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s = Mzy

Iz +

Flujo cortante q = tprom t =

Myz

Iy , tan a =

T 2tAm

T 2Am

Esfuerzo normal My s = I

Flexión asimétrica

Iz

Iy tan u tmáx =

Flexión

sprom =

abs

tan 2us = -

A

2 sx + sy a sx - sy

tmáx =

smáx - smín 2

sprom = smáx + smín 2 1sx - sy2>2 txy

b + t2xy

2

Esfuerzo cortante máximo absoluto 2

0.47 3.60

Abeto Douglas Abeto blanco

9.65

13.1

72.4

131

29.0

22.1

120

200

193

200

44.7

103

101

172

67.0

68.9

–

–

–

–

–

–

44

75

75

75

18

38

37

68

27

26

27

–

–

–

–

–

–

924

703

207

250

152

345

70.0

–

–

255

414

–

–

–

–

–

–

924

703

207

250

152

345

70.0

–

–

255

414

–

–

–

–

38

12

–

–

–

–

–

–

–

–

–

131

172

469

26d 36d

2.5 c

131

483

–

–

1,000

800

517

400

276

655

241

572

669

290

2.1 c

90

717

–

–

1,000

800

517

400

276

655

241

276

179

290

469

290

6.7d

6.2d

–

20.3

–

–

–

–

–

–

152

–

–

–

–

186

10

–

–

–

2.8

–

–

16

22

40

30

1

20

35

5

0.6

12

0.35

0.31e

0.29e

0.34

0.34

0.15

0.15

0.36

0.32

0.27

0.32

0.30

0.34

0.35

0.28

0.28

0.35

23

–

–

–

–

11

11

9.4

12

17

12

26

17

18

12

12

24

Algunos valores específicos pueden variar para un material particular debido a la composición mineral de la aleación, el trabajo mecánico de la probeta o el tratamiento térmico. Para obtener un valor más exacto deben consultarse los manuales de referencia para el material. b Puede suponerse que la resistencia a la cedencia y la resistencia última para los materiales dúctiles son iguales en tensión y en compresión. c Se mide perpendicular a la fibra. d Se mide paralela a la fibra. e Deformación medida en forma perpendicular a la fibra cuando la carga se aplica a lo largo de ésta.

a

Madera de grado estructural

1.45 1.45

Vidrio al 30%

2.38 Kevlar 49

2.38

2

De alta resistencia

2

b + t2xy

De baja resistencia

sx - sy

Plástico reforzado

Esfuerzo cortante máximo en el plano A

a

Concreto

2 ;

No metálicos

sx + sy

4.43

txy

Aleación [Ti-6Al-4V] de titanio

Esfuerzo principal

8.16

s1,2 = sen 2 u + txy cos 2u

De herramienta L2

Esfuerzo cortante promedio en un tubo de pared delgada 1sx - sy2>2

cos 2u + txy sen 2 u

7.86

tan 2up = 2

7.85

TL f = © JG 2

sx - sy

Inoxidable 304

J1x2G

Ecuaciones de transformación del esfuerzo

Estructural A36

tx¿y¿ = 2 sx - sy

+

pr 2t

Aleaciones de acero

T1x2dx s1 = s2 =

1.83

Esfera

pr 2t

Aleaciones [Am 1004-T61] de magnesio

Ángulo de giro sx + sy

s2 =

8.83

P = Tv = 2pfT sx¿ =

pr t

8.74

J =

p 4 c sección transversal sólida 2 p J = 1co4 - ci 42 sección transversal tubular 2 s1 =

Bronce C86100

Cilindro

Latón rojo C83400

Tr t = J

7.28

Esfuerzo cortante en un eje circular

7.19

Esfuerzo en recipientes a presión con pared delgada

Maleable ASTM A-197

Torsión VQ I

Aleaciones de cobre

tprom = q = tt =

Gris ASTM 20

L0 L

Flujo cortante

73.1

dT = a ¢TL VQ It

Aleaciones de hierro fundido

f = t =

2.71

L0 A1x2E PL d = © AE

Esfuerzo cortante transversal

2.79

d =

P1x2dx

2014-T6

Desplazamiento V A

6061-T6

L

tprom =

Aleaciones de aluminio forjado

Potencia P A

Metálicos

s =

Módulo de Resistencia a la cedencia % de elongación Resistencia última Coeficiente de exrigidez G (MPa) sY en probeta de Razón de pansión térmica (MPa) su (GPa) Tens. Comp.b Cortante Tens. Comp.b Cortante 50 mm Poisson v a (10-6)>ºC

Esfuerzo cortante directo promedio

Módulo de elasticidad E (GPa)

Esfuerzo normal

Densidad r (Mg/m3)

Cortante

(Unidades del SI)

Carga axial

Materiales

donde

12/1/11

Propiedades mecánicas promedio para materiales de ingeniería típicosa

2a y 3a Hibbeler.pdf 11:19:56

1

2

14

4

5

6

7

8

9

Secciones I de ala ancha o perfiles W

Peralte d

Grosor del alma tw

Unidades PLS Ala anchura bf

Eje x-x

Designación

Área A

grosor tf

pulg : lb>pie

pulg2

I

pulg

pulg

pulg

pulg

pulg4

S pulg3

W24 W24 W24 W24 W24 W24 W24

* * * * * * *

104 94 84 76 68 62 55

30.6 27.7 24.7 22.4 20.1 18.2 16.2

24.06 24.31 24.10 23.92 23.73 23.74 23.57

0.500 0.515 0.470 0.440 0.415 0.430 0.395

12.750 9.065 9.020 8.990 8.965 7.040 7.005

0.750 0.875 0.770 0.680 0.585 0.590 0.505

3100 2700 2370 2100 1830 1550 1350

258 222 196 176 154 131 114

W18 W18 W18 W18 W18 W18 W18

* * * * * * *

65 60 55 50 46 40 35

19.1 17.6 16.2 14.7 13.5 11.8 10.3

18.35 18.24 18.11 17.99 18.06 17.90 17.70

0.450 0.415 0.390 0.355 0.360 0.315 0.300

7.590 7.555 7.530 7.495 6.060 6.015 6.000

0.750 0.695 0.630 0.570 0.605 0.525 0.425

1070 984 890 800 712 612 510

W16 W16 W16 W16 W16 W16

* * * * * *

57 50 45 36 31 26

16.8 14.7 13.3 10.6 9.12 7.68

16.43 16.26 16.13 15.86 15.88 15.69

0.430 0.380 0.345 0.295 0.275 0.250

7.120 7.070 7.035 6.985 5.525 5.500

0.715 0.630 0.565 0.430 0.440 0.345

W14 W14 W14 W14 W14 W14 W14

* * * * * * *

53 43 38 34 30 26 22

15.6 12.6 11.2 10.0 8.85 7.69 6.49

13.92 13.66 14.10 13.98 13.84 13.91 13.74

0.370 0.305 0.310 0.285 0.270 0.255 0.230

8.060 7.995 6.770 6.745 6.730 5.025 5.000

0.660 0.530 0.515 0.455 0.385 0.420 0.335

Eje y-y

r

I

pulg

pulg4

S pulg3

r pulg

10.1 9.87 9.79 9.69 9.55 9.23 9.11

259 109 94.4 82.5 70.4 34.5 29.1

40.7 24.0 20.9 18.4 15.7 9.80 8.30

2.91 1.98 1.95 1.92 1.87 1.38 1.34

117 108 98.3 88.9 78.8 68.4 57.6

7.49 7.47 7.41 7.38 7.25 7.21 7.04

54.8 50.1 44.9 40.1 22.5 19.1 15.3

14.4 13.3 11.9 10.7 7.43 6.35 5.12

1.69 1.69 1.67 1.65 1.29 1.27 1.22

758 659 586 448 375 301

92.2 81.0 72.7 56.5 47.2 38.4

6.72 6.68 6.65 6.51 6.41 6.26

43.1 37.2 32.8 24.5 12.4 9.59

12.1 10.5 9.34 7.00 4.49 3.49

1.60 1.59 1.57 1.52 1.17 1.12

541 428 385 340 291 245 199

77.8 62.7 54.6 48.6 42.0 35.3 29.0

5.89 5.82 5.87 5.83 5.73 5.65 5.54

57.7 45.2 26.7 23.3 19.6 8.91 7.00

14.3 11.3 7.88 6.91 5.82 3.54 2.80

1.92 1.89 1.55 1.53 1.49 1.08 1.04

10

Apendice B.indd 800

14/1/11 10:58:53

y

tf

1

d

x

x tw

2

y bf

Secciones I de ala ancha o perfiles W

Peralte d

Grosor del alma tw

14

Unidades PLS Ala anchura bf

Eje x-x

Designación

Área A

grosor tf

I

S

pulg : lb>pie

pulg2

pulg

pulg

pulg

pulg

pulg4

pulg3

W12 W12 W12 W12 W12 W12 W12

* * * * * * *

87 50 45 26 22 16 14

25.6 14.7 13.2 7.65 6.48 4.71 4.16

12.53 12.19 12.06 12.22 12.31 11.99 11.91

0.515 0.370 0.335 0.230 0.260 0.220 0.200

12.125 8.080 8.045 6.490 4.030 3.990 3.970

0.810 0.640 0.575 0.380 0.425 0.265 0.225

740 394 350 204 156 103 88.6

118 64.7 58.1 33.4 25.4 17.1 14.9

W10 W10 W10 W10 W10 W10 W10 W10

* * * * * * * *

100 54 45 39 30 19 15 12

29.4 15.8 13.3 11.5 8.84 5.62 4.41 3.54

11.10 10.09 10.10 9.92 10.47 10.24 9.99 9.87

0.680 0.370 0.350 0.315 0.300 0.250 0.230 0.190

10.340 10.030 8.020 7.985 5.810 4.020 4.000 3.960

1.120 0.615 0.620 0.530 0.510 0.395 0.270 0.210

623 303 248 209 170 96.3 68.9 53.8

Eje y-y

r

I

S

r

pulg4

pulg3

pulg

5.38 5.18 5.15 5.17 4.91 4.67 4.62

241 56.3 50.0 17.3 4.66 2.82 2.36

39.7 13.9 12.4 5.34 2.31 1.41 1.19

3.07 1.96 1.94 1.51 0.847 0.773 0.753

112 60.0 49.1 42.1 32.4 18.8 13.8 10.9

4.60 4.37 4.32 4.27 4.38 4.14 3.95 3.90

207 103 53.4 45.0 16.7 4.29 2.89 2.18

40.0 20.6 13.3 11.3 5.75 2.14 1.45 1.10

2.65 2.56 2.01 1.98 1.37 0.874 0.810 0.785

pulg

W8 W8 W8 W8 W8 W8 W8

* * * * * * *

67 58 48 40 31 24 15

19.7 17.1 14.1 11.7 9.13 7.08 4.44

9.00 8.75 8.50 8.25 8.00 7.93 8.11

0.570 0.510 0.400 0.360 0.285 0.245 0.245

8.280 8.220 8.110 8.070 7.995 6.495 4.015

0.935 0.810 0.685 0.560 0.435 0.400 0.315

272 228 184 146 110 82.8 48.0

60.4 52.0 43.3 35.5 27.5 20.9 11.8

3.72 3.65 3.61 3.53 3.47 3.42 3.29

88.6 75.1 60.9 49.1 37.1 18.3 3.41

21.4 18.3 15.0 12.2 9.27 5.63 1.70

2.12 2.10 2.08 2.04 2.02 1.61 0.876

W6 W6 W6 W6 W6 W6

* * * * * *

25 20 16 15 12 9

7.34 5.87 4.74 4.43 3.55 2.68

6.38 6.20 6.28 5.99 6.03 5.90

0.320 0.260 0.260 0.230 0.230 0.170

6.080 6.020 4.030 5.990 4.000 3.940

0.455 0.365 0.405 0.260 0.280 0.215

53.4 41.4 32.1 29.1 22.1 16.4

16.7 13.4 10.2 9.72 7.31 5.56

2.70 2.66 2.60 2.56 2.49 2.47

17.1 13.3 4.43 9.32 2.99 2.19

5.61 4.41 2.20 3.11 1.50 1.11

1.52 1.50 0.966 1.46 0.918 0.905

Apendice B.indd 801

4

5

6

7

8

9

10

14/1/11 10:58:54

y

tf

1

x

d

x

2

tw y bf

14

4

Canales estándar estadounidenses o perfiles C

Designación

Área A

pulg : lb>pie pulg2

5

6

7

8

9

Unidades PLS Ala

Peralte d

Grosor del alma tw

anchura bf

grosor tf

I

pulg

pulg

pulg

pulg

pulg4

pulg3 pulg

Eje x-x

S

Eje y-y

r

I

S

r

pulg4

pulg3

pulg

C15 * 50 C15 * 40 C15 * 33.9

14.7 11.8 9.96

15.00 15.00 15.00

0.716 0.520 0.400

11 16 1 2 3 8

3.716 3.520 3.400

3 34 3 12 3 38

0.650 0.650 0.650

5 8 5 8 5 8

404 349 315

53.8 46.5 42.0

5.24 5.44 5.62

11.0 9.23 8.13

3.78 3.37 3.11

0.867 0.886 0.904

C12 * 30 C12 * 25 C12 * 20.7

8.82 7.35 6.09

12.00 12.00 12.00

0.510 0.387 0.282

1 2 3 8 5 16

3.170 3.047 2.942

3 18 3 3

0.501 0.501 0.501

1 2 1 2 1 2

162 144 129

27.0 24.1 21.5

4.29 4.43 4.61

5.14 4.47 3.88

2.06 1.88 1.73

0.763 0.780 0.799

* * * *

8.82 7.35 5.88 4.49

10.00 10.00 10.00 10.00

0.673 0.526 0.379 0.240

11 1 3 1

16 2 8 4

3.033 2.886 2.739 2.600

3 2 78 2 34 2 58

0.436 0.436 0.436 0.436

7 7 7 7

16 16 16 16

103 91.2 78.9 67.4

20.7 18.2 15.8 13.5

3.42 3.52 3.66 3.87

3.94 3.36 2.81 2.28

1.65 1.48 1.32 1.16

0.669 0.676 0.692 0.713

C9 * 20 C9 * 15 C9 * 13.4

5.88 4.41 3.94

9.00 9.00 9.00

0.448 0.285 0.233

7 16 5 16 1 4

2.648 2.485 2.433

2 58 2 12 2 38

0.413 0.413 0.413

7 16 7 16 7 16

60.9 51.0 47.9

13.5 11.3 10.6

3.22 3.40 3.48

2.42 1.93 1.76

1.17 1.01 0.962

0.642 0.661 0.669

C8 * 18.75 C8 * 13.75 C8 * 11.5

5.51 4.04 3.38

8.00 8.00 8.00

0.487 0.303 0.220

1 2 5 16 1 4

2.527 2.343 2.260

2 12 2 38 2 14

0.390 0.390 0.390

3 8 3 8 3 8

44.0 36.1 32.6

11.0 9.03 8.14

2.82 2.99 3.11

1.98 1.53 1.32

1.01 0.854 0.781

0.599 0.615 0.625

C7 * 14.75 C7 * 12.25 C7 * 9.8

4.33 3.60 2.87

7.00 7.00 7.00

0.419 0.314 0.210

7 16 5 16 3 16

2.299 2.194 2.090

2 14 2 14 2 18

0.366 0.366 0.366

3 8 3 8 3 8

27.2 24.2 21.3

7.78 6.93 6.08

2.51 2.60 2.72

1.38 1.17 0.968

0.779 0.703 0.625

0.564 0.571 0.581

C6 * 13 C6 * 10.5 C6 * 8.2

3.83 3.09 2.40

6.00 6.00 6.00

0.437 0.314 0.200

7 16 5 16 3 16

2.157 2.034 1.920

2 18 2 1 78

0.343 0.343 0.343

5 16 5 16 5 16

17.4 15.2 13.1

5.80 5.06 4.38

2.13 2.22 2.34

1.05 0.866 0.693

0.642 0.564 0.492

0.525 0.529 0.537

C5 * 9 C5 * 6.7

2.64 1.97

5.00 5.00

0.325 0.190

5 16 3 16

1.885 1.750

1 78 1 34

0.320 0.320

5 16 5 16

8.90 7.49

3.56 3.00

1.83 1.95

0.632 0.479

0.450 0.378

0.489 0.493

C4 * 7.25 C4 * 5.4

2.13 1.59

4.00 4.00

0.321 0.184

5 16 3 16

1.721 1.584

1 34 1 58

0.296 0.296

5 16 5 16

4.59 3.85

2.29 1.93

1.47 1.56

0.433 0.319

0.343 0.283

0.450 0.449

C3 * 6 C3 * 5 C3 * 4.1

1.76 1.47 1.21

3.00 3.00 3.00

0.356 0.258 0.170

3 8 1 4 3 16

1.596 1.498 1.410

1 58 1 12 1 38

0.273 0.273 0.273

1 4 1 4 1 4

2.07 1.85 1.66

1.38 1.24 1.10

1.08 1.12 1.17

0.305 0.247 0.197

0.268 0.233 0.202

0.416 0.410 0.404

C10 C10 C10 C10

Apendice B.indd 802

30 25 20 15.3

14/1/11 10:58:55

y x

1

z x

y

Tamaño y grosor

Peso por pie

pulg

lb

2

z

y

Ángulos que tienen patas iguales

x

14

Unidades PLS Eje x-x

Área A

Eje y-y

I

S

r

y

pulg2

pulg4

pulg3

pulg

pulg

I pulg4

Eje z-z

S

r

x

r

pulg3

pulg

pulg

pulg

L8 * 8 * 1

51.0

15.0

89.0

15.8

2.44

2.37

89.0

15.8

2.44

2.37

1.56

3 4 1 2

38.9

11.4

69.7

12.2

12.2

L6 * 6 * 1

37.4

3 4 1 2 3 8

28.7 19.6

3 4 1 2 3 8 3 4 1 2 3 8 1 4

L8 * 8 * L8 * 8 * L6 * 6 * L6 * 6 * L6 * 6 * L5 * 5 * L5 * 5 * L5 * 5 * L4 * 4 * L4 * 4 * L4 * 4 * L4 * 4 * L3 12 L3 12 L3 12

3 12 3 12 3 12

*

L3 * 3 *

1 2 3 8 1 4

* * *

L3 * 3 * L3 * 3 *

* *

L2 12 * 2 12 * L2 12 * 2 12 * L2 12

2 12

*

L2 * 2 *

3 8 1 4 1 8

*

L2 * 2 * L2 * 2 *

Apendice B.indd 803

2.47

2.28

69.7

2.47

2.28

1.58

48.6

8.36

2.50

2.19

48.6

8.36

2.50

2.19

1.59

35.5

8.57

1.80

1.86

35.5

8.57

1.80

1.86

1.17

8.44

28.2

6.66

1.83

1.78

28.2

6.66

1.83

1.78

1.17

5.75

19.9

4.61

1.86

1.68

19.9

4.61

1.86

1.68

1.18

14.9

4.36

15.4

3.53

1.88

1.64

15.4

3.53

1.88

1.64

1.19

23.6

6.94

15.7

4.53

1.51

1.52

15.7

4.53

1.51

1.52

0.975

16.2

4.75

11.3

3.16

1.54

1.43

11.3

3.16

1.54

1.43

0.983

12.3

3.61

8.74

2.42

1.56

1.39

8.74

2.42

1.56

1.39

0.990

18.5

5.44

7.67

2.81

1.19

1.27

7.67

2.81

1.19

1.27

0.778

12.8

3.75

5.56

1.97

1.22

1.18

5.56

1.97

1.22

1.18

0.782

9.8

2.86

4.36

1.52

1.23

1.14

4.36

1.52

1.23

1.14

0.788

6.6

1.94

3.04

1.05

1.25

1.09

3.04

1.05

1.25

1.09

0.795

11.1

3.25

3.64

1.49

1.06

1.06

3.64

1.49

1.06

1.06

0.683

8.5

2.48

2.87

1.15

1.07

1.01

2.87

1.15

1.07

1.01

0.687

5.8

1.69

2.01

0.794

1.09

0.968

2.01

0.794

1.09

0.968

0.694

9.4

2.75

2.22

1.07

0.898

0.932

2.22

1.07

0.898

0.932

0.584

7.2

2.11

1.76

0.833

0.913

0.888

1.76

0.833

0.913

0.888

0.587

4.9

1.44

1.24

0.577

0.930

0.842

1.24

0.577

0.930

0.842

0.592

7.7

2.25

1.23

0.724

0.739

0.806

1.23

0.724

0.739

0.806

0.487

5.9

1.73

0.984

0.566

0.753

0.762

0.984

0.566

0.753

0.762

0.487

4.1

1.19

0.703

0.394

0.769

0.717

0.703

0.394

0.769

0.717

0.491

4.7

1.36

0.479

0.351

0.594

0.636

0.479

0.351

0.594

0.636

0.389

3.19

0.938

0.348

0.247

0.609

0.592

0.348

0.247

0.609

0.592

0.391

1.65

0.484

0.190

0.131

0.626

0.546

0.190

0.131

0.626

0.546

0.398

26.4

1 2 1 2 1 4

1 2 3 8 1 4

7.75 11.0

4

5

6

7

8

9

10

14/1/11 10:58:56

y

tf

1

x

d x tw

2

y bf

14

4

5

6

7

8

9

Secciones I de ala ancha o perfiles W

Unidades SI

Ala Grosor Peralte del alma anchura grosor tw bf tf d

Designación

Área A

mm : kg>m

mm2

mm

mm

mm

mm

Eje x-x

I

S

106 mm4 103 mm3

Eje y-y

r

I

mm 106 mm4

W610 W610 W610 W610 W610 W610 W610

* * * * * * *

155 140 125 113 101 92 82

19 800 17 900 15 900 14 400 12 900 11 800 10 500

611 617 612 608 603 603 599

12.70 13.10 11.90 11.20 10.50 10.90 10.00

324.0 230.0 229.0 228.0 228.0 179.0 178.0

19.0 22.2 19.6 17.3 14.9 15.0 12.8

1 290 1 120 985 875 764 646 560

4 220 3 630 3 220 2 880 2 530 2 140 1 870

255 250 249 247 243 234 231

W460 W460 W460 W460 W460 W460 W460

* * * * * * *

97 89 82 74 68 60 52

12 300 11 400 10 400 9 460 8 730 7 590 6 640

466 463 460 457 459 455 450

11.40 10.50 9.91 9.02 9.14 8.00 7.62

193.0 192.0 191.0 190.0 154.0 153.0 152.0

19.0 17.7 16.0 14.5 15.4 13.3 10.8

445 410 370 333 297 255 212

1 910 1 770 1 610 1 460 1 290 1 120 942

190 190 189 188 184 183 179

W410 W410 W410 W410 W410 W410

* * * * * *

85 74 67 53 46 39

10 800 9 510 8 560 6 820 5 890 4 960

417 413 410 403 403 399

10.90 9.65 8.76 7.49 6.99 6.35

181.0 180.0 179.0 177.0 140.0 140.0

18.2 16.0 14.4 10.9 11.2 8.8

315 275 245 186 156 126

1 510 1 330 1 200 923 774 632

W360 W360 W360 W360 W360 W360 W360

* * * * * * *

79 64 57 51 45 39 33

10 100 8 150 7 200 6 450 5 710 4 960 4 190

354 347 358 355 352 353 349

9.40 7.75 7.87 7.24 6.86 6.48 5.84

205.0 203.0 172.0 171.0 171.0 128.0 127.0

16.8 13.5 13.1 11.6 9.8 10.7 8.5

227 179 160 141 121 102 82.9

1 280 1 030 894 794 688 578 475

108 45.1 39.3 34.3 29.5 14.4 12.1

S

r

103 mm3

mm

667 392 343 301 259 161 136

73.9 50.2 49.7 48.8 47.8 34.9 33.9

22.8 20.9 18.6 16.6 9.41 7.96 6.34

236 218 195 175 122 104 83.4

43.1 42.8 42.3 41.9 32.8 32.4 30.9

171 170 169 165 163 159

18.0 15.6 13.8 10.1 5.14 4.02

199 173 154 114 73.4 57.4

40.8 40.5 40.2 38.5 29.5 28.5

150 148 149 148 146 143 141

24.2 18.8 11.1 9.68 8.16 3.75 2.91

236 185 129 113 95.4 58.6 45.8

48.9 48.0 39.3 38.7 37.8 27.5 26.4

10

Apendice B.indd 804

14/1/11 10:58:57

y

tf

1

d

x

x tw

2

y bf

Secciones I de ala ancha o perfiles W

14

Unidades SI

Grosor Peralte del alma anchura tw bf d

Ala grosor tf

Designación

Área A

mm : kg>m

mm2

mm

mm

mm

mm

Eje x-x

I

S

106 mm4 103 mm3

Eje y-y

r

I

S

r

103 mm3

mm

100 23.4 20.7 7.23 1.92 1.16 0.986

649 228 203 87.6 37.6 23.0 19.5

77.8 49.7 49.3 38.3 21.4 19.5 19.2

mm 106 mm4

W310 W310 W310 W310 W310 W310 W310

* * * * * * *

129 74 67 39 33 24 21

16 500 9 480 8 530 4 930 4 180 3 040 2 680

318 310 306 310 313 305 303

13.10 9.40 8.51 5.84 6.60 5.59 5.08

308.0 205.0 204.0 165.0 102.0 101.0 101.0

20.6 16.3 14.6 9.7 10.8 6.7 5.7

308 165 145 84.8 65.0 42.8 37.0

1940 1060 948 547 415 281 244

137 132 130 131 125 119 117

W250 W250 W250 W250 W250 W250 W250 W250

* * * * * * * *

149 80 67 58 45 28 22 18

19 000 10 200 8 560 7 400 5 700 3 620 2 850 2 280

282 256 257 252 266 260 254 251

17.30 9.40 8.89 8.00 7.62 6.35 5.84 4.83

263.0 255.0 204.0 203.0 148.0 102.0 102.0 101.0

28.4 15.6 15.7 13.5 13.0 10.0 6.9 5.3

259 126 104 87.3 71.1 39.9 28.8 22.5

1840 984 809 693 535 307 227 179

117 111 110 109 112 105 101 99.3

86.2 43.1 22.2 18.8 7.03 1.78 1.22 0.919

656 338 218 185 95 34.9 23.9 18.2

67.4 65.0 50.9 50.4 35.1 22.2 20.7 20.1

W200 W200 W200 W200 W200 W200 W200

* * * * * * *

100 86 71 59 46 36 22

12 700 11 000 9 100 7 580 5 890 4 570 2 860

229 222 216 210 203 201 206

14.50 13.00 10.20 9.14 7.24 6.22 6.22

210.0 209.0 206.0 205.0 203.0 165.0 102.0

23.7 20.6 17.4 14.2 11.0 10.2 8.0

113 94.7 76.6 61.2 45.5 34.4 20.0

987 853 709 583 448 342 194

94.3 92.8 91.7 89.9 87.9 86.8 83.6

36.6 31.4 25.4 20.4 15.3 7.64 1.42

349 300 247 199 151 92.6 27.8

53.7 53.4 52.8 51.9 51.0 40.9 22.3

W150 W150 W150 W150 W150 W150

* * * * * *

37 30 22 24 18 14

4 730 3 790 2 860 3 060 2 290 1 730

162 157 152 160 153 150

8.13 6.60 5.84 6.60 5.84 4.32

154.0 153.0 152.0 102.0 102.0 100.0

11.6 9.3 6.6 10.3 7.1 5.5

274 218 159 168 120 91.2

68.5 67.2 65.0 66.2 63.3 62.9

91.8 72.4 50.9 35.9 24.7 18.2

38.7 38.2 36.8 24.5 23.5 23.0

Apendice B.indd 805

22.2 17.1 12.1 13.4 9.19 6.84

7.07 5.54 3.87 1.83 1.26 0.912

4

5

6

7

8

9

10

14/1/11 10:58:57

y

tf

1

x

x

2

d

tw y bf

14

4

5

6

7

8

9

10

Canales estándar estadounidenses o perfiles C

Designación

Área A

Grosor Peralte del alma tw d

Unidades SI

Ala anchura bf

grosor tf

mm : kg>m

mm2

mm

mm

mm

mm

C380 * 74 C380 * 60 C380 * 50

9 480 7 610 6 430

381.0 381.0 381.0

18.20 13.20 10.20

94.4 89.4 86.4

16.50 16.50 16.50

C310 * 45 C310 * 37 C310 * 31

5 690 4 740 3 930

305.0 305.0 305.0

13.00 9.83 7.16

80.5 77.4 74.7

12.70 12.70 12.70

45 37 30 23

5 690 4 740 3 790 2 900

254.0 254.0 254.0 254.0

17.10 13.40 9.63 6.10

77.0 73.3 69.6 66.0

C230 * 30 C230 * 22 C230 * 20

3 790 2 850 2 540

229.0 229.0 229.0

11.40 7.24 5.92

C200 * 28 C200 * 20 C200 * 17

3 550 2 610 2 180

203.0 203.0 203.0

C180 * 22 C180 * 18 C180 * 15

2 790 2 320 1 850

C150 * 19 C150 * 16 C150 * 12

Eje x-x

I

S

106 mm4 103 mm3

r

I

mm 106 mm4

S

r

103 mm3

mm

882 761 688

133 138 143

4.58 3.84 3.38

61.8 55.1 50.9

22.0 22.5 22.9

67.4 59.9 53.7

442 393 352

109 112 117

2.14 1.86 1.61

33.8 30.9 28.3

19.4 19.8 20.2

11.10 11.10 11.10 11.10

42.9 38.0 32.8 28.1

338 299 258 221

86.8 89.5 93.0 98.4

1.61 1.40 1.17 0.949

27.1 24.3 21.6 19.0

17.0 17.2 17.6 18.1

67.3 63.1 61.8

10.50 10.50 10.50

25.3 21.2 19.9

221 185 174

81.7 86.2 88.5

1.01 0.803 0.733

19.2 16.7 15.8

16.3 16.8 17.0

12.40 7.70 5.59

64.2 59.5 57.4

9.90 9.90 9.90

18.3 15.0 13.6

180 148 134

71.8 75.8 79.0

0.824 0.637 0.549

16.5 14.0 12.8

15.2 15.6 15.9

178.0 178.0 178.0

10.60 7.98 5.33

58.4 55.7 53.1

9.30 9.30 9.30

11.3 10.1 8.87

127 113 99.7

63.6 66.0 69.2

0.574 0.487 0.403

12.8 11.5 10.2

14.3 14.5 14.8

2 470 1 990 1 550

152.0 152.0 152.0

11.10 7.98 5.08

54.8 51.7 48.8

8.70 8.70 8.70

7.24 6.33 5.45

95.3 83.3 71.7

54.1 56.4 59.3

0.437 0.360 0.288

10.5 9.22 8.04

13.3 13.5 13.6

C130 * 13 C130 * 10

1 700 1 270

127.0 127.0

8.25 4.83

47.9 44.5

8.10 8.10

3.70 3.12

58.3 49.1

46.7 49.6

0.263 0.199

7.35 6.18

12.4 12.5

C100 * 11 C100 * 8

1 370 1 030

102.0 102.0

8.15 4.67

43.7 40.2

7.50 7.50

1.91 1.60

37.5 31.4

37.3 39.4

0.180 0.133

5.62 4.65

11.5 11.4

C75 * 9 C75 * 7 C75 * 6

1 140 948 781

76.2 76.2 76.2

9.04 6.55 4.32

40.5 38.0 35.8

6.90 6.90 6.90

0.862 0.770 0.691

22.6 20.2 18.1

27.5 28.5 29.8

0.127 0.103 0.082

4.39 3.83 3.32

10.6 10.4 10.2

C250 C250 C250 C250

* * * *

Apendice B.indd 806

168 145 131

Eje y-y

14/1/11 10:58:58

y x

1

z x

y y

Ángulos que tienen patas iguales

x 2

z

14

Unidades SI

Tamaño y grosor

Masa por metro

Área

I

S

r

y

I

S

r

x

r

mm

kg

mm2

106 mm4

106 mm3

mm

mm

106 mm4

106 mm3

mm

mm

mm

75.9 57.9 39.3

9 680 7 380 5 000

36.9 28.9 20.2

258 199 137

61.7 62.6 63.6

60.1 57.8 55.5

36.9 28.9 20.2

258 199 137

61.7 62.6 63.6

60.1 57.8 55.5

39.6 40.1 40.4

25.4 19.0 12.7 9.5

55.7 42.7 29.2 22.2

7 100 5 440 3 710 2 810

14.6 11.6 8.22 6.35

139 108 75.1 57.4

45.3 46.2 47.1 47.5

47.2 45.0 42.7 41.5

14.6 11.6 8.22 6.35

139 108 75.1 57.4

45.3 46.2 47.1 47.5

47.2 45.0 42.7 41.5

29.7 29.7 30.0 30.2

L127 * 127 * 19.0 L127 * 127 * 12.7 L127 * 127 * 9.5

35.1 24.1 18.3

4 480 3 060 2 330

6.54 4.68 3.64

73.9 51.7 39.7

38.2 39.1 39.5

38.7 36.4 35.3

6.54 4.68 3.64

73.9 51.7 39.7

38.2 39.1 39.5

38.7 36.4 35.3

24.8 25.0 25.1

27.5 19.0 14.6 9.8

3 510 2 420 1 840 1 250

3.23 2.34 1.84 1.28

46.4 32.6 25.3 17.3

30.3 31.1 31.6 32.0

32.4 30.2 29.0 27.9

3.23 2.34 1.84 1.28

46.4 32.6 25.3 17.3

30.3 31.1 31.6 32.0

32.4 30.2 29.0 27.9

19.8 19.9 20.0 20.2

L89 * 89 * 12.7 L89 * 89 * 9.5 L89 * 89 * 6.4

16.5 12.6 8.6

2 100 1 600 1 090

1.52 1.20 0.840

24.5 19.0 13.0

26.9 27.4 27.8

26.9 25.8 24.6

1.52 1.20 0.840

24.5 19.0 13.0

26.9 27.4 27.8

26.9 25.8 24.6

17.3 17.4 17.6

L76 * 76 * 12.7 L76 * 76 * 9.5 L76 * 76 * 6.4

14.0 10.7 7.3

1 770 1 360 927

0.915 0.726 0.514

17.5 13.6 9.39

22.7 23.1 23.5

23.6 22.5 21.3

0.915 0.726 0.514

17.5 13.6 9.39

22.7 23.1 23.5

23.6 22.5 21.3

14.8 14.9 15.0

L64 * 64 * 12.7 L64 * 64 * 9.5 L64 * 64 * 6.4

11.5 8.8 6.1

1 450 1 120 766

0.524 0.420 0.300

12.1 9.46 6.59

19.0 19.4 19.8

20.6 19.5 18.2

0.524 0.420 0.300

12.1 9.46 6.59

19.0 19.4 19.8

20.6 19.5 18.2

12.4 12.4 12.5

L51 * 51 * 9.5 L51 * 51 * 6.4 L51 * 51 * 3.2

7.0 4.7 2.5

877 605 312

0.202 0.146 0.080

5.82 4.09 2.16

15.2 15.6 16.0

16.2 15.1 13.9

0.202 0.146 0.080

5.82 4.09 2.16

15.2 15.6 16.0

16.2 15.1 13.9

9.88 9.93 10.1

L203 * 203 * 25.4 L203 * 203 * 19.0 L203 * 203 * 12.7 L152 L152 L152 L152

L102 L102 L102 L102

* * * *

* * * *

152 152 152 152

102 102 102 102

* * * *

* * * *

19.0 12.7 9.5 6.4

Eje x-x

Eje y-y

Eje z-z 4

5

6

7

8

9

10

Apendice B.indd 807

14/1/11 10:58:59

1

2

14

Pendientes y deflexiones de una viga simplemente apoyada Viga v

P

L 2

4

Pendiente L 2

v

P u1

u2 a

x

b

v L

M0 x

u2

u1

u1 = u2 =

L

6

- PL2 = 16EI

vmáx

Curva elástica v =

-PL3 = 48EI

-Pab1L + b2 6EIL Pab1L + a2

v`

x=a

v =

-Pba 2 = 1L - b2 - a22 6EIL

- M0L 6EI M0L u2 = 3EI

-Pbx 2 1L - b2 - x22 6EIL

0 … x … a

6EIL

u1 =

-M0L2

2243EI

vmáx =

-Px 13L2 - 4x22 48EI

0 … x … L>2

vmáx

umáx

5

umáx

Deflexión

v =

en x = 0.5774L

-M0x 2 1L - x22 6EIL

v L

w

7

x

umáx =

umáx vmáx

8

v w u2 L u1 2

x

L 2

- wL3 24EI

- 3wL3 u1 = 128EI 7wL3 u2 = 384EI

vmáx =

v`

x = L>2

=

-5wL4 384EI

-5wL4 768EI

v =

v =

- wx 3 1x - 2Lx2 + L32 24EI

-wx 116x3 - 24Lx2 + 9L32 384EI

0 … x … L>2 vmáx = - 0.006563

wL4 EI

v =

-wL 18x3 - 24Lx2 384EI

9

en x = 0.4598L v

w0

10

x u1

Apendice C.indd 808

u1 =

L

u2

- 7w0L3 360EI

vmáx = - 0.00652

w0L4 EI

3

u2 =

w0L 45EI

en x = 0.5193L

L>2 … x 6 L

v =

+ 17L2x - L32

- w0x 13x4 - 10L2x2 + 7L42 360EIL

14/1/11 10:59:31

Pendientes y deflexiones de una viga simplemente apoyada Viga

Pendiente

v

1

Deflexión

Curva elástica

P vmáx x

-PL2 2EI

vmáx =

-PL3 3EI

v =

P vmáx x L 2

-Px2 13L - x2 6EI

2

umáx

L v

umáx =

L 2

umáx

-PL2 = 8EI

vmáx

-5PL3 = 48EI

umáx

v =

-Px2 3 A L - xB 6EI 2

v =

-PL2 A 3x - 12 L B 24EI

0 … x … L>2

14

L>2 … x … L 4

v w vmáx x

umáx =

-wL3 6EI

vmáx =

-wL4 8EI

v =

-wx2 2 1x - 4Lx + 6L22 24EI

umáx

L

5

v umáx x M0 vmáx

umáx =

M0L EI

vmáx =

M0L2 2EI

v =

M0x2 2EI

6

L

v

v =

w

vmáx x

L 2

L 2

umáx =

umáx

3

-wL 48EI

vmáx =

- wx2 2 A x - 2Lx + 32 L2 B 24EI

4

-7wL 384EI

7

0 … x … L>2 v =

3

-wL 14x - L>22 192EI L>2 … x … L

8

v w0

vmáx x L

Apendice C.indd 809

umáx =

- w0L3 24EI

vmáx =

-w0L4 30EI

v =

- w0x2 110L3 - 10L2x + 5Lx2 - x32 120EIL

9

umáx

14/1/11 10:59:32