Muro de Corte1 Sante
23
DIAGRAMA DE INTERACCION DE COLUMNA RECTANGULAR 1 2 3 Filas D[mm] # As[cm!] "i [cm] fs[$%f&cm!] T[$%f] M[$%fcm] fs! [$%f&cm!] T! [$%f] M! [$%fcm] fs! [$%f&cm!] T! [$%f] M! [$%fcm] 8 6 3.02 2.50 0.002 4200.00 12667 95002 0.003 4200.00 12667 95002 0.003 4200.00 12667 95002 0.00 ! 8 6 3.02 17.50 -0.002 -4200.00 -12667 95002 0.000 787.50 2375 -17813 0.001 2625.00 7917 -59376 0.00 ( 12 0 0.00 0.00 0.003 4200.00 0 0 0.003 4200.00 0 0 0.003 4200.00 0 0 0.00 ) 12 0 0.00 0.00 0.003 4200.00 0 0 0.003 4200.00 0 0 0.003 4200.00 0 0 0.00 * 12 0 0.00 0.00 0.003 4200.00 0 0 0.003 4200.00 0 0 0.003 4200.00 0 0 0.00 + 12 0 0.00 0.00 0.003 4200.00 0 0 0.003 4200.00 0 0 0.003 4200.00 0 0 0.00 , 12 0 0.00 0.00 0.003 4200.00 0 0 0.003 4200.00 0 0 0.003 4200.00 0 0 0.00 - 12 0 0.00 0.00 0.003 4200.00 0 0 0.003 4200.00 0 0 0.003 4200.00 0 0 0.00 . 12 0 0.00 0.00 0.003 4200.00 0 0 0.003 4200.00 0 0 0.003 4200.00 0 0 0.00 / 12 0 0.00 0.00 0.003 4200.00 0 0 0.003 4200.00 0 0 0.003 4200.00 0 0 0.00 25.4 0 0.00 0.00 0.003 4200.00 0 0 0.003 4200.00 0 0 0.003 4200.00 0 0 0.00 ! 25.4 0 0.00 0.00 0.003 4200.00 0 0 0.003 4200.00 0 0 0.003 4200.00 0 0 0.00 ( 25.4 0 0.00 0.00 0.003 4200.00 0 0 0.003 4200.00 0 0 0.003 4200.00 0 0 0.00 ) 25.4 0 0.00 0.00 0.003 4200.00 0 0 0.003 4200.00 0 0 0.003 4200.00 0 0 0.00 As0 = +/( CARGA MA1IMA Po = 381257 c [cm] a [cm] Cc [$%f] Mc [$%cm] 2 [$%f] M [$%fcm] 2 [$%f] M [$%fcm] / 0.00 0.00 0 0 0 -25334 0 0.90 -22800 0 10.00 8.50 151725 872419 1 151725 1062422 0.90 136553 956180 ! 20.00 17.00 303450 455175 2 318492 532364 0.90 286643 479128 c = 60 ( 30.00 25.50 455175 -1251731 3 475759 -1216106 0.90 428183 -1094495 a= 51 ) 40.00 34.00 606900 -4248300 4 630255 -4233456 0.65 409665 -2751746 Cc = 910350 * 50.00 42.50 758625 -8534531 5 783642 -8532156 0.65 509367 -5545902 + 60.00 51.00 910350 -14110425 6 935684 -14110425 0.65 608194 -9171776 CARGAMA1IMA , 70.00 59.50 1062075 -20975981 7 1087409 -20975981 0.65 706816 -13634388 - 80.00 68.00 1213800 -29131200 8 1239134 -29131200 0.65 805437 -18935280 . 90.00 76.50 1365525 -38576081 9 1390859 -38576081 0.65 904058 -25074453 / 100.00 85.00 1517250 -49310625 10 1542584 -49310625 0.65 1002679 -32051906 110.00 93.50 1668975 -61334831 11 371925 2448 0.65 241752 1591 ) TENSIONMA1IMA ! 120.00 102.00 1820700 -74648700 12 374381 -28862 0.65 243348 -18761 T = -25334 ( 130.00 110.50 1972425 -89252231 13 373409 -29750 0.65 242716 -19337 ) 140.00 119.00 2124150 -105145425 14 372134 -25500 0.65 241887 -16575 * 15.00 12.75 227587.5 825005 15 371178 -22313 0.65 241265 -14503 + 16.00 13.60 242760 776832 16 370434 -19833 0.65 240782 -12892 , 17.00 14.45 257932.5 715763 17 381257 0 0.65 247817 0 - 18.00 15.30 273105 641797 DIAGRAMA DE INTERACCION DE COLUMNA RECTANGULAR . 19.00 16.15 288277.5 554934 !/ 20.00 17.00 303450 455175 2UNTOS ! 21.00 17.85 318622.5 342519 2[$%f] M[$%fcm] 2[$%f] M[$%fcm] MATERIALES SECCI !! 22.00 18.70 333795 216967 -25334 0 0.90 -22800 0 f'c = 210 B = 100 !( 23.00 19.55 348967.5 78518 151725 1062422 0.90 136553 956180 Fy = 4200 H = 20 !) 24.00 20.40 364140 -72828 318492 532364 0.90 286643 479128 Ec = 2.10E+05 A% = 2000 !* 25.00 21.25 379312.5 -237070 371925 2448 0.65 241752 1591 Es = 2.10E+06 L = 660 !+ 26.00 22.10 394485 -414209 381257 0 0.65 247817 0 0.85 !, 27.00 22.95 409657.5 -604245 373409 -29750 0.65 242716 -19337 0.003 372134 -25500 0.65 241887 -16575 !- 28.00 23.80 424830 -807177 371178 -22313 0.65 241265 -14503 !. 29.00 24.65 440002.5 -1023006 370434 -19833 0.65 240782 -12892 ACERO (( 33.00 28.05 500692.5 -2015287 Filas D[mm] # As[cm!] "i [cm () 34.00 28.90 515865 -2295599 SOLICITACIONES 10 6 4.71 2.50 (* 35.00 29.75 531037.5 -2588808 M = 174000 [$%fcm] 1.74 [T3m] ! 10 6 4.71 17.5 (+ 36.00 30.60 546210 -2894913 2 = 354000 [$%f] 354.00 [T3] ( 0 8 0.00 25.0 (, 37.00 31.45 561382.5 -3213915 (- 38.00 32.30 576555 -3545813 (. 39.00 33.15 591727.5 -3890608 )/ 40.00 34.00 606900 -4248300 ) 41.00 34.85 622072.5 -4618888 )! 42.00 35.70 637245 -5002373 )( 43.00 36.55 652417.5 -5398755 )) 44.00 37.40 667590 -5808033 )* 45.00 38.25 682762.5 -6230208 )+ 46.00 39.10 697935 -6665279 ), 47.00 39.95 713107.5 -7113247 )- 48.00 40.80 728280 -7574112 ). 49.00 41.65 743452.5 -8047873 */ 50.00 42.50 758625 -8534531 * 51.00 43.35 773797.5 -9034086 *! 52.00 44.20 788970 -9546537 *( 53.00 45.05 804142.5 -10071885 *) 54.00 45.90 819315 -10610129 ** 55.00 46.75 834487.5 -11161270 *+ 56.00 47.60 849660 -11725308 *, 57.00 48.45 864832.5 -12302242 *- 58.00 49.30 880005 -12892073 *. 59.00 50.15 895177.5 -13494801 +/ 60.00 51.00 910350 -14110425 1.5707963268 20 20 400 0.003926991 0.53 14.491376746 4200 24.17379 4 0.53 210 445.2 ξs ξs! ξs( ξs! φi ! 2UNTOS DEL DIAGRAMA 2ARA c≤ H * HOGNESTAD 2ARAξ =///( φi β= ξc = 0 200000 -50000 0 50000 100000 150000 200000 250000 300000 350000 400000 450000
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Transcript of Muro de Corte1 Sante
7/26/2019 Muro de Corte1 Sante
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DIAGRAMA DE INTERACCION DE COLUMNA RECTANGULAR
334.7
190.32
79.82
182.49
116 -2.56 1.69
30.25 -9.33 0.55
112 -12.87 -0.65
72 -0.78 0.26
28 0.32 0
0 4.21 1.12
1145.58 -21.01 2.97
ex = 0.0025926
ey = -0.01834
8.49366497 72.1423446
8.01581606
ξcm =0.003MODELO DE CONCRETO MODELO DE ACERO
c = 210 !"#$cm2% A& = 6.03 !cm2%
"3 = 0.85 'y = 4200 !"#$cm2%
ξ( = 0.002 '&) = 7000 !"#$cm2%
* = 50 E& = 2100000 !"#$cm2%
ξcm = 0.003 E&+ = 90000 !"#$cm2%
, = 100 !cm% ξ&+ = 0.006
= 17.5 !cm% ξy = 0.002
ec = 2.5 !cm% ξ&m = 0.0682
+ = 20 !cm% ξ = -0.1235
c = 40 !cm% ξ& = -0.0017
/ = 1.5 Fs : Región 1
"1 = 0.76944444 '& = -3543.75 !"#$cm2%
c1 = 0.66666667
c2 = 0.001
c3 = 0.000025
c4 = 0.00095
c5 = 0.00230833
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"2 = 0.40794224
Cc = 54933 !"g# T = $213%5 !"g#
E&&'& = 5%(%59 NO
M)'gnes = $34%(33 !"g*c+# M)'gnes = $252%2*355 !"g*c+#
,)'gnes- = %*5((E$(5 !1.c+#
/'gnes-0 M'e' s's-ic0' e 0ce&'
c = 210 !"#$cm2%
A& = 6.03185789 !cm2%
M !T/.m%
0 0 0
0.0005 -0.25 7.50E-05
0.0010 -0.33 3.75E-05
0.0015 0.72 6.00E-05
0.0020 0.14 3.60E-050.0025 1.88 5.00E-05
0.0030 0.90 3.33E-05
0.0035 3.15 4.286E-05
0.0040 1.85 3.061E-05
0.0045 4.49 3.750E-05
0.0050 2.93 2.813E-05
εcm !1$cm%
0 0.00001 0.00002 0.00003 0.00004 0.00005 0.00006
-1
0
1
2
3
4
5
M'+en-' C&60-&0 $ /'gnes-0 M'e' A
C&60-&0 1.c+
M'+en-' 7-'n*+8
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Filas D[mm] # As[cm!] "i [cm]
8 6 3.02 2.50
! 8 6 3.02 17.50
( 0 0 0.00 0.00
) 0 0 0.00 0.00
* 0 0 0.00 0.00
+ 0 0 0.00 0.00
, 0 0 0.00 0.00
- 0 0 0.00 0.00
. 0 0 0.00 0.00
/ 0 0 0.00 0.00
0 0 0.00 0.00
! 0 0 0.00 0.00
( 0 0 0.00 0.00) 0 0 0.00 0.00
As0 = +/(
c [cm] a [cm] Cc [$%f] Cc [$%f]
! 40.00 34.00 549383 -200813
( 50.00 42.50 686729 -337365
) 60.00 51.00 824075 -476000
* 70.00 59.50 961421 -614621
+ 80.00 68.00 1098767 -752923
, 90.00 76.50 1236113 -891013
) 14.00 11.90
) 14.00 11.90
* 15.00 12.75
+ 16.00 13.60
, 17.00 14.45
- 18.00 15.30
. 19.00 16.15
!/ 20.00 17.00
! 21.00 17.85
2
ξcm =0.003MODELO DE CONCRETO MODELO DE ACERO
c = 210 !"#$cm2% A& = 6.03 !cm2%
"3 = 0.85 'y = 4200 !"#$cm2%
ξ( = 0.002 '&) = 7000 !"#$cm2%
* = 50 E& = 2100000 !"#$cm2%
ξc+ = 0.0015 E&+ = 90000 !"#$cm2%
, = 100 !cm% ξ&+ = 0.006
= 17.5 !cm% ξy = 0.002
ec = 2.5 !cm% ξ&m = 0.0682
+ = 20 !cm% ξ = -0.1100
c = 40 !cm% ξ& = -0.0008
/ = 0.75 Fs : Región 1
"1 = 0.5625 '& = -1771.88 !"#$cm2%
c1 = 1.33333333
c2 = -0.0005
c3 = 0.00000625
c4 = -0.0005125
c5 = 0.00082708
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"2 = 0.36111111
Cc = $2((13 !"g# T = $1( !"g#
E&&'& = $19(125 NO
M)'gnes = 34543%*5 !"g*c+# M)'gnes = $325*55 !"g*c+#
,)'gnes- = 3*%5(E$(5 !1.c+#
M'e' e /'gnes-0
c = 210 !"#$cm2%
M !T/.m%
0 0 0
0.0005 0.0 0.00E00
0.0010 34.6 3.75E-05
0.0015 0.0 0.00E00
0.0020 71.1 3.60E-050.0025 -119.3 5.00E-05
0.0030 119.0 3.33E-05
0.0035 -178.4 4.29E-05
0.0040 178.1 3.06E-05
0.0045 -248.7 3.75E-05
0.0050 248.5 2.81E-05
εcm !1$cm%
0.00007 0.00008
e&'
0 0.00001 0.000
-300
-200
-100
0
100
200
300
M'+en-' C&60-&0 $ /
M'+en-' 7-'n*+8
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fs [$%f&cm!] T [$%f] M [$%fcm] fs! [$%f&cm!] T! [$%f]
0.0028 4200.00 12667 95002 0.0029 4200.00 12667
0.0017 3543.75 10688 -80158 0.0020 4095.00 12350
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 00.0030 4200.00 0 0 0.0030 4200.00 0
Mc [$%cm] Mc [$%cm] 2 [$%f] M [$%fcm]
-3470833.33 3458437.5 371925 2448
-7140000 7108762.5 374381 -28862
-11929750 11900000 373409 -29750
-17840083 17814583.3 372134 -25500
-24871000 24848687.5 371178 -22313
-33022500 33002666.7 370434 -19833
3
ξcm =0.003MODELO DE CONCRETO MODELO DE ACERO MODE
c = 210 !"#$cm2% A& = 6.03 !cm2% c =
"3 = 0.85 'y = 4200 !"#$cm2% "3 =
ξ( = 0.002 '&) = 7000 !"#$cm2% ξ( =
* = 50 E& = 2100000 !"#$cm2% * =
ξcm = 0.003 E&+ = 90000 !"#$cm2% ξc+ =
, = 100 !cm% ξ&+ = 0.006 , =
= 17.5 !cm% ξy = 0.002 =
ec = 2.5 !cm% ξ&m = 0.0682 ec =
+ = 20 !cm% ξ = -0.1278 + =
c = 50 !cm% ξ& = -0.0020 c =
/ = 1.5 Fs : Región 1 / =
"1 = 0.76944444 '& = -4095.00 !"#$cm2% "1 =
c1 = 0.66666667 c1 =
c2 = 0.001 c2 =
c3 = 0.000025 c3 =
c4 = 0.00095 c4 =
c5 = 0.00230833 c5 =
ξs ξs!
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"2 = 0.40794224 "2 =
Cc = %29 !"g# T = $24%(( !"g# Cc =
E&&'& = %1143( NO
M)'gnes = $%14(((( !"g*c+# M)'gnes = %1559*9913% !"g*c+# M)'gnes =
,)'gnes- = *(((E$(5 !1.c+#
M'e' s's-ic0' e 0ce&'
A& = 6.03185789 !cm2%
M !T/.m%
0 0 0
0.0005 -0.25 7.50E-05
0.0010 -0.33 3.75E-05
0.0015 0.72 6.00E-05
0.0020 0.14 3.60E-050.0025 1.88 5.00E-05
0.0030 0.90 3.33E-05
0.0035 3.15 4.29E-05
0.0040 1.85 3.06E-05
0.0045 4.49 3.75E-05
0.0050 2.93 2.81E-05
εcm !1$cm%
02 0.00003 0.00004 0.00005 0.00006
'gnes-0 C'nc&e-' c'nn0'
C&60-&0 1.c+
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M! [$%fcm] fs( [$%f&cm!] T( [$%f] M( [$%fcm] fs) [$%f&cm!]
95002 0.0029 4200.00 12667 95002 0.0029 4200.00
-92627 0.0021 4200.00 12667 -95002 0.0023 4200.00
0 0.0030 4200.00 0 0 0.0030 4200.00
0 0.0030 4200.00 0 0 0.0030 4200.00
0 0.0030 4200.00 0 0 0.0030 4200.00
0 0.0030 4200.00 0 0 0.0030 4200.00
0 0.0030 4200.00 0 0 0.0030 4200.00
0 0.0030 4200.00 0 0 0.0030 4200.00
0 0.0030 4200.00 0 0 0.0030 4200.00
0 0.0030 4200.00 0 0 0.0030 4200.00
0 0.0030 4200.00 0 0 0.0030 4200.00
0 0.0030 4200.00 0 0 0.0030 4200.00
0 0.0030 4200.00 0 0 0.0030 4200.000 0.0030 4200.00 0 0 0.0030 4200.00
ξcm =0.003O DE CONCRETO MODELO DE ACERO MODELO DE CONC
210 !"#$cm2% A& = 6.0318578949 !cm2% c = 210
0.85 'y = 4200 !"#$cm2% "3 = 0.85
0.002 '&) = 7000 !"#$cm2% ξ( = 0.002
50 E& = 2100000 !"#$cm2% * = 50
0.0018 E&+ = 90000 !"#$cm2% ξcm = 0.003
100 !cm% ξ&+ = 0.006 , = 100
17.5 !cm% ξy = 0.002 = 17.5
2.5 !cm% ξ&m = 0.0682 ec = 2.5
20 !cm% ξ = -0.1152 + = 20
50 !cm% ξ& = -0.0012 c = 60
0.9 Fs : Región 1 / = 1.5
0.63 '& = -2457.00 !"#$cm2% "1 = 0.76944444
1.11111111 c1 = 0.66666667
-0.0002 c2 = 0.001
0.000001 c3 = 0.000025
-0.000202 c4 = 0.00095
0.00113233 c5 = 0.00230833
ξs( ξs)
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0.36904762 "2 = 0.40794224
$33%35 !"g# T = $142( !"g# Cc = 24(%5
E&&'& = $322545 NO E&&'& =
%1(%2*5 !"g*c+# M)'gnes = 14114*54%4% !"g*c+# M)'gnes = $11929%5(
,)'gnes- = 3*((E$(5 !1.c+#
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T) [$%f] M) [$%fcm] fs* [$%f&cm!] T* [$%f] M* [$%fcm]
12667 95002 0.0029 4200.00 12667 95002 0.0029
12667 -95002 0.0023 4200.00 12667 -95002 0.0024
0 0 0.0030 4200.00 0 0 0.0030
0 0 0.0030 4200.00 0 0 0.0030
0 0 0.0030 4200.00 0 0 0.0030
0 0 0.0030 4200.00 0 0 0.0030
0 0 0.0030 4200.00 0 0 0.0030
0 0 0.0030 4200.00 0 0 0.0030
0 0 0.0030 4200.00 0 0 0.0030
0 0 0.0030 4200.00 0 0 0.0030
0 0 0.0030 4200.00 0 0 0.0030
0 0 0.0030 4200.00 0 0 0.0030
0 0 0.0030 4200.00 0 0 0.00300 0 0.0030 4200.00 0 0 0.0030
4
ξcm =0.003 ξcm = ETO MODELO DE ACERO MODELO DE CONCRETO
!"#$cm2% A& = 6.03 !cm2% c = 210 !"#$cm2%
'y = 4200 !"#$cm2% "3 = 0.85
'&) = 7000 !"#$cm2% ξ( = 0.002
E& = 2100000 !"#$cm2% * = 50
E&+ = 90000 !"#$cm2% ξc+ = 0.002
!cm% ξ&+ = 0.006 , = 100 !cm%
!cm% ξy = 0.002 = 17.5 !cm%
!cm% ξ&m = 0.0682 ec = 2.5 !cm%
!cm% ξ = -0.1306 + = 20 !cm%
!cm% ξ& = -0.0021 c = 60 !cm%
Fs : Región 1 / = 1
'& = -4462.50 !"#$cm2% "1 = 0.66666667
c1 = 1
c2 = 0
c3 = 0
c4 = 0
c5 = 0.00133333
ξs* ξs+
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"2 = 0.375
!"g# T = $291% !"g# Cc = $4%((( !"g#
5(992 NO E&&'& = $45
!"g*c+# M)'gnes = 1%%*53(% !"g*c+# M)'gnes = 119((((( !"g*c+#
,)'gnes- = 5*(((E$(5 !1.c+#
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fs+ [$%f&cm!] T+ [$%f] M+ [$%fcm] fs, [$%f&cm!] T, [$%f] M, [$%fcm]
4200.00 12667 95002 0.0025 4200.00 12667 95002
4200.00 12667 -95002 -0.0008 -1575.00 -4750 35626
4200.00 0 0 0.0030 4200.00 0 0
4200.00 0 0 0.0030 4200.00 0 0
4200.00 0 0 0.0030 4200.00 0 0
4200.00 0 0 0.0030 4200.00 0 0
4200.00 0 0 0.0030 4200.00 0 0
4200.00 0 0 0.0030 4200.00 0 0
4200.00 0 0 0.0030 4200.00 0 0
4200.00 0 0 0.0030 4200.00 0 0
4200.00 0 0 0.0030 4200.00 0 0
4200.00 0 0 0.0030 4200.00 0 0
4200.00 0 0 0.0030 4200.00 0 04200.00 0 0 0.0030 4200.00 0 0
0.003MODELO DE ACERO
A& = 6.0318578949 !cm2%
'y = 4200 !"#$cm2%
'&) = 7000 !"#$cm2%
E& = 2100000 !"#$cm2%
E&+ = 90000 !"#$cm2%
ξ&+ = 0.006
ξy = 0.002
ξ&m = 0.0682
ξ = -0.1192
ξ& = -0.0014
Fs : Región 1
'& = -2975.00 !"#$cm2%
ξs,
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T = $1%945 !"g#
(55 NO
M)'gnes = 9%23*19!"g*c+#
,)'gnes- = 3*333E$(5 !1.c+#
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fs- [$%f&cm!] T- [$%f] M- [$%fcm] fs. [$%f&cm!] T. [$%f]
0.0025 4200.00 12667 95002 0.0025 4200.00 12667
-0.0008 -1575.00 -4750 35626 -0.0005 -1050.00 -3167
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 0
0.0030 4200.00 0 0 0.0030 4200.00 00.0030 4200.00 0 0 0.0030 4200.00 0
ξs- ξs.
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MATERIALES
f'c = 210
Fy = 4200
M. [$%fcm] fs/ [$%f&cm!] T/ [$%f] M/ [$%fcm] Ec = 2.10E+05
95002 0.0025 4200.00 12667 95002 Es = 2.10E+06
23750 -0.0003 -590.63 -1781 13360 0.85
0 0.0030 4200.00 0 0 0.003
0 0.0030 4200.00 0 0
0 0.0030 4200.00 0 0
0 0.0030 4200.00 0 0
0 0.0030 4200.00 0 0
0 0.0030 4200.00 0 0
0 0.0030 4200.00 0 0
0 0.0030 4200.00 0 0
0 0.0030 4200.00 0 0
0 0.0030 4200.00 0 0
0 0.0030 4200.00 0 00 0.0030 4200.00 0 0
MODELO DE CONC
c = 210
"3 = 0.85
ξ( = 0.002
* = 50
ξcm = 0.003
, = 100
= 17.5
ec = 2.5
+ = 20
c = 70
/ = 1.5
"1 = 0.76944444
c1 = 0.66666667
c2 = 0.001
c3 = 0.000025
c4 = 0.00095
c5 = 0.00230833
ξs/
β =
ξc =
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"2 = 0.40794224
Cc = 91421
E&&'& =
M)'gnes = $1%4((3
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SECCION
[kgf/cm2] B = 100 [cm]
[kgf/cm2] H = 20 [cm]
[kgf/cm2] A% = 2000 [cm2]
[kgf/cm2]
5
ξcm =0.003 ξcm = ETO MODELO DE ACERO MODELO DE CONCRETO
!"#$cm2% A& = 6.03 !cm2% c = 210 !"#$cm2%
'y = 4200 !"#$cm2% "3 = 0.85
'&) = 7000 !"#$cm2% ξ( = 0.002
E& = 2100000 !"#$cm2% * = 50
E&+ = 90000 !"#$cm2% ξc+ = 0.00214286
!cm% ξ&+ = 0.006 , = 100 !cm%
!cm% ξy = 0.002 = 17.5 !cm%
!cm% ξ&m = 0.0682 ec = 2.5 !cm%
!cm% ξ = -0.1326 + = 20 !cm%
!cm% ξ& = -0.0023 c = 70 !cm%
Fs : Región 1 / = 1.07142857
'& = -4725.00 !"#$cm2% "1 = 0.68865079
c1 = 0.93333333
c2 = 0.00014286
c3 = 5.1020E-007
c4 = 0.00014184
c5 = 0.00147568
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"2 = 0.37969344
!"g# T = $25(1 !"g# Cc = $1421 !"g#
99921 NO E&&'& = $59
!"g*c+# M)'gnes = 3151((*(9 !"g*c+# M)'gnes = 1%1453 !"g*c+#
,)'gnes- = 4*2E$(5 !1.c+#
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0.003 ξcm =0.003MODELO DE ACERO MODELO DE CONCRETO MO
A& = 6.0318578949 !cm2% c = 210 !"#$cm2% A& =
'y = 4200 !"#$cm2% "3 = 0.85 'y =
'&) = 7000 !"#$cm2% ξ( = 0.002 '&) =
E& = 2100000 !"#$cm2% * = 50 E& =
E&+ = 90000 !"#$cm2% ξcm = 0.003 E&+ =
ξ&+ = 0.006 , = 100 !cm% ξ&+ =
ξy = 0.002 = 17.5 !cm% ξy =
ξ&m = 0.0682 ec = 2.5 !cm% ξ&m =
ξ = -0.1223 + = 20 !cm% ξ =
ξ& = -0.0016 c = 80 !cm% ξ& =
Fs : Región 1 / = 1.5 Fs :
'& = -3375.00 !"#$cm2% "1 = 0.76944444 '& =
c1 = 0.66666667
c2 = 0.001
c3 = 0.000025
c4 = 0.00095
c5 = 0.00230833
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"2 = 0.40794224
T = $2(35 !"g# Cc = 1(9%% !"g# T =
423 NO E&&'& = 112455
M)'gnes = 141*53 !"g*c+# M)'gnes = $24%1((( !"g*c+# M)'gnes =
,)'gnes- = 3*(1E$(5 !1.c+# ,)'gnes- =
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ξcm =0.003ELO DE ACERO MODELO DE CONCRETO MO
6.03 !cm2% c = 210 !"#$cm2% A& =
4200 !"#$cm2% "3 = 0.85 'y =
7000 !"#$cm2% ξ( = 0.002 '&) =
2100000 !"#$cm2% * = 50 E& =
90000 !"#$cm2% ξc+ = 0.00225 E&+ =
0.006 , = 100 !cm% ξ&+ =
0.002 = 17.5 !cm% ξy =
0.0682 ec = 2.5 !cm% ξ&m =
-0.1341 + = 20 !cm% ξ =
-0.0023 c = 80 !cm% ξ& =
Región 1 / = 1.125 Fs :
-4921.88 !"#$cm2% "1 = 0.70300926 '& =
c1 = 0.88888889
c2 = 0.00025
c3 = 1.5625E-006
c4 = 0.00024688
c5 = 0.00158177
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"2 = 0.38338272
$29 !"g# Cc = $%52923 !"g# T =
NO E&&'& = $%3(5%
449339*991 !"g*c+# M)'gnes = 244 !"g*c+# M)'gnes =
3*%5(E$(5 !1.c+# ,)'gnes- =
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ξcm =0.003ELO DE ACERO MODELO DE CONCRETO MO
6.0318578949 !cm2% c = 210 !"#$cm2% A& =
4200 !"#$cm2% "3 = 0.85 'y =
7000 !"#$cm2% ξ( = 0.002 '&) =
2100000 !"#$cm2% * = 50 E& =
90000 !"#$cm2% ξcm = 0.003 E&+ =
0.006 , = 100 !cm% ξ&+ =
0.002 = 17.5 !cm% ξy =
0.0682 ec = 2.5 !cm% ξ&m =
-0.1247 + = 20 !cm% ξ =
-0.0018 c = 90 !cm% ξ& =
Región 1 / = 1.5 Fs :
-3691.41 !"#$cm2% "1 = 0.76944444 '& =
c1 = 0.66666667
c2 = 0.001
c3 = 0.000025
c4 = 0.00095
c5 = 0.00230833
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"2 = 0.40794224
$222 !"g# Cc = 123113 !"g# T =
NO E&&'& = 12%24
29325%*4%5 !"g*c+# M)'gnes = $33(225(( !"g*c+# M)'gnes =
2*13E$(5 !1.c+# ,)'gnes- =
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%
ξcm =0.003ELO DE ACERO MODELO DE CONCRETO MO
6.03 !cm2% c = 210 !"#$cm2% A& =
4200 !"#$cm2% "3 = 0.85 'y =
7000 !"#$cm2% ξ( = 0.002 '&) =
2100000 !"#$cm2% * = 50 E& =
90000 !"#$cm2% ξc+ = 0.00233333 E&+ =
0.006 , = 100 !cm% ξ&+ =
0.002 = 17.5 !cm% ξy =
0.0682 ec = 2.5 !cm% ξ&m =
-0.1353 + = 20 !cm% ξ =
-0.0024 c = 90 !cm% ξ& =
Región 1 / = 1.16666667 Fs :
-5075.00 !"#$cm2% "1 = 0.71309524 '& =
c1 = 0.85714286
c2 = 0.00033333
c3 = 2.7778E-006
c4 = 0.00032778
c5 = 0.00166389
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"2 = 0.38627872
$3(12 !"g# Cc = $91(13 !"g# T =
NO E&&'& = $%2(3
519%*33!"g*c+# M)'gnes = 33((2%!"g*c+# M)'gnes =
3*333E$(5 !1.c+# ,)'gnes- =
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ELO DE ACERO
6.03185789 !cm2%
4200!"#$cm2%
7000!"#$cm2%
2100000!"#$cm2%
90000 !"#$cm2%
0.006
0.002
0.0682
-0.1266
-0.0019
Región 1
-3947.22 !"#$cm2%
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$23(9 !"g#
NO
411(5*4!"g*c+#
2*593E$(5!1.c+#
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ξcm =0.0005MODELO DE CONCRETO MODELO DE ACERO
c = 250 !"#$cm2% A& = 60.8 !cm2%
"3 = 0.85 'y = 4200 !"#$cm2%
ξ( = 0.002 '&) = 7000 !"#$cm2%
* = 50 E& = 2100000 !"#$cm2%
ξcm = 0.0005 E&+ = 90000 !"#$cm2%
, = 60 !cm% ξ&+ = 0.006
= 55 !cm% ξy = 0.002
ξ&m = 0.0682
ξ = -0.0891
c = 28.78 !cm% ξ& = 0.0005
/ = 0.25 '& Re#/ 1
"1 = 0.22916667 '& = 956.60 !"#$cm2%
c1 = 4
c2 = -0.0015c3 = 0.00005625
c4 = -0.0016125
c5 = -0.00022292
"2 = 0.34090909
Cc = 4(92 !"g# T = 511 !"g#
E&&'& = 2593( NO
M)'gnes = 3%9993 !"g*c+# M)'gnes = 22233*9% !"g*c+#
,)'gnes- = 1*%3%E$(5 !1.c+#
/'gnes-0 M'e' s's-ic0' e 0ce&'
c = 250 !"#$cm2%
A& = 60.8 !cm2%
M !T/.m%
0 0 0
0.0005 26.28 1.74E-05
0.0010 48.76 3.37E-05
0.0015 119.32 6.55E-05
0.0020 122.15 1.05E-040.0025 122.73 1.41E-04
0.0030 -27.24 3.33E-05
0.0035 126.33 2.037E-04
0.0040 127.82 2.294E-04
0.0045 128.72 2.522E-04
0.0050 129.11 2.723E-04
εcm !1$cm%
20
40
60
80
100
120
140
M'+en-' C&60-&0 $ /'gnes-0 M'e' A
M'+en-' 7-'n*+8
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0 0.00005 0.0001 0.00015 0.0002 0.0
-40
-20
0
C&60-&0 1.c+
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ξcm =0.001MODELO DE CONCRETO MODELO DE ACERO MODE
c = 250 !"#$cm2% A& = 60.8 !cm2% c =
"3 = 0.85 'y = 4200 !"#$cm2% "3 =
ξ( = 0.002 '&) = 7000 !"#$cm2% ξ( =
* = 50 E& = 2100000 !"#$cm2% * =
ξcm = 0.001 E&+ = 90000 !"#$cm2% ξcm =
, = 60 !cm% ξ&+ = 0.006 , =
= 55 !cm% ξy = 0.002 =
ξ&m = 0.0682
ξ = -0.0827
c = 29.637 !cm% ξ& = 0.0009 c =
/ = 0.5 '& Re#/ 1 / =
"1 = 0.41666667 '& = 1797.16 !"#$cm2% "1 =
c1 = 2 c1 =
c2 = -0.001 c2 =c3 = 0.000025 c3 =
c4 = -0.00105 c4 =
c5 = 0.00030833 c5 =
"2 = 0.35 "2 =
Cc = 15%44% !"g# T = 1(92% !"g# Cc =
E&&'& = 41( NO
M)'gnes = %(23%5* !"g*c+# M)'gnes = 4%2*524 !"g*c+# M)'gnes =
,)'gnes- = 3*3%4E$(5 !1.c+#
M'e' e /'gnes-0 M'e'
c = 250 !"#$cm2%
A& =
M !T/.m%
0 0 0 0
0.0005 38.0 1.74E-05 0.0005
0.0010 70.3 3.37E-05 0.0010
0.0015 76.8 6.55E-05 0.0015
0.0020 77.7 1.05E-04 0.00200.0025 79.3 1.41E-04 0.0025
0.0030 161.4 3.33E-05 0.0030
0.0035 83.0 2.04E-04 0.0035
0.0040 85.3 2.29E-04 0.0040
0.0045 87.6 2.52E-04 0.0045
0.0050 89.9 2.72E-04 0.0050
εcm !1$cm% ε
cm
e&'
60
80
100
120
140
160
180
M'+en-' C&60-&0 $ /'gnes
M'+en-' 7-'n*+8
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0025 0.0003
0 0.00005 0.0001 0.00
20
40
C&60-
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ξcm =0.0015O DE CONCRETO MODELO DE ACERO MODELO DE CONC
250 !"#$cm2% A& = 60.8 !cm2% c = 250
0.85 'y = 4200 !"#$cm2% "3 = 0.85
0.002 '&) = 7000 !"#$cm2% ξ( = 0.002
50 E& = 2100000 !"#$cm2% * = 50
0.0015 E&+ = 90000 !"#$cm2% ξcm = 0.002
60 !cm% ξ&+ = 0.006 , = 60
55 !cm% ξy = 0.002 = 55
ξ&m = 0.0682
ξ = -0.0627
22.917 !cm% ξ& = 0.0021 c = 19.108
0.75 '& Re#/ 2 / = 1
0.5625 '& = 4200.00 !"#$cm2% "1 = 0.66666667
1.33333333 c1 = 1
-0.0005 c2 = 00.00000625 c3 = 0
-0.0005125 c4 = 0
0.00082708 c5 = 0.00133333
0.36111111 "2 = 0.375
1435 !"g# T = 2553( !"g# Cc = 1241
E&&'& = $91((2 NO E&&'& =
%%9525*1 !"g*c+# M)'gnes = 1193154%*(4 !"g*c+# M)'gnes = %%913*
,)'gnes- = *545E$(5 !1.c+#
's-ic0' e 0ce&'
60.8 !cm2%
M !T/.m%
0 0
26.28 1.74E-05
48.76 3.37E-05
119.32 6.55E-05
122.15 1.05E-04122.73 1.41E-04
-27.24 3.33E-05
126.33 2.04E-04
127.82 2.29E-04
128.72 2.52E-04
129.11 2.72E-04
!1$cm%
0 C'nc&e-' c'nn0'
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015 0.0002 0.00025 0.0003
&0 1.c+
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ξcm =0.002 ξcm = ETO MODELO DE ACERO MODELO DE CONCRETO
!"#$cm2% A& = 60.8 !cm2% c = 250 !"#$cm2%
'y = 4200 !"#$cm2% "3 = 0.85
'&) = 7000 !"#$cm2% ξ( = 0.002
E& = 2100000 !"#$cm2% * = 50
E&+ = 90000 !"#$cm2% ξcm = 0.0025
!cm% ξ&+ = 0.006 , = 60 !cm%
!cm% ξy = 0.002 = 55 !cm%
ξ&m = 0.0682
ξ = -0.0361
!cm% ξ& = 0.0038 c = 17.704 !cm%
'& Re#/ 2 / = 1.25
'& = 4200.00 !"#$cm2% "1 = 0.73083333
c1 = 0.8
c2 = 0.0005c3 = 0.00000625
c4 = 0.0004875
c5 = 0.00182708
"2 = 0.39201824
!"g# T = 2553( !"g# Cc = 149 !"g#
$92942 NO E&&'& = $9
!"g*c+# M)'gnes = 12215(1%*92 !"g*c+# M)'gnes = %9231*2 !"g*c+#
,)'gnes- = 1*(4%E$(4 !1.c+#
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0.0025 ξcm =0.003MODELO DE ACERO MODELO DE CONCRETO MO
A& = 60.8 !cm2% c = 250 !"#$cm2% A& =
'y = 4200 !"#$cm2% "3 = 0.85 'y =
'&) = 7000 !"#$cm2% ξ( = 0.002 '&) =
E& = 2100000 !"#$cm2% * = 50 E& =
E&+ = 90000 !"#$cm2% ξcm = 0.003 E&+ =
ξ&+ = 0.006 , = 60 !cm% ξ&+ =
ξy = 0.002 = 55 !cm% ξy =
ξ&m = 0.0682 ξ&m =
ξ = -0.0118 ξ =
ξ& = 0.0053 c = 90 !cm% ξ& =
'& Re#/ 2 / = 1.5 Fs :
'& = 4200.00 !"#$cm2% "1 = 0.76944444 '& =
c1 = 0.66666667
c2 = 0.001c3 = 0.000025
c4 = 0.00095
c5 = 0.00230833
"2 = 0.40794224
T = 2553( !"g# Cc = 293 !"g# T =
392 NO E&&'& = 1(319
M)'gnes = 122%252%*29 !"g*c+# M)'gnes = 1144 !"g*c+# M)'gnes =
,)'gnes- = 1*412E$(4 !1.c+# ,)'gnes- =
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ξcm =0.0035ELO DE ACERO MODELO DE CONCRETO MO
60.8 !cm2% c = 250 !"#$cm2% A& =
4200 !"#$cm2% "3 = 0.85 'y =
7000 !"#$cm2% ξ( = 0.002 '&) =
2100000 !"#$cm2% * = 50 E& =
90000 !"#$cm2% ξcm = 0.0035 E&+ =
0.006 , = 60 !cm% ξ&+ =
0.002 = 55 !cm% ξy =
0.0682 ξ&m =
-0.1152 ξ =
-0.0012 c = 17.186 !cm% ξ& =
Región 1 / = 1.75 Fs :
-2450.00 !"#$cm2% "1 = 0.79345238 '& =
c1 = 0.57142857
c2 = 0.0015c3 = 0.00005625
c4 = 0.0013875
c5 = 0.00277708
"2 = 0.42149823
$149( !"g# Cc = 1%32 !"g# T =
NO E&&'& = $9(%
$2%23%3*1 !"g*c+# M)'gnes = 3(2999*2 !"g*c+# M)'gnes =
3*333E$(5 !1.c+# ,)'gnes- =
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ξcm =0.004ELO DE ACERO MODELO DE CONCRETO MO
60.8 !cm2% c = 250 !"#$cm2% A& =
4200 !"#$cm2% "3 = 0.85 'y =
7000 !"#$cm2% ξ( = 0.002 '&) =
2100000 !"#$cm2% * = 50 E& =
90000 !"#$cm2% ξcm = 0.004 E&+ =
0.006 , = 60 !cm% ξ&+ =
0.002 = 55 !cm% ξy =
0.0682 ξ&m =
0.0273 ξ =
0.0077 c = 17.436 !cm% ξ& =
Región 3 / = 2 Fs :
4351.00 !"#$cm2% "1 = 0.80833333 '& =
c1 = 0.5
c2 = 0.002c3 = 0.0001
c4 = 0.0018
c5 = 0.00323333
"2 = 0.43298969
24541 !"g# Cc = 1%9%(( !"g# T =
NO E&&'& = $92
1233432*(9 !"g*c+# M)'gnes = 5224*% !"g*c+# M)'gnes =
2*(3%E$(4 !1.c+# ,)'gnes- =
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ξcm =0.0045ELO DE ACERO MODELO DE CONCRETO MO
60.8 !cm2% c = 250 !"#$cm2% A& =
4200 !"#$cm2% "3 = 0.85 'y =
7000 !"#$cm2% ξ( = 0.002 '&) =
2100000 !"#$cm2% * = 50 E& =
90000 !"#$cm2% ξcm = 0.0045 E&+ =
0.006 , = 60 !cm% ξ&+ =
0.002 = 55 !cm% ξy =
0.0682 ξ&m =
0.0421 ξ =
0.0086 c = 17.845 !cm% ξ& =
Región 3 / = 2.25 '&
4430.63 !"#$cm2% "1 = 0.81712963 '& =
c1 = 0.44444444
c2 = 0.0025c3 = 0.00015625
c4 = 0.0021875
c5 = 0.00367708
"2 = 0.44287063
2932 !"g# Cc = 1591 !"g# T =
NO E&&'& = $%32
12%225*23 !"g*c+# M)'gnes = %5(99*% !"g*c+# M)'gnes =
2*294E$(4 !1.c+# ,)'gnes- =
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ξcm =0.005ELO DE ACERO MODELO DE CONCRETO MO
60.8 !cm2% c = 250 !"#$cm2% A& =
4200 !"#$cm2% "3 = 0.85 'y =
7000 !"#$cm2% ξ( = 0.002 '&) =
2100000 !"#$cm2% * = 50 E& =
90000 !"#$cm2% ξcm = 0.005 E&+ =
0.006 , = 60 !cm% ξ&+ =
0.002 = 55 !cm% ξy =
0.0682 ξ&m =
0.0542 ξ =
0.0094 c = 18.365 !cm% ξ& =
Re#/ 3 / = 2.5 '&
4495.04 !"#$cm2% "1 = 0.82166667 '& =
c1 = 0.4
c2 = 0.003c3 = 0.000225
c4 = 0.00255
c5 = 0.00410833
"2 = 0.4515213
2%329 !"g# Cc = 19239 !"g# T =
NO E&&'& = $4(1
12%1523*1 !"g*c+# M)'gnes = 9411*5 !"g*c+# M)'gnes =
2*522E$(4 !1.c+# ,)'gnes- =
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ELO DE ACERO
60.8 !cm2%
4200!"#$cm2%
7000!"#$cm2%
2100000 !"#$cm2%
90000 !"#$cm2%
0.006
0.002
0.0682
0.0639
0.0100
Re#/ 3
4546.25 !"#$cm2%
2%412 !"g#
NO
1291(599*3% !"g*c+#
2*%23E$(4!1.c+#
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