SECCION SIMPLEMENTE REFORZADA (S-A). ING. ELIUD HERNANDEZ
DATOS GEOMETRICOS b(cm)= 40 h(cm)= 55 d"(cm)= 5 50 d(cm)=
DATOS PARTICULARES εcu(rad)= 0.003 As(cm)= 0!00 0.0020 ε#(rad)= 0.85 $%=
CARACTERISTICAS DE LOS MATERIALES &"c('cm)= *0 Ec('cm)= 252671 &#('cm)= 400 += 8.31 Es('cm)= %00000 Asm,+(cm) 6.67 β%= 0.85 0.85 %!05-&"c%40 0.85 0!5≤β%B(%!05-&"c%400)
%! ./r,cac,1+ s, 2a s/cc,1+ /s3 sub-r/&r6ada! Asb=
50
cm2
O78 SECCIO9 SU:-RE;OR
AGRIETAMIENTO AMIENTO! Mm/+3 # Cura3ura d/ Ar,/3am,/+3! ! AGRIET Ar,/3am,/+3!
AREA DE SECCION EQUIVALENTE $ODULO DE ROTURA %RO&. E'E NEUTRO INERCIA DE SECCION EQUIVALENTE
As/= ;r= ;r= C= Is/=
33.47 28.90 623995.64
kg/cm2 cm cm4
Ma= @a=
8001 00180.22 .22 5.1E06
kg.c kg.cm m !"#/cm
2346.22
cm2
%
SECCION DOBLEMENTE REFORZADA (D-A). ING. ELIUD HERNANDEZ
DATOS GEOMETRICOS b(cm)= 40 h(cm)= 55 d"(cm)= 5 d(cm)= 50
DI(U'O
DATOS PARTICULARES εcu(rad)= 0.003 As(cm)= % ε#(rad)= 0.0020 $%= 0.85 As"(cm)= %0
CARACTERISTICAS DE LOS MATERIALES &"c('cm)=
*0
Ec('cm)=
252671
&#('cm)= Es('cm)= β%=
400 %00000
+= Asm,+(cm) %!05-&"c%40
8.31 6.67
0.85
0!5≤β%B(%!05-&"c%400)
0.85
%! ./r,cac,1+ s, 2a s/cc,1+ /s3 sub-r/&r6ada!
Asb=
50
cm2
O78 SECCIO9 SU:-RE;OR
! AGRIETAMIENTO! Mm/+3 # Cura3ura d/ Ar,/3am,/+3!
AREA DE SECCION EQUIVALENTE $ODULO DE ROTURA %RO&. DEL E'E NEUTRO INERCIA DE SECCION EQUIVALENTE
As/= ;r = C= Is/=
650409.31
Ma= @a=
803589 4.9E06
2390.09 33.47 27.91
cm2 kg/cm2 cm cm4
kg.cm !"#/cm
0.85
%
! CEDENCIA. Mm/+3 # Cura3ura C/d/+3/! IP>TESIS %? Cmr3am,/+3 /2s3,c 2,+/a2 d/2 C+cr/3 E2 ac/r /s3 /+ C/d/+c,a Cmr3am,/+3 /r&/c3am/+3/ 2s3,c d/2 ac/r E2 C+cr/3 + ha a2ca+6ad /2 a3am,/+3
!%! D/3/rm,+ac,1+ d/2 EFE 9EUTRO!
T=C=
84000
c²=
c= 3!,!=
)Ec*+,*- c² + (2*AsFy) c - 2*AsFyd=0
Pr&! D/2 // +/u3r c=
1 0
0
16.65
!! ./r,cac,1+ d/ h,13/s,s! 0.000998 !"# εc= ;c= 0!*5H;"C= M#=
252.27 238.00
kg/cm2 kg/cm2
*0
'!cm
cm
O7 9O CUMPLE
@#= !00E-05
IP>TESIS ? Cmr3am,/+3 + 2,+/a2 d/2 C+cr/3 E2 ac/r /s3 /+ C/d/+c,a Cmr3am,/+3 /r&/c3am/+3/ 2s3,c d/2 ac/r E2 C+cr/3 + ha a2ca+6ad /2 a3am,/+3
!! D/3/rm,+ac,1+ d/2 EFE 9EUTRO! εc#= m=
0.0009 15.70
Pr&! D/2 // +/u3r c=
1 1 1
!"# cm 16.67
!4! ./r,cac,1+ d/ h,13/s,s! 0.001000 !"# εcd/&!= 252.79 kg/cm2 ;c= 0!*5H;"C= 238.00 kg/cm2
cm
O7 O7
A2,ca
M#=
55J0
'!cm
@#= !00E-05
!! C2cu2 d/ Mm/+3 C/d/+3/ # Cura3ura C/d/+3/! M#= 3735590 kg.cm @#= 6.00E05 !"#/cm
! CEDENCIA. Mm/+3 # Cura3ura C/d/+3/! IP>TESIS %? E/ +/u3r /+3r/ As # As" Cmr3am,/+3 2,+/a2 /2s3,c d/2 c+cr/3 E2 As /s3a c/d,/+d #a c/d,1 E2 C+cr/3 + ha a2ca+6ad /2 a3am,/+3 # As" /s3a a cmr/s E2 As" /s3a c/d,/+d #a c/d,
!%! D/3/rm,+ac,1+ d/2 EFE 9EUTRO! TAs = Cc K CAs"
67200
c²= )Ec*+,*- c² + (2*Fy(As-As')) c - 2*(As-As')Fy*d=0
1
1
Pr&! D/2 // +/u3r c=
1
0 1
0
9.99
!! ./r,cac,1+ d/ h,13/s,s! εc= 0.000499 !"# ε"s= 0.000249 !"# 126.15 kg/cm2 ;c= 0!*5H;"C= 238.00 kg/cm2 C=CcKCAs"= 67200 kg M#= Cc= @#=
CAs'=
c= 3!,!=
00JJ 500 5!00E-05 4000
cm
'
O7 9 Cum2/ O7
'!cm ' radcm '
IP>TESIS ? E/ +/u3r /+3r/ As # As" Cmr3am,/+3 2,+/a2 /2s3,c d/2 c+cr/3 E2 As /s3a c/d,/+d #a c/d,1 E2 C+cr/3 + s/ ha a3ad # As" /s3a a cmr/s,1 E2 As" + /s3 c/d,/+d TAs = Cc K CAs"
A2,ca
67200
!%! D/3/rm,+ac,1+ d/2 EFE 9EUTRO! c²=
)Ec*+,*-/2 c² + Fy(As+As') c - (Asd+As'd')Fy=0
c= 3!,!=
1
1
Pr&! D/2 // +/u3r c=
1
1 1
1
14.15
!! ./r,cac,1+ d/ h,13/s,s! 0.000790 !"# εc= 0.000511 !"# ε"s= ;c= 199.52 kg/cm2 0!*5H;"C= 238.00 kg/cm2 67200 kg C=CcKCAs"= M#= Cc= @#=
CAs'=
0JJ44 54 5!5*E-05 %04
'!cm ' radcm '
cm
' ' '
'
kg 20214 168000 8400000
radcm
,13/s,s
radcm
,1+
kg
20214 50400 2520000
,13/s,s kg
10107
109200 3570000
4! AGOTAMIENTO! Mm/+3 # Cura3ura 23,ma! IP>TESIS? E2 ac/r /s3 c/d,/+d #a c/d,1 Cmr3am,/+3 /r&/c3am/+3/ 2s3,c d/2 ac/r E2 C+cr/3 /s3 /+ c+d,c,1+ d/ a3am,/+3
T=C=
84000
kg
4!%! D/3/rm,+ac,1+ d/2 EFE 9EUTRO! Pr&! D/2 // +/u3r c= a=
10.38
cm
8.82
cm
4!! C2cu2 d/ Mm/+3 U23,ma # Cura3ura U23,ma!
Mu= @u=
3829412 2.89E04
kg.cm !"#/cm
Tab2a d/ Mm/+3 Cura3ura C+d,c,1+ Cura3ura (Radcm) Mm/+3 (T-m) 0 0 I+,c,a2 5!0*E-0 *!00 Ar,/3am,/+3 !00E-05 ! C/d/+c,a !*JE-04 *!J 23,ma ) m T (
DUCTILIDAD
μ=
Diagrama de Momento-Curvatura
o t n e 44 m 40 o M 36 32 28 24 20 16 12 8 4 0 0
0.00005
0.0001
0.00015
0.0002
Curvatura (rad/cm)
0.00025
0.0003
0.00035
4!*
4! AGOTAMIENTO! Mm/+3 # Cura3ura 23,ma! IP>TESIS %? E2 As # /2 As" /s3 c/d,/+d #a c/d,1 Cmr3am,/+3 /2s3,c /r&/c3am/+3/ 2s3,c d/2 ac/r E2 C+cr/3 a2ca+61 /2 a3am,/+3 E/ +/u3r /+3r/ As # As" As" /+ cmr/s,1+
DI(U'O
0
1
4!%! D/3/rm,+ac,1+ d/2 EFE 9EUTRO! Pr&! D/2 // +/u3r c= 0 0
TAs = Cc K CAs" cm
+ cum2/
0.0018166667 !"# 2.65 cm
+ cum2/
3.11
ε"s= a=
67200
Mu= Cc= @u=
CAs'=
%%4 500 0!000J 4000
'!cm ' radcm '
A2,ca
IP>TESIS ? As" + ha c/d,d Cmr3am,/+3 /2s3,c /r&/c3am/+3/ 2s3,c d/2 ac/r As /s3a /+ c/d/+c,a # /2 C+cr/3 + ha a3ad E/ +/u3r /+3r/ As # As" As" /+ cmr/s,1+
4!! D/3/rm,+ac,1+ d/2 EFE 9EUTRO!
TAs = Cc K CAs"
67200
cN=
c= 3!,!=
)0.85cβ1- c )AEεcA&, c A#Eεc0
1
Pr&! D/2 // +/u3r c=
1 6.50
cm
'
1
ε"s= Mu= Cc= @u=
CAs'=
0.000694
!"#
%4%% 5%!0* 0!0004 %45J
'!cm ' radcm '
'
kg
,13/s,s
kg 8092 4200 315000
DUCT!DAD "#TMADA D"! ##T"MA (#"CC$% #M&!"M"%T" "$ADA)
Lc
*+, 55
cs cs
(Longi!d Li"#$ d$ %& o%!n&) (A%!#& o&% d$ %& $ccin d$ %& ig&)
(Long %&sic& A#o/) 2,.5 c L = 2 1 + 3*( L Lc)*( mf -1 ) md **.
md m f
+0
(e1aci2n de Ducti1idades)
Ductlidad Est
Tab2a d/ Mm/+3 Cura3ura C+d,c,1+ Cura3ura (Radcm) Mm/+3 (T-m) 0 0 I+,c,a2 4!*JE-0 *!04 Ar,/3am,/+3 5!5*E-05 0!40 C/d/+c,a 4!%E-04 %!4 23,ma
DUCTILIDAD
μ=
*!
Diagrama de Momento-Curvatura
) m T ( o t n 36 e m 32 o M
28 24 20 16 12 8 4 0 0
0.0001
0.0002
0.0003
0.0004
0.0005
Curvatura (rad/cm)
"#TMAC$% D"! ACT$ D" "DUCC3% D" "#&U"#TA (#"CC$% D$4!"M"%T"
Lc
*+, 55
cs cs
(Longi!d Li"#$ d$ %& o%!n&) (A%!#& o&% d$ %& $ccin d$ %& ig&)
(Long %&sic& A#o/) 2,.5 c L = 2 1 + 3*( L Lc)*( mf -1 ) md 5+,
md m f
+*
(e1aci2n de Ducti1idades)
Ductlidad Estm
ada del Sisema
"$ADA)
ada del Sisema
4
