¡Descarga Ejercicios de Resistencia de Materiales: Aplicación del Método de Rigidez Directa y más Exámenes en PDF de Análisis Estructural solo en Docsity!
1 Calcular las reacciones en los apoyos y dibujar el diagrama de fuerzas cortantes y el diagrama de momento fle 1 2 3 4 L 4 0.188 0.375 -0.188 0. Elemento DC q 6 0.375 1.000 -0.375 0. P 0 -0.188 -0.375 0.188 -0. 0.375 0.375 -0.375 1. 3 4 5 L 5 0.024 0.120 -0.024 3 Elemento DAq 0 -0.120 0.600 -0.120 4 P 20 -0.024 -0.120 0.024 5 5 6 7 L 3 0.111 -0.111 0.333 5 Elemento AB q 4 -0.111 0.111 -0.333 6 P 0 0.333 -0.333 1.000 7 7 8 9
KED=EI
KEA=EI
KAB=EI
A B
D E
D E B
C
C
L 2 0.375 -0.375 0.750 7
Elemento BC q 0 -0.375 0.375 -0.750 8 P 25 0.750 -0.750 1.500 9 Matriz de rigidez consolidada 1 2 3 4 5 6 0.188 0.375 -0.188 0.375 0 0 0.375 1.000 -0.375 0.500 0 0 -0.188 -0.375 0.212 -0.495 -0.024 0 0.375 0.375 -0.120 1.600 -0.120 0 0 0 -0.024 -0.120 0.135 -0. 0 0 0 -0.120 -0.111 0. 0 0 0 0 0.333 0. 0 0 0 0 0 0 0 0 0 0 0 0 0.00 1 0.00 2 w 6 12 3 L 4 -12 4 13.75 3 L 3 11.25 4 6.25 5 p 20 0 5.625 5 q 5 0. 9.375 6 L 3 -5.625 7 q 25 0.000 8 0 L 2 0.000 9
KBC=EI
FED=
FEA=
FAB=
FBC=
F=KU + ∑Fext
el diagrama de momento flector. Considerar EI= Constante (10 puntos) 1 2 3 4
Momentos y reacciones en vigas articulada-empotrada
EI 150000 Tn/m2 0.09 0. L 5.2 m EI 0.22 0. Elemento AB W 9 Tn/m -0.09 -0. P 0 0.22 0. 3 4 Kresorte L= 700 -700 3 1 2 -700 700 4 12,801.55 33,284. 1 2 33,284.02 115,384. Kresorte R= 40000 -40000 1 -12,801.55 -33,284. -40000 40000 2 33,284.02 57,692. Matriz reducida 2 3 155,384.62 -33,284.02 2 -33,284.02 13,501.55 3 q 9 L 5. F=KU + ∑Fext 0 2 8.11 2 F= 0 3 ∑Fext= 16.38 3 Practica Dirigida
- Aplicando el método de rigidez directa, calcular las deformaciones en los nodos A, B, C, D y E. Dibujar los diagramas de fuerzas cortantes y de momentos flectores, sabiendo que EI= 1.5x105 ton-m2, los apoyos elásticos tienen coeficientes 700, 500 y 900 ton/m (B, C y D) y en los rotacionales son 40000 y 35,000 ton-m/rad (A y E) respectivamente KAB= FAB= KAB=
0.00001 0.00003 -0.0006612317 u 0.00003 0.00016 = -0.0028432631 u 7.02 12801.548 33284.024 -12801.548 33284. 8.11 + 33284.024 115384.615 -33284.024 57692. 16.38 -12801.548 -33284.024 12801.548 -33284. -12.17 33284.024 57692.308 -33284.024 115384. 3 4 EI 150000 Tn/m2 0.22 0. L 3.8 m EI 0.42 1. Elemento BC W 20 Tn/m -0.22 -0. P 0 0.42 0. 3 4 Kresorte L= 40000 -40000 3 3 4 -40000 40000 4 32,803.62 62,326. 5 6 62,326.87 157,894. Kresorte L= 35000 -35000 5 -32,803.62 -62,326. -35000 35000 6 62,326.87 78,947. Matriz reducida 3 5 72,803.62 -32,803.62 3 -32,803.62 67,803.62 5 q L F=KU + ∑Fext 0 3 0.00 3 F= 0 5 ∑Fext= 0.00 5 0.00002 0.00001 0 u 0.00001 0.00002 = 0 u 0.00 32803.616 62326.870 -32803.616 62326. 0.00 + 62326.870 157894.737 -62326.870 78947.
K-1=
FAB=
KAB=
FAB=
KAB=
K-1=
FAB=
EI 150000 Tn/m2 0.19 0. L 4 m EI 0.38 1. Elemento DE W 7 Tn/m -0.19 -0. P 0 0.38 0. 7 8 Kresorte L= 900 -900 7 7 8 -900 900 8 28,125.00 56,250. 9 10 56,250.00 150,000. Kresorte R= 35000 -35000 9 -28,125.00 -56,250. -35000 35000 10 56,250.00 75,000. Matriz reducida 7 10 29,025.00 56,250.00 7 56,250.00 185,000.00 10 q 7 L 4 F=KU + ∑Fext 0 7 14.00 7 F= 0 10 ∑Fext= -9.33 10 0.00008 -0.00003 -0.0014122531 u -0.00003 0.00001 = 0.0004798337 u 14.00 28125.000 56250.000 -28125.000 56250. 9.33 + 56250.000 150000.000 -56250.000 75000. 14.00 -28125.000 -56250.000 28125.000 -56250. -9.33 56250.000 75000.000 -56250.000 150000.
KAB=
FAB=
KAB=
K-1=
FAB=
- RyA 3 25.75
- F= 0 4 ∑Fext= -0.750 - 0 5 11.875 - RyB 6 9.375 - MB 7 -5.625 - 0 8 0.000 - 0 9 0.000 - F - ∑Fext= 0.750 - -11.875 - 0.188 0.375 0.375 0.000 - 0.375 1.000 0.500 0.000 - 0.375 0.375 1.600 -0.120 - 0.000 0.000 -0.120 0.135 - 0.000000 0.188 0.375 0.375 0.000 u F - ∑Fext = Ku - 0.000000 = 0.375 1.000 0.500 0.000 u - 0.750000 0.375 0.375 1.600 -0.120 u
- -11.875000 0.000 0.000 -0.120 0.135 u - 75.619 -24.2857143 -10.8571429 -9. - -21.571 8.071 2.714 2. - -13.571 4.071 2.714 2. - -12.054 3.616 2.411 9. - u1 -14. - u2 = 4. - u3 4. - u4 -11. - RyA 25.75 -0.188 -0.375 -0. F ∑Fext K - RyB = 9.375 + 0.000 0.000 0. - MB -5.625 0.000 0.000 0. - RyA 25.75 2.875 28. Ku - RyB = 9.375 + 1.25 = 10. - Matriz inversa: K-
- MB -5.625 -3.75 -9. - 0 0.444 0.667 -0.444 0.667 -14.
- FED= 0 + 0.667 1.333 -0.667 0.667 4. - 12 -0.444 -0.667 0.444 -0.667 - -12 0.667 0.667 -0.667 1.333 4. - 13.75 0.111 0.333 -0.111 0 2.
- FEA= 11.25 + -0.333 1.000 -0.333 4.88 8. - 6.25 -0.111 -0.333 0.111 -11.25 -2. - 5.625 0.111 -0.111 0.333 -11.25 -1.
- FAB= 9.375 + -0.111 0.111 -0.333 0 1. - -5.625 0.333 -0.333 1.000 0 -3. - 0 0.375 -0.375 0.750 9.38 -1.
- FBC= 0 + -0.375 0.375 -0.750 0 1. - 0 0.750 -0.750 1.500 0 -3.
- 0.00 0.0000
- 0.00 = 0.0000
- 0.00 12.0000
- 0.00 -12.0000
- = 19.8750 - 3.3750 - 4.3750
- = 10.6250 - -9.3750 - -1.2500
- = 1.2500 - -3.7500 - 0.000000 14.3897158083 21.410
- -0.000661 18.33926902 = 26.449
- -0.002843 -14.3897158083 1.990
- 0.000000 56.4872531834 44.317
- -0.22 0.42
- -0.42 0.53
- -0.42 1.05
- -32,803.62 62,326.87
- -62,326.87 78,947.37
- -62,326.87 157,894.74 - 0.00 Ay - 0.00 Ma - 0.00 By - 0.00 Mb - 0.000 - F - ∑Fext= 0.000 - 0.000000 0 0.000 - 0.000000 0 = 0.000 - 0.000000 0 0.000 - 0.000000 0 20.000 - -0.09 0.22 - -0.22 0.38 - 0.09 -0.22 - -0.22 0.77
- -12,801.55 33,284.02
- -33,284.02 57,692.31
- -33,284.02 115,384.62 - 7.50 Ay - 9.75 Ma - 7.50 By - 9.75 Mb - -7.500 - F - ∑Fext= -7.500 - 0.000000 -223.695567826 -216.196
- -0.010819 -893.702461997 = -883.952
- -0.010656 223.695567826 231.196
- 0.000000 -269.514490699 -259.764
