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1er Casoaligerado 3 tramos 3.10 21 = 0.15 > 0.2
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Luz 0.50 1.35 3.10 ,igideces 1.00 0.30 0.0 1.00
1 2 3udo .0-1 !1- !1- !-3 !-3 !3-6
W 0 0 0 0 0 0
L 0.5 1.35 1.35 3.1 3.1 0
const 6 1 1 1 1 6
L)con ". 133. 133. 06. 06. 0.0
1 -1 1 -1 1 -1
". -133. 133. -06. 06. 0.0
udo 1 2 37ramo 0-1 1- 1- -3 -3 3-6
1.00 0.30 0.0 0.0 0.00
)sum 1.00 0.30 0.0 1.00 0.00
CR!!-1.00 -0.30 -0.0 -1.00
M.+. " #134 134 #705 705 0
16 -16 8 -35 05 -05
-81
131 81 800 300
0.00 -131 131 -300 0
-85 -150
85 150 -15
33 5
0.00 -33 33 -5 0
-18 -3
18 3 -56
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1O
1"
0.00 - -1" 0
-6 -"
6 " -13
" #" 457 #457 0 0
A/SCD " " 457 457 0 0
der iB$ der iB$ der iB$
6. AAL'S'S 7,AMO EO, 7,AMO
,i = L ) C Mi - Md D ) L +SF;+,(O de &O,7+ 4i = ,i - n
,d = L - ,i 4d = ,d - n
GCD = ,i ) MOM+7OS + 'S+HO
GICD = L - GCD G = ancho de apoJo )
MCD = ,i ) C D - Mi M@ = ,i G - Mi - G )
Gi = GCD - C GCD - Mi ) D MI@ = ,d G - Md - G )
Gd = GICD - C GICD - Md ) D MCD = ,i ) C D - Mi
1 2 3
L 1.6 3.1
Ancho apoJo = 0.5 es apoJado 0.5 es apoJado
/ase = 0.10 0.10
losa = h = 0.1 0.1
ecurimiento 0.03 0.03
d 0.0" 0.0"
n 0.1" 0.1"
G 0.10
0.0 0.0
L 1.10 .5
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4
03/10/2016 ING.CIVL1Omo
Mi " 65
Md 65 0
,i 1616
,d "1 10"6
GCD 0.0" 1.81
GICD 1.01 1.6
MCD -8 80
Gi -1.00 0.38
Gd -1.00 0.00
+SF;+,(O de &O,7+
4i -"0 16
4d 6 "8
MOM+7OS + 'S+HO
M@ -" -30
MI@ -3 105
CD -8 80
7ramo LuB ancho de d % Momento C-D ,eacciones Momentos de di+s#uerB cortant Eunto de in#le@
apoJo ' ' GCD ' CD ' '
1er Caso M@ MK@ MCD1- 1.10 0.5 0.1" 0 -". -3.6 8. "1.3 0.1 -". -3.6 -5. -"0.5 6.1 -1.00 -1.00
-3 .5 0.5 0.1" 0 -30.1 105.0 1616.6 10"3.8 1.8 -30.1 105.0 8".5 16. "8.6 0.38 0.00
7ramo LuB ancho de d % Momento C-D ,eacciones Momentos de di+s#uerB cortant Eunto de in#le@
apoJo ' ' GCD ' CD ' '
2do Caso M@ MK@ MCD1- .55 0.5 0.3 50 -3. -8.5 68". 100". 0. -3. -8.5 15.5 6. 3.8 0.0 1.01
-3 3.60 0.5 0.3 50 -80".1 53. 11"3.0 ".0 .1 -80".1 53. 501.6 100.6 5"3.6 0.6 0.03
3-6 0.00 0.00 0.00 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.00
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1Omo
7ramo LuB ancho de d % Momento C-D ,eacciones Momentos de di+s#uerB cortant Eunto de in#le@
apoJo ' ' GCD ' CD ' '
3er Caso M@ MK@ MCD1- .55 0.5 0.3 50 -3. -8.5 68". 100". 0. -3. -8.5 15.5 6. 3.8 0.0 1.01
-3 3.60 0.5 0.3 50 -80".1 53. 11"3.0 ".0 .1 -80".1 53. 501.6 100.6 5"3.6 0.6 0.03
3-6 0.00 0.00 0.00 0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.00
EA,A LOS *,AF'&OS M@ = ,i G - Mi - G )
MI@ = ,d G - Md - G )
1er &asdo &aso3er &as 0 0.0 1er &asodo &aso 3er &aso 0.0 0.0
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1Omo
1- 1- 1- 0 0.0 -3 -3 -3 0.0 0.0
,i 8. 68". 68". 0.0 0.0 1616.6 11"3.0 11"3.0 0.0 0.0
0.0 50.0 50.0 0.0 0.0 0.0 50.0 50.0 0.0 0.0
Mi ". 3. 3. 0.0 0.0 30.1 80".1 80".1 0.0 0.0L 1.10 .55 .55 0 0.0 .5 3.6 3.6 0.0 0.0
0 " 3 3 0 0 30.1 16055.3 38"05.1 0.0 0.0
0. 11 -65 -65 0 0 56.
0.6 6" -106 -106 0 0 -15.3
0.8 1 -160 -160 0 0 -30.1
0. " -15 -15 0 0 -5".
1 3 -16 -16 0 0 -856.3
1. 551 -10 -10 0 0 -63.8
1.6 86 -5 -5 0 0 -".
1.8 1013 " " 0 0 -18.5
1. 1" 13 13 0 0 -00.
1818 5 5 0 0 -6.
. 1"0 60 60 0 0 -88.0
.6 35" 51 51 0 0 -560.1
.8 6 0 0 -3."
. 366 ""8 ""8 0 0 -1"0.8
30.1
30.1
30.1
30.1
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1Omo
0
0.0 0.0 0.0
' ' '
-1.00 -1.00 0.38 0.00 0.00 0.00
0.0 1.01 0.6 0.03 0.00 0.00
Ma@imos 0.0 1.01 0.6 0.03 0.00 0.00
0.0 0.0 0.0
0.0 0.0 0.0
M@ MK@ MCD M@ MK@ MCD M@ MK@ MCD
". 3.6 -5. 30.1 105.0 8".5 0.0 0.0 0.0
3. 8.5 15.5 80".1 53. 501.6 0.0 0.0 0.0
0.0 3. 8.5 15.5 80".1 105.0 8".5 0.0 0.0 0.0
0.0 80".1 105.0 8".5
0.0 8".5 0.0 0.0
0.0 0
$%#& $%'& ' 1 37.8 0.0 152.5 0.1 1.0
627.5 0.0 67".5 0. 0.0
3 67".5 0.0 0.0 0.0 0.0
6 0.0TRAMO1-2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15-500
0
500
1000
1500
2000
2500
3000
3500
1 - 2
Lux
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C ( L C ) L ( C * R +ormulasEara 175 usar AsC-D = 8.0 - C 38.5 - Mu ? 100 ) 5338.6Eara #Ic = 15 g ) cm
AsCD = 6.0 - C 50.00 - MuCD ? 100 ) 1136.1 D C 1) D
Eara 210 usar AsC-D = .3 - C 5.0 - Mu ? 100 ) 666.08Eara #Ic = 10 g ) cm
AsCD = ."0 - C 35.1 - MuCD ? 100 ) 1111.8 D C 1) D
(C*R %#&175 D,ame-ro diametros
(s%#& (s m, (s d,seo
0.08 cm 0.58 0.56 cm
1.0 cm 0.58 1.07 cm
1.1 cm 0.58 1.17 cm
0.00 cm 0.58 0.56 cm0.00 cm 0.58 0.56 cm
(C*R %'&175
(s%'& (s d,seo
0.6 cm 0.24 cm
1.0 cm 1.08 cm
0.00 cm 0.00 cm
0.00 cm 0.00 cm
(C*R %#& 210
(s%#& (s m,
0.08 cm 0.58 0.56 cm
1.08 cm 0.58 1.06 cm
1.15 cm 0.58 1.15 cm
0.01 cm 0.58 0.56 cm
(C*R %'&210
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1O
1 Metrado de cargas g)cm
1.1 &argas permanentes Eeso
Eeso losa aligerada 60 peso C Eeso-iB$ Ees 100 g ) ml
Eeso piso acaado 100 peso C Eeso-iB$ Ees 50 g ) ml
Eeso s)%iga 100 peso ? A-%ig 5 g ) ml
Eeso de trai$ueria 0 peso C L-iB$ L-der 0 g ) ml
Wm 12"5 Kg / ml
1. &argas 4i%as
Sore carga 500 peso C L-iB$ L-der 135
W 1375 Kg / ml1.3 &argasss de dise9o cargas #actoriBadas
Wu 1.4 Wm ' 1.7 W 6150.50 Kg / ml
6.15 / m
Wu 1.4 Wm 1.1 / m AAL'S'S +L EO,7'&O
M+7OO A'
.1 Momento de inercia L
'%1 = A-%ig ? peralte3 ) 1 8061 cm6 5.5 55000
'% = A-%ig ? peralte3 ) 1 8061 cm6 0 0
'c1 = piCD ? d6 ) 86 diamet 30 cm2
'c = A-col ? lado ) 1 3"81 cm6 3 30000
. ,igideces columnas %1 = '%1 ) 6.3
,igideces %igas % = '% ) L
c = 'c ) 1.33
.3 &oe#icientes de distriucion
&c = - c ) C sumatoria C c % D D &%1 &%
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&% = - c ) C sumatoria C c % D D 6.3 0.00
&c 1.33 &c 1.33 &c 1.33
A / &
.6 Momentos de empotramiento L ) 1
M A/ 10.68 7-m
M /A 10.68 7-m
M /& 0.00 7-m
M &/ 0.00 7-m
,+O+O = +&'AL+S
#10.46 -0.3" -10.68 10.68 -0.3" 10.46 0 0.00 0 0.00 0.00-0.11 6.0 -0.11 -0.5
1.15
'S+HO + 4'*AS
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6. 8.01 "."6 8.01
5. 10.86 1.68 10.86
5.8 15." 15. 15."
8 1. 1.3 1.8.6 .6" 1.8 .6"
8. 35. 5.63 35.
3".8 .3 3".8
.6
.
ancho de apoJo 0.5 0.5 0.5 0.5 0.5 0.5
apoJo ) 0.15 0.15 0.15 0.15 0.15 0.15
MiC-D 1.1 13.18 1." 13.18 1.1 13.16 7-m
MdC-D 1. 0.1 13.85 0.1 1. 0.18 7-m
,+S;M+
7,AMO A - /
&ASO MiC-D MdC-D MCD
1 1.1 1. .
1." 13.85 -0.13 1.1 1. .
1." 13.85 .
7,AMO / - &
&ASO MiC-D MdC-D MCD
1 13.18 0.1 0.00
13.18 0.1 0.00
3 13.16 0.18 0.00
13.18 0.1 0.00
13.85 13.18
1 2 3 4 5 6 7 8 9 10111213141516171819202122
0.00
2.00
4.00
6.00
8.00
10.00
12.00
TRAMO B - C
Column!
Column
G
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1." 13.85 0.1
. 0.00
A / &
recurimiento = 6 cm
+strio 3) A,+A 0.1 cm
&AL&;LO +L A&+,O /arra 3)6 A,+A .6 cm
A&+,O + 1 &AEA d = peralte - C recurimiento diametro estrio mitad diametro de la arra D
d = 66 cm
A&+,O + &d = peralte - C recurimiento diametro estrio diametro de la arra espacio de aceros )
d = 61 cm
A&+,O + ,+F;+,(O
A&+,O +*A7'4O % # & d = 66 cmase 5 cm d = 61 cm
#Ic = 15 g)cm
#J = 600 g)cm
iametro ,u = Mu ) C d D
&uantia min = 0.0033 As = cuantia ? ? d
As min = cuantia min ? ? d 3.8300 &uanti ase d =
Mu ase d ,u L As min ,u >= As min V"# $a%la &s
A 1"000 5 66 6.0 5.5 3.8300 %er tala 6.0 0.0033 3.83
/ 1+008 5 61 3.6 0 3.8300 %er tala 3.6 0.0101 10.35
& 1000 5 66 0.3 3 3.8300 &uant min. 3.83 0.0033 3.83
A&+,O EOS'7'4O % ' & d = 66 cmase 5 cm d = 61 cm
#Ic = 15 g)cm
#J = 600 g)cm
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iametro ,u = Mu ) C d D
&uantia min = 0.0033 As = cuantia ? ? d
As min = cuantia min ? ? d 0.0000 &uanti ase =
AEONO ase d ,u As min ,u >= As min 4er ta &s
A-/ 000 5 66 3".03 3.83 3.83 %er tala 3".03 0.0033 3.83
/-& 0 5 66 0.00 3.83 3.83 uant min. 0.00 0.00
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2do Casoaligerado de 3 tramos 3.65 21 = 0.1 > 0.2
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Luz 1.25 2.80 3.65 0.95 ,igideces 1.00 0.63 0.5 1.00
1 2 3udo .0-1 !1- !1- !-3 !-3 !3-6
W 50 50 50 50 50 50
L 1.5 . . 3.85 3.85 0."5
const 6 1 1 1 1 6
L)const 3. 3." 3." 863." 863." 1.
1 -1 1 -1 1 -1
3. -3." 3." -863." 863." -1.
udo 1 2 37ramo 0-1 1- 1- -3 -3 3-6
1.00 0.63 0.5 0.5 0.00
)sum 1.00 0.63 0.5 1.00 0.00
CR!!
-1.00 -0.63 -0.5 -1.00
M.+. 38 #37" 37" #644 644 #22
361 -361 11 -311 8 -8
-605
18 "
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38 #38 726 #726 22 #22
A/SCD 38 38 726 726 22 22
der iB$ der iB$ der iB$
6. AAL'S'S 7,AMO EO, 7,AMO
,i = L ) C Mi - Md D ) L +SF;+,(O de &O,7+ 4i = ,i - n
,d = L - ,i 4d = ,d - n
GCD = ,i ) MOM+7OS + 'S+HO
GICD = L - GCD G = ancho de apoJo )
MCD = ,i ) C D - Mi M@ = ,i G - Mi - G )
Gi = GCD - C GCD - Mi ) D C1)D MI@ = ,d G - Md - G )
Gd = GICD - C GICD - Md ) D C1)D MCD = ,i ) C D - Mi
1 2 3
L . 3.
Ancho apoJo = 0.5 es apoJado 0.5 es apoJado
/ase = 0.10 0.10
losa = h = 0.5 0.5
,ecurimiento 0.03 0.03
d 0. 0.
n 0.3 0.3
G 0.10
50.0 50.0
L .55 3.60
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Mi 3 8
Md 8
,i 60 11"3
,d 100" "
GCD 0.1 .08
GICD 1.6 1.36
MCD 15 501
Gi 0.0 0.6
Gd 1.01 0.03
+SF;+,(O de &O,7+
4i 6 100
4d 6 5"3
MOM+7OS + 'S+HO
M@ -3 -80"
MI@ -8 53
CD 15 501
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3er Casoaligerado de 3 tramos 3.65 21 = 0.1
1. Metrado de cargas Ancho de LOSA = 0.25 m&arga permanentes m
peso de losa aligerada 320 g)m
peso de piso acaado 100 g)m
peso carga e$ui%alente o tai$ueria 0 g)m
D 420
&argas %i%as
sore carga 500 0
L 500
. &argas ultimas de dise9o
A&:O de 4'*;+7A = 0.4 m
&argas en %iguetas
&arga ultima muerta
&arga ultima %i%a
3. eterminacion de momentos&onsiderando %olados imaginarios
+@termos M = L ) i
Medios M = L ) 1 d
&alculo de las rigideces
1 1- 1.00 = 3.85 ? 0."5
-3 0.5 = .0 ? 0."5
1 ? !5 0.5
3 ? !5 0.00
1.
4olado
1 2
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Luz 1.25 2.80 3.65 ,igideces 1.00 0.63 0.5 1.00
1 2 3udo .0-1 !1- !1- !-3 !-3 !3-
W 50 50 50 50 50 5
L 1.5 . . 3.85 3.85 0.
const 6 1 1 1 1
L)const 3. 3." 3." 863." 863." 1
1 -1 1 -1 1 -
3. -3." 3." -863." 863." -1
udo 1 2 37ramo 0-1 1- 1- -3 -3 3-
1.00 0.63 0.5 0.5
)sum 1.00 0.63 0.5 1.00
CR!!-1.00 -0.63 -0.5 -1.00
M.+. 38 #37" 37" #644 644
361 -361 11 -311 8 -8
-605
18 "
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38 #38 726 #726 22 #22
A/SCD 38 38 726 726 22 22
der iB$ der iB$ der iB$
6. AAL'S'S 7,AMO EO, 7,AMO
,i = L ) C Mi - Md D ) L +SF;+,(O de &O,7
,d = L - ,i
GCD = ,i ) MOM+7OS +
GICD = L - GCD G = anch
MCD = ,i ) C D - Mi M@ = ,i G
Gi = GCD - C GCD - Mi ) D C1)D MI@ = ,d G
Gd = GICD - C GICD - Md ) D C1)D MCD = ,i )
1 2 3
L . 3.
Ancho apoJo = 0.5 es apoJado 0.5 es apoJado
/ase = 0.10 0.10
losa = h = 0.5 0.5
,ecurimiento 0.03 0.03
d 0. 0.
n 0.3 0.3
G 0.10
50.0 50.0
L .55 3.60
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Mi 3 8
Md 8
,i 60 11"3
,d 100" "
GCD 0.1 .08
GICD 1.6 1.36
MCD 15 501
Gi 0.0 0.6
Gd 1.01 0.03
+SF;+,(O de &O,7+
4i 6 100
4d 6 5"3
MOM+7OS + 'S+HO
M@ -3 -80"
MI@ -8 53
CD 15 501
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308803335 l
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ple la condicion de ser menor
O,*+ /+A,AO OLO,'+,
'*. &'4'L
&O&,+7O A,MAO 1
3.50 e)1 350 g)m
= 163 55.
Kg/ml
= 575.2 580 Kg/ml
= 235.2 235.2 g)ml
= 360 360 g)ml
e@tremo iB$uierdo cara e@terior
e@tremo derecho cara e@teior
3.85
308803335 xlsx
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4i = ,i - n
4d = ,d - n
)
)
Mi
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8/19/2019 LOSA Maciza 3 Tramos 2 Luces
53/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
54/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
55/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
56/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
57/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
58/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
59/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
60/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
61/105
03/10/2016
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
62/105
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
63/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
64/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
65/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
66/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
67/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
68/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
69/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
70/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
71/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
72/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
73/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
74/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
75/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
76/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
77/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
78/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
79/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
80/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
81/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
82/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
83/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
84/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
85/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
86/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
87/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
88/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
89/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
90/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
91/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
92/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
93/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
94/105
03/10/2016
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
95/105
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
96/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
97/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
98/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
99/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
100/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
101/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
102/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
103/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
104/105
03/10/2016
308803335.xlsx
8/19/2019 LOSA Maciza 3 Tramos 2 Luces
105/105
03/10/2016