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7/25/2019 Modulo Minimo de Seccion
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Luz Libre 20 m
Peso propio 0.6 kg/m
Losa 0.3 5 1.5 kg/m
Piso terminado 0.1 5 0.5 kg/m
s/c 0.1 5 0.5 kg/m
M1= 105 ton-m M1/M2=
Ms= 50 ton-m
s= 0.0391253m!du"o m#nimo superior
i= 0.0380498m!du"o m#nimo in$erior
PREDIMENSIONAMIENTO
b%/b= 0.1
t/&= 0.1
's= 0.0(0)* b&2
'i= 0.05++* b&2
&= 0.(
b= 0.60+00(5((*
0.5b= 0.30200+2)+3
b%= 0.060+00(5()
t= 0.0(
seccion constructiv
,= 0.315 m2 0.15
= 0.0338585m+
r2= 0.10!48!2m2
s= 0.2134498m 0.6
i= 0.2!1139 m
s= 0.0854088m3
i= 0.0"!23"!m3 0.15
0.6
1s= 132.0*0*25 ss=
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1i= 16*.*65516 si=
b1= -2.1((31-006
b2= -0.00000(02(
b3= ).+5+(22-00*b+= 1.2*205(-006
-100 -50 0
-5
0
5
10
15
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#$ER%A DE TENSADO
,= 0.315 m
$ts= -300 ton/m2
Miga= 3*.( ton-m
M"osa= *5 ton-m P1=
Ms= 50 ton-m
i= 0.06*236*%i= 0.+*)
n= 0.(5
e= 0.+2
s 0.213++)(5
TRA%ADO DE& 'A(&E RES$&TANTE
s= 0.+0
i= 0.50
ri= 0.0(
L= 20
,= 3150
= 2*.113())6
P1= 1(+031.)62
i= 3).6+
-10
-15 -10 -5
TRA
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= 33(5(+(.21
L= 2000 cm
s1= 5(.+22(+52 116.(+56)03)
s2= 5(.+22(+52 0
u= 1))5.)2)6613 kg/m"
POSTENSADO INI'IA&
5(.+22(+52 -0.5621)2)55(.+22(+52 2.5621)2)5
POSTENSADO ESTA(&E
+).65)+1(+ -0.5621)2)5
+).65)+1(+ 2.5621)2)5
ES#$ER%OS DE(IDOS A M1
112.(
ES#$ER%OS DE(IDOS A M
10500000
)ERI#I'A'I*N DE $NA SE''I*N
4L,4 7P848 ,9M:L
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-32.(++)11(
132.0*0*25 )).225(132)1 -13
-2*.)1(1*5 10+.15255005 -30
122)3(1*.5 122)3)21.6++ 15*
;848 ,9M:L
1+).6)0602
-16*.*65516 -1(.0*+)13+55 16(
12*.23*012 -+0.52(503*** 15*
-156.16+*0) -1)6.6)3212+5 -30
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Mpp= 30
M"osa= *5
Mpt= 25
Msc= 25
2.1
0.002025 0.00016(*5
0.032+ 0.002* 0.003121((
0.00303*5 0.00025313
Luz Libre
0.) cg= 0.50 Peso propio
i= 0.50 Losa
s= 0.+0 Piso termina
s/c
0.15 0.)
M1=
5(.5+1)((1
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*+.36+1+*
b1 -2.61b2 -3.6*
b3 1.15
b+ 1.13
s -21.3++)(+(
i 2*.113())6
253
7n 215.05
50 100 150 200
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2
k=
?
0
2
+
6
(
100 5 10 15
-0.2
-0.1
0
0.1
0.2
0.3
0.+
0.5
ADO DEL CABLE RESULTANTE
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-32.(++)11(1+).6)0602
-2*.)1(1*5
12*.23*012
132.0*0*25
-16*.*65516
122)3(1*.5
-156.16+*0)
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$ci= 16( kg/cm2
$ti= -13 kg/cm2
$c= 15* kg/cm2
$t= -30 kg/cm2
20 m
*56 kg/m 3*.(
300 5 1500 kg/m *5
100 5 500 kg/m
100 5 500 kg/m
112.( ton-m
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ecuaci!n :+ ecuaci!n :3
> > -55 -55 -1.(1322535
-50 -50 -1.5+3(+122
-+5 -+5 -1.2*++5*1
-+0 -0.)(*5)3+5 -+0 -1.0050*2)(
-35 -0.*22()+2* -35 -0.*356(((6
-30 -0.+5(1)50) -30 -0.+6630+*3
-25 -0.1)3+)5)1 -25 -0.1)6)2061
-20 0.0*12032( -20 0.0*2+6351
-15 0.335)02+6 -15 0.3+1(+*63
-10 0.6006016+ -10 0.611231*6-5 0.(65300(2 -5 0.((0615((
0 1.13 0 1.15
5 1.3)+6))1( 5 1.+1)3(+12
10 1.65)3)(36 10 1.6((*6(2+
15 1.)2+0)*5+ 15 1.)5(1523*
20 2.1((*)6*2 20 2.22*536+)
25 2.+53+)5)1 25 2.+)6)2061
30 2.*1(1)50) 30 2.*6630+*3
35 2.)(2()+2* 35 3.0356(((6
+0 3.2+*5)3+5 +0 3.3050*2)(
+5 3.5122)263 +5 3.5*++5*1
50 3.**6))1(1 50 3.(+3(+122
55 +.0+16)0)) 55 +.11322535
60 +.3063)01* 60 +.3(260)+*
65 +.5*10()36 65 +.651))35)
*0 +.(35*((5+ *0 +.)213***1
*5 5.100+(**2 *5 5.1)0*61(+
(0 5.3651(6) (0 5.+601+5)6
(5 5.62)((60( (5 5.*2)5300(
)0 5.()+5(526 )0 5.))()1+2
)5 6.15)2(+++ )5 6.26(2)(33
100 6.+23)(362 100 6.53*6(2+5
105 6.(0*0665*
110 *.0*6+506)
115 *.3+5(3+(2
120 *.61521()+
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0.00+235*1
?
0 -0.0( 0.+0 0 0
0.016)+2(6 -0.0( 0.+0 -2 0.016)+2(6
0.06***1+3 -0.0( 0.3)6+2(5* -+ 0.06***1+3
0.152+(5*1 -0.0( 0.3)6+2(5* -6 0.152+(5*1
0.2*10(5*1 -0.0( 0.3)6+2(5* -( 0.2*10(5*1
0.+235*1+3 -0.0( 0.3)6+2(5* -10 0.+235*1+3
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, d ,d2
1 0.0) 0.+2(5*1+3 0.01653061
2 0.0) -0.0535*1+3 0.00025(2)
3 0.135 0.321+2(5* 0.013)+**
0.030*3661
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ecuaci!n :1 ecuaci!n :2
> > -55
-50
-+5
-+0
-35
-30
-25
-20
-15
-10 -3.5*2605)0)6 -10 -5.0235+)31-5 -3.0)1302)5+( -5 -+.3+6**+65
0 -2.61 0 -3.6*
5 -2.12(6)*0+52 5 -2.))322535
10 -1.6+*3)+0)0+ 10 -2.316+506)
15 -1.1660)11356 15 -1.63)6*60+
20 -0.6(+*((1(0( 20 -0.)62)013)
25 -0.203+(52261 25 -0.2(6126*+
30 0.2**(1**2(* 30 0.3)06+*)2
35 0.*5)1206(35 35 1.06*+225*
+0 1.2+0+2363(3 +0 1.*++1)*22
+5 1.*21*265)31 +5 2.+20)*1((
50 2.20302)5+*) 50 3.0)**+653
55 2.6(+332502* 55 3.**+5211(
60 3.165635+5*5 60 +.+512)5(3
65 3.6+6)3(+122 65 5.12(0*0+)
*0 +.12(2+136* *0 5.(0+(+51+
*5 +.60)5++321( *5 6.+(161)*)
(0 5.0)0(+*2*66 (0 *.15(3)++5
(5 5.5*2150231+ (5 *.(3516)1
)0 6.053+531(62 )0 (.511)+3*5
)5 6.53+*561+1 )5 ).1((*1(+1
100 *.01605)0)5( 100 ).(65+)306
105 *.+)*3620506 105 10.5+226**
110 *.)*(6650053 110 11.21)0+2+
115 (.+5))6*)601 115 11.()5(1*
120 (.)+12*0)1+) 120 12.5*25)1*
125 ).+225*3(6)* 125 13.2+)3663
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-0.0( 0.3)6+2(5*
-0.0( 0.3)6+2(5*
-0.0( 0.3)6+2(5*
-0.0( 0.3)6+2(5*
-0.0( 0.3)6+2(5*
-0.0( 0.3)6+2(5*
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ecuaci!n 1/. ecuaci!n 1/.u
> > -55 -55
-50 -50
-+5 -+5
-+0 -+0
-35 -35
-30 -30
-25 3.)5256)1* -25 +.6500(13(
-20 3.)5256)1* -20 +.6500(13(
-15 3.)5256)1* -15 +.6500(13(
-10 3.)5256)1* -10 +.6500(13(-5 3.)5256)1* -5 +.6500(13(
0 3.)5256)1* 0 +.6500(13(
5 3.)5256)1* 5 +.6500(13(
10 3.)5256)1* 10 +.6500(13(
15 3.)5256)1* 15 +.6500(13(
20 3.)5256)1* 20 +.6500(13(
25 3.)5256)1* 25 +.6500(13(
30 3.)5256)1* 30 +.6500(13(
35 3.)5256)1* 35 +.6500(13(
+0 3.)5256)1* +0 +.6500(13(
+5 3.)5256)1* +5 +.6500(13(
50 3.)5256)1* 50 +.6500(13(
55 3.)5256)1* 55 +.6500(13(
60 3.)5256)1* 60 +.6500(13(
65 3.)5256)1* 65 +.6500(13(
*0 3.)5256)1* *0 +.6500(13(
*5 3.)5256)1* *5 +.6500(13(
(0 3.)5256)1* (0 +.6500(13(
(5 3.)5256)1* (5 +.6500(13(
)0 3.)5256)1* )0 +.6500(13(
)5 3.)5256)1* )5 +.6500(13(
100 3.)5256)1* 100 +.6500(13(
105 3.)5256)1* 105 +.6500(13(
110 3.)5256)1* 110 +.6500(13(
115 3.)5256)1* 115 +.6500(13(
120 3.)5256)1* 120 +.6500(13(
125 3.)5256)1* 125 +.6500(13(
130 3.)5256)1* 130 +.6500(13(
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135 3.)5256)1* 135 +.6500(13(
1+0 3.)5256)1* 1+0 +.6500(13(
1+5 3.)5256)1* 1+5 +.6500(13(
150 3.)5256)1* 150 +.6500(13(
155 +.6500(13(
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DIA+RAMA DE MA+NE&
-100 -50 0 50 100 150
-5
0
5
10
15
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-10
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0
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X (m) 0 1 3 5 7
P1(ton) 625 625 625 625 625
e(m)
P1e(ton.m)
Mviga(ton.m)s (kg/cm2)
i (kg/cm2)
adms (kg/cm2)
admi (kg/cm2)
Cum!e
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" 11 13 15
625 625 625 625