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PRACTICA DOMICILIARIA n 4EJERCICIO N 1M= 10000 m.kg7200 kg10800 kg10000 kg4 m 6 m 5 m 3I 4I 2I 2 m 2 m 2 m 2 m Solucin:ADBCMAB = MA + (2EI/L)*(2A + B) = 1200 + (2E*3I/5)(2A + B) .. (1)MBA = MB + (2EI/L)*(2B + A) = 3200 + (2E*3I/5)(2B + A) .. (2)MBC = MB + (2EI/L)*(2B + C) = -11200 + (2E*4I/6)(2B + C) .. (3)MCB = MC + (2EI/L)*(2C + B) = 12800 + (2E*4I/6)(2C + B) .. (4)MCD = MC + (2EI/L)*(2C + D) = -5000 + (2E*2I/4)(2C + D) .. (5)MDC = MD + (2EI/L)*(2D + C) = 5000 + (2E*2I/4)(2D + C) .. (6)

Ahora:MA = (-10000*3/5*5)*(5-3*2) = 1200MB = (10000*2)*(2*5-3*2) = 3200MB = ((-7200*2*4*4)/6*6) ((10800*4*2*2)/6*6) = -11200MC = ((7200*2*2*4)/6*6) + ((10800*4*4*2)/6*6) = -12800MC = -MD = -10000*4/8 = -5000

Entonces:K = I/L tramo AB =3/5 tramo BC= 4/6 =2/3 tramo CD = 2/4 =1/2MAB = 1200 + 18(2A + B) = 1200 + 36 A + 18 BMBA = 3200 + 18(2B + A) = 3200 + 18 A + 36B MBC = -11200 + 20(2B + C) = -11200 + 40 B + 20 C MCB = 12800 + 20(2C + B) = 12800 + 20 B + 40 C MCD = -5000 + 15(2C + D) = -5000 + 30 C + 15 D MDC = 5000 + 15(2D + C) = 5000 + 30 D + 15 C Tenemos:()MAB = 0MBA + MBC = 0MCB + MCD = 0MDC = 0Entonces: () en las condicionesCondiciones:MAB = 0 = 1200 + 36A + 18 B = 200 + 6 A + 3 BMBA + MBC = 0 = -8000 + 18 A + 76 B + 20 C = 9 A + 38 B + 10 C = 4000MCB + MDC = 0 = 7800 + 20 B + 70 C + 15 D = 4 B + 14 C + 3 D = -1560MDC = 0 = 5000 + 30 D + 15 C 1000 = 6 D + 3 C

Resolviendo: A = -118.2838 B = 169.90 C =-139.168 D = -97.082

Reemplazando:MAB = 0MBA = 7187MBC = -7187MCB = 10.631MCD = -10.631MDC = 0

()ADBC2m2m2m2m2m2m3m68757187106313125343778266261017476582342Reacciones en los apoyos:RA = -3437 kgRB = 3437 + 7826 = 11263 kgRC = 10174 + 7658 = 17832 kgRD = 2342 kgEJERCICIO N 26m5m3mM = 15000q = 4000 kg/mABCConsiderar: E = 21 * 10 ^5 kg/cm^2 I = 15 * 10 ^3 cm4Solucin:

MA = (-4000*6*6)/20 = -7200MB = (4000*6*6)/30 = 4800MB = ((-15000*2)/5*5)*(5-3*3) = 4800MC = ((15000*3)/5*5)*(2*5-3*3) = 1800

Tenemos:MAB = -7200 + (2EI/6)*(2A + B 0.009/6)MBA = 4800 + (2EI/6)*(2B + A 0.009/6) MBC = 4800 + (2EI/5)*(2B + C +0.009/5) MCB = 1800 + (2EI/5)*(2C + B + 0.009/5) Nudo B:MBA + MBC = 0

Nudo C:MCB = 0MBA + MBC = 0 = 9600 + 1/3*EI(2B 0.003/2) + 2EI/5(2B + c + 0.00915)-9600*15/EI = 22B + 6C + 0.0033Ahora:22B + 6C = - 0.0033 9600*15/21*15*10^4 = - 0.049

MCB = 0 = 1800 + 2EI/5 *(2C + B + 0.009/5) 4500/EI= 2 C + B + 0.00182 C + B = -0.0018 45000/21*15*10^4 = -0.0032

Obtenemos:c = -0.000579 B = -0.0020699

MAB = -10.948MBA = -1122MBC = 1122MCB = 0800040004000kg/m6m30003000M = 150003m2m-1094811226000900010012-1988-3224.4

Reacciones: RA = 10012RB = -12364RB = 1236.4RC = 3.224.4

EJERCICIO N3P = 3500 kgABCDEFM= 14700q = 4000 kg/m2I3.5I2I2m120003m5m2I2m5m6m7mKBC = 2/5KCD = 3.5/7 = KD/E = 2/6KDF = 2/5Tenemos:MBA = 7000MBC = 0 + 12(B + C) = 24B + 12CMCB = 0 + 12(C + B) = 12B + 24CMCD = 1500 + 15(C + D) = 15000 + 30C + 15DMDC = -4800 + 15(2D + C) = -4800 + 15C + 30DMDE = -4800 + 10(2D + E) = -4800 + 20D + 10EMED = 7200 + 10(2E + D) = 7200 +10D + 20EMDF = 8640 + 12(2D + F) = 8640 + 24D + 12FMFD = -5760 + 12(2F + D) = -5760 + 12D + 24FSe tiene las condiciones:MBA + MBC = 0MCB + MCD = 0MDC + MDF + MDE = 0MED = 0F = 0Resolviendo:B = -302.9397c = 22.5461D = 61.1856E = -390.5928F = 0MBA = 7000MBC = -7000MCB = -3094MCD = 3094MDC = -2626MDE = -7482MED = 0MDF = 10108MFD = -5026Reemplazando:0 = 7000 + 24B + 12C -1750 = 6B + 3C0 = 1500 + 12B + 54C + 15D -500 = 4B + 18C + 5D0 = -4800*2 + 8640 + 15C + 74D + 10E + 12F 960 = 15C + 74D + 10E0 = 7200 + 10D + 20E -720 = D + 2E

ABCDEF-3500378420335247-675320198216BCDEFMB= -7000MC= 30944200-50262626-7482Reacciones:RB = 5519 kgRC = 14 kgRE = 6753 kgRFy = 3214 kgRFx = 3784 kgRE = 8216 kgEJERCICIO N 4ABCDIEG2I2I2IF2500 kg3000kg/m10000kg.m3m5m2m4m5m4mMAB = 0 + 15(2A + B)MAB = 15 bMBA = 0 + 15(2B + A)MBA = 30 BMBF = 0 + 20(2B + F)MBF = 40 BMFB = 0 + 20(2F + B)MFB = 20 BMBC = -1250 + 30(2 b + c)MBC = -1250 + 60 b + 30cMCB = 1250 + 30(2 C + B)MCB = 1250 + 30 B + 60cMBG = 0 + 24(2 B + G)MBG = 48B + 24GMGB = 0 + 24(2 G + B)MGB = 24 B + 48GMCD = 0 + 24(2 C + D)MCD = 48 C + 24DMDC = 0 + 24(2 D + c)MDC = 24 C + 48DMDE = -3000 *2*1 = -6000 MDE = -6000Se tiene las condiciones:MBA + MBF + MBC + MBG = 0MCB + MCD = 10000MDC + MDE = 0MGB = 0Reemplazando:30 B + 40 B + (-1250 + 60 B + 30 C) + (48 B + 24 G) = 0 89 B + 15 C + 12 G = 6251250 + 30 B + 60 C + 48 C + 24 D = 10000 5 B + 18 C + 4 D = 4375/324 C + 48 D 6000 = 0 C + 2 D = 25024 B + 48 G = 0 B + 2 G = 089 B + 15 C +12 G = 6255 B + 18 C + 4 D = 4375/3C + 2 D = 250 B + 2G = 0

Resolviendo:B = -3.4916B = 60.9869D = 94.5065G = 1.7458

Finalmente:MAB = -52.37MBA = -104.75MBF = -139.66MFB = -69.83MBC = 370.11MCB = 4804.47MBG = -125.70MGB = 0MCD = 5195.53MDC = 6000ABCDEGFMD= -6000-480570-521051265196