diagrama de interaccion columnas circulares

DIAGRAMA DE INTERACCION COLUMNAS RECTANGULARES

406 28 6

40

0 Ø 1/2" 0 Ø 1/2" 0 Ø 1/2"0 Ø 5/8" 0 Ø 5/8" 0 Ø 5/8"3 Ø 3/4" 2 Ø 3/4" 3 Ø 3/4"0 Ø 1" 0 Ø 1" 0 Ø 1"

P1 P2 P3

Es = 2039400 Kg/cm2Fy = 4200 Kg/cm2f'c = 210 Kg/cm2εc = 0.003

DEFORMACION UNITARIA DE FLUENCIA EN EL ACEROEje neutro para la condicion de falla balanceada

εy = Fy / Es = 4200 Kg/cm2 = 0.002059432039400 Kg/cm2

PUNTO 1

CALCULO DE LA FUERZA DE COMPRESION EN EL CONCRETO

Cc = ,85 f'c b d = 0.85 210 40 40 = 285600

CALCULO DE LA FUERZA DE COMPRESION DEL ACERO

P1 = As1 fs1 = 7.8 4200 = 32760 KgP2 = As2 fs2 = 5.2 4200 = 21840 KgP3 = As3 fs3 = 7.8 4200 = 32760 Kg

CALCULO CARGA AXIAL NOMINAL

Pn = Cc + P1 + P2 + P3 = 372960 Kg = 372.96 Ton

CALCULO DEL MOMENTO FLECTOR NOMINAL

Mn = 285600 0 +32760 14 +21840 0 -32760 14 = 0 Kg-cm

0 T-cm0 T-m

PUNTO 2

ε1εc =

εc = ε20.003 ε3

34

6 28 640

CALCULO DE DEFORMACIONES UNITARIAS

ε1 = 0.003 34 = 0.00255 0.0020594340

ε2 = 0.003 20 = 0.0015 0.0020594340

ε3 = 0.003 6 = 0.00045 0.0020594340

CALCULO DE ESFUERZOS EN EL ACERO

fs1 = 4200 Kg/cm2

fs2 = 3059.1 Kg/cm2

fs1 = 917.73 Kg/cm2

CALCULO DE LA FUERZA DE COMPRESION EN EL HORMIGON

Cc = ,85 f'c b d = 0.85 210 34 40 = 242760


P1 = As1 fs1 = 7.8 4200 = 32760 KgP2 = As2 fs2 = 5.2 3059.1 = 15907.32 KgP3 = As3 fs3 = 7.8 917.73 = 7158.294 Kg


Pn = Cc + P1 + P2 + P3 = 298585.614 Kg = 298.585614 Ton


Mn = 242760 3 +32760 14 +

15907.32 0 -7158.294 14 = 1086703.88 Kg-cm

1086.70388 T-cm10.8670388 T-m

e = 3.63950516

PUNTO e = 10% H = 4 cm ENTRE 40 y 39.15467

ε1εc =

εc = ε20.003 ε3

33.2814695

6 28 639.15467


ε1 = 0.003 33.15467 = 0.00254028 0.0020594339.15467

ε2 = 0.003 19.15467 = 0.00146762 0.0020594339.15467

ε3 = 0.003 5.15467 = 0.00039495 0.0020594339.15467


fs1 = 4200 Kg/cm2

fs2 = 2993.05554 Kg/cm2

fs1 = 805.454419 Kg/cm2


Cc = ,85 f'c b d = 0.85 210 33.2814695 40 = 237629.69223


P1 = As1 fs1 = 7.8 4200 = 32760 KgP2 = As2 fs2 = 5.2 2993.05554 = 15563.8888 KgP3 = As3 fs3 = 7.8 805.454419 = 6282.54447 Kg


Pn = Cc + P1 + P2 + P3 = 292236.126 Kg = 292.236126 Ton


Mn = 237629.692 3.35926525 +32760 14 +

15563.8888 0 -6282.54447 14 = 1168945.54 Kg-cm

1168.94554 T-cm11.6894554 T-m

e = 4.00000357

PUNTO e = 10% H = 4 cm ENTRE 34 y 20

ε1

εc =εc = ε2

0.003 ε3

28.9

6 28 634


ε1 = 0.003 28 = 0.00247059 0.0020594334

ε2 = 0.003 14 = 0.00123529 0.0020594334

ε3 = 0.003 0 = 0 0.0020594334


fs1 = 4200 Kg/cm2

fs2 = 2519.25882 Kg/cm2

fs1 = 0 Kg/cm2


Cc = ,85 f'c b d = 0.85 210 28.9 40 = 206346


P1 = As1 fs1 = 7.8 4200 = 32760P2 = As2 fs2 = 5.2 2519.25882 = 13100.1459P3 = As3 fs3 = 7.8 0 = 0


Pn = Cc + P1 + P2 - P3 = 252206.146 Kg = 252.206146 Ton


Mn = 206346 5.55 +32760 14 +

13100.1459 0 -0 14 = 1603860.3 Kg-cm

1603.8603 T-cm16.038603 T-m

e = 6.35932282 cm

PUNTO 3

ε1εc =

εc = ε20.003 ε3

25.5

6 28 630


ε1 = 0.003 24 = 0.0024 0.0020594330

ε2 = 0.003 10 = 0.001 0.0020594330

ε3 = 0.003 4 = 0.0004 0.0020594330


fs1 = 4200 Kg/cm2

fs2 = 2039.4 Kg/cm2

fs1 = 815.76 Kg/cm2


Cc = ,85 f'c b d = 0.85 210 25.5 40 = 182070


P1 = As1 fs1 = 7.8 4200 = 32760P2 = As2 fs2 = 5.2 2039.4 = 10604.88P3 = As3 fs3 = 7.8 815.76 = 6362.928


Pn = Cc + P1 + P2 - P3 = 219071.952 Kg = 219.071952 Ton


Mn = 182070 7.25 +32760 14 +

10604.88 0 -6362.928 14 = 1867728.49 Kg-cm

1867.72849 T-cm18.6772849 T-m

e = 8.52563952 cm

PUNTO 4

ε1εc =

εc = ε20.003 ε3

17

6 28 620


ε1 = 0.003 14 = 0.0021 0.0020594320

ε2 = 0.003 0 = 0 0.0020594320

ε3 = 0.003 14 = 0.0021 0.0020594320


fs1 = 4200 Kg/cm2

fs2 = 0 Kg/cm2

fs1 = 4200 Kg/cm2


Cc = ,85 f'c b d = 0.85 210 17 40 = 121380


P1 = As1 fs1 = 7.8 4200 = 32760P2 = As2 fs2 = 5.2 0 = 0P3 = As3 fs3 = 7.8 4200 = 32760


Pn = Cc + P1 + P2 - P3 = 121380 Kg = 121.38 Ton


Mn = 121380 11.5 +32760 14 +

0 0 -32760 14 = 2313150 Kg-cm

2313.15 T-cm23.1315 T-m

PUNTO 5

ε1εc =

εc = ε20.003 ε3

6.34015

6 28 67.459


ε1 = 0.003 1.459 = 0.00058681 0.002059437.459

ε2 = 0.003 12.541 = 0.00504397 0.002059437.459

ε3 = 0.003 26.541 = 0.01067476 0.002059437.459


fs1 = 1196.736 Kg/cm2

fs2 = 4200 Kg/cm2

fs1 = 4200 Kg/cm2


Cc = ,85 f'c b d = 0.85 210 6.34015 40 = 45268.671


P1 = As1 fs1 = 7.8 1196.736 = 9334.54077P2 = As2 fs2 = 5.2 4200 = 21840P3 = As3 fs3 = 7.8 4200 = 32760


Pn = Cc + P1 + P2 - P3 = 3.2117749 Kg = 0.00321177 Ton


Mn = 45268.671 16.829925 +9334.54077 14 -

21840 0 -32760 14 = 1351191.91 Kg-cm

1351.19191 T-cme= 420699.442 13.5119191 T-m

Mu Pu .9 Mu .9 Pu .7 Mu .7 Pu e = Mu / Pu =punt 1 0 372.96 0 335.664 0 261.072 0punt 2 1086.70388 298.585614 978.033496 268.727053 760.692719 209.00993 596.736punt 3 1867.72849 219.071952 1680.95564 197.164757 1307.40994 153.350366 895.104punt 4 2313.15 121.38 2081.835 109.242 1619.205 84.966 1193.472

punt 5 1351.19191 0.00321177 1216.07272 0.0028906 945.834336 0.00224824 1491.84

La carga axial que define una variación en el factor de reducción de capacidad es:

.1 f'c Ag = 0.1 210 1600 = 33600 Kg33.6 T

POR NO SER ZUNCHADA e = 10% h

e = 0.1 40 = 4 cms

DE LA ECUACION = e = Mu / Pu = 4 cms

CARGA AXIAL QUE DEFINE REDUCCION DE CARGA

0.1 210 1600 = 33600 Kg33.6 T

0 500 1000 1500 2000 25000

50

100

150

200

250

300

350

400

f(x) = − 65.6426488033962 ln(x) + 572.180599188307

DIAGRAMA DE INTERACCION

P nominal, M nominal90% Pn Mn70% Pn MnLogarithmic (70% Pn Mn)e = 10% hMAX PMIN P

Mnominal

Pnom

inal

Kg

4 M Max P Min P0 0 204.565288 0 33.6

149.184 925.26 204.565288 925.26 33.6223.776 1387.89 204.565288 1387.89 33.6298.368 1850.52 204.565288 1850.52 33.6

372.96 2313.15 204.565288 2313.15 33.6

0 500 1000 1500 2000 25000

50

100

150

200

250

300

350

400

f(x) = − 65.6426488033962 ln(x) + 572.180599188307


P nominal, M nominal90% Pn Mn70% Pn MnLogarithmic (70% Pn Mn)e = 10% hMAX PMIN P

Mnominal

Pnom

inal

DIAGRAMA DE INTERACCION COLUMNAS RECTANGULARES

1207.5 105 7.5

40

Long

10 Ø 1/2" Ps 20 Ø 5/8" 30 Ø 3/4" 4

16 Ø 1" 567

Es = 2039400 Kg/cm2 8Fy = 4200 Kg/cm2 9f'c = 210 Kg/cm2 10εc = 0.003

DEFORMACION UNITARIA DE FLUENCIA EN EL ACEROEje neutro para la condicion de falla balanceada

εy = Fy / Es = 4200 Kg/cm2 = 0.00205942922039400 Kg/cm2

Ag = PI r2 = 11309.733553 cm2

PUNTO 1

CALCULO DE LA FUERZA DE COMPRESION EN EL CONCRETO

Cc = ,85 f'c b d = 0.85 210 11309.733553 =


Ps = As fs = 81.6 4200 = 342720 Kg


Pn = Cc + Ps = 2361507.44 Kg = 2361.5074392 Ton


Mn = 2018787.44 0 = 0.000

8400 10.242 = 86032.8008400 29.167 = 245002.8008400 43.652 = 366676.8008400 51.491 = 432524.400

0 0 = 0.0000 0 = 0.0000 0 = 0.0000 0 = 0.0000 0 = 0.0000 0 = 0.0000 0 = 0.0000 0 = 0.0000 0 = 0.0000 0 = 0.0000 0 = 0.0000 0 = 0.000

8400 -51.491 = -432524.4008400 -43.652 = -366676.8008400 -29.167 = -245002.8008400 -10.242 = -86032.800

0.000 Kg-cm0.000 T-cm0.000 T-m

PUNTO 2

ε1εc =

εc = ε20.003 ε3

102

7.5 105 7.5120120


ε1 = 0.003 49.757758094 = 0.001243944 1120

ε2 = 0.003 30.832562766 = 0.0007708141 2120

ε3 = 0.003 16.347845354 = 0.0004086961 3120

ε4 = 0.003 8.5087727788 = 0.0002127193 4120

ε5 = 0.003 60 = 0 5120

ε6 = 0.003 60 = 0 6120

ε7 = 0.003 60 = 0 7120

ε8 = 0.003 60 = 0 8120

ε9 = 0.003 60 = 0 9120

ε10 = 0.003 60 = 0 10120

ε1 = 0.003 70.242241906 = 0.001756056 1120

ε2 = 0.003 89.167437234 = 0.0022291859 2120

ε3 = 0.003 103.65215465 = 0.0025913039 3120

ε4 = 0.003 111.49122722 = 0.0027872807 4120

ε5 = 0.003 60 = 0 5120

ε6 = 0.003 60 = 0 6120

ε7 = 0.003 60 = 0 7120

ε8 = 0.003 60 = 0 8120

ε9 = 0.003 60 = 0 9120

ε10 = 0.003 60 = 0 10120


fs1 = 2536.8993 Kg/cm2fs2 = 1571.99821 Kg/cm2fs3 = 833.494895 Kg/cm2fs4 = 433.81978 Kg/cm2fs5 = 0 Kg/cm2fs6 = 0 Kg/cm2fs7 = 0 Kg/cm2fs8 = 0 Kg/cm2fs9 = 0 Kg/cm2fs10 = 0 Kg/cm2

fs1 = 3581.3007 Kg/cm2fs2 = 4200 Kg/cm2fs3 = 4200 Kg/cm2fs4 = 4200 Kg/cm2fs5 = 0 Kg/cm2fs6 = 0 Kg/cm2fs7 = 0 Kg/cm2fs8 = 0 Kg/cm2

fs9 = 0 Kg/cm2fs10 = 0 Kg/cm2


Cc = ,85 f'c Asc = 0.85 210 10245.937728 =

area = 1799.639964102 8446.2977643

10245.937728 cm2


P1 = As1 fs1 = 10.2 2536.8993 = 25876.372824 KgP2 = As2 fs2 = 10.2 1571.99821 = 16034.381769 KgP3 = As3 fs3 = 10.2 833.494895 = 8501.6479329 KgP4 = As4 fs4 = 10.2 433.81978 = 4424.9617573 KgP5 = As5 fs5 = 0 0 = 0 KgP6 = As6 fs6 = 0 0 = 0 KgP8 = As7 fs7 = 0 0 = 0 KgP8 = As8 fs8 = 0 0 = 0 KgP9 = As9 fs9 = 0 0 = 0 KgP10 = As10 fs10 = 0 0 = 0 Kg

P11 = As11 fs11 = 10.2 3581.3007 = 36529.267176 KgP12 = As12 fs12 = 10.2 4200 = 42840 KgP13 = As13 fs13 = 10.2 4200 = 42840 KgP14 = As14 fs14 = 10.2 4200 = 42840 KgP15 = As15 fs15 = 0 0 = 0 KgP16 = As16 fs16 = 0 0 = 0 KgP17 = As17 fs17 = 0 0 = 0 KgP18 = As18 fs18 = 0 0 = 0 KgP19 = As19 fs19 = 0 0 = 0 KgP20 = As20 fs20 = 0 0 = 0 Kg

219886.63146 KgCALCULO CARGA AXIAL NOMINAL

Pn = Cc + SUM Pi = 2048786.52 Kg = 2048.786516 Ton


Mn = 1828899.88 9 = 16460098.9625876.3728 -10.24224191 = -265032.0701116034.3818 -29.16743723 = -467681.823838501.64793 -43.65215465 = -371115.250314424.96176 -51.49122722 = -227846.71129

0 0 = 00 0 = 00 0 = 00 0 = 00 0 = 00 0 = 00 0 = 0

36529.2672 10.242241906 = 374141.5910642840 29.167437234 = 1249533.011142840 43.652154646 = 1870058.30542840 51.491227221 = 2205884.1742

0 0 = 00 0 = 00 0 = 00 0 = 00 0 = 00 0 = 0

20828040.186 Kg-cm208.28040186 T-cm

e = 0.10166037 2.0828040186 T-m

PUNTO e = 10% H = 12 cm ENTRE 0 y

ε1εc =

εc = ε20.003 ε3

71.999675

7.5 105 7.584.7055

120


ε1 = 0.003 14.463258094 = 0.0005122427 1

84.7055

ε2 = 0.003 -4.461937234 = -0.0001580277 284.7055

ε3 = 0.003 -18.94665465 = -0.0006710304 384.7055

ε4 = 0.003 -26.78572722 = -0.0009486655 484.7055

ε5 = 0.003 24.7055 = 0 584.7055

ε6 = 0.003 24.7055 = 0 684.7055

ε7 = 0.003 24.7055 = 0 784.7055

ε8 = 0.003 24.7055 = 0 884.7055

ε9 = 0.003 24.7055 = 0 984.7055

ε10 = 0.003 24.7055 = 0 1084.7055

ε1 = 0.003 34.947741906 = 0.0012377381 184.7055

ε2 = 0.003 53.872937234 = 0.0019080085 284.7055

ε3 = 0.003 68.357654646 = 0.0024210112 384.7055

ε4 = 0.003 76.196727221 = 0.0026986463 484.7055

ε5 = 0.003 24.7055 = 0 584.7055

ε6 = 0.003 24.7055 = 0 6

84.7055

ε7 = 0.003 24.7055 = 0 784.7055

ε8 = 0.003 24.7055 = 0 884.7055

ε9 = 0.003 24.7055 = 0 984.7055

ε10 = 0.003 24.7055 = 0 1084.7055


fs1 = 1044.66777 Kg/cm2fs2 = -322.281604 Kg/cm2fs3 = -1368.49936 Kg/cm2fs4 = -1934.70833 Kg/cm2fs5 = 0 Kg/cm2fs6 = 0 Kg/cm2fs7 = 0 Kg/cm2fs8 = 0 Kg/cm2fs9 = 0 Kg/cm2fs10 = 0 Kg/cm2

fs1 = 2524.24311 Kg/cm2fs2 = 3891.19248 Kg/cm2fs3 = 4200 Kg/cm2fs4 = 4200 Kg/cm2fs5 = 0 Kg/cm2fs6 = 0 Kg/cm2fs7 = 0 Kg/cm2fs8 = 0 Kg/cm2fs9 = 0 Kg/cm2fs10 = 0 Kg/cm2


Cc = ,85 f'c Asc = 0.85 210 5105.1962394 =

area = 896.698322871.999675 4208.4979166

5105.1962394 cm2


P1 = As1 fs1 = 10.2 1044.66777 = 10655.61124 KgP2 = As2 fs2 = 10.2 -322.281604 = -3287.2723577 KgP3 = As3 fs3 = 10.2 -1368.49936 = -13958.693462 KgP4 = As4 fs4 = 10.2 -1934.70833 = -19734.024946 KgP5 = As5 fs5 = 0 0 = 0 KgP6 = As6 fs6 = 0 0 = 0 KgP8 = As7 fs7 = 0 0 = 0 KgP8 = As8 fs8 = 0 0 = 0 KgP9 = As9 fs9 = 0 0 = 0 KgP10 = As10 fs10 = 0 0 = 0 Kg

P11 = As11 fs11 = 10.2 2524.24311 = 25747.279695 KgP12 = As12 fs12 = 10.2 3891.19248 = 39690.163292 KgP13 = As13 fs13 = 10.2 4200 = 42840 KgP14 = As14 fs14 = 10.2 4200 = 42840 KgP15 = As15 fs15 = 0 0 = 0 KgP16 = As16 fs16 = 0 0 = 0 KgP17 = As17 fs17 = 0 0 = 0 KgP18 = As18 fs18 = 0 0 = 0 KgP19 = As19 fs19 = 0 0 = 0 KgP20 = As20 fs20 = 0 0 = 0 Kg


Pn = Cc + SUM Pi = 1036070.59 Kg = 1036.0705922 Ton


Mn = 911277.529 24.0001625 = 21870808.77210655.6112 -10.24224191 = -109137.34797

-3287.27236 -29.16743723 = 95881.310164-13958.6935 -43.65215465 = 609327.04565-19734.0249 -51.49122722 = 1016129.1625

0 0 = 0

0 0 = 00 0 = 00 0 = 00 0 = 00 0 = 00 0 = 0

25747.2797 10.242241906 = 263709.8670539690.1633 29.167437234 = 1157660.3466

42840 43.652154646 = 1870058.30542840 51.491227221 = 2205884.1742

0 0 = 00 0 = 00 0 = 00 0 = 00 0 = 00 0 = 0

28980321.635 Kg-cm289.80321635 T-cm

e = 0.27971377 2.8980321635 T-m

PUNTO 3

ε1εc =

εc = ε20.003 ε3

76.5

7.5 105 7.590

120


ε1 = 0.003 19.757758094 = 0.0006585919 190

ε2 = 0.003 0.8325627665 = 2.7752092E-05 290

ε3 = 0.003 -13.65215465 = -0.0004550718 390

ε4 = 0.003 -21.49122722 = -0.0007163742 490

ε5 = 0.003 30 = 0 590

ε6 = 0.003 30 = 0 690

ε7 = 0.003 30 = 0 790

ε8 = 0.003 30 = 0 890

ε9 = 0.003 30 = 0 990

ε10 = 0.003 30 = 0 1090

ε1 = 0.003 40.242241906 = 0.0013414081 190

ε2 = 0.003 59.167437234 = 0.0019722479 290

ε3 = 0.003 73.652154646 = 0.0024550718 390

ε4 = 0.003 81.491227221 = 0.0027163742 490

ε5 = 0.003 30 = 0 590

ε6 = 0.003 30 = 0 690

ε7 = 0.003 30 = 0 790

ε8 = 0.003 30 = 0 890

ε9 = 0.003 30 = 0 990

ε10 = 0.003 30 = 0 1090


fs1 = 1343.1324 Kg/cm2fs2 = 56.5976169 Kg/cm2fs3 = -928.073473 Kg/cm2fs4 = -1460.97363 Kg/cm2fs5 = 0 Kg/cm2fs6 = 0 Kg/cm2fs7 = 0 Kg/cm2fs8 = 0 Kg/cm2fs9 = 0 Kg/cm2fs10 = 0 Kg/cm2



Cc = ,85 f'c Asc = 0.85 210 7609.619489 =

area = 951.8297838976.5 6657.7897051

7609.619489 cm2


P1 = As1 fs1 = 10.2 1343.1324 = 13699.950431 KgP2 = As2 fs2 = 10.2 56.5976169 = 577.29569202 KgP3 = As3 fs3 = 10.2 -928.073473 = -9466.3494228 KgP4 = As4 fs4 = 10.2 -1460.97363 = -14901.93099 KgP5 = As5 fs5 = 0 0 = 0 KgP6 = As6 fs6 = 0 0 = 0 KgP8 = As7 fs7 = 0 0 = 0 KgP8 = As8 fs8 = 0 0 = 0 KgP9 = As9 fs9 = 0 0 = 0 KgP10 = As10 fs10 = 0 0 = 0 KgPctr = Asctr fsctr = 2 0 = 0 KgP11 = As11 fs11 = 10.2 2735.6676 = 27903.809569 KgP12 = As12 fs12 = 10.2 4022.20238 = 41026.464308 KgP13 = As13 fs13 = 10.2 4200 = 42840 KgP14 = As14 fs14 = 10.2 4200 = 42840 KgP15 = As15 fs15 = 0 0 = 0 KgP16 = As16 fs16 = 0 0 = 0 KgP17 = As17 fs17 = 0 0 = 0 KgP18 = As18 fs18 = 0 0 = 0 KgP19 = As19 fs19 = 0 0 = 0 KgP20 = As20 fs20 = 0 0 = 0 Kg


Pn = Cc + SUM Pi = 1502836.32 Kg = 1502.8363184 Ton


Mn = 1358317.08 21.75 = 29543396.46313699.9504 -10.24224191 = -140318.20642577.295692 -29.16743723 = -16838.235862

-9466.34942 -43.65215465 = 413226.54894-14901.931 -51.49122722 = 767318.71465

0 0 = 00 0 = 00 0 = 00 0 = 00 0 = 00 0 = 00 0 = 0

27903.8096 10.242241906 = 285797.5677

41026.4643 29.167437234 = 1196636.822642840 43.652154646 = 1870058.30542840 51.491227221 = 2205884.1742

0 0 = 00 0 = 00 0 = 00 0 = 00 0 = 00 0 = 0

36125162.154 Kg-cm361.25162154 T-cm

e = 0.24037989 3.6125162154 T-m

PUNTO 4

ε1εc =

εc = ε20.003 ε3

51

7.5 105 7.560

120


ε1 = 0.003 -10.24224191 = -0.0005121121 160

ε2 = 0.003 -29.16743723 = -0.0014583719 260

ε3 = 0.003 -43.65215465 = -0.0021826077 360

ε4 = 0.003 -51.49122722 = -0.0025745614 460

ε5 = 0.003 0 = 0 560

ε6 = 0.003 0 = 0 6

60

ε7 = 0.003 0 = 0 760

ε8 = 0.003 0 = 0 860

ε9 = 0.003 0 = 0 960

ε10 = 0.003 0 = 0 1060

ε1 = 0.003 10.242241906 = 0.0005121121 160

ε2 = 0.003 29.167437234 = 0.0014583719 260

ε3 = 0.003 43.652154646 = 0.0021826077 360

ε4 = 0.003 51.491227221 = 0.0025745614 460

ε5 = 0.003 0 = 0 560

ε6 = 0.003 0 = 0 660

ε7 = 0.003 0 = 0 760

ε8 = 0.003 0 = 0 860

ε9 = 0.003 0 = 0 960

ε10 = 0.003 0 = 0 1060


fs1 = -1044.40141 Kg/cm2fs2 = -2974.20357 Kg/cm2fs3 = -4200 Kg/cm2fs4 = -4200 Kg/cm2fs5 = 0 Kg/cm2fs6 = 0 Kg/cm2fs7 = 0 Kg/cm2fs8 = 0 Kg/cm2fs9 = 0 Kg/cm2fs10 = 0 Kg/cm2



Cc = ,85 f'c Asc = 0.85 210 4578.9305563 =

area = 533.890438251 69 6196.9125585

4578.9305563 cm2


P1 = As1 fs1 = 10.2 -1044.40141 = -10652.894353 KgP2 = As2 fs2 = 10.2 -2974.20357 = -30336.876462 KgP3 = As3 fs3 = 10.2 -4200 = -42840 KgP4 = As4 fs4 = 10.2 -4200 = -42840 Kg

P5 = As5 fs5 = 0 0 = 0 KgP6 = As6 fs6 = 0 0 = 0 KgP8 = As7 fs7 = 0 0 = 0 KgP8 = As8 fs8 = 0 0 = 0 KgP9 = As9 fs9 = 0 0 = 0 KgP10 = As10 fs10 = 0 0 = 0 Kg

P11 = As11 fs11 = 10.2 1044.40141 = 10652.894353 KgP12 = As12 fs12 = 10.2 2974.20357 = 30336.876462 KgP13 = As13 fs13 = 10.2 4200 = 42840 KgP14 = As14 fs14 = 10.2 4200 = 42840 KgP15 = As15 fs15 = 0 0 = 0 KgP16 = As16 fs16 = 0 0 = 0 KgP17 = As17 fs17 = 0 0 = 0 KgP18 = As18 fs18 = 0 0 = 0 KgP19 = As19 fs19 = 0 0 = 0 KgP20 = As20 fs20 = 0 0 = 0 Kg

-1.455192E-11 KgCALCULO CARGA AXIAL NOMINAL

Pn = Cc + SUM Pi = 817339.104 Kg = 817.33910429 Ton


Mn = 817339.104 34.5 = 28198199.098-10652.8944 -10.24224191 = 109109.52096-30336.8765 -29.16743723 = 884848.94007

-42840 -43.65215465 = 1870058.305-42840 -51.49122722 = 2205884.1742

0 0 = 00 0 = 00 0 = 00 0 = 00 0 = 00 0 = 00 0 = 0

10652.8944 10.242241906 = 109109.5209630336.8765 29.167437234 = 884848.94007

42840 43.652154646 = 1870058.30542840 51.491227221 = 2205884.1742

0 0 = 00 0 = 00 0 = 00 0 = 00 0 = 0

0 0 = 038338000.979 Kg-cm383.38000979 T-cm

e = 0.46905869 3.8338000979 T-m

PUNTO 5

ε1εc =

εc = ε20.003 ε3

12.570072

7.5 105 7.514.78832

120


ε1 = 0.003 -55.45392191 = -0.0112495379 114.78832

ε2 = 0.003 -74.37911723 = -0.015088756 214.78832

ε3 = 0.003 -88.86383465 = -0.0180271663 314.78832

ε4 = 0.003 -96.70290722 = -0.0196174225 414.78832

ε5 = 0.003 -45.21168 = 0 514.78832

ε6 = 0.003 -45.21168 = 0 614.78832

ε7 = 0.003 -45.21168 = 0 714.78832

ε8 = 0.003 -45.21168 = 0 814.78832

ε9 = 0.003 -45.21168 = 0 914.78832

ε10 = 0.003 -45.21168 = 0 1014.78832

ε1 = 0.003 -34.96943809 = -0.0070939981 114.78832

ε2 = 0.003 -16.04424277 = -0.00325478 214.78832

ε3 = 0.003 -1.559525354 = -0.0003163697 314.78832

ε4 = 0.003 6.2795472212 = 0.0012738865 414.78832

ε5 = 0.003 -45.21168 = 0 514.78832

ε6 = 0.003 -45.21168 = 0 614.78832

ε7 = 0.003 -45.21168 = 0 714.78832

ε8 = 0.003 -45.21168 = 0 814.78832

ε9 = 0.003 -45.21168 = 0 914.78832

ε10 = 0.003 -45.21168 = 0 1014.78832


fs1 = -4200 Kg/cm2fs2 = -4200 Kg/cm2fs3 = -4200 Kg/cm2

fs4 = -4200 Kg/cm2fs5 = 0 Kg/cm2fs6 = 0 Kg/cm2fs7 = 0 Kg/cm2fs8 = 0 Kg/cm2fs9 = 0 Kg/cm2fs10 = 0 Kg/cm2

fs1 = -4200 Kg/cm2fs2 = -4200 Kg/cm2fs3 = -645.204325 Kg/cm2fs4 = 2597.96419 Kg/cm2fs5 = 0 Kg/cm2fs6 = 0 Kg/cm2fs7 = 0 Kg/cm2fs8 = 0 Kg/cm2fs9 = 0 Kg/cm2fs10 = 0 Kg/cm2


Cc = ,85 f'c Asc = 0.85 210 630.07779383 =

area = 1742.946234212.570072 107.429928 8936.7095249

630.07779383 cm2


P1 = As1 fs1 = 10.2 -4200 = -42840 KgP2 = As2 fs2 = 10.2 -4200 = -42840 KgP3 = As3 fs3 = 10.2 -4200 = -42840 KgP4 = As4 fs4 = 10.2 -4200 = -42840 KgP5 = As5 fs5 = 0 0 = 0 KgP6 = As6 fs6 = 0 0 = 0 KgP8 = As7 fs7 = 0 0 = 0 KgP8 = As8 fs8 = 0 0 = 0 KgP9 = As9 fs9 = 0 0 = 0 KgP10 = As10 fs10 = 0 0 = 0 Kg

P11 = As11 fs11 = 10.2 -4200 = -42840 KgP12 = As12 fs12 = 10.2 -4200 = -42840 KgP13 = As13 fs13 = 10.2 -645.204325 = -6581.0841137 KgP14 = As14 fs14 = 10.2 2597.96419 = 26499.234751 KgP15 = As15 fs15 = 0 0 = 0 KgP16 = As16 fs16 = 0 0 = 0 KgP17 = As17 fs17 = 0 0 = 0 KgP18 = As18 fs18 = 0 0 = 0 KgP19 = As19 fs19 = 0 0 = 0 KgP20 = As20 fs20 = 0 0 = 0 Kg

-237121.84936 KgCALCULO CARGA AXIAL NOMINAL

Pn = Cc + SUM Pi = -124652.963 Kg = -124.65296316 Ton


Mn = 112468.886 53.714964 = 6041262.1733-42840 -10.24224191 = 438777.64325-42840 -29.16743723 = 1249533.0111-42840 -43.65215465 = 1870058.305-42840 -51.49122722 = 2205884.1742

0 0 = 00 0 = 00 0 = 00 0 = 00 0 = 00 0 = 00 0 = 0

-42840 10.242241906 = -438777.64325-42840 29.167437234 = -1249533.0111

-6581.08411 43.652154646 = -287278.5014726499.2348 51.491227221 = 1364478.1177

0 0 = 00 0 = 00 0 = 00 0 = 00 0 = 00 0 = 0

11194404.269 Kg-cm111.94404269 T-cm

e = -0.89804558 1.1194404269 T-m

Mu Pu .9 Mu .9 Pu .7 Mu .7 Pu

punt 1 0 2361.5074392 0 2125.3566953 0 1653.05521punt 2 208.280402 2048.786516 187.452362 1843.9078644 145.7962813 1434.15056punt 3 361.251622 1502.8363184 325.126459 1352.5526865 252.87613508 1051.98542punt 4 383.38001 817.33910429 345.042009 735.60519386 268.36600685 572.137373punt 5 111.944043 -124.6529632 100.749638 -112.18766685 78.360829881 -87.2570742

La carga axial que define una variación en el factor de reducción de capacidad es:

.1 f'c Ag = 0.1 210 4800 = 100800100.8

POR NO SER ZUNCHADA e = 10% h

e = 0.1 120 = 12 cms

DE LA ECUACION = e = Mu / Pu = 12 cms

CARGA AXIAL QUE DEFINE REDUCCION DE CARGA

0.1 210 4800 = 100800 Kg100.8 T

Nro de varillas = 16Nro varillas al lado = 8Nro espacios al lado = 4Radio de distribucion = 52.5Angulo interno = 22.5

ang acum dist acum Nro var int

11.25 10.242241906 233.75 29.167437234 256.25 43.652154646 278.75 51.491227221 2

0 0 00 0 00 0 00 0 00 0 00 0 0

2018787.4392 Kg

1828899.8845 Kg

911277.52873 Kg

1358317.0788 Kg

817339.10429 Kg

112468.8862 Kg

e = Mu / Pu = 12 M Max P=.8 P Min P

0 0 0 1322.44417 0 100.8113.35235708 944.60297568 153.352004 1322.44417 153.352004 100.8170.02853562 1416.9044635 230.028006 1322.44417 230.028006 100.8226.70471416 1889.2059514 306.704008 1322.44417 306.704008 100.8

283.3808927 2361.5074392 383.38001 1322.44417 383.38001 100.8

KgT

0 50 100 150 200 250 300 350 400 450

-500

0

500

1000

1500

2000

2500

3000

f(x) = 588.508748790996 ln(x) − 2268.76084289057


P nominal, M nominal90% Pn Mn70% Pn MnLogarithmic (70% Pn Mn)MAX PMIN P

Mnominal

Pnom

inal

diagrama de interaccion columnas circulares

Documents

la carga axial

carga axial

p6 as6

p8 as8

p8 as7

p10 as1

p2 as2

p4 as4