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BARRA aBARRA bP1a-1313.380-2298.420.0101090304-6.37010-35.42P1b1313.380.00-2298.420.0101090304-1313.380760-2298.416330.026240523120.19-26.38-6.20010-26.640-100571.4285700.0003521805=-35.42-1006.370.00100571.430.000.0003521805+0-100571.4285700.0006170702=35.42+-62.06=-26.64-1006.202298.4202681.49-0.003005721215.1700115.17-2298.420.005362.97-0.00300572122298.4163302681.48571-0.0035153082-39.3550.8911.5300111.53

P2a1313.3802298.420.01010903046.3701035.42P2b-1313.3807602298.416330.01010903041313.3807602298.416330.0262405231-20.1926.386.2001026.640100571.4300.0003521805=35.42-100-6.370-100571.4285700.0003521805+0100571.4285700.0006170702=-35.42+62.06=26.64-100-6.202298.4205362.97-0.00300572127.120017.12-2298.4163302681.48571-0.00300572122298.4163305362.97143-0.0035153082-31.2941.4610.1600110.16

BARRA cBARRA dP1c1313.380760-2298.416330.0262405231-1313.380760-2298.416330.04321057142.54-48.55-6.00010-16.81P1d1313.380-2298.420.043210571-1313.380-2298.420.05983019264.96-70.48-5.53010-7.310100571.4285700.0006170702+0-100571.4285700.0007841861=62.06+-78.87=-16.81-1006.000.00100571.4300.0007841861+0-100571.4300.0008568889=78.87+-86.18=-7.31-1005.53-2298.4163305362.97143-0.00351530822298.4163302681.48571-0.0035697433-79.1689.7410.5800110.58-2298.4205362.97-0.00356974332298.4202681.49-0.0035229102-118.46128.079.610019.61k1,1a1313.380-2298.42k1,2a-1313.380-2298.420.00100571.4300-100571.430P2c-1313.3807602298.416330.02624052311313.3802298.420.043210571-42.5448.556.0001016.81P2d-1313.3802298.420.0432105711313.3802298.420.059830192-64.9670.485.530107.31-2298.4205362.972298.4202681.490-100571.4285700.0006170702+0100571.4300.0007841861=-62.06+78.87=16.81-100-6.000-100571.4300.0007841861+0100571.4300.0008568889=-78.87+86.18=7.31-100-5.53-2298.4163302681.48571-0.00351530822298.4205362.97-0.0035697433-69.7480.1710.4300110.43-2298.4202681.49-0.00356974332298.4205362.97-0.0035229102-108.89118.629.730019.73k2,1a-1313.3802298.42k2,2a1313.3802298.420-100571.4300100571.430BARRA e-2298.4202681.492298.4205362.97P1e1313.380-2298.420.059830192-1313.380-2298.420.075309258786.68-92.24-5.560101.410.00100571.4300.0008568889+0-100571.4300.0008429074=86.18+-84.77=1.41-1005.56BARRA g=h,i,j,k,l-2298.4205362.97-0.00352291022298.4202681.49-0.0029023658-156.41165.318.900018.90

k1,1g8800000k1,2g-88000.0000P2e-1313.3802298.420.0598301921313.3802298.420.0753092587-86.676937527192.245.56010-1.410879.861759.730-879.861759.730-100571.4300.0008568889+0100571.4300.0008429074=-86.1785412669+84.77=-1.41-100-5.5601759.734692.600-1759.732346.30-2298.4202681.49-0.00352291022298.4205362.97-0.0029023658-146.9613238855157.5310.5700110.57

k2,1g-8800000k2,2g88000.0000.00BARRA f0-879.86-1759.730879.86-1759.73P1f1313.380-2298.420.0753092587-1313.380-2298.420.0881266624105.58-107.87-2.290108.8101759.732346.300.00-1759.734692.600.00100571.4300.0008429074+0-100571.4300.000755312=84.77+-75.96=8.81-1002.29-2298.4205362.97-0.00290236582298.4202681.49-0.0034247594-188.66193.374.710014.71

P2f-1313.3802298.420.07530925871313.3802298.420.0881266624-105.5805764324107.872.29010-8.810-100571.4300.0008429074+0100571.4300.000755312=-84.7724006015+75.96=-8.81-100-2.29-2298.4202681.49-0.00290236582298.4205362.97-0.0034247594-180.8746824941184.183.310013.31

BARRA gP1g88000000.0881266624-88000.00000.08804827347755.15-7748.256.901006.900879.861759.730.000755312+0-879.861759.73-0.0025904256=-5.36+0.69=-4.67010-4.6701759.734692.60-0.00342475940-1759.732346.30-0.0009021622-14.742.44-12.30001-12.30

P2g-88000000.088126662488000.0000.000.0880482734-7755.14629190147748.25-6.90100-6.900-879.86-1759.730.000755312+0879.86-1759.73-0.0025904256=5.3620640076+-0.69=4.670104.6701759.732346.30-0.00342475940.00-1759.734692.60-0.0009021622-6.70637155970.32-6.38001-6.38

BARRA hP1h88000000.0753092587-88000.00000.07533176086627.21-6629.19-1.98100-1.980879.861759.730.0008429074+0-879.861759.73-0.0024099528=-4.37+-3.80=-8.16010-8.1601759.734692.60-0.00290236580-1759.732346.30-0.0033631166-12.14-3.65-15.79001-15.79

P2h-88000000.075309258788000.0000.000.0753317608-6627.216629.191.981001.980-879.86-1759.730.0008429074+0879.86-1759.73-0.0024099528=4.37+3.80=8.160108.1601759.732346.30-0.00290236580.00-1759.734692.60-0.0033631166-5.33-11.54-16.87001-16.87

BARRA iP1i88000000.059830192-88000.00000.05981830655265.06-5264.011.051001.050879.861759.730.0008568889+0-879.861759.73-0.0021407525=-5.45+-4.03=-9.48010-9.4801759.734692.60-0.00352291020-1759.732346.30-0.003361958-15.02-4.12-19.14001-19.14

P2i-88000000.05983019288000.0000.000.0598183065-5265.05689905635264.01-1.05100-1.050-879.86-1759.730.0008568889+0879.86-1759.73-0.0021407525=5.4454088211+4.03=9.480109.4801759.732346.30-0.00352291020.00-1759.734692.60-0.003361958-6.7579154856-12.01-18.77001-18.77

BARRA jP1j88000000.043210571-88000.00000.04320770413802.53-3802.280.251000.250879.861759.730.0007841861+0-879.861759.73-0.0017697543=-5.59+-4.66=-10.26010-10.2601759.734692.60-0.00356974330-1759.732346.30-0.0035349933-15.37-5.18-20.55001-20.55

P2j-88000000.04321057188000.0000.000.0432077041-3802.533802.28-0.25100-0.250-879.86-1759.730.0007841861+0879.86-1759.73-0.0017697543=5.59+4.66=10.2601010.2601759.732346.30-0.00356974330.00-1759.734692.60-0.0035349933-7.00-13.47-20.47001-20.47

BARRA kP1k88000000.0262405231-88000.00000.02623751192309.17-2308.900.261000.260879.861759.730.0006170702+0-879.861759.73-0.0012892293=-5.64+-4.95=-10.59010-10.5901759.734692.60-0.00351530820-1759.732346.30-0.0034576738-15.41-5.84-21.25001-21.25

P2k-88000000.026240523188000.0000.000.0262375119-2309.172308.90-0.26100-0.260-879.86-1759.730.0006170702+0879.86-1759.73-0.0012892293=5.64+4.95=10.5901010.5901759.732346.30-0.00351530820.00-1759.734692.60-0.0034576738-7.16-13.96-21.12001-21.12

BARRA lP1l88000000.0101090304-88000.00000.0101085742889.59-889.550.041000.040879.861759.730.0003521805+0-879.861759.73-0.0006958168=-4.98+-4.56=-9.54010-9.5401759.734692.60-0.00300572120-1759.732346.30-0.0029389863-13.48-5.67-19.16001-19.16

0.0101090304BP2l-88000000.010109030488000.0000.000.0101085742-889.59889.55-0.04100-0.040.00035218050-879.86-1759.730.0003521805+0879.86-1759.73-0.0006958168=4.98+4.56=9.540109.54-0.003005721201759.732346.30-0.00300572120.00-1759.734692.60-0.0029389863-6.43-12.57-19.00001-19.000.0262405231C0.0006170702BARRA m-0.0035153082P1m1313.380-2298.420-1313.380-2298.420.01010857420.00-6.52-6.5201069.980.043210571D0.00100571.4300+0-100571.430-0.0006958168=0.00+69.98=69.98-1006.520.0007841861-2298.4205362.9702298.4202681.49-0.00293898630.0015.3515.3500115.35-0.00356974330.059830192EP2m-1313.3802298.4201313.3802298.420.01010857420.006.526.52010-69.980.00085688890-100571.4300+0100571.430-0.0006958168=0.00+-69.98=-69.98-100-6.52-0.0035229102-2298.4202681.4902298.4205362.97-0.00293898630.007.477.470017.470.0753092587F0.0008429074BARRA n-0.0029023658P1n1313.380-2298.420.0101085742-1313.380-2298.420.026237511920.03-26.51-6.4801059.680.0881266624G0.00100571.430-0.0006958168+0-100571.430-0.0012892293=-69.98+129.66=59.68-1006.480.000755312-2298.4205362.97-0.00293898632298.4202681.49-0.0034576738-39.0051.0312.0400112.04-0.00342475940.0880482734HP2n-1313.3802298.420.01010857421313.3802298.420.0262375119-20.0326.516.48010-59.68-0.00259042560-100571.430-0.0006958168+0100571.430-0.0012892293=69.98+-129.66=-59.68-100-6.48-0.0009021622-2298.4202681.49-0.00293898632298.4205362.97-0.0034576738-31.1141.7610.6500110.650.0753317608I -0.0024099528BARRA o-0.0033631166P1o1313.380-2298.420.0262375119-1313.380-2298.420.043207704142.41-48.62-6.2201048.330.0598183065J0.00100571.430-0.0012892293+0-100571.430-0.0017697543=-129.66+177.99=48.33-1006.22-0.0021407525-2298.4205362.97-0.00345767382298.4202681.49-0.0035349933-78.8589.8310.9800110.98-0.0033619580.0432077041KP2o-1313.3802298.420.02623751191313.3802298.420.0432077041-42.4148.626.22010-48.33-0.00176975430-100571.430-0.0012892293+0100571.430-0.0017697543=129.66+-177.99=-48.33-100-6.22-0.0035349933-2298.4202681.49-0.00345767382298.4205362.97-0.0035349933-69.5880.3510.7700110.770.0262375119L-0.0012892293BARRA p-0.0034576738P1p1313.380-2298.420.0432077041-1313.380-2298.420.059818306564.87-70.84-5.9601037.310.0101085742M0.00100571.430-0.0017697543+0-100571.430-0.0021407525=-177.99+215.30=37.31-1005.96-0.0006958168-2298.4205362.97-0.00353499332298.4202681.49-0.003361958-118.27128.4710.2000110.20-0.0029389863P2p-1313.3802298.420.04320770411313.3802298.420.0598183065-64.8770.845.96010-37.310-100571.430-0.0017697543+0100571.430-0.0021407525=177.99+-215.30=-37.31-100-5.96-2298.4202681.49-0.00353499332298.4205362.97-0.003361958-108.79119.4610.6700110.67

BARRA qP1q1313.380-2298.420.0598183065-1313.380-2298.420.075331760886.29-91.21-4.9201027.070.00100571.430-0.0021407525+0-100571.430-0.0024099528=-215.30+242.37=27.07-1004.92-2298.4205362.97-0.0033619582298.4202681.49-0.0033631166-155.52164.138.610018.61

P2q-1313.3802298.420.05981830651313.3802298.420.0753317608-86.2991.214.92010-27.070-100571.430-0.0021407525+0100571.430-0.0024099528=215.30+-242.37=-27.07-100-4.92-2298.4202681.49-0.0033619582298.4205362.97-0.0033631166-146.50155.118.610018.61

BARRA rP1r1313.380-2298.420.0753317608-1313.380-2298.420.0880482734106.67-113.57-6.9001018.150.00100571.430-0.0024099528+0-100571.430-0.0025904256=-242.37+260.52=18.15-1006.90-2298.4205362.97-0.00336311662298.4202681.49-0.0009021622-191.18199.958.770018.77

P2r-1313.3802298.420.07533176081313.3802298.420.0880482734-106.67113.576.90010-18.150-100571.430-0.0024099528+0100571.430-0.0025904256=242.37+-260.52=-18.15-100-6.90-2298.4202681.49-0.00336311662298.4205362.97-0.0009021622-182.16197.5315.3700115.37

EQUILIBRIO EN LOS NUDOS

NUDO B

2.786.37-6.200.040.21-0.76=35.42+-26.64+-9.54=-0.76-0.517.1211.53-19.16-0.51

NUDO C

2.78B6.346.20-6.000.260.46-0.76-0.76=26.64+-16.81+-10.59=-0.76-0.51-0.5110.1610.58-21.25-0.516.34C-0.76NUDO D-0.5110.28D10.286.00-5.530.250.73-0.76-0.76=16.81+-7.31+-10.26=-0.76-0.51-0.5110.439.61-20.55-0.5114.48E-0.76-0.51NUDO E18.88F-0.7614.485.53-5.561.051.01-0.51-0.76=7.31+1.41+-9.48=-0.76130.52G-0.519.738.90-19.14-0.51-11.38-7.590HNUDO F-11.387.5918.88-2.29-1.985.561.290I-0.76=8.81+-8.16+-1.41=-0.76-0.76-0.514.71-15.7910.57-0.510.510J-0.76NUDO G0.510K130.522.296.909.19-0.76-11.38=-8.81+-4.67=-13.480.51-7.593.31-12.30-8.990L-0.760.51NUDO H0M-0.760-6.906.90-0.000.51-11.38=4.67+-18.15=-13.487.59-6.3815.378.99

NUDO I

0-6.904.921.98-0.00-0.76=18.15+-27.07+8.16=-0.760.518.778.61-16.870.51

NUDO J

0-4.925.96-1.050.00-0.76=27.07+-37.31+9.48=-0.760.518.6110.67-18.770.51

NUDO K

06.22-0.25-5.960.00-0.76=-48.33+10.26+37.31=-0.760.5110.77-20.4710.200.51

NUDO L

06.48-0.26-6.220.00-0.76=-59.68+10.59+48.33=-0.760.5110.65-21.1210.980.51

NUDO M

06.52-0.04-6.48-0.00-0.76=-69.98+9.54+59.68=-0.760.517.47-19.0012.040.51

Hoja3NIVELWxMxhx{mx.hx^kCVxFxVxFX/2FX/R667.356.86544342513.521207.75630027920.5662143.48143.4871.7410.25522.082.2507645263.517.555.53063966590.151339.54183.0219.772.82422.082.2507645263.51443.25073195290.117930.80213.8215.402.20322.082.2507645263.510.531.33733617960.085422.32236.1411.161.59222.082.2507645263.5719.89939471180.054214.17250.317.091.01122.082.2507645263.53.59.15558863430.02506.52256.833.260.47177.7518.119266055366.92999142371.0261.29218.751.9113.57.514.330.539626.3026.3013.151.881303.0584412.230.460422.4548.7511.221.6048.754.9697.526.571.048.75

Hoja4

BARRASAREA (m^2)I(m^4)E((T/m^2)EA(T)EI(T.m^2)L(m)lmBARRASEA/L2EI/L4EI/L6EI/L^212EI/L^3a0.160.00213322000003520004693.33401a88000.002346.674693.331760.00880.00b0.150.00312522000003300006875.00610b55000.002291.674583.331145.83381.94c0.160.00213322000003520004693.33401c88000.002346.674693.331760.00880.00d0.090.00067522000001980001485.003.501d56571.43848.571697.14727.35415.63e0.1050.00107222000002310002358.13610e38500.00786.041572.08393.02131.01f0.090.00067522000001980001485.003.501f56571.43848.571697.14727.35415.63EA/L2EI/L4EI/L6EI/L^212EI/L^3MATRIZ FUERZA DE DESPLAZAMIENTOBARRA a=cBARRA bBCDEk1,1a880.000.00-1760.00k1,2a-880.000.00-1760.00k1,1b55000.000.000.00k1,2b-55000.000.000.00PB56295.630.001032.65-415.630.00-727.35000-55000000.28B0.0088000.000.000.00-88000.000.000.00381.941145.830.00-381.941145.830.00144953.371145.830.00-56571.430.000000-381.941145.83-12.00-1760.000.004693.331760.000.002346.670.001145.834583.330.00-1145.832291.671032.651145.8310973.81727.350.00848.570000-1145.832291.67-12.00PC-415.630.00727.3538915.630.00727.35-38500.000.000.000000.33Ck2,1a-880.000.001760.00k2,2a880.0001760.00k2,1b-55000.000.000.00k2,2b55000.000.000.000.00-56571.430.000.0056702.44393.020.00-131.01393.02000-7.500.00-88000.000.00088000.0000.00-381.94-1145.830.00381.94-1145.83-727.350.00848.57727.35393.023269.230.00-393.02786.04000-7.50-1760.000.002346.671760.0004693.330.001145.832291.670.00-1145.834583.33PD000-385000038915.630.00727.35-415.630.00727.350.00D0000-131.01-393.020.0056702.44-393.020.00-56571.430.00-11.25BARRA d=fBARRA e0000393.02786.04727.35-393.023269.22-727.350.00848.574.69PE-5500000000-415.630.00-727.3556295.630.001032.650.00Ek1,1d415.630.00-727.35k1,2d-415.630.00-727.35k1,1e38500.000.000.00k1,2e-38500.000.000.000-381.94-1145.830000.00-56571.430.000.00144953.37-1145.83-18.000.0056571.430.000.00-56571.430.000.00131.01393.020.00-131.01393.0201145.832291.67000727.350.00848.571032.65-1145.8310973.817.50-727.350.001697.14727.350.00848.570.00393.021572.080-393.02786.048.12E-043.26E-06-1.21E-041.05E-033.51E-06-1.77E-050.0010514105-0.0000035066-0.00002082150.000803418-0.0000032551-0.00011918341.1952E-03Bk2,1d-415.630.00727.35k2,2d415.630.00727.35k2,1e-38500.000.000.00k2,2e38500.000.000.003.26E-061.14E-05-1.63E-069.34E-061.14E-05-1.85E-060.00000934280.0000000078-0.00000185110.00000325510.0000000072-0.0000016276-2.0514E-040.00-56571.430.000.0056571.430.000.00-131.01-393.020.00131.01-393.02-1.21E-04-1.63E-061.20E-04-2.42E-04-1.75E-06-1.09E-05-0.00024125030.00000175330.000030131-0.00011918340.00000162760.0000002305-1.3412E-03-727.350.00848.57727.350.001697.140.00393.02786.040.00-393.021572.080.00105144270.0000093428-0.00024199453.31E-031.42E-05-3.57E-043.29E-03-1.42E-05-3.54E-040.0010514105-0.0000093428-0.00024125033.6092E-03C0.00000350660.0000113558-0.00000175331.42E-052.90E-05-4.37E-061.42E-051.43E-08-4.37E-060.00000350660.0000000078-0.0000017533-3.2844E-04-0.0000177182-0.0000018511-0.0000108611-3.57E-04-4.37E-063.92E-04-3.54E-044.37E-06-2.69E-05-0.00002082140.00000185110.0000301309-2.8583E-030.00105141050.0000093428-0.00024125030.00329262710.0000142142-0.00035356993.31E-03-1.42E-05-3.57E-041.05E-03-9.34E-06-2.42E-043.5473E-03D-0.00000350660.00000000780.0000017533-0.00001421420.00000001430.0000043653-1.42E-052.90E-054.37E-06-3.51E-061.14E-051.75E-06-5.5698E-04-0.0000208215-0.00000185110.000030131-0.0003535703-0.0000043653-0.0000269274-3.57E-044.37E-063.92E-04-1.77E-051.85E-06-1.09E-051.4462E-030.0008034180.0000032551-0.00011918340.00105141050.0000035066-0.00002082141.05E-03-3.51E-06-1.77E-058.12E-04-3.26E-06-1.21E-041.2037E-03E-0.00000325510.00000000720.0000016276-0.00000934280.00000000780.0000018511-9.34E-061.14E-051.85E-06-3.26E-061.14E-051.63E-06-3.4883E-04-0.0001191834-0.00000162760.0000002305-0.0002412503-0.00000175330.0000301309-2.42E-041.75E-06-1.09E-05-1.21E-041.63E-061.20E-044.8831E-04

BARRA aP1a-880.000-1760.000.00119524151.310-880000-0.0002051433=18.051760.0002346.67-0.001341161-1.04

P2a880.0001760.000.0011952415-1.31088000.000-0.0002051433=-18.051760.0004693.33-0.001341161-4.19

BARRA bP1b55000.000.000.000.0011952415-55000.000.000.000.001203650665.74-66.20-0.460.00381.941145.83-0.0002051433+0.00-381.941145.83-0.0003488339=-1.62+0.69=-0.920.001145.834583.33-0.0013411610.00-1145.832291.670.0004883058-6.381.52-4.86

P2b-55000.000.000.000.001195241555000.000.000.000.0012036506-65.7466.200.460.00-381.94-1145.83-0.0002051433+0.00381.94-1145.83-0.0003488339=1.62+-0.69=0.920.001145.832291.67-0.0013411610.00-1145.834583.330.0004883058-3.312.64-0.67

BARRA cP1c-880.000.00-1760.000.0012036506-1.920.00-88000.000.00-0.0003488339=30.701760.000.002346.670.00048830583.26

P2c880.000.001760.000.00120365061.920.0088000.000.00-0.0003488339=-30.701760.000.004693.330.00048830584.41

BARRA dP1d415.630-727.350.0011952415-415.630.00-727.350.00360918041.470.582.050.0056571.430-0.0002051433+0.00-56571.430.00-0.0003284381=-11.61+18.58=6.97-727.3501697.14-0.001341161727.350.00848.57-0.0028582516-3.150.20-2.95

P2d-415.630.00727.350.0011952415415.630.00727.350.0036091804-1.47-0.58-2.050.00-56571.430.00-0.0002051433+0.0056571.430.00-0.0003284381=11.61+-18.58=-6.97-727.350.00848.57-0.001341161727.350.001697.14-0.0028582516-2.01-2.23-4.23

BARRA eP1e38500.000.000.000.0036091804-38500.000.000.000.0035473328138.95-136.572.380.00131.01393.02-0.0003284381+0.00-131.01393.02-0.0005569785=-1.17+0.64=-0.530.00393.021572.08-0.00285825160.00-393.02786.040.0014461699-4.621.36-3.27

P2e-38500.000.000.000.003609180438500.0000.000.0035473328-138.95136.57-2.380.00-131.01-393.02-0.0003284381+0131.01-393.0208333333-0.0005569785=1.17+-0.64=0.530.00393.02786.04-0.00285825160.00-393.021572.080.0014461699-2.382.490.12

BARRA fP1f415.630-727.350.0012036506-415.630.00-727.350.00354733280.15-2.53-2.380.0056571.430-0.0003488339+0.00-56571.430.00-0.0005569785=-19.73+31.51=11.78-727.3501697.140.0004883058727.350.00848.570.0014461699-0.053.813.76

P2f-415.630.00727.350.0012036506415.630.00727.350.0035473328-0.152.532.380.00-56571.430.00-0.0003488339+0.0056571.430.00-0.0005569785=19.73+-31.51=-11.78-727.350.00848.570.0004883058727.350.001697.140.0014461699-0.465.034.57

EQUILIBRIO EN LOS NUDOS

NUDO B

0.28-1.31-0.462.050.28-12.00=-18.05+-0.92+6.97=-12.00-12.00-4.19-4.86-2.95-12.00

NUDO C

0.33-2.052.380.33-7.50=-6.97+-0.53=-7.50-7.50-4.23-3.27-7.50

NUDO D

0.00-2.382.38-0.00-11.25=0.53+-11.78=-11.254.690.124.574.69

NUDO E

0.000.461.92-2.380.00-18.00=0.92+-30.70+11.78=-187.50-0.674.413.767.5

CALCULO DE LAS REACCIONES