quinta-practica-calificada-analisis-estrucctural-i (1).pdf

UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA

ESCUELA PROFESIONAL DE INGENIERIA CIVIL

ANALISIS ESTRUCTURAL I

PREGUNTA:

En el prtico 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

PRTICO

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




SOLUCIN:

A. CALCULO DE MOMENTOS.

1. PORTICO SIN DESLIZAMIENTO

1.1. 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

4T 4T

4 T/m

6T 6T

6 T/m

4.8T 4.8T

4.8 T/m

22 T

33 T

6 7 8




1.2. FACTORES DE DISTRIBUCION

Nudo 1

Nudo 2

Nudo 3

Nudo 4

Nudo 5

(

)




1.3. PROCESO ITERATIVO

1 5

2 4

0.212 0.788 0.788 0.212

-20.513

20.513 -0.165

1.246 -8.017

-16.034 -4.314

5.784 21.500

10.750 0.046

-0.050 -4.254

-8.507 -2.289

0.912 3.391

1.695 0.036

-0.037 -0.682

-1.364 -0.367

0.153 0.567

0.283 0.010

-0.018 -0.116

-0.232 -0.062

0.028 0.105

0.053 0.002

-0.005 -0.022

-0.043 -0.012

0.006 0.021

0.010 0.001

-0.001 -0.005

-0.009 -0.002

0.001 0.005

0.002 0.000

-0.001 -0.002

-0.003 0.000

0.001 0.002

8.020 -8.020

7.115 -7.115

3 1

4 3

5 2

0.081 0.090 0.829 0.434 0.219 0.043 0.304 0.913 0.087

-30.770

30.770

-24.616

24.616

2.492 2.769 25.508

12.754

-11.237

-22.474 -2.142

2.892 -1.665

-3.329 -1.680 -0.330 -2.332

-1.166

-0.099 -0.110 -1.018

-0.509

-2.157 0.532

1.065 0.101

0.456 0.463

0.926 0.467 0.092 0.649

0.324

-0.074 -0.083 -0.762

-0.381

-1.144 -0.148

-0.296 -0.028

0.076 0.363

0.726 0.366 0.072 0.509

0.254

-0.036 -0.040 -0.364

-0.182

-0.184 -0.116

-0.232 -0.022

0.014 0.105

0.209 0.106 0.021 0.146

0.073

-0.010 -0.011 -0.098

-0.049

-0.031 -0.033

-0.067 -0.006

0.003 0.025

0.049 0.025 0.005 0.035

0.017

-0.002 -0.002 -0.023

-0.011

-0.006 -0.008

-0.016 -0.002

0.001 0.005

0.011 0.006 0.001 0.008

0.004

-0.001 0.000 -0.005

-0.003 -0.001 -0.002

-0.004 0.000

0.002 0.002 0.000 0.002

5.712 2.523 -8.236

2.098 -2.098

40.984 -0.708 -3.662 -36.612

1.262

-0.354

0.000




1.4. CORTANTES EN LAS COLUMNAS

( )

( )

2. PORTICO CON DESPLAZAMIENTO EN PRIMER NIVEL (3-4-5)

2.1. MOMENTOS EMPOTRAMIENTO

(

)(

)

22 T

33 T H1

3.349

3.349

3.349

0.769

0.769

0.769

8.020

5.712

2.523

1.262

3.349

2.629

2.629

2.629

0.216

0.216

0.216

7.115

3.662

0.708

0.354

2.629

0.426

0.426

0.426

2.098

H2

1

3 54

? ?

2




(

)(

)

(

)(

)

SI


1 5

2

4

0.212 0.788 0.788 0.212

9.035

19.327

-7.615

-15.229 -4.097

-0.301 -1.119

-0.559 3.122

-7.894 -1.010

-2.019 -0.543

1.888 7.016

3.508 0.512

-1.314 -1.584

-3.168 -0.852

0.614 2.284

1.142 0.093

-0.222 -0.487

-0.973 -0.262

0.150 0.558

0.279 0.018

-0.041 -0.117

-0.234 -0.063

0.034 0.125

0.062 0.004

-0.008 -0.026

-0.052 -0.014

0.007 0.027

0.013 0.001

-0.002 -0.006

-0.011 -0.003

0.002 0.006

0.003 0.000

0.000 -0.001

-0.002 -0.001

0.000 0.001

-17.242 17.242

1.947 -1.947

3 1

4 3

5 2

0.081 0.090 0.829 0.434 0.219 0.043 0.304 0.913 0.087

-223.081

-1032.785

-181.374

18.070 20.077 184.934

92.467

41.399

90.687

-0.151 195.065

390.131 196.863 38.654 273.271

82.797 7.890

-15.788 -17.542 -161.585

-80.792

-2.049 -62.374

136.636

0.944 31.512

63.023 31.802 6.244 44.145

-124.748 -11.887

-2.629 -2.921 -26.906

-13.453

-0.272 -10.076

22.073

0.307 5.165 10.329 5.212 1.023 7.235 -20.152 -1.920

-0.443 -0.492 -4.536

-2.268

-0.426 -1.651

3.618




0.075 0.943

1.886 0.952 0.187 1.321

-3.303 -0.315

-0.082 -0.092 -0.844

-0.422

-0.131 -0.302

0.661

0.017 0.185

0.371 0.187 0.037 0.260

-0.603 -0.057

-0.016 -0.018 -0.168

-0.084

-0.032 -0.059

0.130

0.004 0.038

0.076 0.038 0.008 0.053

-0.119 -0.011

-0.003 -0.004 -0.034

-0.017

-0.007 -0.013

0.027

0.001 0.008

0.016 0.008 0.002 0.011

-0.025 -0.002

-0.001 -0.001 -0.007

-0.004

-0.002 -0.003

0.006

0.303 -224.074 223.771

0.004 0.002 0.000 0.003

-0.005 0.001

461.264 -797.720 43.237 293.221

96.990 -96.990

-223.081

-1032.785

-181.374

-0.496

117.532

181.374

-223.577

-915.253

0.000

2.3. CORTANTES EN LAS COLUMNAS

( )

( )

H'20.549

0.549

0.549

90.986

90.986

90.986

1.947

0.303

224.074

223.577

0.549

14.751

14.751

14.751

348.165

348.165

348.165

17.242

43.237

797.720

915.253

14.751

19.713

19.713

19.713

96.990

H'1




3. PORTICO CON DESPLAZAMIENTO EN EL SEGUNDO NIVEL (1-2)

3.1. MOMENTOS DE EMPOTRAMIENTO

(

)(

)

(

)(

)

SI

1

3 54

2

??





1 2 2

1

0.212 0.788 0.788 0.212

-240.928

-240.928

94.926

189.851 51.077

30.953 115.050

57.525 2.622

9.131 -23.698

-47.396 -12.751

3.088 11.479

5.739 0.569

-1.134 -2.485

-4.971 -1.337

0.767 2.852

1.426 0.108

-0.248 -0.605

-1.209 -0.325

0.181 0.672

0.336 0.022

-0.048 -0.141

-0.282 -0.076

0.040 0.149

0.074 0.004

-0.010 -0.031

-0.062 -0.017

0.009 0.032

0.016 0.001

-0.002 -0.007

-0.013 -0.004

0.002 0.007

0.003 0.000

0.000 -0.001

-0.003 -0.001

0.000 0.001

201.036 -201.036

-198.200 198.200

3 3

4 4

5 5

0.081 0.090 0.829 0.434 0.219 0.043 0.304 0.913 0.087

-240.928

-240.928

15.476

25.538

18.262 20.291 186.899

93.450

1.544 26.461

52.922 26.705 5.243 37.070

18.535

-2.268 -2.520 -23.216

-11.608

-6.376 -8.461

-16.922 -1.613

0.384 5.739

11.477 5.791 1.137 8.039

4.020

-0.496 -0.551 -5.075

-2.538

-0.669 -1.835

-3.670 -0.350

0.090 1.094

2.188 1.104 0.217 1.533

0.766

-0.096 -0.107 -0.982

-0.491

-0.163 -0.350

-0.700 -0.067

0.020 0.218

0.435 0.220 0.043 0.305

0.153

-0.019 -0.021 -0.197

-0.099

-0.038 -0.070

-0.139 -0.013

0.004 0.045

0.089 0.045 0.009 0.063

0.031

-0.004 -0.004 -0.041

-0.020

-0.008 -0.014

-0.029 -0.003

0.001 0.009

0.019 0.009 0.002 0.013

0.007

-0.001 -0.001 -0.008

-0.004

-0.002 -0.003

-0.006 -0.001

0.000 0.002

0.004 0.002 0.000 0.003

0.001

0.000 0.000 -0.002

-0.001

0.000 -0.001

-0.001 0.000

-208.031 17.086 190.945

0.001 0.000 0.000 0.001

0.000

145.824 33.877 -215.993 36.292

0.000 0.000

2.046 -2.046

8.543

16.938

0.000




3.3. CORTANTES EN COLUMNA

( )

( )

4. CALCULO DE LAS CONSTANTES

H"2

5.209

198.200

208.031

17.086

8.543

101.714

99.081

10.328

10.328

201.036

215.993

33.877

16.938

99.081

0.416

0.416

0.416

2.046

H"1

10.328

5.209

5.209

99.081

99.081

101.714

101.714

101.714

H2 = 22.720

H1 = 32.406

H'2 = 15.300

H'1 = 474.164




( ) ( )

( ) ( )

5. CALCULOS DE LOS MOMENTOS FINALES

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

H"2 = 200.795

H"1 = 215.917

UNIVERSIDAD NACIONAL PEDRO RUIZ GALLO FACULTAD DE INGENIERIA CIVIL, SISTEMAS Y ARQUITECTURA ESCUELA PROFESIONAL DE INGENIERIA CIVIL


B. CALCULO DE LAS REACCIONES

22 T

33 T

4T

4 T/m

6T 6T

6 T/m4.8 T/m

4.8T 4.8T

10.885 24.315

22.61319.62749.7933.007

93.73515.913

19.757

42.953116.120

23.193

25.444

25.444

25.444

111.888

4.235

24.778

24.778

14.388

42.167

13.269

31.845

16.040

2.9249.886

8.731

16.040

16.040

29.623

29.623

29.623

95.576

19.757

23.193

14.388

14.388

13.269

9.886

8.731

8.731

8.731

13.269

13.269

13.269

13.269

31.845

24.315

24.315

24.315

49.7935.028

10.885

10.885

10.885

15.913

15.913

4T

13.269+31.845 = 45.114

2.924 +42.167 = 45.091el error es 0.023

9.886

9.886

9.886

2.924

2.924

2.924

2.924

2.9242.924

22.613

22.613

22.613

22.613

19.627

111.888

111.888

95.576

42.167

42.167

42.167

42.167

93.735

93.735




C. DIAGRAMAS N, V, y M.

--

-

-

13.269

31.845

93.73515.913

10.885 13.269

2.924

22.613

DIAGRAMA DE FUERZAS NORMALES

-

-

--

+

++

++

+

10.885

24.315

13.269

19.627

22.613

2.92442.16749.793

3.007

8.731

9.886

DIAGRAMA DE FUERZAS CORTANTES

-

--

+

+

++

+

+

+

+

+

-

-

-

--

-

29.623

29.623

24.778 95.5764.235

14.388

14.388

111.88825.444

42.953

19.75723.193

16.040 16.040

DIAGRAMA DE MOMENTOS FLECTORES

116.120




D. CALCULO DE LA DEFLEXION EN LOS CENTROS DE LAS VIGAS TRAMO 1-2

(

)

(

) ( )

(

)

(

) ( )

( ) (

)

( ( )) (

)

( )

(

)

( ( ))

(

)

T/m

4T

4 T/m

10.885 +Q/2 24.315+ Q/2

13.269

16.040 29.623

13.268

4T

Q

1A C B

2




TRAMO 3-4

(

)

(

) ( )

(

)

(

) ( )

( ) (

)

( ( )) (

)

( )

(

)

( ( ))

(

)

T/m

6 T/m

49.793 +Q/23.007 +Q/2

Q

3 A C B 442.953116.120

31.845 31.845




TRAMO 4-5

(

)

(

) ( )

(

)

(

) ( )

( ) (

)

( ( )) (

)

( )

(

)

( ( ))

(

)

T/m

4.8 T/m

4.8T 4.8T

22.613 +Q/219.627 +Q/2

Q

4A C B

54.235 14.388

2.9242.924

quinta-practica-calificada-analisis-estrucctural-i (1).pdf

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