20 m Ø 3/8"
* ZONAS NO CONFINADAS ( R.C.N.)
16 Ø L = 16 x 0.953 = 15.248 cm
Ø 3/8" 48 Ø e = 48 x 0.953 = 45.744 cm Para diseño tomamos el menor
0.953 b = 40 cm
1 @ 0.05
2 @ 0.10
0.40 2 @ 0.15
resto @ 0.20
0.4
0 4 Ø 1 1/4" + 8 Ø 1''
Ø 3/8"