quinta practica calificada analisis estrucctural i metodo kani

UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO

ESCUELA PROFESIONAL DE INGENIERIA CIVILANALISIS ESTRUCTURAL I

PREGUNTA:

En el pórtico calcular:

A. Los momentos en las barras

B. Las reacciones en los apoyos

C. Diagramas de N, V, y M.

D. Las deflexiones en el centro de las vigas.

P = 4.0, w = 4.0, H = 22, a = 3.4, b = 4.1

PÓRTICO

1.7 1.73.4 1.7 1.7 3.4

4.92

4.1

4T 4T

4 T/m

6T 6T

6 T/m

4.8T 4.8T

4.8 T/m

22 T

33 T

1 2

3 5

6

4

7 8

a/2 a/2a a/2 a/2 a

1.2b

b

P

w

1.5P

1.5w

1.2P

1.2w

H

1.5H

1 2

3 5

6

4

7 8

P

1.5P1.2P

30x55

40x70 35x65

30x30

30x30

40x30

40x50

40x28

30x55

40x70 35x65

30x30

30x30

40x30

40x50

40x28

UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO

ESCUELA PROFESIONAL DE INGENIERIA CIVILANALISIS ESTRUCTURAL I

SOLUCIÓN:

A. CALCULO DE MOMENTOS EN LAS BARRAS.

1. MOMENTOS DE EMPOTRAMIENTO

ME12 = -20.513 Tm ME21 = 20.513 Tm ME34 = -30.770 Tm

ME43 = 30.770 Tm ME45 = -24.616 Tm ME54 = 24.616 Tm

2. COEFICIENTE DE GIRO

u12=−0.394 ,u21=−0.394 , u13=−0.106

u24=−0.106 , u31=−0.041 , u34=−0.414

u36=−0.045 ,u42=−0.021 ,u43=−0.217

u45=−.152, u47=−0.109 , u54=−0.457

u58=−0.043

UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO

ESCUELA PROFESIONAL DE INGENIERIA CIVILANALISIS ESTRUCTURAL I

3. COEFICIENTE DE DESPLAZAMIENTO

Coef. De desplazamiento

γ13 -0.750γ 24 -0.750γ 36 -0.240γ 47 -1.113γ 58 -0.147

4. MOMENTO DE PISO

MP1 30.067MP2 90.200

UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO

ESCUELA PROFESIONAL DE INGENIERIA CIVILANALISIS ESTRUCTURAL I

5. PROCESO ITERATIVO

4° 3°

-20.513 -0.394 -20.513 20.513 -0.394 20.513

-0.106 10.773 -8.081 -0.106

2.900 17.441 -2.847 -2.175

4.694 20.282 -4.207 -0.766

5.459 21.122 -5.454 -1.132

5.685 21.314 -5.941 -1.468

5.737 21.349 -6.083 -1.599

5.746 21.354 -6.117 -1.637

5.747 21.354 -6.125 -1.647

5.747 21.354 -6.126 -1.649

5.747 21.354 -6.127 -1.649

5.747 -1.649

-0.750 30.067 -0.750

-23.942 1.248 -23.942 -0.117

-29.259 3.033 -29.259 1.984

-29.819 2.497 -29.819 2.867

-29.702 2.172 -29.702 3.148

-29.614 2.054 -29.614 3.227

-29.581 2.019 -29.581 3.247

-29.572 2.010 -29.572 3.252

-29.570 2.007 -29.570 3.253

-29.569 2.007 -29.569 3.254

-29.569 2.007 -29.569 3.254

UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO

ESCUELA PROFESIONAL DE INGENIERIA CIVILANALISIS ESTRUCTURAL I

1° -0.041 5° -0.021 2°-30.77 -0.414 -30.77 30.77 -0.217 6.154 -0.152 -24.616 24.616 -0.457 24.616-0.045 12.750 -1.191 -0.109 -0.835 -11.243 -0.0431.387 30.972 20.265 -0.600 14.197 -5.049 -1.0653.370 25.505 29.285 10.207 20.516 -13.489 -0.4782.775 22.180 32.146 14.750 22.520 -16.883 -1.2772.413 20.981 32.952 16.191 23.085 -17.953 -1.5992.283 20.621 33.163 16.598 23.233 -18.256 -1.7002.243 20.524 33.214 16.704 23.269 -18.335 -1.7292.233 20.500 33.226 16.730 23.277 -18.355 -1.7362.230 20.494 33.229 16.736 23.279 -18.360 -1.7382.230 20.493 33.230 16.737 23.280 -18.361 -1.7392.230 16.737 -1.739

-0.240 90.200 -1.113 -0.147-21.746 -100.676 -13.260 0.532-26.485 -122.617 -16.150 6.869-27.686 -128.174 -16.882 8.714-27.995 -129.604 -17.070 9.240-28.071 -129.960 -17.117 9.385-28.089 -130.044 -17.128 9.423-28.094 -130.063 -17.131 9.432-28.095 -130.067 -17.131 9.435-28.095 -130.068 -17.132 9.435-28.095 -130.068 -17.132 9.435

0 0 -0.5

6. CALCULOS DE LOS MOMENTOS FINALES

MOMENTOS KANI

M12= 16.068M21= 29.613M13= -16.068M31= -19.808M24= -29.613M42= -24.711M34= 43.445M43= 117.722M36= -23.636M63= -25.865

UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO

ESCUELA PROFESIONAL DE INGENIERIA CIVILANALISIS ESTRUCTURAL I

M47= -96.594M74= -113.331M45= 3.583M54= 11.174M58= -11.174M85= 0.000

UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL

ANALISIS ESTRUCTURAL I

B. CALCULO DE LAS REACCIONES

UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL

ANALISIS ESTRUCTURAL I

C. DIAGRAMAS N, V, y M.

D. CALCULO DE LA DEFLEXION EN LOS CENTROS DE LAS VIGAS

TRAMO 1-2

M 1 A=(10.885+Q2 ) x−2x2+16.040 dM 1A

dQ= x2

M AC=(10.885+Q2 )x−2x2+16.040−4(x−1.7) dM AC

dQ= x2

M 2B=(24.315+Q2 ) x−2 x2−29.623 dM 4B

dQ= x2

MBC=(24.315+Q2 ) x−2 x2−29.623−4(x−1.7) dMBC

dQ= x2

dc 1−2=1

0.0041593E∫0

1.7

(10.885x−2x2+16.040 )( x2 )dx+ 10.0041593 E

∫1.7

3.4

(10.885x−2x2+16.040−4 ( x−1.7 ) )( x2 )dx+ 10.0041593 E

∫0

1.7

(24.315 x−2 x2−29.623 )( x2 )dx+ 10.0041593 E

∫1.7

3.4

(24.315x−2x2−29.623−4 (x−1.7 ) )( x2 )dx

dc 1−2=15855.1747489

E↓ T/m

TRAMO 3-4

UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL

ANALISIS ESTRUCTURAL I

M 3 A=(3.007+Q2 ) x−3 x2+42.953 dM 3A

dQ= x2

M AC=(3.007+Q2 )x−3x2+42.953−6 (x−1.7) dM AC

dQ= x2

M 4 B=(49.793+Q2 ) x−3 x2−116.120 dM 4 B

dQ= x2

MBC=(49.793+Q2 )x−3 x2−116.120−6 (x−1.7) dM BC

dQ= x2

dc 3−4=1

0.011433 E∫0

1.7

(3.007 x−3 x2+42.953 )( x2 )dx+ 10.011433 E

∫1.7

3.4

(3.007 x−3 x2+42.953−6 (x−1.7 ) )( x2 )dx+ 10.011433E

∫0

1.7

(49.793 x−3 x2−116.120 )( x2 )dx+ 10.011433E

∫1.7

3.4

(49.793 x−3 x2−116.120−6 ( x−1.7 )) ( x2 )dx

dc 3−4=422.954984

E↓ T/m

TRAMO 4-5

M 4 A=(19.627+Q2 )x−2.4 x2−4.235 dM 4 A

dQ= x2

M AC=(19.627+Q2 )x−2.4 x2−4.235−4.8 (x−1.7) dM AC

dQ= x2

M 5B=(22.613+Q2 ) x−2.4 x2−14.388 dM 5B

dQ= x2

UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO ESCUELA PROFESIONAL DE INGENIERIA CIVIL

ANALISIS ESTRUCTURAL I

MBC=(22.613+Q2 ) x−2.4 x2−14.388−4.8 (x−1.7) dMBC

dQ= x2

dc 4−5=1

0.0080099 E∫0

1.7

(19.628 x−2.4 x2−4.235 )( x2 )dx+ 10.0080099E

∫1.7

3.4

(19.628 x−2.4 x2−4.235−4.8 ( x−1.7 ) )( x2 )dx+ 10.0080099 E

∫0

1.7

(22.613 x−2.4 x2−14.388 )( x2 )dx+ 10.0080099 E

∫1.7

3.4

(22.613 x−2.4 x2−14.388−4.8 ( x−1.7 ) )( x2 )dx

dc 4−5=15090.787026

E↓ T/m