PENDIENTE DEFLEXION - VIGAS
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ANALISIS ESTRUCTURAL - VIGA DE 4 LUCES Y 5 APOYOS (METODO PENDIENTE DFLEXION) UNIDADES DE LONGITUD m UNIDADES DE FUERZA kg INGRESAR DATOS: E 2.00E+10 E 2.00E+10 E 2.00E+10 E 2.00E+10 I 0.0040 I 0.0040 I 0.0040 I 0.0060 L 5.00 L 8.00 L 8.00 L 10.00 MEPi -166.67 MEPi -640.00 MEPi -117.19 MEPi -250.00 MEPj 250.00 MEPj 426.67 MEPj 70.31 MEPj 250.00 P= 100.00 Q= 200.00 w= 200.00 a= 3.00 a= 5.00 b= 5.00 b= 5.00 A B C D E K1 = 2EI/L K2 = 2EI/L K3 = 2EI/L K4 = 2EI/L L L L L MATRIZ DE RIGIDECES GIROS 2° MIEMBRO M EC. PEND. DEFLEX. 2EI/L MEP AB 32,000,000 -166.667 BA 250.000 BC 20,000,000 -640.000 CB 426.667 CD 20,000,000 -117.188 DC 70.313 DE 24,000,000 -250.000 ED 250.000 MATRIZ DE RIGIDECES GIROS 2° MIEMBRO GIROS 64,000,000 32,000,000 - - - 166.667 1.18E-07 32,000,000 104,000,000 20,000,000 - - 390.000 4.97E-06 - 20,000,000 80,000,000 20,000,000 - -309.479 -6.54E-06 - - 20,000,000 88,000,000 24,000,000 179.688 5.73E-06 - - - 24,000,000 48,000,000 -250.000 -8.07E-06 RESOLVIENDO EL SISTEMA DE ECUACIONES CON METODOS ITERATIVOS - METODOS DE SOBRERELAJACION ϐ = 1.10 K ### 0 0 0 0 0 1 2.86E-06 3.16E-06 -5.12E-06 3.53E-06 -7.67E-06 2 8.43E-07 4.61E-06 -5.98E-06 5.69E-06 -8.09E-06 3 2.46E-07 4.85E-06 -6.55E-06 5.74E-06 -8.08E-06 4 1.75E-07 4.97E-06 -6.55E-06 5.73E-06 -8.07E-06 5 1.15E-07 4.97E-06 -6.54E-06 5.73E-06 -8.07E-06 6 1.17E-07 4.97E-06 -6.54E-06 5.73E-06 -8.07E-06 7 1.18E-07 4.97E-06 -6.54E-06 5.73E-06 -8.07E-06 8 1.18E-07 4.97E-06 -6.54E-06 5.73E-06 -8.07E-06 9 1.18E-07 4.97E-06 -6.54E-06 5.73E-06 -8.07E-06 10 1.18E-07 4.97E-06 -6.54E-06 5.73E-06 -8.07E-06 M MATRIZ DE MOMENTOS (DEBIDO A GIROS) MATRIZ DE MOMENTOS (DEBIDO A GIROS) M FINALES AB 64,000,000 32,000,000 - - - -0.00 AB BA 32,000,000 64,000,000 - - - 572.00 BA BC - 40,000,000 20,000,000 - - -572.00 BC CB - 20,000,000 40,000,000 - - 264.34 CB CD - - 40,000,000 20,000,000 - -264.34 CD DC - - 20,000,000 40,000,000 - 168.68 DC DE - - - 48,000,000 24,000,000 -168.68 DE ED - - - 24,000,000 48,000,000 0.00 ED 2K1 K1 θA -(MEPAB) 2EI/L(2 θA + θB - 3Ψ) + MEP K1 2(K1 + K2) K2 θB -(MEPBA + MEPBC) 2EI/L( θA + 2θB - 3Ψ) + MEP K2 2(K2 + K3) K3 θC -(MEPCB + MEPCD) 2EI/L(2 θB + θC - 3Ψ) + MEP K3 2(K3 + K4) K4 θD -(MEPDC + MEPDE) 2EI/L( θB + 2θC - 3Ψ) + MEP K4 2K4 θE -(MEPED) 2EI/L( 2θC+ θD - 3Ψ) + MEP 2EI/L( θC+ 2θD - 3Ψ) + MEP 2EI/L( 2θD+ θE - 3Ψ) + MEP 2EI/L( θD+ 2θE - 3Ψ) + MEP θA θA θB θB θC θC θD θD θE θE x (k+1) i = x (k) i + ϐr (k) i θA θB θC θD θE r (k) 1 = (b1 - a11 x (k) 1 - a12 x (k) 2 - a13 x (k) 3 - a14 x (k) 4 - a15 x (k) 5) / a11 r (k) 2 = (b2 - a21 x (k+1) 1 - a22 x (k) 2 - a23 x (k) 3 - a24 x (k) 4 - a25 x (k) 5 / a22 r (k) 3 = (b3 - a31 x (k+1) 1 - a32 x (k+1) 2 - a33 x (k) 3 - a34 x (k) 4 - a35x (k) 5 / a33 r (k) 4 = (b4 - a41 x (k+1) 1 - a42 x (k+1) 2 - a43 x (k+1) 3 - a44 x (k) 4 - a45x (k) 5) / a44 r (k) 5 = (b5 - a51 x (k+1) 1 - a52 x (k+1) 2 - a53 x (k+1) 3 - a54 x (k+1) 4 - a55x (k) 5) / a55 2K1 K1 K1 2K1 2K2 K2 K2 2K2 2K3 K3 K3 2K3 2K4 K4 K4 2K4
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Transcript of PENDIENTE DEFLEXION - VIGAS
VIGA
ANALISIS ESTRUCTURAL - VIGA DE 4 LUCES Y 5 APOYOS (METODO PENDIENTE DFLEXION)
UNIDADES DE LONGITUDmUNIDADES DE FUERZAkg
INGRESAR DATOS:E2.00E+10E2.00E+10E2.00E+10E2.00E+10I0.0040I0.0040I0.0040I0.0060L5.00L8.00L8.00L10.00MEPi-166.67MEPi-640.00MEPi-117.19MEPi-250.00MEPj250.00MEPj426.67MEPj70.31MEPj250.00
P=100.00Q=200.00w=200.00a=3.00a=5.00b=5.00b=5.00
A BCDEK1 = 2EI/LK2 = 2EI/LK3 = 2EI/LK4 = 2EI/L
LLLL
MATRIZ DE RIGIDECESGIROS2 MIEMBROMEC. PEND. DEFLEX.2EI/LMEP2K1K1A-(MEPAB)AB2EI/L(2 A + B - 3) + MEP32,000,000-166.667K12(K1 + K2)K2B-(MEPBA + MEPBC)BA2EI/L( A + 2B - 3) + MEP250.000K22(K2 + K3)K3C-(MEPCB + MEPCD)BC2EI/L(2 B + C - 3) + MEP20,000,000-640.000K32(K3 + K4)K4D-(MEPDC + MEPDE)CB2EI/L( B + 2C - 3) + MEP426.667K42K4E-(MEPED)CD2EI/L( 2C+ D - 3) + MEP20,000,000-117.188DC2EI/L( C+ 2D - 3) + MEP70.313DE2EI/L( 2D+ E - 3) + MEP24,000,000-250.000ED2EI/L( D+ 2E - 3) + MEP250.000
MATRIZ DE RIGIDECESGIROS2 MIEMBROGIROS64,000,00032,000,0000.00.00.0A166.6671.18E-07A32,000,000104,000,00020,000,0000.00.0B390.0004.97E-06B0.020,000,00080,000,00020,000,0000.0C-309.479-6.54E-06C0.00.020,000,00088,000,00024,000,000D179.6885.73E-06D0.00.00.024,000,00048,000,000E-250.000-8.07E-06E
RESOLVIENDO EL SISTEMA DE ECUACIONES CON METODOS ITERATIVOS - METODOS DE SOBRERELAJACION =1.10x(k+1)i = x(k)i + r(k)iKABCDE0.000000r(k)1 = (b1 - a11 x(k)1 - a12 x (k)2 - a13 x(k)3 - a14 x(k)4 - a15 x(k)5) / a1112.86E-063.16E-06-5.12E-063.53E-06-7.67E-06r(k)2 = (b2 - a21 x(k+1)1 - a22 x (k)2 - a23 x(k)3 - a24 x(k)4 - a25 x(k)5 / a2228.43E-074.61E-06-5.98E-065.69E-06-8.09E-06r(k)3 = (b3 - a31 x(k+1)1 - a32 x (k+1)2 - a33 x(k)3 - a34 x(k)4 - a35x (k)5 / a3332.46E-074.85E-06-6.55E-065.74E-06-8.08E-06r(k)4 = (b4 - a41 x(k+1)1 - a42 x (k+1)2 - a43 x(k+1)3 - a44 x(k)4 - a45x(k)5) / a4441.75E-074.97E-06-6.55E-065.73E-06-8.07E-06r(k)5 = (b5 - a51 x(k+1)1 - a52 x (k+1)2 - a53 x(k+1)3 - a54 x(k+1)4 - a55x(k)5) / a5551.15E-074.97E-06-6.54E-065.73E-06-8.07E-0661.17E-074.97E-06-6.54E-065.73E-06-8.07E-0671.18E-074.97E-06-6.54E-065.73E-06-8.07E-0681.18E-074.97E-06-6.54E-065.73E-06-8.07E-0691.18E-074.97E-06-6.54E-065.73E-06-8.07E-06101.18E-074.97E-06-6.54E-065.73E-06-8.07E-06
MMATRIZ DE MOMENTOS (DEBIDO A GIROS)MATRIZ DE MOMENTOS (DEBIDO A GIROS)M FINALESAB2K1K164,000,00032,000,0000.00.00.0-0.00ABBAK12K132,000,00064,000,0000.00.00.0572.00BABC2K2K20.040,000,00020,000,0000.00.0-572.00BCCBK22K20.020,000,00040,000,0000.00.0264.34CBCD2K3K30.00.040,000,00020,000,0000.0-264.34CDDCK32K30.00.020,000,00040,000,0000.0168.68DCDE2K4K40.00.00.048,000,00024,000,000-168.68DEEDK42K40.00.00.024,000,00048,000,0000.00ED
