DISEÑO DE COLUMNAS.xls
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BASE DISEÑO DE COLUMNA DE HORMIGON ARMADO 1.0 DIRECCION X-X SECCION RECTANGULAR CASO Mu xx [Ton-m] Pu [Ton] H: ALTURA 40 cm 1 2.9 13.93 B: ANCHO 40 cm 2 2.12 13.69 R: RECUBRIMIENTO 5 cm 3 1.79 5.49 D: PERALTE EFECTIVO 35 cm 4 8.54 12.1 L:LARGO DE LA COLUMNA 4.2 m 5 4.62 7.07 6 1.92 12.58 MATERIALES 7 1.59 4.38 8 8.34 10.99 fc': 250 kg/cm2 9 4.82 5.97 fy 2800 kg/cm2 Ec 254842 kg/cm2 Ey 2100000 kg/cm2 ρ calculado ρ min 10.9.2 ρ max 10.9.2 Eu 0.003 0.040 0.01 0.08 ρ max 21.4.3 POSICION [cm] ACERO [cm2] 0.06 2Φ26+2Φ26 1 35 21.2 cm2 26 2Φ26 2 25 10.62 cm2 26 2Φ26 3 15 10.62 cm2 2Φ26+2Φ26 4 5 21.2 cm2 B/H<0,4 B>30 cm 0 5 10 15 20 25 30 35 40 -300 -200 -100 0 100 200 300 400 500 600 DIAGRAMA DE INTERACCION XX MOMENTO [Ton-m] CARGA AXIAL [Ton]
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Transcript of DISEÑO DE COLUMNAS.xls
BASE
DISEÑO DE COLUMNA DE HORMIGON ARMADO1.0 DIRECCION X-XSECCION RECTANGULAR
CASO Mu xx [Ton-m] Pu [Ton] CUMPLEH: ALTURA 40 cm 1 2.9 13.93 okaB: ANCHO 40 cm 2 2.12 13.69 okaR: RECUBRIMIENTO 5 cm 3 1.79 5.49 okaD: PERALTE EFECTIVO 35 cm 4 8.54 12.1 okaL:LARGO DE LA COLUMNA 4.2 m 5 4.62 7.07 oka
6 1.92 12.58 oka
MATERIALES 7 1.59 4.38 oka8 8.34 10.99 oka
fc': 250 kg/cm2 9 4.82 5.97 okafy 2800 kg/cm2
Ec 254842 kg/cm2Ey 2100000 kg/cm2 ρ calculado ρ min 10.9.2 ρ max 10.9.2 ρ normal Eu 0.003 0.040 0.01 0.08 0.04
ρ max 21.4.3POSICION [cm] ACERO [cm2] 0.06
2Φ26+2Φ26 1 35 21.2 cm2 26 5.312Φ26 2 25 10.62 cm2 26 5.312Φ26 3 15 10.62 cm2
2Φ26+2Φ26 4 5 21.2 cm2
B/H<0,4 B>30 cm
0 5 10 15 20 25 30 35 40
-300
-200
-100
0
100
200
300
400
500
600
DIAGRAMA DE INTERACCION XX
MOMENTO [Ton-m]
CA
RG
A A
XIA
L [
To
n]
2.0 DIRECCION Y-YSECCION RECTANGULAR
CASO Mu yy [Ton-m] Pu [Ton] CUMPLEH: ALTURA 40 cm 1 2.9 13.93 okaB: ANCHO 40 cm 2 2.12 13.69 okaR: RECUBRIMIENTO 5 cm 3 1.79 5.49 okaD: PERALTE EFECTIVO 35 cm 4 8.54 12.1 okaL:LARGO DE LA COLUMNA 4.2 m 5 4.62 7.07 oka
6 1.92 12.58 oka
MATERIALES 7 1.59 4.38 oka8 8.34 10.99 oka
fc': 250 kg/cm2 9 4.82 5.97 okafy 2800 kg/cm2
Ec 254842 kg/cm2Ey 2100000 kg/cm2Eu 0.003
POSICION [cm] ACERO [cm2]2Φ26+2Φ22 1 35 21.2 cm2
3Φ22 2 25 10.6 cm23Φ22 3 15 10.6 cm2
2Φ26+2Φ22 4 5 21.2 cm2
0 5 10 15 20 25 30 35 40
-300
-200
-100
0
100
200
300
400
500
600DIAGRAMA DE INTERACCION YY
MOMENTO [Ton-m]
CA
RG
A A
XIA
L [
To
n]
3.0 DISEÑO CONSIDERANDO MOMENTO BIAXIAL
3.1METODO DE LAS CARGAS RECIPROCAS DE BRESLER
CASO Mu xx [Ton-m] Mu yy [Ton-m] Pu [Ton] exu eyu1 2.9 2.9 13.93 0.21 0.212 2.12 2.12 13.69 0.15 0.153 1.79 1.79 5.49 0.33 0.334 8.54 8.54 12.1 0.71 0.715 4.62 4.62 7.07 0.65 0.656 1.92 1.92 12.58 0.15 0.157 1.59 1.59 4.38 0.36 0.368 8.34 8.34 10.99 0.76 0.769 4.82 4.82 5.97 0.81 0.81
CASO ex ey Pnex [Ton] Pney [Ton] Po [Ton] Pn biax [Ton]1 0.21 0.21 174.432 174.432 518.392 104.8582 0.15 0.15 223.202 223.202 518.392 142.2183 0.33 0.33 109.627 109.627 518.392 61.2944 0.71 0.71 45.585 45.585 518.392 23.8415 0.65 0.65 49.066 49.066 518.392 25.7526 0.15 0.15 225.508 225.508 518.392 144.0967 0.36 0.36 97.056 97.056 518.392 53.5408 0.76 0.76 42.053 42.053 518.392 21.9169 0.81 0.81 38.827 38.827 518.392 20.169
CASO Pu [Ton] Φ Pn biax [Ton] CUMPLE1 13.93 94.365 oka2 13.69 127.986 oka3 5.49 55.163 oka4 12.1 21.455 oka5 7.07 23.176 oka6 12.58 129.677 oka7 4.38 48.185 oka8 10.99 19.723 oka9 5.97 18.151 oka
0 5 10 15 20 25 30 35 40
-300
-200
-100
0
100
200
300
400
500
600DIAGRAMA DE INTERACCION YY
MOMENTO [Ton-m]
CA
RG
A A
XIA
L [
To
n]
Pn≤1
1Pox
+ 1Poy
− 1Po
3.2 METODO DEL CONTORNO DE CARGA PCA
CASO Mu xx [Ton-m] Mu yy [Ton-m] Pu [Ton] Φ Mnxx [Ton-m] Φ Mnyy [Ton-m]1 2.9 2.9 13.93 24.292 24.29172752 2.12 2.12 13.69 24.292 24.29172753 1.79 1.79 5.49 24.782 24.78197254 8.54 8.54 12.1 24.564 24.564165 4.62 4.62 7.07 24.782 24.78197256 1.92 1.92 12.58 24.564 24.564167 1.59 1.59 4.38 24.782 24.78197258 8.34 8.34 10.99 24.564 24.564169 4.82 4.82 5.97 24.782 24.7819725
CASO Mu xx [Ton-m] Mu yy [Ton-m] Φ Mnxx [Ton-m] Φ Mnyy [Ton-m] INTERACCION CUMPLE1 2.9 2.9 24.292 24.292 0.051 oka2 2.12 2.12 24.292 24.292 0.029 oka3 1.79 1.79 24.782 24.782 0.021 oka4 8.54 8.54 24.564 24.564 0.321 oka5 4.62 4.62 24.782 24.782 0.109 oka6 1.92 1.92 24.564 24.564 0.024 oka7 1.59 1.59 24.782 24.782 0.017 oka8 8.34 8.34 24.564 24.564 0.308 oka9 4.82 4.82 24.782 24.782 0.118 oka
VALOR DE BETA UTILIZADO0.67
cuantida de acero 0.040fy 2800 kg/cm2fc 250 kg/cm2w 0.446
ω=ρg f yf c '(M ux
M nx)(log0 .5log β )+(M uy
M ny)(log 0.5log β )≤1.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
4.0 DISEÑO DE COLUMNAS HORMIGON AL CORTE
CASO MAS DESFABORABLE
SECCION RECTANGULAR Pu [Ton] Vn [Ton]5.97 3.96
H: ALTURA 40 cmB: ANCHO 40 cmR: RECUBRIMIENTO 5 cmD: PERALTE EFECTIVO 35 cmL:LARGO DE LA COLUMNA 3 m
MATERIALES
fc': 250 kg/cm2fy 2800 kg/cm2
Ec 254842 kg/cm2Ey 2100000 kg/cm2Eu 0.003
4.1 DISEÑO AL CORTE DE COLUMNA
Vu<Φ(Vc+Vs)s: DISTANCIA ENTRE ESTRIBOS
numero de barras Φ barra [mm] As [cm2] Avmin [cm2] sdiseño [cm] scalculado [cm] smax [cm]2 10 1.57 0.93333333333 20 -26.82 17.5
Vu 3.960 TonVc 12.34 Ton corte no detalladoVs 7.697 Ton oka
Vsmax 46.485 TonVn 20.037 Ton
ΦVn 12.022 Ton okaVu/ΦVn 0.33
CASO Pu [Ton] Vu [Ton] Φ barra [mm] sdiseño [cm] Vu/ΦVn1 5.970 3.960 10 20 0.33
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0.0
0.2
0.4
0.6
0.8
1.0
1.2
4.2 DISEÑO AL CORTE DE COLUMNA. CORTE POR CAPACIDAD
SE CONSIDERA EN LAS ZONAS CERCANAS A LOS NUDOS DONDE SE ESPERA PLASTIFICACION
Vu<Φ(Vc+Vs)s: DISTANCIA ENTRE ESTRIBOS zonas sin fluencia
numero de barras Φ barra [mm] As [cm2] Avmin [cm2] sdiseño [cm] scalculado [cm] smax [cm]4 10 3.14 0.46666666667 10 10.91 17.5
Vu(PP+SC): CORTE DE PESO PROPIO MAS SOBRECARGA SIN MAYORARVu(DPC): CORTE DETERMINADO DEL DISEÑO POR CAPACIDAD CONSIDERANDO LA SOBRERESISTENCIA DE LOS MATERIALES
Vu(PP+SC) 2.15 TonVu(DPC) 21.835 Ton
Vu 24 TonVc 0 Ton corte no detalladoVs 30.788 Ton oka
Vsmax 46.485 TonVn 30.788 Ton
ΦVn 26.169 Ton okaVu/ΦVn 0.9
L: LONGITUD ALREDEDOR DE NUDOS, O ZONAS QUE SE ESPEREN QUE SE EXCEDA LA FLUENCIAL= 50 cm LONGITUD A CONFINAR
CASO Mu xx [Ton-m] Mu yy [Ton-m] Pu [Ton] Mn xx [Ton-m] Mn yy [Ton-m] Vu(DPC) [Ton]1 2.9 2.9 13.93 36.682 36.682 21.8352 2.12 2.12 13.69 36.648 36.648 21.8143 1.79 1.79 5.49 35.401 35.401 21.0724 8.54 8.54 12.1 36.419 36.419 21.6785 4.62 4.62 7.07 35.652 35.652 21.2226 1.92 1.92 12.58 36.488 36.488 21.7197 1.59 1.59 4.38 35.225 35.225 20.9678 8.34 8.34 10.99 36.259 36.259 21.5839 4.82 4.82 5.97 35.477 35.477 21.117
CASO Vu(PP+SC) Vu(DPC) [Ton] Vu [Ton] As [cm2] sdiseño [cm] armadura1 2.15 21.835 23.985 3.14 102 2.15 21.814 23.964 3.14 103 2.15 21.072 23.222 3.14 10
4 2.15 21.678 23.828 3.14 105 2.15 21.222 23.372 3.14 106 2.15 21.719 23.869 3.14 107 2.15 20.967 23.117 3.14 108 2.15 21.583 23.733 3.14 109 2.15 21.117 23.267 3.14 10
4.3 DISEÑO DE LA ARMADURA DE CONFINAMIENTO
SE CONSIDERA EN LAS ZONAS CERCANAS A LOS NUDOS DONDE SE ESPERA PLASTIFICACION
Ash 2.81 cm2 s min[cm] smax[cm]s 10 cm 10 10fc 250 kg/cm2fy 2800 kg/cm2Ag 1600 cm2Ach 1376 cm2hc 35 cmhx 40 cmΦ longitudinal 2.2 cm
Ash: ARMADURA DE CONFINAMIENTO DE LA COLUMNA CON CERCOSs: SEPARACION ENTRE CERCOSAg: AREA TOTAL DE LA SECCIONAch: AREA DEL NUCLEO CONFINADOhx: MAXIMA SEPARACION ENTRE CERCOS DE UNA SECCION
12 1.1312 1.13
ESTRIBOS Φ10 S=10
SE DEBE CONFINAR EN UNA ZONA DE LONGITUD IHUAL A 50 DESDE EL TERMINODE LA CARA DEL NUDO
5 RESISTENCIA MINIMA A LA FLEXION DE LAS COLUMNAS
NUDO CENTRALANALISIS DEL NUDO
Mn VIGA+ izq 7.109Mn VIGA- IZQ 13.659
SUMA(Mn+izq + Mn-der) 20.768
Mn VIGA- der 13.659Mn VIGA+ der 7.109
SUMA(Mn-izq + Mn+der) 20.768FS 1.2SUMA DE LAS VIGAS*FS 24.922SUMA DE LAS COLUMNAS 27.582 oka
Pu [Ton] Mn [Ton-m] CONSIDERANSO SOLO UNA DIRECCION0 27.582
Pu [Ton] Mn [Ton-m] CONSIDERANDO EN FORMA SIMULTANEA EN AMBAS DIRECIONES EL SISMO0 18.48
EN EL CASO MAS DESFABORABLE LAS COLUMNAS QUE SE ENCUENTRAN EN LOS EXTREMOS TIENEN UNA CAPACIDADA FLEXION MAYOR QUE LAS VIGAS
Mn [Ton-m] Pn [Ton] Φ Mn [Ton-m] ΦPn [Ton] ex
0 -178.39218139648 0 -160.552963257 0.000
2.767175 -163.94218444824 2.4904575 -147.547973633 -0.017
3.7542922 -158.45118713379 3.37886281 -142.606063843 -0.024Φ Mn [Ton-m] 5.1873931 -149.75048828125 4.66865375 -134.775436401 -0.035
24.292 11.165608 -110.512550354 10.0490463 -99.4612884521 -0.10124.292 15.5817 -81.452270507813 14.02353 -73.3070373535 -0.19124.782 19.035806 -58.568756103516 17.132225 -52.7118797302 -0.32524.564 21.849945 -39.715225219727 19.6649488 -35.7437019348 -0.55024.782 24.2124 -23.636419296265 21.79116 -21.2727775574 -1.02424.564 26.24062 -9.549388885498 23.6165575 -8.59444999695 -2.748
24.782 28.01166 3.0595977306366 24.7819725 2.706832170486 9.15524.564 28.881333 9.89593982696533 24.56416 8.416697502136 2.91924.782 29.51373 15.3869342803955 24.2917275 12.6644525528 1.918
30.430168 27.268180847168 23.238275 20.823595047 1.11631.280265 38.5320434570313 22.125775 27.25524520874 0.81232.060183 49.1016998291016 22.4421275 34.37118911743 0.65332.77582 59.0952529907227 22.943075 41.36667633057 0.555
33.431823 68.6054992675781 23.402275 48.0238494873 0.48734.031878 77.7062759399414 23.822315 54.3943901062 0.43834.578965 86.4571151733398 24.205275 60.51998519897 0.40035.075513 94.9065704345703 24.5528575 66.43460083008 0.37035.523515 103.094581604004 24.86646 72.16620635986 0.34535.749153 114.563873291016 25.024405 80.19470977783 0.31235.91575 126.103668212891 25.141025 88.27256774902 0.285
36.052778 137.171478271484 25.2369425 96.02004241943 0.26336.159565 147.82048034668 25.311695 103.4743423462 0.24536.23555 158.096160888672 25.364885 110.6673049927 0.22936.28024 168.03759765625 25.3961675 117.6263122559 0.216
36.293213 177.678634643555 25.40525 124.3750457764 0.20436.274103 187.048736572266 25.39187 130.9341125488 0.19436.222585 196.173553466797 25.3558075 137.3214874268 0.18535.473005 209.511459350586 24.8311025 146.6580200195 0.16934.513698 223.825134277344 24.1595875 156.6775970459 0.15433.56987 237.629318237305 23.4989075 166.3405151367 0.141
32.631743 250.857070922852 22.84222 175.5999603271 0.13031.655895 262.754669189453 22.159125 183.9282684326 0.12030.686688 274.311737060547 21.48068 192.0182342529 0.11229.720853 285.554809570313 20.8045963 199.8883666992 0.10428.755448 296.507598876953 20.1288138 207.5552978516 0.09727.787825 307.191467285156 19.4514775 215.0340270996 0.09026.815585 317.625946044922 18.7709088 222.3381500244 0.08425.836553 327.828491210938 18.0855875 229.4799499512 0.07924.848768 337.815063476563 17.3941363 236.4705352783 0.07423.850425 347.600158691406 16.6952975 243.3201141357 0.06922.839885 357.197082519531 15.98792 250.0379486084 0.06421.81566 366.617889404297 15.2709613 256.6325073242 0.060
20.776365 375.873718261719 14.543455 263.1116027832 0.05519.720755 384.974670410156 13.8045275 269.4822387695 0.05118.647659 393.93017578125 13.0533613 275.7511291504 0.04717.556024 402.748809814453 12.2892163 281.9241638184 0.04416.444853 411.438598632813 11.5113975 288.0069885254 0.04015.313251 420.006744384766 10.719275 294.0047302246 0.036
0 518.392211914063 0 362.8745422363 0.000
Mn [Ton-m] Pn [Ton] Φ Mn [Ton-m] ΦPn [Ton] ey
0 -178.39218139648 0 -160.552963257 0.000
2.767175 -163.94218444824 2.4904575 -147.547973633 -0.017
3.7542922 -158.45118713379 3.37886281 -142.606063843 -0.024Φ Mn [Ton-m] 5.1873931 -149.75048828125 4.66865375 -134.775436401 -0.035
24.292 11.165608 -110.512550354 10.0490463 -99.4612884521 -0.10124.292 15.5817 -81.452270507813 14.02353 -73.3070373535 -0.19124.782 19.035806 -58.568756103516 17.132225 -52.7118797302 -0.32524.564 21.849945 -39.715225219727 19.6649488 -35.7437019348 -0.55024.782 24.2124 -23.636419296265 21.79116 -21.2727775574 -1.02424.564 26.24062 -9.549388885498 23.6165575 -8.59444999695 -2.748
24.782 28.01166 3.0595977306366 24.7819725 2.706832170486 9.15524.564 28.881333 9.89593982696533 24.56416 8.416697502136 2.91924.782 29.51373 15.3869342803955 24.2917275 12.6644525528 1.918
30.430168 27.268180847168 23.238275 20.823595047 1.11631.280265 38.5320434570313 22.125775 27.25524520874 0.81232.060183 49.1016998291016 22.4421275 34.37118911743 0.65332.77582 59.0952529907227 22.943075 41.36667633057 0.555
33.431823 68.6054992675781 23.402275 48.0238494873 0.48734.031878 77.7062759399414 23.822315 54.3943901062 0.43834.578965 86.4571151733398 24.205275 60.51998519897 0.40035.075513 94.9065704345703 24.5528575 66.43460083008 0.37035.523515 103.094581604004 24.86646 72.16620635986 0.34535.749153 114.563873291016 25.024405 80.19470977783 0.31235.91575 126.103668212891 25.141025 88.27256774902 0.285
36.052778 137.171478271484 25.2369425 96.02004241943 0.26336.159565 147.82048034668 25.311695 103.4743423462 0.24536.23555 158.096160888672 25.364885 110.6673049927 0.22936.28024 168.03759765625 25.3961675 117.6263122559 0.216
36.293213 177.678634643555 25.40525 124.3750457764 0.20436.274103 187.048736572266 25.39187 130.9341125488 0.19436.222585 196.173553466797 25.3558075 137.3214874268 0.18535.473005 209.511459350586 24.8311025 146.6580200195 0.16934.513698 223.825134277344 24.1595875 156.6775970459 0.15433.56987 237.629318237305 23.4989075 166.3405151367 0.141
32.631743 250.857070922852 22.84222 175.5999603271 0.13031.655895 262.754669189453 22.159125 183.9282684326 0.12030.686688 274.311737060547 21.48068 192.0182342529 0.11229.720853 285.554809570313 20.8045963 199.8883666992 0.10428.755448 296.507598876953 20.1288138 207.5552978516 0.09727.787825 307.191467285156 19.4514775 215.0340270996 0.09026.815585 317.625946044922 18.7709088 222.3381500244 0.08425.836553 327.828491210938 18.0855875 229.4799499512 0.07924.848768 337.815063476563 17.3941363 236.4705352783 0.07423.850425 347.600158691406 16.6952975 243.3201141357 0.06922.839885 357.197082519531 15.98792 250.0379486084 0.06421.81566 366.617889404297 15.2709613 256.6325073242 0.060
20.776365 375.873718261719 14.543455 263.1116027832 0.05519.720755 384.974670410156 13.8045275 269.4822387695 0.05118.647659 393.93017578125 13.0533613 275.7511291504 0.04717.556024 402.748809814453 12.2892163 281.9241638184 0.04416.444853 411.438598632813 11.5113975 288.0069885254 0.04015.313251 420.006744384766 10.719275 294.0047302246 0.036
0 518.392211914063 0 362.8745422363 0.000
0 1.0000.1 0.9910.2 0.9690.3 0.9360.4 0.8920.5 0.8360.6 0.7660.7 0.6790.8 0.5660.9 0.408
1 0.000
Φ Φ 0.85 reduccion de corte utilizada normalmente. Utilizar con diseño por capacidad para zonas sismicas0.6 Φ 0.6 reduccion de corte utilizada normalmente sin diseño por capacidad para zonas sismicas
zonas sin fluenciaΦ Φ 0.85 reduccion de corte utilizada normalmente. Utilizar con diseño por capacidad para zonas sismicas
0.85 Φ 0.6 reduccion de corte utilizada normalmente sin diseño por capacidad para zonas sismicas
Vu(DPC): CORTE DETERMINADO DEL DISEÑO POR CAPACIDAD CONSIDERANDO LA SOBRERESISTENCIA DE LOS MATERIALES
Vu(DPC) [Ton]
1.522.81
CONSIDERANDO EN FORMA SIMULTANEA EN AMBAS DIRECIONES EL SISMO
EN EL CASO MAS DESFABORABLE LAS COLUMNAS QUE SE ENCUENTRAN EN LOS EXTREMOS TIENEN UNA CAPACIDAD
reduccion de corte utilizada normalmente. Utilizar con diseño por capacidad para zonas sismicasreduccion de corte utilizada normalmente sin diseño por capacidad para zonas sismicas
reduccion de corte utilizada normalmente. Utilizar con diseño por capacidad para zonas sismicasreduccion de corte utilizada normalmente sin diseño por capacidad para zonas sismicas
