Hoja1

METODO DE LA RIGIDEZW13.53.5W2DATOS:MSECCION DE LA VIGA0.85W1=5Tn/mW2=7Tn/m3712L1=3m0.40L2=7mL3=12mCUADRO DE CARACTERISTICAS DE LA VIGAM=2Tn*mb=0.40m0.40mL2/2=3.5mh=0.86m0.85mE=2173706.51Tn/mI=0.0204708333m4f'c=210kg/cm2EI=44497.5837212679Tn*m3

1. GRADOS DE LIBERTAD DE LA VIGA

123N.N=4N.R=9G.L=3

2. CALULO DE LAS RIGIDESESBCK11==84757.3023262247

K21==12713.5953489337

K31=0CDK12==12713.5953489337

K22==40259.7186049567

K32==7416.2639535447

CD

K13=0

K23==7416.2639535447

K33==14832.52790708933. MATRIZ DE RIGIDEZ

84757.302326224712713.5953489337012713.595348933740259.71860495677416.263953544707416.263953544714832.5279070893

4. MATRIZ INVERSA DE RIGIDEZ0.0000124478-0.00000432970.0000021648-0.00000432970.0000288646-0.00001443230.0000021648-0.00001443230.0000746355

5. CALCULO DE LOS MOMENTOS DE EMPOTRAMIENTOTRAMO A-BW1MEP=3MEP=3.75TRAMO B-CMEP=3.53.5MEP=0.50M7

TRAMO C-DMEP=W2

MEP=8412

3.75-3.750.50-0.5084-84

M.E.P. A1=3.75M.E.P. B1=-3.75M.E.P. B2=0.50M.E.P. C1=-0.50M.E.P. C2=84M.E.P. D1=-84

5. MATRIZ DE MOMENTO TRAMO A-BTRAMO B-CTRAMO C-D

MEXT=0MEXT=0MEXT=0

3.25=-83.50846. CALCULO DEL DESPLAZAMIENTO ( )A=0B=0.0005838311C=-0.0036365752D=0.00748151647. CALCULO DE LOS MOMENTOS ABMA=21.0693807339OK

ABCBMB1=30.8887614679MB2-30.8887615OK

BCCD

MC1-85.5452982MC285.5452982OK

CD

MD0.0000000OK

8. CALCULO DE REACCIONES8.1. CALCULO DE LAS REACCIONES ISOSTATICASTRAMO A-B

W1 MA=0 MB=0

L1*RB - L1*W1*(L1/2) =0L1*W1*(L1/2)-L1*VA=03RA=7.5TnRB=7.5TnTRAMO B-C3.53.5 MB=0 MC=0ML2*RC+M=0M-L2*RB=07RB=0.29TnRC=-0.29TnTRAMO C-DW2 MC=0 MD=012L3*RD-L3*W2(10/2)=0L3*W2(L3/2)-L3*RC=0RC=42TnRD=42Tn8.2. CALCULO DE LAS REACCIONES HIPERESTATICASTRAMO A-BR'1=(MA-MB)/L1R'1=17.32

TRAMO B-CR'2=(MB-MC)/L2R'2=-16.63TRAMO C-DR'3=(MC-MD)/L3R'3=7.138.3. CALCULO DE LAS REACCIONES FINALES

REAC. ISOS7.507.500.29-0.2942.0042.00REAC. HIPER.17.32-17.32-16.6316.637.13-7.13REAC. TOTAL24.82-9.82-16.3516.3549.1334.87

RA=24.82TnRB=-26.17TnRC=65.48TnRD=34.87Tn9. DIAGRAMA DE FUERZA CORTANTEREACCION DXY220.002234.87

CORTE 1-1XY=RD-W2*XX12234.87010-49.1312

REACCION CXY10-49.131016.35

CORTE 2-2XY=RC+RD-W2*L31016.35316.35

REACCION BXY316.353-9.82CORTE 3-3XY=W1*X-RA3-9.820-24.82

REACCION AXY0-24.8200.00

DIAGRAMA DE FUERZA CORTANTE GENERAL

XY220.002234.8710-49.131016.35316.353-9.820-24.8200.00

10. DIAGRAMA DE MOMENTO FLEXIONANTEXY=RD*X1-W2*X1*(X1/2)X1220017.0286.864.9810.00-85.5512.00XY=RD*X2+RC*(X2-L3)-W2*L3*(X2-L3/2)X210.00-85.5512.006.50-28.3315.50XY=RD*X3+RC*(X3-L3)-W2*L3*(X2-L3/2)+Mn X36.50-26.3315.503.0030.8919.00XYX43.0030.8919.000.00-21.0722XY0-21.07220022

ABCD2EI/L14EI/L14EI/L22EI/L22EI/L24EI/L24EI/L32EI/L32EI/L22EI/L34EI/L3-1-1RARBRBRCRCRD4EI/L12EI/L12EI/L14EI/L12EI/L24EI/L22EI/L22EI/L22EI/L24EI/L22EI/L24EI/L32EI/L32EI/L22EI/L34EI/L3