A12
APPENDIX APPENDI X B Typical Properties of Selected Materials Used in Engineering 1,5 (U.S. Customary Units) Ultimate Strength
Material Steel Structural (ASTM-A36) High-strength-low-alloy ASTM-A709 Grade 50 ASTM-A913 Grade 65 ASTM-A992 Grade 50 Quenched & tempered ASTM-A709 Grade 100 Stainless, AISI 302 Cold-rolled Annealed Reinforcing Steel Medium strength High strength Cast Iron Gray Cast Iron 4.5% C, ASTM A-48 Malleable Cast Iron 2% C, 1% Si, ASTM A-47 Aluminum Alloy 1100-H14 (99% Al) Alloy 2014-T6 Alloy 2024-T4 Alloy 5456-H116 Alloy 6061-T6 Alloy 7075-T6
Yield Strength3
Modulus Specific Compresof Weight, Tension, sion, 2 Shear, Tension, Shear, Elastici Elasticity, ty, 3 6 lb/in ksi ksi ksi ksi ksi 10 psi
Modulus of Rigidity, 106 psi
0.284
58
36
29
11.2
6.5
21
0.284 0.284 0.284
65 80 65
50 65 50
29 29 29
11.2 11.2 11.2
6.5 6.5 6.5
21 17 21
0.284
110
100
29
11.2
6.5
18
0.286 0.286
125 95
75 38
28 28
10.8 10.8
9.6 9.6
12 50
0.283 0.283
70 90
40 60
29 29
11 11
6.5 6.5
0.260
25
95
35
0.264
50
90
48
33
0.098 0.101 0.101 0.095 0.098 0.101
16 66 68 46 38 83
10 40 41 27 24 48
14 58 47 33 35 73
32 57
22 29
10 53
74 46
43 32
60 15
85 39 45
46 31
Copper Oxygen-free copper (99.9% Cu) Annealed 0.322 Hard-drawn 0.322 Yellow Brass (65% Cu, 35% Zn) Cold-rolled 0.306 Annealed 0.306 Red Brass (85% Cu, 15% Zn) Cold-rolled 0.316 Annealed 0.316 Tin bronze 0.318 (88 Cu, 8Sn, 4Zn) Manganese bronze 0.302 (63 Cu, 25 Zn, 6 Al, 3 Mn, 3 Fe) Aluminum bronze 0.301 (81 Cu, 4 Ni, 4 Fe, 11 Al)
95 90
130
21
22
Coefficient of Thermal Expans ion, Expansion, 1026/8F
Ductili ty, Ductility, Percent Elongation Elongati on in 2 in.
10
4.1
6.7
24
9.3
6.7
10
10.1 10.9 10.6 10.4 10.1 10.4
3.7 3.9 3.7 4
13.1 12.8 12.9 13.3 13.1 13.1
9 13 19 16 17 11
17 17
6.4 6.4
9.4 9.4
45 4
15 15
5.6 5.6
11.6 11.6
8 65
63 10 21
17 17 14
6.4 6.4
10.4 10.4 10
3 48 30
48
15
12
20
40
16
9
6
8 33 19 20
36 9
6.1
0.5
(Table continued on page A13)
APPENDIX B Typical Properties of Selected Materials Used in Engineering 1,5 (SI Units) Ultimate Strength
Material Steel Structural (ASTM-A36) High-strength-low-alloy ASTM-A709 Grade 345 ASTM-A913 Grade 450 ASTM-A992 Grade 345 Quenched & tempered ASTM-A709 Grade 690 Stainless, AISI 302 Cold-rolled Annealed Reinforcing Steel Medium strength High strength Cast Iron Gray Cast Iron 4.5% C, ASTM A-48 Malleable Cast Iron 2% C, 1% Si, ASTM A-47 Aluminum Alloy 1100-H14 (99% Al) Alloy 2014-T6 Alloy-2024-T4 Alloy-5456-H116 Alloy 6061-T6 Alloy 7075-T6
A13
Yield Strength3
Modulus Compresof Density Tension, sion,2 Shear, Tension, Shear, Elasticity, kg/m3 MPa MPa MPa MPa MPa GPa
Modulus of Rigidity, GPa
Coefficient of Thermal Expansion, 1026/8C
Ductility, Percent Elongation in 50 mm
7860
400
250
200
77.2
11.7
21
7860 7860 7860
450 550 450
345 450 345
200 200 200
77.2 77.2 77.2
11.7 11.7 11.7
21 17 21
7860
760
690
200
77.2
11.7
18
7920 7920
860 655
520 260
190 190
75 75
17.3 17.3
12 50
7860 7860
480 620
275 415
200 200
77 77
11.7 11.7
7200
170
655
240
69
28
12.1
7300
345
620
330
230
165
65
12.1
10
2710 2800 2800 2630 2710 2800
110 455 470 315 260 570
70 275 280 185 165 330
95 400 325 230 240 500
70 75 73 72 70 72
26 27 26 28
23.6 23.0 23.2 23.9 23.6 23.6
9 13 19 16 17 11
220 390
150 200
70 265
120 120
44 44
16.9 16.9
45 4
510 320
300 220
410 100
105 105
39 39
20.9 20.9
8 65
585 270 310
320 210
435 70 145
120 120 95
44 44
18.7 18.7 18.0
3 48 30
330
105
21.6
20
275
110
16.2
6
Copper Oxygen-free copper (99.9% Cu) Annealed 8910 Hard-drawn 8910 Yellow-Brass (65% Cu, 35% Zn) Cold-rolled 8470 Annealed 8470 Red Brass (85% Cu, 15% Zn) Cold-rolled 8740 Annealed 8740 Tin bronze 8800 (88 Cu, 8Sn, 4Zn) Manganese bronze 8360 (63 Cu, 25 Zn, 6 Al, 3 Mn, 3 Fe) Aluminum bronze 8330 (81 Cu, 4 Ni, 4 Fe, 11 Al)
655 620
900
145
150
55 230 130 140
250 60
42
0.5
(Table continued on page A14)
A14
APPENDIX B Typical Properties of Selected Materials Used in Engineering 1,5 (U.S. Customary Units) Continued from page A13 Ultimate Strength
Material
Modulus Specific Compresof Weight, Tension, sion,2 Shear, Tension, Shear, Elasticity, lb/in3 ksi ksi ksi ksi ksi 106 psi
Magnesium Alloys Alloy AZ80 (Forging) Alloy AZ31 (Extrusion)
0.065 0.064
50 37
Titanium Alloy (6% Al, 4% V)
0.161
Monel Alloy 400(Ni-Cu) Cold-worked Annealed
Ductility, Percent Elongation in 2 in.
14 14
6 12
130
120
16.5
5.3
10
0.319 0.319
98 80
85 32
26 26
7.7 7.7
22 46
Cupronickel (90% Cu, 10% Ni) Annealed Cold-worked
0.323 0.323
53 85
16 79
9.5 9.5
35 3
Timber, air dry Douglas fir Spruce, Sitka Shortleaf pine Western white pine Ponderosa pine White oak Red oak Western hemlock Shagbark hickory Redwood
0.017 0.015 0.018 0.014 0.015 0.025 0.024 0.016 0.026 0.015
15 8.6
Concrete Medium strength High strength
0.084 0.084 0.0412
13 9.4
7.2 5.6 7.3 5.0 5.3 7.4 6.8 7.2 9.2 6.1
1.1 1.1 1.4 1.0 1.1 2.0 1.8 1.3 2.4 0.9
0.0433 0.0484
9.5 8
0.0433 0.0374 0.0520 0.033 0.100 0.100 0.083 0.079
6.5 8 6 2 3 2 1
20 20 1.9 1.5 1.7 1.5 1.3 1.8 1.8 1.6 2.2 1.3
4.0 6.0 11
50 18
2.4 2.4
Coefficient of Thermal Expansion, 1026/8F
6.5 6.5
8.4
23 19
Modulus of Rigidity, 106 psi
36 29
Plastics Nylon, type 6/6, (molding compound) Polycarbonate Polyester, PBT (thermoplastic) Polyester elastomer Polystyrene Vinyl, rigid PVC Rubber Granite (Avg. values) Marble (Avg. values) Sandstone (Avg. values) Glass, 98% silica 1
Yield Strength3
7.5 7.5 .1 .07
3.6 4.5
Varies 1.7 to 2.5
5.5 5.5
14
6.5
0.4
80
50
12.5 11
9 8
0.35 0.35
68 75
110 150
8 6.5
0.03 0.45 0.45
5.5 13 10 35 18 12 7
5 4 2
10 8 6 9.6
4 3 2 4.1
70 75 90 4 6 5 44
500 2 40 600
Properties of metals vary widely as a result of variations in composition, heat treatment, and mechanical working. For ductile metals the compression strength is generally assumed to be equal to the tension strength. 3 Offset of 0.2 percent. 4 Timber properties are for loading parallel to the grain. 5 See also Marks’ Mechanical Engineering Handbook, 10th ed., McGraw-Hill, New York, 1996; Annual Book of ASTM, American Society for Testing Materials, Philadelphia, Pa.; Metals Handbook, American Society for Metals, Metals Park, Ohio; and Aluminum Design Manual, The Aluminum Association, Washington, DC. 2
APPENDIX B Typical Properties of Selected Materials Used in Engineering 1,5 (SI Units) Continued from page A14 Ultimate Strength
Material
Modulus of Rigidity, GPa
Magnesium Alloys Alloy AZ80 (Forging) Alloy AZ31 (Extrusion)
1800 1770
345 255
16 16
Titanium Alloy (6% Al, 4% V)
4730
Monel Alloy 400(Ni-Cu) Cold-worked Annealed Cupronickel (90% Cu, 10% Ni) Annealed Cold-worked Timber, air dry Douglas fir Spruce, Sitka Shortleaf pine Western white pine Ponderosa pine White oak Red oak Western hemlock Shagbark hickory Redwood Concrete Medium strength High strength Plastics Nylon, type 6/6, (molding compound) Polycarbonate Polyester, PBT (thermoplastic) Polyester elastomer Polystyrene Vinyl, rigid PVC Rubber Granite (Avg. values) Marble (Avg. values) Sandstone (Avg. values) Glass, 98% silica 1
Yield Strength3
Modulus Compresof Density Tension, sion,2 Shear, Tension, Shear, Elasticity, kg/m3 MPa MPa MPa MPa MPa GPa 250 200
45 45
900
830
8830 8830
675 550
585 220
8940 8940
365 585
110 545
470 415 500 390 415 690 660 440 720 415
100 60 55 90 65
2320 2320
160 130
50 39 50 34 36 51 47 50 63 42
A15
7.6 7.6 9.7 7.0 7.6 13.8 12.4 10.0 16.5 6.2
345 125
Ductility, Percent Elongation in 50 mm
25.2 25.2
6 12
115
9.5
10
180 180
13.9 13.9
22 46
17.1 17.1
35 3
140 140 13 10 12 10 9 12 12 11 15 9
28 40
Coefficient of Thermal Expansion, 1026/8C
52 52 0.7 0.5
25 30
Varies 3.0 to 4.5
9.9 9.9
1140
75
95
45
2.8
144
50
1200 1340
65 55
85 75
35 55
2.4 2.4
122 135
110 150
1200 1030 1440 910 2770 2770 2300 2190
45 55 40 15 20 15 7
55 45
0.2 3.1 3.1
40 90 70 240 125 85 50
35 28 14
70 55 40 65
4 3 2 4.1
125 135 162 7.2 10.8 9.0 80
500 2 40 600
Properties of metals very widely as a result of variations in composition, heat treatment, and mechanical working. For ductile metals the compression strength is generally assumed to be equal to the tension strength. 3 Offset of 0.2 percent. 4 Timber properties are for loading parallel to the grain. 5 See also Marks’ Mechanical Engineering Handbook, 10th ed., McGraw-Hill, New York, 1996; Annual Book of ASTM, American Society for Testing Materials, Philadelphia, Pa.; Metals Handbook, American Society of Metals, Metals Park, Ohio; and Aluminum Design Manual, The Aluminum Association, Washington, DC. 2
t f
A16
APPENDIX C Properties of Rolled-Steel Shapes (U.S. Customary Units) W Shapes (Wide-Flange Shapes)
d
Y
X
X t w Y b f
Flange
Designation†
Area A , in2
Depth d , in.
Width b f, in.
Thickness t f, in.
Web Thickness t w, in.
Axis
X-X
Axis
Y-Y
I x , in4
S x , in3
r x , in.
I y , in4
S y , in3
r y , in.
W36
3
302 135
88.8 39.7
37.3 35.6
16.7 12.0
1.68 0.790
0.945 0.600
21100 7800
1130 439
15.4 14.0
1300 225
156 37.7
3.82 2.38
W33
3
201 118
59.2 34.7
33.7 32.9
15.7 11.5
1.15 0.740
0.715 0.550
11600 5900
686 359
14.0 13.0
749 187
95.2 32.6
3.56 2.32
W30
3
173 99
51.0 29.1
30.4 29.7
15.0 10.50
1.07 0.670
0.655 0.520
8230 3990
541 269
12.7 11.7
598 128
79.8 24.5
3.42 2.10
W27
3
146 84
43.1 24.8
27.4 26.70
14.0 10.0
0.975 0.640
0.605 0.460
5660 2850
414 213
11.5 10.7
443 106
63.5 21.2
3.20 2.07
W24
3
104 68
30.6 20.1
24.1 23.7
12.8 8.97
0.750 0.585
0.500 0.415
3100 1830
258 154
10.1 9.55
259 70.4
40.7 15.7
2.91 1.87
W21
3
101 62 44
29.8 18.3 13.0
21.4 21.0 20.7
12.3 8.24 6.50
0.800 0.615 0.450
0.500 0.400 0.350
2420 1330 843
227 127 81.6
9.02 8.54 8.06
248 57.5 20.7
40.3 14.0 6.37
2.89 1.77 1.26
W18
3
106 76 50 35
31.1 22.3 14.7 10.3
18.7 18.2 18.0 17.7
11.2 11.0 7.50 6.00
0.940 0.680 0.570 0.425
0.590 0.425 0.355 0.300
1910 1330 800 510
204 146 88.9 57.6
7.84 7.73 7.38 7.04
220 152 40.1 15.3
39.4 27.6 10.7 5.12
2.66 2.61 1.65 1.22
77 57 40 31 26
22.6 16.8 11.8 9.13 7.68
16.5 16.4 16.0 15.9 15.7
10.3 7.12 7.00 5.53 5.50
0.76 0.715 0.505 0.440 0.345
0.455 0.430 0.305 0.275 0.250
1110 758 518 375 301
134 92.2 64.7 47.2 38.4
7.00 6.72 6.63 6.41 6.26
138 43.1 28.9 12.4 9.59
26.9 12.1 8.25 4.49 3.49
2.47 1.60 1.57 1.17 1.12
370 145 82 68 53 43 38 30 26 22
109 42.7 24.0 20.0 15.6 12.6 11.2 8.85 7.69 6.49
17.9 14.8 14.3 14.0 13.9 13.7 14.1 13.8 13.9 13.7
16.5 15.5 10.1 10.0 8.06 8.00 6.77 6.73 5.03 5.00
2.66 1.09 0.855 0.720 0.660 0.530 0.515 0.385 0.420 0.335
1.66 0.680 0.510 0.415 0.370 0.305 0.310 0.270 0.255 0.230
5440 1710 881 722 541 428 385 291 245 199
607 232 123 103 77.8 62.6 54.6 42.0 35.3 29.0
7.07 6.33 6.05 6.01 5.89 5.82 5.87 5.73 5.65 5.54
1990 241 677 87.3 148 29.3 121 24.2 57.7 14.3 45.2 11.3 26.7 7.88 19.6 5.82 8.91 3.55 7.00 2.80
4.27 3.98 2.48 2.46 1.92 1.89 1.55 1.49 1.08 1.04
W16
W14
3
3
†A wide-flange shape is designated by the letter W followed by the nominal depth in inches and the weight in pounds per foot.
(Table continued on page A17)
t f
APPENDIX C Properties of Rolled-Steel Shapes (SI Units) W Shapes (Wide-Flange Shapes)
d
A17
Y
X
X t w Y b f
Flange
Designation†
Area A , mm2
Depth d , mm
Width b f, mm
Thickness t f, mm
Web Thickness t w, mm
Axis
X-X
Axis
Y-Y
I x S x r x 6 4 3 3 10 mm 10 mm mm
I y S y r y 6 4 3 3 10 mm 10 mm mm
W920
3
449 201
57300 25600
947 904
424 305
42.7 20.1
24.0 15.2
8780 3250
18500 7190
391 356
541 93.7
2560 618
97.0 60.5
W840
3
299 176
38200 22400
856 836
399 292
29.2 18.8
18.2 14.0
4830 2460
11200 5880
356 330
312 77.8
1560 534
90.4 58.9
W760
3
257 147
32900 18800
772 754
381 267
27.2 17.0
16.6 13.2
3430 1660
8870 4410
323 297
249 53.3
1310 401
86.9 53.3
W690
3
217 125
27800 16000
696 678
356 254
24.8 16.3
15.4 11.7
2360 1190
6780 3490
292 272
184 44.1
1040 347
81.3 52.6
W610
3
155 101
19700 13000
612 602
325 228
19.1 14.9
12.7 10.5
1290 762
4230 2520
257 243
108 29.3
667 257
73.9 47.5
W530
3
150 92 66
19200 11800 8390
544 533 526
312 209 165
20.3 15.6 11.4
12.7 10.2 8.89
1010 554 351
3720 2080 1340
229 217 205
103 23.9 8.62
660 229 104
73.4 45.0 32.0
W460
3
158 113 74 52
20100 14400 9480 6650
475 462 457 450
284 279 191 152
23.9 17.3 14.5 10.8
15.0 10.8 9.02 7.62
795 554 333 212
3340 2390 1460 944
199 196 187 179
91.6 63.3 16.7 6.37
646 452 175 83.9
67.6 66.3 41.9 31.0
W410
3
114 14600 85 10800 60 7610 46.1 5890 38.8 4950
419 417 406 404 399
262 181 178 140 140
19.3 18.2 12.8 11.2 8.76
11.6 10.9 7.75 6.99 6.35
462 316 216 156 125
2200 1510 1060 773 629
178 171 168 163 159
57.4 17.9 12.0 5.16 3.99
441 198 135 73.6 57.2
62.7 40.6 39.9 29.7 28.4
W360
3
551 216 122 101 79 64 57.8 44 39 32.9
455 376 363 356 353 348 358 351 353 348
419 394 257 254 205 203 172 171 128 127
67.6 27.7 21.7 18.3 16.8 13.5 13.1 9.78 10.7 8.51
42.2 17.3 13.0 10.5 9.40 7.75 7.87 6.86 6.48 5.84
2260 712 367 301 225 178 160 121 102 82.8
9950 3800 2020 1690 1270 1030 895 688 578 475
180 161 154 153 150 148 149 146 144 141
828 282 61.6 50.4 24.0 18.8 11.1 8.16 3.71 2.91
3950 1430 480 397 234 185 129 95.4 58.2 45.9
108 101 63.0 62.5 48.8 48.0 39.4 37.8 27.4 26.4
70300 27500 15500 12900 10100 8130 7230 5710 4960 4190
†A wide-flange shape is designated by the letter W followed by the nominal depth in millimeters and the mass in kilograms per meter.
(Table continued on page A18)
t f
A18
APPENDIX C Properties of Rolled-Steel Shapes (U.S. Customary Units) Continued from page A17 W Shapes (Wide-Flange Shapes)
d
Y
X
X t w Y b f
Flange
Designation†
Area A , in2
Depth d , in.
Width b f, in.
Thickness t f, in.
Web Thickness t w, in.
Axis X-X
Axis Y-Y
I x , in4
S x , in3
r x , in.
I y , in4
S y , in3
r y , in.
W12
3
96 72 50 40 35 30 26 22 16
28.2 21.1 14.6 11.7 10.3 8.79 7.65 6.48 4.71
12.7 12.3 12.2 11.9 12.5 12.3 12.2 12.3 12.0
12.2 12.0 8.08 8.01 6.56 6.52 6.49 4.03 3.99
0.900 0.670 0.640 0.515 0.520 0.440 0.380 0.425 0.265
0.550 0.430 0.370 0.295 0.300 0.260 0.230 0.260 0.220
833 597 391 307 285 238 204 156 103
131 97.4 64.2 51.5 45.6 38.6 33.4 25.4 17.1
5.44 5.31 5.18 5.13 5.25 5.21 5.17 4.91 4.67
270 195 56.3 44.1 24.5 20.3 17.3 4.66 2.82
44.4 32.4 13.9 11.0 7.47 6.24 5.34 2.31 1.41
3.09 3.04 1.96 1.94 1.54 1.52 1.51 0.848 0.773
W10
3
112 68 54 45 39 33 30 22 19 15
32.9 20.0 15.8 13.3 11.5 9.71 8.84 6.49 5.62 4.41
11.4 10.4 10.1 10.1 9.92 9.73 10.5 10.2 10.2 10.0
10.4 10.1 10.0 8.02 7.99 7.96 5.81 5.75 4.02 4.00
1.25 0.770 0.615 0.620 0.530 0.435 0.510 0.360 0.395 0.270
0.755 0.470 0.370 0.350 0.315 0.290 0.300 0.240 0.250 0.230
716 394 303 248 209 171 170 118 96.3 68.9
126 75.7 60.0 49.1 42.1 35.0 32.4 23.2 18.8 13.8
4.66 4.44 4.37 4.32 4.27 4.19 4.38 4.27 4.14 3.95
236 134 103 53.4 45.0 36.6 16.7 11.4 4.29 2.89
45.3 26.4 20.6 13.3 11.3 9.20 5.75 3.97 2.14 1.45
2.68 2.59 2.56 2.01 1.98 1.94 1.37 1.33 0.874 0.810
W8
3
58 48 40 35 31 28 24 21 18 15 13
17.1 14.1 11.7 10.3 9.12 8.24 7.08 6.16 5.26 4.44 3.84
8.75 8.50 8.25 8.12 8.00 8.06 7.93 8.28 8.14 8.11 7.99
8.22 8.11 8.07 8.02 8.00 6.54 6.50 5.27 5.25 4.01 4.00
0.810 0.685 0.560 0.495 0.435 0.465 0.400 0.400 0.330 0.315 0.255
0.510 0.400 0.360 0.310 0.285 0.285 0.245 0.250 0.230 0.245 0.230
228 184 146 127 110 98.0 82.7 75.3 61.9 48.0 39.6
52.0 43.2 35.5 31.2 27.5 24.3 20.9 18.2 15.2 11.8 9.91
3.65 3.61 3.53 3.51 3.47 3.45 3.42 3.49 3.43 3.29 3.21
75.1 60.9 49.1 42.6 37.1 21.7 18.3 9.77 7.97 3.41 2.73
18.3 15.0 12.2 10.6 9.27 6.63 5.63 3.71 3.04 1.70 1.37
2.10 2.08 2.04 2.03 2.02 1.62 1.61 1.26 1.23 0.876 0.843
W6
3
25 20 16 12 9
7.34 5.87 4.74 3.55 2.68
6.38 6.20 6.28 6.03 5.90
6.08 6.02 4.03 4.00 3.94
0.455 0.365 0.405 0.280 0.215
0.320 0.260 0.260 0.230 0.170
53.4 41.4 32.1 22.1 16.4
16.7 13.4 10.2 7.31 5.56
2.70 2.66 2.60 2.49 2.47
17.1 13.3 4.43 2.99 2.20
5.61 4.41 2.20 1.50 1.11
1.52 1.50 0.967 0.918 0.905
W5
3
19 16
5.56 4.71
5.15 5.01
5.03 5.00
0.430 0.360
0.270 0.240
26.3 21.4
10.2 8.55
2.17 2.13
9.13 7.51
3.63 3.00
1.28 1.26
W4
3
13
3.83
4.16
4.06
0.345
0.280
11.3
5.46
1.72
3.86
1.90
1.00
†A wide-flange shape is designated by the letter W followed by the nominal depth in inches and the weight in pounds per foot.
t f
APPENDIX C Properties of Rolled-Steel Shapes (SI Units) Continued from page A18 W Shapes (Wide-Flange Shapes)
d
A19
Y
X
X t w Y b f
Flange
Designation†
Area Depth 2 A , mm d , mm
Width b f, mm
Thickness t f, mm
Web Thickness t w, mm
Axis X-X
Axis Y-Y
I x S x r x 6 4 3 3 10 mm 10 mm mm
I y S y r y 6 4 3 3 10 mm 10 mm mm
W310
3
143 107 74 60 52 44.5 38.7 32.7 23.8
18200 13600 9420 7550 6650 5670 4940 4180 3040
323 312 310 302 318 312 310 312 305
310 305 205 203 167 166 165 102 101
22.9 17.0 16.3 13.1 13.2 11.2 9.65 10.8 6.73
14.0 10.9 9.40 7.49 7.62 6.60 5.84 6.60 5.59
347 248 163 128 119 99.1 84.9 64.9 42.9
2150 1600 1050 844 747 633 547 416 280
138 135 132 130 133 132 131 125 119
112 81.2 23.4 18.4 10.2 8.45 7.20 1.94 1.17
728 531 228 180 122 102 87.5 37.9 23.1
78.5 77.2 49.8 49.3 39.1 38.6 38.4 21.5 19.6
W250
3
167 101 80 67 58 49.1 44.8 32.7 28.4 22.3
21200 12900 10200 8580 7420 6260 5700 4190 3630 2850
290 264 257 257 252 247 267 259 259 254
264 257 254 204 203 202 148 146 102 102
31.8 19.6 15.6 15.7 13.5 11.0 13.0 9.14 10.0 6.86
19.2 11.9 9.4 8.89 8.00 7.37 7.62 6.10 6.35 5.84
298 164 126 103 87.0 71.2 70.8 49.1 40.1 28.7
2060 1240 983 805 690 574 531 380 308 226
118 113 111 110 108 106 111 108 105 100
98.2 55.8 42.9 22.2 18.7 15.2 6.95 4.75 1.79 1.20
742 433 338 218 185 151 94.2 65.1 35.1 23.8
68.1 65.8 65.0 51.1 50.3 49.3 34.8 33.8 22.2 20.6
31.3 25.3 20.4 17.7 15.4 9.03 7.62 4.07 3.32 1.42 1.14
300 246 200 174 152 109 92.3 60.8 49.8 27.9 22.5
53.3 52.8 51.8 51.6 51.3 41.1 40.9 32.0 31.2 22.3 21.4
W200
3
86 71 59 52 46.1 41.7 35.9 31.3 26.6 22.5 19.3
11000 9100 7550 6650 5880 5320 4570 3970 3390 2860 2480
222 216 210 206 203 205 201 210 207 206 203
209 206 205 204 203 166 165 134 133 102 102
20.6 17.4 14.2 12.6 11.0 11.8 10.2 10.2 8.38 8.00 6.48
13.0 10.2 9.14 7.87 7.24 7.24 6.22 6.35 5.84 6.22 5.84
94.9 76.6 60.8 52.9 45.8 40.8 34.4 31.3 25.8 20.0 16.5
852 708 582 511 451 398 342 298 249 193 162
92.7 91.7 89.7 89.2 88.1 87.6 86.9 88.6 87.1 83.6 81.5
W150
3
37.1 29.8 24 18 13.5
4740 3790 3060 2290 1730
162 157 160 153 150
154 153 102 102 100
11.6 9.27 10.3 7.11 5.46
8.13 6.60 6.60 5.84 4.32
22.2 17.2 13.4 9.20 6.83
274 220 167 120 91.1
68.6 67.6 66.0 63.2 62.7
7.12 5.54 1.84 1.24 0.916
91.9 72.3 36.1 24.6 18.2
38.6 38.1 24.6 23.3 23.0
W130
3
28.1 23.8
3590 3040
131 127
128 127
10.9 9.14
6.86 6.10
10.9 8.91
167 140
55.1 54.1
3.80 3.13
59.5 49.2
32.5 32.0
W100
3
19.3
2470
106
103
8.76
7.11
4.70
43.7
1.61
31.1
25.4
89.5
†A wide-flange shape is designated by the letter W followed by the nominal depth in millimeters and the mass in kilograms per meter.
t f
A20
APPENDIX C Properties of Rolled-Steel Shapes (U.S. Customary Units) S Shapes (American Standard Shapes)
d
Y
X
X t w Y b f
Flange
3
I x , in4
S x , in3
r x , in.
I y , in4
S y , in3
r y , in.
Axis X-X
Axis Y-Y
Area A , in2
Depth d , in.
Width b f, in.
121 106 100 90 80
35.5 31.1 29.3 26.5 23.5
24.5 24.5 24.0 24.0 24.0
8.05 7.87 7.25 7.13 7.00
1.09 1.09 0.870 0.870 0.870
0.800 0.620 0.745 0.625 0.500
3160 2940 2380 2250 2100
258 240 199 187 175
9.43 9.71 9.01 9.21 9.47
83.0 76.8 47.4 44.7 42.0
20.6 19.5 13.1 12.5 12.0
1.53 1.57 1.27 1.30 1.34
165 155 128 119
7.71 7.89 7.62 7.83
49.9 46.6 29.5 27.5
13.9 13.2 9.25 8.78
1.33 1.36 1.16 1.19
Designation† S24
Web Thickness t w, in.
Thickness t f, in.
S20
3
96 86 75 66
28.2 25.3 22.0 19.4
20.3 20.3 20.0 20.0
7.20 7.06 6.39 6.26
0.920 0.920 0.795 0.795
0.800 0.660 0.635 0.505
1670 1570 1280 1190
S18
3
70 54.7
20.5 16.0
18.0 18.0
6.25 6.00
0.691 0.691
0.711 0.461
923 801
103 89.0
6.70 7.07
24.0 20.7
7.69 6.91
1.08 1.14
S15
3
50 42.9
14.7 12.6
15.0 15.0
5.64 5.50
0.622 0.622
0.550 0.411
485 446
64.7 59.4
5.75 5.95
15.6 14.3
5.53 5.19
1.03 1.06
S12
3
50 40.8 35 31.8
14.6 11.9 10.2 9.31
12.0 12.0 12.0 12.0
5.48 5.25 5.08 5.00
0.659 0.659 0.544 0.544
0.687 0.462 0.428 0.350
303 270 228 217
50.6 45.1 38.1 36.2
4.55 4.76 4.72 4.83
15.6 13.5 9.84 9.33
5.69 5.13 3.88 3.73
1.03 1.06 0.980 1.00
S10
3
35 25.4
10.3 7.45
10.0 10.0
4.94 4.66
0.491 0.491
0.594 0.311
147 123
29.4 24.6
3.78 4.07
8.30 6.73
3.36 2.89
0.899 0.950
S8
3
23 18.4
6.76 5.40
8.00 8.00
4.17 4.00
0.425 0.425
0.441 0.271
64.7 57.5
16.2 14.4
3.09 3.26
4.27 3.69
2.05 1.84
0.795 0.827
S6
3
17.2 12.5
5.06 3.66
6.00 6.00
3.57 3.33
0.359 0.359
0.465 0.232
26.2 22.0
8.74 7.34
2.28 2.45
2.29 1.80
1.28 1.08
0.673 0.702
S5
3
10
2.93
5.00
3.00
0.326
0.214
12.3
4.90
2.05
1.19
0.795
0.638
S4
3
9.5 7.7
2.79 2.26
4.00 4.00
2.80 2.66
0.293 0.293
0.326 0.193
6.76 6.05
3.38 3.03
1.56 1.64
0.887 0.748
0.635 0.562
0.564 0.576
S3
3
7.5 5.7
2.20 1.66
3.00 3.00
2.51 2.33
0.260 0.260
0.349 0.170
2.91 2.50
1.94 1.67
1.15 1.23
0.578 0.447
0.461 0.383
0.513 0.518
†An American Standard Beam is designated by the letter S followed by the nominal depth in inches and the weight in pounds per foot.
t f
APPENDIX C Properties of Rolled-Steel Shapes (SI Units) S Shapes (American Standard Shapes)
d
A21
Y
X
X t w Y b f
Flange
Designation†
Area A , mm2
Depth d , mm
Width b f, mm
Thickness t f, mm
Web Thickness t w, mm
Axis X-X
Axis Y-Y
I x S x 6 4 10 mm 103 mm3
r x mm
I y S y r y 6 4 3 3 10 mm 10 mm mm
S610
3
180 158 149 134 119
22900 20100 18900 17100 15200
622 622 610 610 610
204 200 184 181 178
27.7 27.7 22.1 22.1 22.1
20.3 15.7 18.9 15.9 12.7
1320 1220 991 937 874
4230 3930 3260 3060 2870
240 247 229 234 241
34.5 32.0 19.7 18.6 17.5
338 320 215 205 197
38.9 39.9 32.3 33.0 34.0
S510
3
143 128 112 98.2
18200 16300 14200 12500
516 516 508 508
183 179 162 159
23.4 23.4 20.2 20.2
20.3 16.8 16.1 12.8
695 653 533 495
2700 2540 2100 1950
196 200 194 199
20.8 19.4 12.3 11.4
228 216 152 144
33.8 34.5 29.5 30.2
S460
3
104 81.4
13200 10300
457 457
159 152
17.6 17.6
18.1 11.7
384 333
1690 1460
170 180
10.0 8.62
126 113
27.4 29.0
74 64
9480 8130
381 381
143 140
15.8 15.8
14.0 10.4
202 186
1060 973
146 151
6.49 5.95
90.6 85.0
26.2 26.9
74 60.7 52 47.3
9420 7680 6580 6010
305 305 305 305
139 133 129 127
16.7 16.7 13.8 13.8
17.4 11.7 10.9 8.89
126 112 94.9 90.3
829 739 624 593
116 121 120 123
6.49 5.62 4.10 3.88
93.2 84.1 63.6 61.1
26.2 26.9 24.9 25.4
52 37.8
6650 4810
254 254
125 118
12.5 12.5
15.1 7.90
61.2 51.2
482 403
96.0 103
3.45 2.80
55.1 47.4
22.8 24.1
34 27.4
4360 3480
203 203
106 102
10.8 10.8
11.2 6.88
26.9 23.9
265 236
78.5 82.8
1.78 1.54
33.6 30.2
20.2 21.0
25.7 18.6
3260 2360
152 152
90.7 84.6
9.12 9.12
11.8 5.89
10.9 9.16
143 120
57.9 62.2
0.953 0.749
21.0 17.7
17.1 17.8
15
1890
127
76.2
8.28
5.44
5.12
80.3
52.1
0.495
13.0
16.2
102 102
71.1 67.6
7.44 7.44
8.28 4.90
2.81 2.52
55.4 49.7
39.6 41.7
0.369 0.311
10.4 9.21
14.3 14.6
63.8 59.2
6.60 6.60
8.86 4.32
1.21 1.04
31.8 27.4
29.2 31.2
0.241 0.186
7.55 6.28
13.0 13.2
S380
3
S310
3
S250
3
S200
3
S150
3
S130
3
S100
3
14.1 11.5
1800 1460
S75
3
11.2 8.5
1420 1070
76.2 76.2
†An American Standard Beam is designated by the letter S followed by the nominal depth in millimeters and the mass in kilograms per meter.
A22
t f
Y
APPENDIX C Properties of Rolled-Steel Shapes (U.S. Customary Units) C Shapes (American Standard Channels)
t w X
X
d
x Y b f
Flange
Designation†
Area A , in2
Depth d , in.
Width b f, in.
Thickness t f, in.
Web Thickness t w, in.
14.7 11.8 10.0
15.0 15.0 15.0
3.72 3.52 3.40
0.650 0.650 0.650
0.716 0.520 0.400
404 348 315
53.8 46.5 42.0
5.24 5.45 5.62
11.0 9.17 8.07
3.77 3.34 3.09
0.865 0.883 0.901
0.799 0.778 0.788
Axis X-X
Axis Y-Y
I x , in4
S x , in3 r x , in.
I y , in4
S y , in3 r y , in. x , in.
C15
3
50 40 33.9
C12
3
30 25 20.7
8.81 7.34 6.08
12.0 12.0 12.0
3.17 3.05 2.94
0.501 0.501 0.501
0.510 0.387 0.282
162 144 129
27.0 24.0 21.5
4.29 4.43 4.61
5.12 4.45 3.86
2.05 1.87 1.72
0.762 0.779 0.797
0.674 0.674 0.698
C10
3
30 25 20 15.3
8.81 7.34 5.87 4.48
10.0 10.0 10.0 10.0
3.03 2.89 2.74 2.60
0.436 0.436 0.436 0.436
0.673 0.526 0.379 0.240
103 91.1 78.9 67.3
20.7 18.2 15.8 13.5
3.42 3.52 3.66 3.87
3.93 3.34 2.80 2.27
1.65 1.47 1.31 1.15
0.668 0.675 0.690 0.711
0.649 0.617 0.606 0.634
C9
3
20 15 13.4
5.87 4.41 3.94
9.00 9.00 9.00
2.65 2.49 2.43
0.413 0.413 0.413
0.448 0.285 0.233
60.9 51.0 47.8
13.5 11.3 10.6
3.22 3.40 3.49
2.41 1.91 1.75
1.17 1.01 0.954
0.640 0.659 0.666
0.583 0.586 0.601
C8
3
18.7 13.7 11.5
5.51 4.04 3.37
8.00 8.00 8.00
2.53 2.34 2.26
0.390 0.390 0.390
0.487 0.303 0.220
43.9 36.1 32.5
11.0 9.02 8.14
2.82 2.99 3.11
1.97 1.52 1.31
1.01 0.848 0.775
0.598 0.613 0.623
0.565 0.554 0.572
C7
3
12.2 9.8
3.60 2.87
7.00 7.00
2.19 2.09
0.366 0.366
0.314 0.210
24.2 21.2
6.92 6.07
2.60 2.72
1.16 0.957
0.696 0.617
0.568 0.578
0.525 0.541
C6
3
13 10.5 8.2
3.81 3.08 2.39
6.00 6.00 6.00
2.16 2.03 1.92
0.343 0.343 0.343
0.437 0.314 0.200
17.3 15.1 13.1
5.78 5.04 4.35
2.13 2.22 2.34
1.05 0.860 0.687
0.638 0.561 0.488
0.524 0.529 0.536
0.514 0.500 0.512
C5
3
9 6.7
2.64 1.97
5.00 5.00
1.89 1.75
0.320 0.320
0.325 0.190
8.89 7.48
3.56 2.99
1.83 1.95
0.624 0.470
0.444 0.372
0.486 0.489
0.478 0.484
C4
3
7.2 5.4
2.13 1.58
4.00 4.00
1.72 1.58
0.296 0.296
0.321 0.184
4.58 3.85
2.29 1.92
1.47 1.56
0.425 0.312
0.337 0.277
0.447 0.444
0.459 0.457
C3
3
6 5 4.1
1.76 1.47 1.20
3.00 3.00 3.00
1.60 1.50 1.41
0.273 0.273 0.273
0.356 0.258 0.170
2.07 1.85 1.65
1.38 1.23 1.10
1.08 1.12 1.17
0.300 0.241 0.191
0.263 0.228 0.196
0.413 0.405 0.398
0.455 0.439 0.437
†An American Standard Channel is designated by the letter C followed by the nominal depth in inches and the weight in pounds per foot.
t f
Y
APPENDIX C Properties of Rolled-Steel Shapes (SI Units) C Shapes (American Standard Channels)
Designation†
Y b f
Area Depth Width 2 A , mm d , mm b f, mm
Axis X-X
Axis Y-Y
Thickness t f, mm
Web Thickness t w, mm
I x S x r x 6 4 3 3 10 mm 10 mm mm
I y S y r y x 6 4 3 3 10 mm 10 mm mm mm
168 145 131
3
74 60 50.4
9480 7610 6450
381 381 381
94.5 89.4 86.4
16.5 16.5 16.5
18.2 13.2 10.2
C310
3
45 37 30.8
5680 4740 3920
305 305 305
80.5 77.5 74.7
12.7 12.7 12.7
13.0 9.83 7.16
C250
3
45 37 30 22.8
5680 4740 3790 2890
254 254 254 254
77.0 73.4 69.6 66.0
11.1 11.1 11.1 11.1
C230
3
30 22 19.9
3790 2850 2540
229 229 229
67.3 63.2 61.7
10.5 10.5 10.5
C200
3
27.9 20.5 17.1
3550 2610 2170
203 203 203
64.3 59.4 57.4
C180
3
18.2 14.6
2320 1850
178 178
C150
3
19.3 15.6 12.2
2460 1990 1540
C130
3
13 10.4
C100
3
C75
d
Flange
C380
t w X x
X
A23
882 762 688
133 138 143
4.58 3.82 3.36
61.8 54.7 50.6
22.0 22.4 22.9
20.3 19.8 20.0
67.4 59.9 53.7
442 393 352
109 113 117
2.13 1.85 1.61
33.6 30.6 28.2
19.4 19.8 20.2
17.1 17.1 17.7
17.1 13.4 9.63 6.10
42.9 37.9 32.8 28.0
339 298 259 221
86.9 89.4 93.0 98.3
1.64 1.39 1.17 0.945
27.0 24.1 21.5 18.8
17.0 17.1 17.5 18.1
16.5 15.7 15.4 16.1
11.4 7.24 5.92
25.3 21.2 19.9
221 185 174
81.8 86.4 88.6
1.00 0.795 0.728
19.2 16.6 15.6
16.3 16.7 16.9
14.8 14.9 15.3
9.91 9.91 9.91
12.4 7.70 5.59
18.3 15.0 13.5
180 148 133
71.6 75.9 79.0
0.820 0.633 0.545
16.6 13.9 12.7
15.2 15.6 15.8
14.4 14.1 14.5
55.6 53.1
9.30 9.30
7.98 5.33
10.1 8.82
113 100
66.0 69.1
0.483 0.398
11.4 10.1
14.4 14.7
13.3 13.7
152 152 152
54.9 51.6 48.8
8.71 8.71 8.71
11.1 7.98 5.08
7.20 6.29 5.45
94.7 82.6 71.3
54.1 56.4 59.4
0.437 0.358 0.286
10.5 9.19 8.00
13.3 13.4 13.6
13.1 12.7 13.0
1700 1270
127 127
48.0 44.5
8.13 8.13
8.26 4.83
3.70 3.11
58.3 49.0
46.5 49.5
0.260 0.196
7.28 6.10
12.3 12.4
12.1 12.3
10.8 8
1370 1020
102 102
43.7 40.1
7.52 7.52
8.15 4.67
1.91 1.60
37.5 31.5
37.3 39.6
0.177 0.130
5.52 4.54
11.4 11.3
11.7 11.6
8.9 7.4 6.1
1140 948 774
40.6 38.1 35.8
6.93 6.93 6.93
9.04 6.55 4.32
0.862 0.770 0.687
22.6 20.2 18.0
27.4 28.4 29.7
0.125 0.100 0.0795
4.31 3.74 3.21
10.5 10.3 10.1
11.6 11.2 11.1
3
76.2 76.2 76.2
†An American Standard Channel is designated by the letter C followed by the nominal depth in millimeters and the mass in kilograms per meter.
A24
Y x Z
APPENDIX C Properties of Rolled-Steel Shapes (U.S. Customary Units) Angles Equal Legs
X
X y Y
Z
Axis X-X and Axis Y-Y Weight per Foot, lb/ft
Area, in2
I , in4
S , in3
r , in.
1 ⁄ 4 1 ⁄ 2
51.0 38.9 26.4
15.0 11.4 7.75
89.1 69.9 48.8
15.8 12.2 8.36
2.43 2.46 2.49
2.36 2.26 2.17
1.56 1.57 1.59
Size and Thickness, in. L8
3
8
3
Axis Z-Z r z , in.
3
x or y , in.
L6
3
6
3
1 3 4 ⁄ 5 ⁄ 8 1 2 ⁄ 3 ⁄ 8
37.4 28.7 24.2 19.6 14.9
11.0 8.46 7.13 5.77 4.38
35.4 28.1 24.1 19.9 15.4
8.55 6.64 5.64 4.59 3.51
1.79 1.82 1.84 1.86 1.87
1.86 1.77 1.72 1.67 1.62
1.17 1.17 1.17 1.18 1.19
L5
3
5
3
3 4 ⁄ 5 ⁄ 8 1 2 ⁄ 3 ⁄ 8
23.6 20.0 16.2 12.3
6.94 5.86 4.75 3.61
15.7 13.6 11.3 8.76
4.52 3.85 3.15 2.41
1.50 1.52 1.53 1.55
1.52 1.47 1.42 1.37
0.972 0.975 0.980 0.986
L4
3
4
3
3 4 ⁄ 5 ⁄ 8 1 2 ⁄ 3 ⁄ 8 1 ⁄ 4
18.5 15.7 12.8 9.80 6.60
5.44 4.61 3.75 2.86 1.94
7.62 6.62 5.52 4.32 3.00
2.79 2.38 1.96 1.50 1.03
1.18 1.20 1.21 1.23 1.25
1.27 1.22 1.18 1.13 1.08
0.774 0.774 0.776 0.779 0.783
312
3
1 2 ⁄ 3 8 ⁄ 1 ⁄ 4
11.1 8.50 5.80
3.25 2.48 1.69
3.63 2.86 2.00
1.48 1.15 0.787
1.05 1.07 1.09
1.05 1.00 0.954
0.679 0.683 0.688
3
3
1 ⁄ 2 3 ⁄ 8 1 ⁄ 4
9.40 7.20 4.90
2.75 2.11 1.44
2.20 1.75 1.23
1.06 0.825 0.569
0.895 0.910 0.926
0.929 0.884 0.836
0.580 0.581 0.585
212
3
½ 3 8 ⁄ 1 ⁄ 4 3 ⁄ 16
7.70 5.90 4.10 3.07
2.25 1.73 1.19 0.900
1.22 0.972 0.692 0.535
0.716 0.558 0.387 0.295
0.735 0.749 0.764 0.771
0.803 0.758 0.711 0.687
0.481 0.481 0.482 0.482
2
3
3 8 ⁄ ⁄ 4 1 ⁄ 8
4.70 3.19 1.65
1.36 0.938 0.484
0.476 0.346 0.189
0.348 0.244 0.129
0.591 0.605 0.620
0.632 0.586 0.534
0.386 0.387 0.391
L312
3
L3
L212
3
3
L2
3
1
A25
Y x Z
APPENDIX C Properties of Rolled-Steel Shapes (SI Units) Angles Equal Legs
X
X y Y
Z
Axis X-X
Size and Thickness, mm L203
3
L152
3
Mass per Meter, kg/m
Area, mm
I 106 mm4
S 103 mm3
r mm
x or y mm
Axis Z-Z r z mm
2
203
3
25.4 19 12.7
75.9 57.9 39.3
9680 7350 5000
37.1 29.1 20.3
259 200 137
61.7 62.5 63.2
59.9 57.4 55.1
39.6 39.9 40.4
152
3
25.4 19 15.9 12.7 9.5
55.7 42.7 36.0 29.2 22.2
7100 5460 4600 3720 2830
14.7 11.7 10.0 8.28 6.41
140 109 92.4 75.2 57.5
45.5 46.2 46.7 47.2 47.5
47.2 45.0 43.7 42.4 41.1
29.7 29.7 29.7 30.0 30.2
19 15.9 12.7 9.5
35.1 29.8 24.1 18.3
4480 3780 3060 2330
6.53 5.66 4.70 3.65
74.1 63.1 51.6 39.5
38.1 38.6 38.9 39.4
38.6 37.3 36.1 34.8
24.7 24.8 24.9 25.0
19 15.9 12.7 9.5 6.4
27.5 23.4 19.0 14.6 9.80
3510 2970 2420 1850 1250
3.17 2.76 2.30 1.80 1.25
45.7 39.0 32.1 24.6 16.9
30.0 30.5 30.7 31.2 31.8
32.3 31.0 30.0 28.7 27.4
19.7 19.7 19.7 19.8 19.9
L127
3
127
3
L102
3
102
3
L89
3
89
3
12.7 9.5 6.4
16.5 12.6 8.60
2100 1600 1090
1.51 1.19 0.832
24.3 18.8 12.9
26.7 27.2 27.7
26.7 25.4 24.2
17.2 17.3 17.5
L76
3
76
3
12.7 9.5 6.4
14.0 10.7 7.30
1770 1360 929
0.916 0.728 0.512
17.4 13.5 9.32
22.7 23.1 23.5
23.6 22.5 21.2
14.7 14.8 14.9
L64
3
64
3
12.7 9.5 6.4 4.8
11.4 8.70 6.10 4.60
1450 1120 768 581
0.508 0.405 0.288 0.223
11.7 9.14 6.34 4.83
18.7 19.0 19.4 19.6
20.4 19.3 18.1 17.4
12.2 12.2 12.2 12.2
9.5 6.4 3.2
7.00 4.70 2.40
877 605 312
0.198 0.144 0.0787
5.70 4.00 2.11
15.0 15.4 15.7
16.1 14.9 13.6
L51
3
51
3
9.80 9.83 9.93
A26
Y x Z
APPENDIX C Properties of Rolled-Steel Shapes (U.S. Customary Units) Angles Unequal Legs
X
y
X
Y
Size and Weight per Thickness, in. Foot, lb/ft Area, in2 L8
3
6
3
Axis X-X
Z
Axis Y-Y
Axis Z-Z
I x , in4
S x , in3
r x , in. y , in.
I y , in4
S y , in3 r y , in. x , in. r z , in. tan
38.8 30.8 21.7
8.92 6.92 4.79
1.72 1.75 1.79
1.65 1.56 1.46
1.28 1.29 1.30
0.542 0.550 0.557
a
1 ⁄ 4 1 2 ⁄
44.2 33.8 23.0
13.0 9.94 6.75
80.9 63.5 44.4
15.1 11.7 8.01
2.49 2.52 2.55
2.65 2.55 2.46
24.5 17.3 13.4
6.23 4.31 3.30
1.88 1.91 1.93
2.07 1.98 1.93
8.63 6.22 4.86
2.95 2.06 1.58
1.12 1.14 1.16
1.07 0.981 0.933
0.856 0.864 0.870
0.428 0.440 0.446
3
L6
3
4
3
3 4 ⁄ 1 ⁄ 2 3 8 ⁄
23.6 16.2 12.3
6.94 4.75 3.61
L5
3
3
3
1 2 ⁄ 3 8 ⁄ 1 ⁄ 4
12.8 9.80 6.60
3.75 2.86 1.94
9.43 7.35 5.09
2.89 2.22 1.51
1.58 1.60 1.62
1.74 1.69 1.64
2.55 2.01 1.41
1.13 0.874 0.600
0.824 0.838 0.853
0.746 0.698 0.648
0.642 0.646 0.652
0.357 0.364 0.371
L4
3
3
3
1 ⁄ 2 3 ⁄ 8 1 4 ⁄
11.1 8.50 5.80
3.25 2.48 1.69
5.02 3.94 2.75
1.87 1.44 0.988
1.24 1.26 1.27
1.32 1.27 1.22
2.40 1.89 1.33
1.10 0.851 0.585
0.858 0.873 0.887
0.822 0.775 0.725
0.633 0.636 0.639
0.542 0.551 0.558
212
3
1
⁄ 2 3 8 ⁄ 1 4 ⁄
9.40 7.20 4.90
2.75 2.11 1.44
3.24 2.56 1.81
1.41 1.09 0.753
1.08 1.10 1.12
1.20 1.15 1.10
1.36 0.756 1.09 0.589 0.775 0.410
0.701 0.716 0.731
0.701 0.655 0.607
0.532 0.535 0.541
0.485 0.495 0.504
L312
3
L3
3
2
3
1
⁄ 2 3 8 ⁄ 1 ⁄ 4
7.70 5.90 4.10
2.25 1.73 1.19
1.92 1.54 1.09
1.00 0.779 0.541
0.922 0.937 0.953
1.08 1.03 0.980
0.667 0.470 0.539 0.368 0.390 0.258
0.543 0.555 0.569
0.580 0.535 0.487
0.425 0.426 0.431
0.413 0.426 0.437
L212
3
2
3
3 8 ⁄ 1 4 ⁄
5.30 3.62
1.55 1.06
0.914 0.656
0.546 0.381
0.766 0.782
0.826 0.779
0.513 0.361 0.372 0.253
0.574 0.589
0.578 0.532
0.419 0.423
0.612 0.624
A27
Y x Z
APPENDIX C Properties of Rolled-Steel Shapes (SI Units) Angles Unequal Legs
X
y
X
Y
Axis X-X
Size and Thickness, mm
Z
Axis Y-Y
Axis Z-Z
Mass per Meter kg/m
Area mm2
I x S x r x y 6 4 3 3 10 mm 10 mm mm mm
I y S y r y x 6 4 3 3 10 mm 10 mm mm mm
r z mm
tan
L203 3 152 3 25.4 19 12.7
65.5 50.1 34.1
8390 6410 4350
33.7 26.4 18.5
247 192 131
63.2 67.3 64.0 64.8 64.8 62.5
16.1 12.8 9.03
146 113 78.5
43.7 41.9 44.5 39.6 45.5 37.1
32.5 32.8 33.0
0.542 0.550 0.557
L152
19 12.7 9.5
35.0 24.0 18.2
4480 3060 2330
10.2 7.20 5.58
102 70.6 54.1
47.8 52.6 48.5 50.3 49.0 49.0
3.59 2.59 2.02
48.3 33.8 25.9
28.4 27.2 29.0 24.9 29.5 23.7
21.7 21.9 22.1
0.428 0.440 0.446
102
3
3
a
L127
3
76
3
12.7 9.5 6.4
19.0 14.5 9.80
2420 1850 1250
3.93 3.06 2.12
47.4 36.4 24.7
40.1 44.2 40.6 42.9 41.1 41.7
1.06 0.837 0.587
18.5 14.3 9.83
20.9 18.9 21.3 17.7 21.7 16.5
16.3 16.4 16.6
0.357 0.364 0.371
L102
3
76
3
12.7 9.5 6.4
16.4 12.6 8.60
2100 1600 1090
2.09 1.64 1.14
30.6 23.6 16.2
31.5 33.5 32.0 32.3 32.3 31.0
0.999 0.787 0.554
18.0 13.9 9.59
21.8 20.9 22.2 19.7 22.5 18.4
16.1 16.2 16.2
0.542 0.551 0.558
L89
3
64
3
12.7 9.5 6.4
13.9 10.7 7.30
1770 1360 929
1.35 1.07 0.753
23.1 17.9 12.3
27.4 30.5 27.9 29.2 28.4 27.9
0.566 0.454 0.323
12.4 9.65 6.72
17.8 17.8 18.2 16.6 18.6 15.4
13.5 13.6 13.7
0.485 0.495 0.504
L76
3
51
3
12.7 9.5 6.4
11.5 8.80 6.10
1450 1120 768
0.799 0.641 0.454
16.4 12.8 8.87
23.4 27.4 23.8 26.2 24.2 24.9
0.278 0.224 0.162
7.70 6.03 4.23
13.8 14.7 14.1 13.6 14.5 12.4
10.8 10.8 10.9
0.413 0.426 0.437
9.5 6.4
7.90 5.40
1000 684
0.380 0.273
8.95 6.24
19.5 21.0 19.9 19.8
0.214 0.155
5.92 4.15
14.6 14.7 15.0 13.5
10.6 10.7
0.612 0.624
L64
3
51
3
A28
APPENDIX D Beam Deflections and Slopes Beam and Loading
Maximum Deflection
Elastic Curve
Slope at End
Equation of Elastic Curve
1 P
y
L
O L
PL3 3EI
2
2
wL4 8EI
2
ML2 2 2EI
2
x ymax
2
x ymax
x ymax
PL2 2EI
y 5
wL3 6EI
y 5 2
w 1 x4 2 4 Lx3 1 6 L2 x2 2 24EI
ML EI
y 5 2
M 2 x 2EI
P 3 1 x 2 3 Lx2 2 6EI
2
w
y
L
O L 3
y
L
O L
M
4 1
L
2
y
P
L x
O
6
PL2 16EI
ymax
1
L
L
PL3 2 48EI
For x # 12 L: P 1 4 x3 2 3 L2 x 2 y 5 48EI
2
5 P
a
y
L
b
b
a
A
B
B x ymax
A x m
L
For a . b: Pb 1 L2 2 b2 2 3y2 2
1 B
9 3EIL L2 2 b2 at x m 5 3
Pb 1 L2 2 b2 2 u A 5 2 6EIL Pa 1 L2 2 a2 2 uB 5 1 6EIL
For x
,
a:
Pb 3 x3 2 1 L2 2 b2 2 x 4 6EIL Pa2 b2 5 5 2 x a: y For 3EIL
y 5
6
w
y
L x
O 1
L
L
5 wL4 2 384EI
6
wL3 24EI
y 5 2
w 1 x4 2 2 Lx3 1 L3 x 2 24EI
y 5 2
M 1 x3 2 L2 x 2 6EIL
ymax
2
7 M
A
B
y
L B x
A L
ymax 3
L
1
ML2 9 3EI
ML 6EI ML uB 5 2 3EI u A 5 1
