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