Hoja1

00.20.40.60.811.2NOTA:1.4Donde:1.6i=es le nodo y tiene que ser mayor q uno1.82i-1=Representara a una fuerza externa vertical y/o a una reaccion22i=Representara a un momento externo y/o a un giro de la viga2.22.4SOLUCION:2.62.8

1)Reacciones y momentos:(R,M)={1,2,3,5,7,8}LONGITUDDesplazamientos Conocidos:= Dk=10110.220223.530395070802)Identificando Desplazamientos y Giros desconocidos.(,)={4,6}fuerzas Conocidas=40ton-m60ton-m

3)Matriz Rigidez de los elementosE=1EI=1I=10.00094232230.00007705420.0013717421

1234567810.0113078680.0576701269-0.0113078680.057670126950.01646090530.0740740741-0.01646090530.0740740741k1= 20.05767012690.3921568627-0.05767012690.1960784314k3= 60.07407407410.4444444444-0.07407407410.22222222223-0.011307868-0.05767012690.011307868-0.05767012697-0.0164609053-0.07407407410.0164609053-0.074074074140.05767012690.1960784314-0.05767012690.392156862780.07407407410.2222222222-0.07407407410.4444444444

345630.00092465060.0108646446-0.00092465060.0108646446k2= 40.01086464460.170212766-0.01086464460.0851063835-0.0009246506-0.01086464460.0009246506-0.010864644660.01086464460.085106383-0.01086464460.170212766

4)Matriz rigidez de la viga4612357840.56236962870.0851063830.05767012690.1960784314-0.0468054822-0.01086464460060.0851063830.6146572104000.01086464460.0632094294-0.07407407410.222222222210.057670126900.0113078680.0576701269-0.01130786800020.196078431400.05767012690.3921568627-0.05767012690003-0.04680548220.0108646446-0.011307868-0.05767012690.0122325186-0.0009246506005-0.01086464460.063209429400-0.00092465060.017385556-0.01646090530.074074074170-0.0740740741000-0.01646090530.0164609053-0.0740740741800.22222222220000.0740740741-0.07407407410.44444444445)Reacciones y Momentos de empotramiento perfectoELEMENTORiMiRjMj1234161.1999104.0461.2-104.043456288.182248.791845.617989-146.61455678362.64103.6888.56-123.12

6)Desplazamiento y giros DesconocidosDk=0

Qk=404144.7518=4-144.7518606-42.9345642.9345

46Du=41.816247896-0.2514805325*-144.75186-0.25148053251.661743493442.9345

Du=4-273.702343rad6107.748385radReaccionesdonde:Dk=0

Q'k=161.19992104.043149.3825108.257989788.568-123.12Qu=10.057670126900000-273.702343161.199920.196078431400000107.748385+2104.043-0.04680548220.0108646446000003149.3825-0.01086464460.0632094294000005108.25798970-0.074074074100000788.56800.2222222222000008-123.12

Qu=145.41555Ton250.3728Ton-m3163.3634Ton5118.0423Ton780.5786Ton8-99.17591Ton-m

DISTANCIACORTANTE046.094134.094222.094310.0944-1.9065-13.9066-25.9067-37.9068-49.9069-61.90610-73.90610.2-76.30610.285.5925051175.9925051263.9925051351.9925051439.9925051527.9925051615.992505173.99250517.7-4.40749517.7-4.4074818-4.4074819-4.4074820-4.4074821-4.4074822-4.4074822.7-4.4074822.7-13.4074928-13.4074928.7-13.4074928.7-19.4067839829-19.48391230-20.8552931-23.94095232-28.74089833-35.25512833.7-40.8350879833.765.740102023463.0915483553.148753641.4916683728.1203023813.03465239-3.76528240-22.279541-42.50800242-64.45078842.7-80.830737180-52.680691-12.58637215.50795331.60227435.69659527.7909167.885237-24.020458-67.926139-123.8318110-191.7374910.2-206.75862610.2-206.758611-142.124612-72.132113-14.13961431.85291565.8454TRAMO ABTRAMO ABTRAMO ABTRAMO ABTRAMO ABTRAMO AB1687.83791797.8304DISTANACIAGIROFLECHADISTANACIAGIROFLECHADISTANACIAGIROFLECHADISTANACIAGIROFLECHADISTANACIAGIROFLECHADISTANACIAGIROFLECHA17.797.6851500010.2-261.93275340.0005752817.7-249.09748763-3343.38880560622.7184.23061837-3459.56128330628.7-201991.937809199-1474.800136707933.785.75318570830.670650419317.797.6852590.2-9.6302516-0.99295290410.4-301.5886368-56.4079057617.8-239.35108948-3367.80940666422.8191.72826952-3440.76034086428.8-202723.159212378-1435.14239543933.872.32658700498.56137467661896.3630120.4-17.5127304-3.73557523210.6-337.9168202-120.4132034418-219.990518-3413.73768323206.321347-3400.94265430-211513.157168-970.10316800043447.410729609620.47683019981991.9555220.6-23.7434364-7.88791240810.8-371.0133036-191.3593780818.2-200.80624628-3455.81144157623.2220.37812472-3358.25994777630.2-212980.997357646-895.940276795534.225.018277944527.66270726172087.5480320.8-28.4183696-13.12920985611-400.974087-268.6096918.4-181.79827432-3494.06594232823.4233.89860268-3312.81948212830.4-214449.69118345-823.172323421334.45.075174866830.61633257992183.1405421-31.63353-19.15791311.2-427.8951704-351.5465995218.6-162.96660212-3528.53644519223.6246.88278088-3264.72851699231.1-219597.183502487-582.00908571134.6-12.495379623129.81994724932278.7330521.2-33.4849176-25.69166726411.4-451.8725538-439.5717669618.8-144.31122968-3559.25821010423.8259.33065932-3214.09431230431.6-223281.201274138-425.896495622134.8-27.772928382425.740158174722.775.6478091.4-34.0685324-32.46731807211.6-473.0022372-532.1060526419-125.832157-3586.26649724271.242238-3161.02412832.1-226971.881753231-286.819352444735-40.83975712518.827389500122.775.6477771.6-33.4803744-39.24091084811.8-491.3802206-628.5895168819.2-107.52938408-3609.59656581624.2282.61751692-3105.62522401632.6-230669.899932942-168.273305412335.2-51.78089442239.515334032284.588081.8-31.8164436-45.78769101612-507.102504-728.4814219.4-89.40291092-3629.28367648824.4293.45649608-3048.00486028833.1-234376.037949195-74.118286032935.4-60.6841117026-1.77959532228.7-4.7971632-29.17274-51.90210412.2-520.2650874-831.2602223219.6-71.45273752-3645.36308895224.6303.75917548-2988.27029675233.6-238091.185080666-8.632079465535.6-67.6399232515-14.658814131328.7-4.79702791482.2-25.6452636-57.39779522412.4-530.9639708-936.4235841619.8-53.67886388-3657.87006314424.8313.52555512-2926.52879334433.7-238835.3814001590.615874323135.8-72.7415862114-28.742115014729-10.626984922.4-21.3300144-62.10761011212.6-539.2951542-1043.4883658420-36.08129-3666.83985925322.755635-2862.8876136-76.0851005824-43.668216199630-30.654462.6-16.3229924-65.88359408812.8-545.3546376-1151.9906276820.2-18.66001588-3672.30773645625.2331.44941512-2797.45400665636.2-77.7692092214-59.095310109231-52.910505482.8-10.7201976-68.59699257613-549.238421-1261.4856320.4-1.41504152-3674.30895544825.4339.60689548-2730.33524324836.4-77.8953978423-74.701611919332-79.109407043-4.61763-70.13825113.2-551.0425044-1371.5478331220.615.65363308-3672.87877591225.6347.22807608-2661.63857971236.6-76.5678950166-90.185908137833-110.965450363.21.8887104-70.41701478413.4-550.8628878-1481.7708973620.832.54600792-3668.05245778425.8354.31295692-2591.47127598436.8-73.8936721724-105.268105172133.7-137.54868001283.48.7028236-69.36212935213.6-548.7955712-1591.767683042149.262083-3659.86526126360.861538-2519.94059237-69.9824435954-119.689777933.7-137.5378606423.615.7287096-66.92164012813.8-544.9365546-1701.1702504821.265.80185832-3648.35244549626.2366.87381932-2447.15378769637.2-64.9466664282-133.214718242634-118.2092563.822.8703684-63.06279253614-539.381838-1809.6298621.482.16533388-3633.54927120826.4372.34980088-2373.21812300837.4-58.9015406706-145.629483732935-59.94625430.0318-57.77203214.2-532.2274214-1916.8169719221.698.35250968-3615.49099807226.6377.28948268-2298.24085787237.6-51.9650091795-156.74394608836-12.4831844.237.1170044-51.05500394414.4-523.5693048-2022.4212465621.8114.36338572-3594.21288602426.8381.69286472-2222.32925222437.8-44.257757669-166.39183977813722.4656584.444.0299816-42.93655379214.6-513.5034882-2126.1515442422130.197962-3569.75019527385.559947-2145.59056638-35.9032147104-174.43131060113843.1859924.650.6747316-33.46072696814.8-502.1259716-2227.7359252822.2145.85623852-3542.13818493627.2388.89072952-2068.13205913638.2-27.027551732-180.74546424853947.9635344.856.9552544-22.69076889615-489.532755-2326.9216522.4161.33821528-3511.41211576827.4391.68521228-1990.06099156838.4-17.7596830192-185.24291488344035.084562.77555-10.70912515.2-475.8198384-2423.4751787222.6176.64389228-3477.60724743227.6393.94339528-1911.48462323238.6-8.2312657148-187.8583337007412.8331065.268.03961842.38255929615.4-461.0832218-2517.1821717622.7184.23061837-3459.56128230627.8395.66527852-1832.51021406438.81.4233001814-188.552997510942-50.5034325.472.651459616.46343856815.6-445.4189052-2607.8474894428396.850862-1753.2450243911.0668718125-187.315337299842.7-101.3029658625.676.515073631.39346739215.8-428.9228886-2695.2951920828.2397.50014572-1673.79631297639.220.5595634646-184.16148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9Ton6Ton12Ton/m24Ton/m10.2m5m5m6m7.5m9m2i2i-1i9Ton6Ton12Ton/m24Ton/m10.2m5m5m6m7.5m9m2134756812349Ton6Ton12Ton/m24Ton/m10.2m5m5m6m7.5m9m50.372845.4155163.3680.58118.04699.18