columna b-5 planta ii

1.6864 -0.0007 0 1.6297 -0.0007 0 1.58421.683 0.0016 0 1.6161 0.0067 0 1.5232

1.6721 0.0055 0 1.4629 0.0739 0 1.43971.6594 0.006 0 1.404 0.096 0 1.38361.6416 0.0156 0 1.3617 0.1129 0 1.34061.4832 0.0825 0 1.3069 0.1345 0 1.28111.4277 0.1058 0 1.2687 0.1499 0 1.25171.385 0.1227 0 1.2406 0.1586 0 1.2098

1.3297 0.1446 0 1.1917 0.1735 0 1.16441.2928 0.1579 0 1.1362 0.1907 0 1.11521.2464 0.1717 0 1.0824 0.2053 0 1.05351.2011 0.1855 0 1.0184 0.222 0 0.99681.1509 0.2009 0 0.9363 0.2422 0 0.91371.0821 0.2189 0 0.8614 0.2584 0 0.84641.0305 0.2324 0 0.7772 0.2769 0 0.75010.9453 0.2532 0 0.6945 0.2952 0 0.67490.8728 0.2697 0 0.6107 0.3131 0 0.59550.7798 0.2905 0 0.5467 0.3245 0 0.52920.7066 0.3064 0 0.498 0.3316 0 0.48680.6219 0.3244 0 0.4096 0.339 0 0.41820.5551 0.3369 0 0.3652 0.3414 0 0.36180.5043 0.3439 0 0.3141 0.3429 0 0.31290.4157 0.3525 0 0.2771 0.3429 0 0.28010.3687 0.3551 0 0.2174 0.3411 0 0.22050.3153 0.3567 0 0.1753 0.3392 0 0.17920.2758 0.3567 0 0.1351 0.3372 0 0.14080.2142 0.3548 0 0.1075 0.3347 0 0.11420.1714 0.3528 0 0.0717 0.332 0 0.07960.1295 0.3508 0 0.0556 0.3305 0 0.05360.1008 0.3481 0 0.0337 0.3283 0 0.0310.0649 0.3454 00.0479 0.3438 00.0254 0.3416 0

0 0.3388 0

-0.0007 0 1.5414 -0.0007 0 1.5013 -0.00070.0295 0 1.4875 0.0264 0 1.4626 0.01960.0646 0 1.4202 0.0549 0 1.3928 0.04780.0873 0 1.3604 0.0776 0 1.3428 0.06890.1042 0 1.3228 0.0947 0 1.2937 0.08660.1274 0 1.2584 0.1174 0 1.2462 0.1060.1383 0 1.2352 0.1287 0 1.2136 0.11920.1529 0 1.2028 0.1413 0 1.1771 0.13280.1669 0 1.1496 0.1572 0 1.133 0.14640.1814 0 1.0956 0.1725 0 1.0782 0.1630.1988 0 1.0407 0.1882 0 1.0242 0.17860.2134 0 0.9776 0.2045 0 0.9634 0.19460.2333 0 0.896 0.2239 0 0.8868 0.2120.249 0 0.8312 0.2392 0 0.8204 0.228

0.2695 0 0.7369 0.2604 0 0.723 0.24870.2854 0 0.6588 0.2753 0 0.6455 0.26480.3022 0 0.5798 0.2921 0 0.5666 0.28040.3138 0 0.5172 0.3011 0 0.5017 0.29070.3198 0 0.4779 0.3066 0 0.4568 0.29580.3256 0 0.4133 0.3121 0 0.4083 0.29860.3278 0 0.3591 0.3142 0 0.3563 0.30060.3292 0 0.3133 0.3155 0 0.3137 0.30180.3279 0 0.282 0.3143 0 0.2839 0.30070.3275 0 0.2227 0.3138 0 0.225 0.30020.3255 0 0.1846 0.312 0 0.19 0.29860.3221 0 0.1457 0.3086 0 0.1506 0.29510.3212 0 0.1207 0.3078 0 0.1265 0.29240.3168 0 0.0878 0.3036 0 0.096 0.29030.3147 0 0.0616 0.3015 0 0.0767 0.2870.312 0 0.041 0.2989 0 0.0517 0.2839

0.0019 0.2778

1.4566 -0.00070 1.415 0.0206 0 1.4128 -0.0007 00 1.371 0.0384 0 1.3577 0.0261 00 1.3187 0.0597 0 1.2962 0.0505 00 1.2771 0.0764 0 1.2479 0.0687 00 1.2213 0.0985 0 1.2005 0.0884 00 1.1922 0.1094 0 1.1656 0.1013 00 1.1554 0.1236 0 1.1291 0.1159 00 1.1172 0.1362 0 1.0974 0.1265 00 1.0665 0.1518 0 1.0467 0.1432 00 1.0066 0.1685 0 0.9883 0.1609 00 0.946 0.1848 0 0.9351 0.1738 00 0.8719 0.2025 0 0.8604 0.1925 00 0.8071 0.2178 0 0.7862 0.2086 00 0.7072 0.2392 0 0.6989 0.228 00 0.6314 0.2539 0 0.6206 0.244 00 0.5516 0.2692 0 0.5408 0.2576 00 0.49 0.2792 0 0.4842 0.2663 00 0.4526 0.2826 0 0.4526 0.2693 00 0.4034 0.2851 0 0.3984 0.2733 00 0.3536 0.287 0 0.3509 0.2734 00 0.3141 0.2881 0 0.3145 0.2745 00 0.2858 0.287 0 0.2877 0.2734 00 0.2337 0.286 0 0.2395 0.2717 00 0.2055 0.2839 0 0.2005 0.2693 00 0.1747 0.2822 0 0.1606 0.2663 00 0.1381 0.2781 0 0.1381 0.2649 00 0.1157 0.2764 0 0.1107 0.2608 00 0.0816 0.2724 0 0.0875 0.2581 00 0.0468 0.2683 0 0.0625 0.2554 000

1.3235 -0.0007 0 1.28191.3716 -0.0007 0 1.3201 0.0009 0 1.11111.3375 0.0163 0 1.2495 0.0328 0 0.95721.2777 0.04 0 1.2045 0.0516 0 0.83951.2368 0.0565 0 1.1497 0.0717 0 0.74341.1778 0.0792 0 1.1181 0.0846 0 0.64381.1504 0.0897 0 1.0822 0.0976 0 0.56261.1129 0.1031 0 1.0456 0.1122 0 0.47291.0805 0.1167 0 1.004 0.1249 0 0.37441.0307 0.1326 0 0.9533 0.1415 0 0.26580.9856 0.1473 0 0.8999 0.1555 0 0.16730.9208 0.1647 0 0.8293 0.1725 0 0.06480.8492 0.1814 0 0.7662 0.1878 0 00.7744 0.1994 0 0.6637 0.2083 0 1.23910.6944 0.2158 0 0.5881 0.2222 0 1.07470.6044 0.2332 0 0.5158 0.2358 0 0.9560.5371 0.2451 0 0.4565 0.2431 0 0.82790.4889 0.2526 0 0.4316 0.2448 0 0.73040.4424 0.2566 0 0.3885 0.2446 0 0.6440.395 0.2604 0 0.3454 0.2462 0 0.55

0.3481 0.2598 0 0.3153 0.2471 0 0.4550.3149 0.2608 0 0.2915 0.2462 0 0.37130.2896 0.2598 0 0.2428 0.2444 0 0.27110.2445 0.258 0 0.2112 0.2424 0 0.18210.2046 0.2556 0 0.1822 0.2407 0 0.07750.1672 0.2526 0 0.1546 0.2376 0 0.00280.143 0.2515 0 0.1373 0.2363 0 0

0.1206 0.2481 0 0.1098 0.2325 00.094 0.245 0 0.0682 0.2264 0

0.0557 0.2393 0 0 0.2147 0

0.0006 0 1.1995 -0.0012 0 1.1514 0.00050.0699 0 1.0308 0.0651 0 1.0102 0.05570.1251 0 0.9154 0.1063 0 0.8896 0.09840.1566 0 0.8105 0.137 0 0.7901 0.12860.1793 0 0.7123 0.1597 0 0.6929 0.15090.1999 0 0.6213 0.1785 0 0.6008 0.16940.2143 0 0.5413 0.1929 0 0.5315 0.18070.2279 0 0.4501 0.2043 0 0.4768 0.1890.234 0 0.3749 0.2094 0 0.3753 0.1957

0.2328 0 0.2763 0.2058 0 0.2816 0.19230.2248 0 0.1827 0.1969 0 0.1939 0.18380.2104 0 0.0892 0.1833 0 0.1117 0.17240.2007 0 0.0038 0.1668 0 0.0315 0.15580.0001 0 0 0.1653 0 0 0.14470.066 0

0.1103 00.1461 00.1698 00.1859 00.2038 00.2169 00.2209 00.2193 00.2117 00.1978 00.1829 00.1819 0

0 1.1066 0.0005 0 1.062 -0.0001 00 0.987 0.0463 0 0.9599 0.0399 00 0.8832 0.0853 0 0.8503 0.0802 00 0.7794 0.1164 0 0.7525 0.1102 00 0.6876 0.1391 0 0.6689 0.1312 00 0.5946 0.1575 0 0.5806 0.1482 00 0.5295 0.168 0 0.5136 0.1581 00 0.4405 0.1804 0 0.435 0.1668 00 0.3757 0.1821 0 0.3762 0.1684 00 0.2868 0.1788 0 0.2921 0.1653 00 0.2035 0.1709 0 0.2139 0.1579 00 0.1329 0.1593 0 0.1349 0.1441 00 0.0549 0.1436 0 0.0622 0.1284 00 0 0.1259 0 0.002 0.1092 0

0 0.1079 0

1.026 -0.0007 0 0.9742 -0.0005 0 0.93210.8747 0.0537 0 0.8478 0.046 0 0.82550.8108 0.0778 0 0.7743 0.0725 0 0.7560.7293 0.103 0 0.7124 0.0933 0 0.69350.6548 0.1209 0 0.6407 0.1106 0 0.62660.5746 0.1353 0 0.5586 0.1265 0 0.54760.517 0.1443 0 0.4992 0.1352 0 0.49190.433 0.1537 0 0.4263 0.1417 0 0.4241

0.3898 0.1553 0 0.378 0.1419 0 0.38940.3027 0.1522 0 0.3066 0.1389 0 0.3130.2301 0.145 0 0.2346 0.1307 0 0.24360.173 0.1353 0 0.1718 0.1199 0 0.1876

0.0923 0.1189 0 0.1048 0.104 0 0.12840.0347 0.0997 0 0.0327 0.0802 0 0.05810.0034 0.0879 0 0.0014 0.0684 0 0.0042

0 0.0861 0 0 0.0676 0 0

-0.0007 0 0.8792 0.0006 0 0.8374 -0.00050.0371 0 0.8037 0.0279 0 0.8088 0.01050.0634 0 0.7326 0.0545 0 0.7316 0.03820.0822 0 0.6752 0.0731 0 0.669 0.06060.1004 0 0.6084 0.0915 0 0.617 0.07590.1156 0 0.5312 0.1057 0 0.565 0.08790.1238 0 0.4852 0.1114 0 0.5216 0.09540.1284 0 0.4311 0.115 0 0.4791 0.10030.1288 0 0.3955 0.1164 0 0.4288 0.10320.1252 0 0.3192 0.1122 0 0.3634 0.10180.1171 0 0.2533 0.1045 0 0.3218 0.09860.1071 0 0.2063 0.0941 0 0.2671 0.09040.0918 0 0.1497 0.0794 0 0.2185 0.08160.0693 0 0.0825 0.0579 0 0.1665 0.0670.0477 0 0.031 0.0373 0 0.1073 0.04670.0457 0 0 0.0229 0 0.0579 0.0269

0 0

0 1.728 -0.0011 00 1.7109 0.0105 00 1.6852 0.0212 00 1.6674 0.0286 00 1.6554 0.027 00 1.5047 0.0917 00 1.4683 0.1073 00 1.4223 0.1259 00 1.3498 0.1543 00 1.326 0.1632 00 1.2767 0.1777 00 1.2206 0.1948 00 1.1702 0.2099 00 1.0966 0.2295 00 1.0425 0.2436 00 0.9572 0.2642 00 0.8841 0.2805 0

0.7652 0.3068 00.7188 0.3174 00.6356 0.335 00.576 0.3472 0

0.5434 0.3523 00.511 0.3571 0

0.4627 0.3622 00.4163 0.3658 00.3705 0.3681 00.3155 0.3696 00.2753 0.3694 00.2121 0.3692 00.1674 0.3671 00.1236 0.3649 00.0938 0.3622 00.0578 0.3595 00.0398 0.3578 00.0167 0.3555 0

0 0.3537 0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.05

0.1

0.15

0.2

0.25

0.3

0.35 w=0.95

w=0.90

w=0.85

w=0.80

w=0.75

w=0.70

w=0.65

w=0.60

w=0.55

w=0.50

w=0.45

w=0.40

w=0.35

w=0.30

w=0.25

w=0.2

w=0.15

w=0.10

w=0.05

w=0

w=1

xz

yzV

U

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.05

0.1

0.15

0.2

0.25

0.3

0.35w=0.95

w=0.90

w=0.85

w=0.80

w=0.75

w=0.70

w=0.65

w=0.60

w=0.55

w=0.50

w=0.45

w=0.40

w=0.35

w=0.30

w=0.25

w=0.2

w=0.15

w=0.10

w=0.05

w=0

w=1

CALCULO DE ARMADURA DE COLUMNA B-5 NIVEL II PARA EL N - MymaxCOLUMNA Nº 111

yfck = 225 Kg/cm² γc = 1.7 fcd = 119.12 Kg/cm²fyk = 4600 Kg/cm² γf = 1.8 fyd = 3833 Kg/cm²

5.609 Es = 2100 Ton/cm² γs = 1.240 0.6325

x N= 129.46 T ex = 0.4885 cm.Mx= 5.609 T-m ey= 4.3326 cm.My= 0.6325 T-m

0.1128 < 0.25 FLEXION SIMPLE

40 Los momentos Mx y My se

utilizara en funcion al eje de rotacion

ANALISIS EN EL PLANO XZ

0.25 35 35 I= 125052.08333 14.00

6.00 6.00

0.1799 30 60 I= 135000 1.0796Ø= 1.8799 0.1799 30 60 I= 135000 1.0796

4.00 0.4265 40 40 I= 213333.33333 1.706

Ø= 1.9145 0.1799 30 60 I= 135000 1.07960.1799 30 60 I= 135000 1.0796

6.00 6.006.50 0.2625 40 40 I= 213333.33333 1.706

a = 1.5867 > 1 TRANSLACIONALi = 11.547 cm.

λm= 46.721 > 35 EXITE EFECTO DE PANDEO

I. CALCULO DE LA EXCENTRICIDAD etx = ec + ea TOMAR EN CUENTA EFECTO DE PANDEOa) Excentricidad minima en columnas

2.00 cm.7.698 → emin = 2.00 cm.

4.33262 ec ea emin = 2.00 cm.40 b) Excentricidad calculado inicial

ec < emin → ec = 2 cm.

c) Excentricidad adicional por pandeo40

5.698 cmd) Excentricidad total

Ng= 44.756 0.3457 < 70 → ε = 0.003etx = ec + ea etx = 7.698 cm. N = 129.46ey > emin ey = 4.33 cm. 0.0022

ex /bey /h

=

=

=

=IL=

IL=

IL=

ea=(1+0 .12∗β ) (ε y+ε ) h+20∗ech+10∗ec

∗(α ln )2

50∗i

ε y=fydEs

=

e min=h

20=

=

NgN

=

=

=IL=

IL=

λ=α(H−

h1

2−

h2

2 )i

=IL=

=IL=

Para aceros en las 4 caras tenemos que: β = 1.5CALCULO DE LA CUANTIA

1.2227 0.2353 0.1324

v β Interpolando la v = 1.2227 → β = 0.50001.2 0.5

1.2227 0.5000 1.7095 0.02511.3 0.5

RESUMEN: μ = 0.0251 v = 1.2227 → ω = 0.430

II. CALCULO DE LA EXCENTRICIDAD

ety = ec + ea TOMAR EN CUENTA EFECTO DE PANDEO

a) Excentricidad minima en columnasea

11.623 2.00 cm.ec → emin = 2.00 cm.

40 emin = 2.00 cm.

2 b) Excentricidad calculado inicial

40 ec > emin → ec = 4.33 cm.

c) Excentricidad adicional por pandeo

7.290 cm

Ng= 44.756 0.3457 > 0.7 → ε = 0.004N = 129.46

0.0018

Para aceros en las 4 caras tenemos que: β = 1.5

d) Excentricidad total

ety = ec + ea ety = 11.623 cm.ex < emin ex = 2 cm.

CALCULO DE LA CUANTIA

1.2227 0.061 0.3553


1.2227 0.5000 1.7095 0.05281.3 0.5

v=Nd

b∗h∗fcd= μx=

Nd∗ex

h∗b2∗fcd= μ y=

Nd∗ey

h2∗b∗fcd=

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

ea=(1+0 .12∗β ) (ε y+ε ) h+20∗ech+10∗ec

∗(α ln )2

50∗i

ε y=fydEs

=

e min=h

20=

v=Nd

b∗h∗fcd= μx=

Nd∗ex

h∗b2∗fcd= μ y=

Nd∗ey

h2∗b∗fcd=

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

NgN

=

v=Nd

b∗h∗fcd=

v=Nd

b∗h∗fcd=

RESUMEN: μ = 0.0528 v = 1.2227 → ω = 0.520


yfck = 225 Kg/cm² γc = 1.7 fcd = 119.12 Kg/cm²fyk = 4600 Kg/cm² γf = 1.8

5.609 Es = 2100 Ton/cm² γs = 1.2 fyd = 3833 Kg/cm²40 0.6325





ANALISIS EN EL PLANO YZ

0.25 35 35 I= 125052.08333 14.00

5.00 7.00

0.1542 30 60 I= 135000 1.0796Ø= 1.8277 0.2159 30 60 I= 135000 1.0796

4.00 0.4265 40 40 I= 213333.33333 1.706

Ø= 1.8613 0.1542 30 60 I= 135000 1.07960.2159 30 60 I= 135000 1.0796

5.00 7.006.50 0.2625 40 40 I= 213333.33333 1.706




2.00 cm.7.60254 → emin = 2.00 cm.





Ng= 44.756 0.3457 < 70 → ε = 0.003etx = ec + ea etx = 7.603 cm. N = 129.46

ex /bey /h

=

ea=(1+0 .12∗β ) (ε y+ε ) h+20∗ech+10∗ec

∗(α ln )2

50∗i

ε y=fydEs

=

e min=h

20=

NgN

=

=

=

=IL=

IL=

IL= =

=

=IL=

IL=

λ=α(H−

h1

2−

h2

2 )i

=IL=

=IL=

ey > emin ey = 4.33 cm. 0.0022


1.2227 0.2324 0.1324


1.2227 0.5000 1.7095 0.02441.3 0.5

RESUMEN: μ = 0.0244 v = 1.2227 → ω = 0.425




11.950 0 cm. → emin = 2 cm.ec

40b) Excentricidad calculado inicial

2ec > emin → ec = 4.3326 cm.

40


7.617 cm

Ng= 44.756 0.3457 > 0.7 ® ε = 0.004N = 129.46

0.0022



ety = ec + ea ety = 11.950 cm.ex > emin ex = 2 cm.


1.2227 0.0611 0.3653


1.2227 0.5000 1.7095 0.057

ea=(1+0 .12∗β ) (ε y+ε ) h+20∗ech+10∗ec

∗(α ln )2

50∗i

ε y=fydEs

=

e min=h

20=

v=Nd

b∗h∗fcd= μx=

Nd∗ex

h∗b2∗fcd= μ y=

Nd∗ey

h2∗b∗fcd=

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

ε y=fydEs

=

v=Nd

b∗h∗fcd= μx=

Nd∗ex

h∗b2∗fcd= μ y=

Nd∗ey

h2∗b∗fcd=

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

NgN

=

v=Nd

b∗h∗fcd=

v=Nd

b∗h∗fcd=

1.3 0.5

RESUMEN: μ = 0.057 v = 1.2227 → ω = 0.530

CALCULO DE ACERO DE LA COLUMNA

fck = 225 Kg/cm² γc = 1.7 fcd = 119.12 Kg/cm²fyk = 4600 Kg/cm² γs = 1.2 fyd = 3833 Kg/cm²

ρ min = 0.0054 (TABLA SEGÚN GIMENEZ MONTOYA)

N - Mymax Mxmaxμ v ω μ v ω

PLANO xzetx 0.025 1.223 0.430 0.148 0.402 0.160ety 0.053 1.223 0.520 0.135 0.402 0.110

PLANO yzetx 0.024 1.223 0.425 0.146 0.402 0.150ety 0.057 1.223 0.530 0.138 0.402 0.125

Para el diseño se utiliza el valor:

ω = 0.530> 0.20 No se ajusta< 0.60 No se ajusta

26.351 cm² 8 Ø 20 25.133 cm²

CALCULO DEL ACERO MINIMO

8.64 cm² 4 Ø 16 8.0425 cm²

CALCULO DEL ESTRIBO DE LA COLUMNA

6 mmSe asume el mayor: 6 mm

5 mm

CALCULO DE LA SEPARACION DEL ESTRIBO.

S = 30 cm.

S = 40 cm.Se asume el menor: S = 30 cm.

S = 30 cm.

3 Ø 16

2 Ø 16

Æe =Æe =

Æe =

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

φe≥6mm

⇒

φe≥14

φmax

S≤15φminS≤b ⇒

S≤30cm

A min= ρmin .b .h=

As=ωb .h . fcd

fyd=

403 Ø 16

40Ø #REF! c / #REF!

CALCULO DE ARMADURA DE COLUMNA B-5 NIVEL II PARA MxmaxCOLUMNA Nº 111


1.7246 Es = 2100 Ton/cm² γs = 1.240 3.2456






0.25 35 35 I= 125052.08333 14.00

6.00 6.00

0.1799 30 60 I= 135000 1.0796Ø= 1.8799 0.1799 30 60 I= 135000 1.0796

4.00 0.4265 40 40 I= 213333.33333 1.706

Ø= 1.9145 0.1799 30 60 I= 135000 1.07960.1799 30 60 I= 135000 1.0796

6.00 6.006.50 0.2625 40 40 I= 213333.33333 1.706




2.00 cm.16.075 → emin = 2.00 cm.


ec > emin → ec = 7.6337 cm.



Ng= 44.756 1.0527 > 0.7 → ε = 0.004etx = ec + ea etx = 16.075 cm. N = 42.516ey > emin ey = 4.06 cm. 0.0022

ex /bey /h

=

ea=(1+0 .12∗β ) (ε y+ε ) h+20∗ech+10∗ec

∗(α ln )2

50∗i

ε y=fydEs

=

e min=h

20=

NgN

=

λ=α(H−

h1

2−

h2

2 )i

=

=

=IL=

IL=

IL= =

=

=IL=

IL=

=IL=

=IL=


0.4015 0.1614 0.0407


0.4015 0.8985 1.0813 0.14770.5 0.8

RESUMEN: μ = 0.1477 v = 0.4015 → ω = 0.160




11.267 2.00 cm.ec → emin = 2.00 cm.

40 emin = 2.00 cm.

7.6337 b) Excentricidad calculado inicial

40 ec > emin → ec = 4.06 cm.


7.211 cm

Ng= 44.756 1.0527 > 0.7 → ε = 0.004N = 42.516

0.0018



ety = ec + ea ety = 11.267 cm.ex > emin ex = 7.6337 cm.


0.4015 0.077 0.1131


0.4015 0.8985 1.0813 0.1350.5 0.8

v=Nd

b∗h∗fcd= μx=

Nd∗ex

h∗b2∗fcd= μ y=

Nd∗ey

h2∗b∗fcd=

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

ea=(1+0 .12∗β ) (ε y+ε ) h+20∗ech+10∗ec

∗(α ln )2

50∗i

ε y=fydEs

=

e min=h

20=

v=Nd

b∗h∗fcd= μx=

Nd∗ex

h∗b2∗fcd= μ y=

Nd∗ey

h2∗b∗fcd=

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

NgN

=

RESUMEN: μ = 0.135 v = 0.4015 → ω = 0.110









0.25 35 35 I= 125052.08333 14.00

5.00 7.00

0.1542 30 60 I= 135000 1.0796Ø= 1.8277 0.2159 30 60 I= 135000 1.0796

4.00 0.4265 40 40 I= 213333.33333 1.706

Ø= 1.8613 0.1542 30 60 I= 135000 1.07960.2159 30 60 I= 135000 1.0796

5.00 7.006.50 0.2625 40 40 I= 213333.33333 1.706




2.00 cm.15.9335 → emin = 2.00 cm.


ec > emin → ec = 7.6337 cm.



Ng= 44.756 1.0527 > 0.7 → ε = 0.004etx = ec + ea etx = 15.934 cm. N = 42.516

ex /bey /h

=

ea=(1+0 .12∗β ) (ε y+ε ) h+20∗ech+10∗ec

∗(α ln )2

50∗i

ε y=fydEs

=

e min=h

20=

NgN

=

=

=

=IL=

IL=

IL= =

=

=IL=

IL=

λ=α(H−

h1

2−

h2

2 )i

=IL=

=IL=

ey > emin ey = 4.06 cm. 0.0022


0.4015 0.1599 0.0407


0.4015 0.8985 1.0813 0.14640.5 0.8

RESUMEN: μ = 0.1464 v = 0.4015 → ω = 0.150




11.591 0 cm. → emin = 2 cm.ec


7.6337ec > emin → ec = 4.0563 cm.

40


7.535 cm

Ng= 44.756 1.0527 > 0.7 ® ε = 0.004N = 42.516

0.0022





0.4015 0.0766 0.1164


0.4015 0.8985 1.0813 0.1377

ea=(1+0 .12∗β ) (ε y+ε ) h+20∗ech+10∗ec

∗(α ln )2

50∗i

ε y=fydEs

=

e min=h

20=

v=Nd

b∗h∗fcd= μx=

Nd∗ex

h∗b2∗fcd= μ y=

Nd∗ey

h2∗b∗fcd=

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

ε y=fydEs

=

v=Nd

b∗h∗fcd= μx=

Nd∗ex

h∗b2∗fcd= μ y=

Nd∗ey

h2∗b∗fcd=

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

NgN

=

0.5 0.8

RESUMEN: μ = 0.1377 v = 0.4015 → ω = 0.125

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

MOMENTOS REDUCIDOS

COL DATOS FrameStation Comb P Mx My x Mrx Mry

m Text Ton Ton-m Ton-m m. Ton-m Ton-m

B5 - I

107 0 COMB1 -98.978 0.927 1.260

Altura de la columna = 6.50 107 0 COMB4 -124.433 0.857 1.487 1.275 0.857 1.487

Altura de viga superior= 0.60 107 6.5 COMB4 -114.006 3.513 -2.789 4.239 3.264 -2.591

Altura de viga inferior= 0.00 107 4 COMB5 -127.894 -1.196 -1.800 1.128 -1.196 -1.800

107 6.5 COMB5 -118.213 5.696 -1.100 2.465 5.003 -0.966

VALORES EXTREMO MIN -127.894 -1.196 -2.591

MAX -98.978 5.003 1.487

B5 - II

111 0 COMB1 -44.756 -1.247 1.851

Altura de la columna = 4.00 111 0 COMB4 -42.516 -1.951 3.672 2.581 -1.725 3.246

Altura de viga superior= 0.60 111 4 COMB4 -42.516 1.073 -2.131 1.469 0.854 -1.695

Altura de viga inferior= 0.60 111 0 COMB13 -129.461 -2.739 0.513 1.194 -2.051 0.384

111 4 COMB13 -129.461 6.433 -0.725 2.342 5.609 -0.632


MAX -42.516 5.609 3.246

B5 - III

115 0 COMB1 -34.799 -0.131 0.430




115 4 COMB13 -95.792 6.173 -0.457 1.885 5.190 -0.385


MAX -34.799 5.190 1.470

B5 - IV

119 0 COMB1 -24.408 -0.419 0.524




119 4 COMB13 -63.154 6.956 -0.365 1.946 5.883 -0.309


MAX -24.408 5.883 1.530

A5 - V

123 0 COMB1 -13.859 -0.245 0.286




123 4 COMB13 -30.290 4.413 -0.201 2.027 3.760 -0.171

123 0 COMB21 -31.867 -0.020 -0.071 0.988 -0.014 -0.049

123 4 COMB21 -31.867 -0.061 0.111 2.441 -0.053 0.097


Ng -13.859 MAX -30.290 3.760 0.924

B5 - VI

127 0 COMB1 -3.015 -0.254 0.236




127 4 COMB21 -35.053 3.599 -0.450 2.889 3.599 -0.450


MAX -3.015 3.599 0.689

Mt1

Mt2

Mr1

Mr2

xM t1

=H

M t1+M t2

⇒ x=H

M t 1+M t 2

M t1

M r 1

x−h2

=M t 1

x⇒ M r 1=

M t1

x (x−h2 )

OBS

Ng

Mxmax

N

Mymax

Ng

Mxmax

N-Mymax

Ng

Mxmax

N-Mymax

Ng

Mxmax

N-Mymax

Mxmax

Mymax

N

Ng

Mxmax

N-Mymax



5.609 Es = 2100 Ton/cm² γs = 1.240 0.6325






0.25 35 35 I= 125052.08333 14.00

6.00 6.00

0.7197 30 60 I= 540000 4.3182Ø= 0.47 0.7197 30 60 I= 540000 4.3182

4.00 0.4265 40 40 I= 213333.33333 1.706

Ø= 0.4786 0.7197 30 60 I= 540000 4.31820.7197 30 60 I= 540000 4.3182

6.00 6.006.50 0.2625 40 40 I= 213333.33333 1.706


λm= 34.583 < 35 NOEXITEEFECTODEPANDEO

I. CALCULO DE LA EXCENTRICIDAD etx = e NO TOMAR EN CUENTA EL EFECTO DE PANDEOa) Excentricidad minima en columnas

2.00 cm.5.122 → emin = 2.00 cm.





Ng= 44.756 0.3457 < 70 → ε = 0.003etx = ec + ea etx = 5.122 cm. N = 129.46ey > emin ey = 4.33 cm. 0.0022

ex /bey /h

=

=

=

=IL=

IL=

IL=

ea=(1+0 .12∗β ) (ε y+ε ) h+20∗ech+10∗ec

∗(α ln )2

50∗i

ε y=fydEs

=

e min=h

20=

=

NgN

=

=

=IL=

IL=

λ=α(H−

h1

2−

h2

2 )i

=IL=

=IL=


1.2227 0.1566 0.1324


1.2227 0.5000 1.7095 0.01151.3 0.5

RESUMEN: μ = 0.0115 v = 1.2227 → ω = 0.380


ety = e NO TOMAR EN CUENTA EL EFECTO DE PANDEO


8.327 2.00 cm.ec → emin = 2.00 cm.

40 emin = 2.00 cm.

2 b) Excentricidad calculado inicial

40 ec > emin → ec = 4.33 cm.


3.994 cm

Ng= 44.756 0.3457 > 0.7 → ε = 0.004N = 129.46

0.0018



ety = ec + ea ety = 8.327 cm.ex < emin ex = 2 cm.


1.2227 0.061 0.2545


1.2227 0.5000 1.7095 0.02121.3 0.5

v=Nd

b∗h∗fcd= μx=

Nd∗ex

h∗b2∗fcd= μ y=

Nd∗ey

h2∗b∗fcd=

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

ea=(1+0 .12∗β ) (ε y+ε ) h+20∗ech+10∗ec

∗(α ln )2

50∗i

ε y=fydEs

=

e min=h

20=

v=Nd

b∗h∗fcd= μx=

Nd∗ex

h∗b2∗fcd= μ y=

Nd∗ey

h2∗b∗fcd=

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

NgN

=

v=Nd

b∗h∗fcd=

v=Nd

b∗h∗fcd=

RESUMEN: μ = 0.0212 v = 1.2227 → ω = 0.400









0.25 35 35 I= 125052.08333 14.00

5.00 7.00

0.6169 30 60 I= 540000 4.3182Ø= 0.4569 0.8636 30 60 I= 540000 4.3182

4.00 0.4265 40 40 I= 213333.33333 1.706

Ø= 0.4653 0.6169 30 60 I= 540000 4.31820.8636 30 60 I= 540000 4.3182

5.00 7.006.50 0.2625 40 40 I= 213333.33333 1.706




2.00 cm.5.098 → emin = 2.00 cm.





Ng= 44.756 0.3457 < 70 → ε = 0.003etx = ec + ea etx = 5.098 cm. N = 129.46

ex /bey /h

=

ea=(1+0 .12∗β ) (ε y+ε ) h+20∗ech+10∗ec

∗(α ln )2

50∗i

ε y=fydEs

=

e min=h

20=

NgN

=

=

=

=IL=

IL=

IL= =

=

=IL=

IL=

λ=α(H−

h1

2−

h2

2 )i

=IL=

=IL=

ey > emin ey = 4.33 cm. 0.0022


1.2227 0.1558 0.1324


1.2227 0.5000 1.7095 0.01151.3 0.5

RESUMEN: μ = 0.0115 v = 1.2227 → ω = 0.320




8.545 0 cm. → emin = 2 cm.ec


2ec > emin → ec = 4.3326 cm.

40


4.212 cm

Ng= 44.756 0.3457 > 0.7 ® ε = 0.004N = 129.46

0.0022



ety = ec + ea ety = 8.545 cm.ex > emin ex = 2 cm.


1.2227 0.0611 0.2612


1.2227 0.5000 1.7095 0.0227

ea=(1+0 .12∗β ) (ε y+ε ) h+20∗ech+10∗ec

∗(α ln )2

50∗i

ε y=fydEs

=

e min=h

20=

v=Nd

b∗h∗fcd= μx=

Nd∗ex

h∗b2∗fcd= μ y=

Nd∗ey

h2∗b∗fcd=

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

ε y=fydEs

=

v=Nd

b∗h∗fcd= μx=

Nd∗ex

h∗b2∗fcd= μ y=

Nd∗ey

h2∗b∗fcd=

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

NgN

=

v=Nd

b∗h∗fcd=

v=Nd

b∗h∗fcd=

1.3 0.5

RESUMEN: μ = 0.0227 v = 1.2227 → ω = 0.430

CALCULO DE ACERO DE LA COLUMNA

fck = 225 Kg/cm² γc = 1.7 fcd = 119.12 Kg/cm²fyk = 4600 Kg/cm² γs = 1.2 fyd = 3833 Kg/cm²

ρ min = 0.0054 (TABLA SEGÚN GIMENEZ MONTOYA)

N - Mymax Mxmaxμ v ω μ v ω

PLANO xzetx 0.012 1.223 0.380 0.115 0.402 0.065ety 0.021 1.223 0.400 0.108 0.402 0.090

PLANO yzetx 0.011 1.223 0.320 0.115 0.402 0.065ety 0.023 1.223 0.430 0.110 0.402 0.085

Para el diseño se utiliza el valor:

ω = 0.430> 0.20 No se ajusta< 0.60 No se ajusta

21.379 cm² 12 Ø 16 24.127 cm²

CALCULO DEL ACERO MINIMO

8.64 cm² 4 Ø 16 8.0425 cm²

CALCULO DEL ESTRIBO DE LA COLUMNA

6 mmSe asume el mayor: 6 mm

4 mm

CALCULO DE LA SEPARACION DEL ESTRIBO.

S = 24 cm.

S = 40 cm.Se asume el menor: S = 24 cm.

S = 30 cm.

2 Ø 16

Ø 6 c / 24

40 8 Ø 16

Æe =Æe =

Æe =

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

φe≥6mm

⇒

φe≥14

φmax

S≤15φminS≤b ⇒

S≤30cm

A min= ρmin .b .h=

As=ωb .h . fcd

fyd=

2 Ø 1640



1.7246 Es = 2100 Ton/cm² γs = 1.240 3.2456






0.25 35 35 I= 125052.08333 14.00

6.00 6.00

0.7197 30 60 I= 540000 4.3182Ø= 0.47 0.7197 30 60 I= 540000 4.3182

4.00 0.4265 40 40 I= 213333.33333 1.706

Ø= 0.4786 0.7197 30 60 I= 540000 4.31820.7197 30 60 I= 540000 4.3182

6.00 6.006.50 0.2625 40 40 I= 213333.33333 1.706




2.00 cm.12.259 → emin = 2.00 cm.


ec > emin → ec = 7.6337 cm.



Ng= 44.756 1.0527 > 0.7 → ε = 0.004etx = ec + ea etx = 12.259 cm. N = 42.516ey > emin ey = 4.06 cm. 0.0022

ex /bey /h

=

ea=(1+0 .12∗β ) (ε y+ε ) h+20∗ech+10∗ec

∗(α ln )2

50∗i

ε y=fydEs

=

e min=h

20=

NgN

=

λ=α(H−

h1

2−

h2

2 )i

=

=

=IL=

IL=

IL= =

=

=IL=

IL=

=IL=

=IL=

=

=

=

=


0.4015 0.1231 0.0407


0.4015 0.8985 1.0813 0.11490.5 0.8

RESUMEN: μ = 0.1149 v = 0.4015 → ω = 0.065




8.007 2.00 cm.ec → emin = 2.00 cm.

40 emin = 2.00 cm.

7.6337 b) Excentricidad calculado inicial

40 ec > emin → ec = 4.06 cm.


3.951 cm

Ng= 44.756 1.0527 > 0.7 → ε = 0.004N = 42.516

0.0018





0.4015 0.077 0.0804


0.4015 0.8985 1.0813 0.1080.5 0.8

v=Nd

b∗h∗fcd= μx=

Nd∗ex

h∗b2∗fcd= μ y=

Nd∗ey

h2∗b∗fcd=

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

ea=(1+0 .12∗β ) (ε y+ε ) h+20∗ech+10∗ec

∗(α ln )2

50∗i

ε y=fydEs

=

e min=h

20=

v=Nd

b∗h∗fcd= μx=

Nd∗ex

h∗b2∗fcd= μ y=

Nd∗ey

h2∗b∗fcd=

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

NgN

=

RESUMEN: μ = 0.108 v = 0.4015 → ω = 0.090









0.25 35 35 I= 125052.08333 14.00

5.00 7.00

0.6169 30 60 I= 540000 4.3182Ø= 0.4569 0.8636 30 60 I= 540000 4.3182

4.00 0.4265 40 40 I= 213333.33333 1.706

Ø= 0.4653 0.6169 30 60 I= 540000 4.31820.8636 30 60 I= 540000 4.3182

5.00 7.006.50 0.2625 40 40 I= 213333.33333 1.706




2.00 cm.12.2232 → emin = 2.00 cm.


ec > emin → ec = 7.6337 cm.



Ng= 44.756 1.0527 > 0.7 → ε = 0.004etx = ec + ea etx = 12.223 cm. N = 42.516

ex /bey /h

=

ea=(1+0 .12∗β ) (ε y+ε ) h+20∗ech+10∗ec

∗(α ln )2

50∗i

ε y=fydEs

=

e min=h

20=

NgN

=

=

=

=IL=

IL=

IL= =

=

=IL=

IL=

λ=α(H−

h1

2−

h2

2 )i

=IL=

=IL=

=

=

=

=

ey > emin ey = 4.06 cm. 0.0022


0.4015 0.1227 0.0407


0.4015 0.8985 1.0813 0.11460.5 0.8

RESUMEN: μ = 0.1146 v = 0.4015 → ω = 0.065




8.223 0 cm. → emin = 2 cm.ec


7.6337ec > emin → ec = 4.0563 cm.

40


4.166 cm

Ng= 44.756 1.0527 > 0.7 ® ε = 0.004N = 42.516

0.0022





0.4015 0.0766 0.0825


0.4015 0.8985 1.0813 0.1098

ea=(1+0 .12∗β ) (ε y+ε ) h+20∗ech+10∗ec

∗(α ln )2

50∗i

ε y=fydEs

=

e min=h

20=

v=Nd

b∗h∗fcd= μx=

Nd∗ex

h∗b2∗fcd= μ y=

Nd∗ey

h2∗b∗fcd=

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

ε y=fydEs

=

v=Nd

b∗h∗fcd= μx=

Nd∗ex

h∗b2∗fcd= μ y=

Nd∗ey

h2∗b∗fcd=

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

NgN

=

0.5 0.8

RESUMEN: μ = 0.1098 v = 0.4015 → ω = 0.085

α=log2log(1+ β )

= μ=α√μx

α+μ yα=

etx = e NO TOMAR EN CUENTA EL EFECTO DE PANDEO

columna b-5 planta ii

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