Steel: Jonathan Ochshorn's Structural Elements text, Third Edition

Table A-4.1: Steel properties¹

Category	ASTM designation		Yield stress, F_y (ksi)	(Ultimate) tensile stress, F_u (ksi)	Preferred for these shapes
Carbon	A36 A500 Gr. B A500 Gr. B A53 Gr. B		36 42 46 ²35	58 58 58 60	M, S, C, MC, L, plates⁴ and bars HSS round⁵ HSS rectangular⁵ Pipe
High-strength, low-alloy	A992 A572 Gr. 50		50 50	65 65	³W HP
Corrosion resistant, high-strength, low-alloy	A588 A242		50 42–50	70 63–70
Low alloy reinforcing bars	A615		40 60 75	60 90 100	Rebar
Bolts	F3125	A325	n/a	120	High-strength bolts, 0.5 – 1.5 in. diameter
	F3125	A490	n/a	150	High-strength bolts, 0.5 – 1.5 in. diameter
	F3043		n/a	200	Check availability for these bolts, 1 – 1.25 in. diameter
	A307 Gr. A		n/a	60	Common bolts
Cold-formed	A653 Gr. 33		33	45	Connector plates⁴ in wood construction

Notes:

1. The modulus of elasticity, E, for these steels can be taken as 29,000 ksi.

2. Steel with F_y = 35 ksi may be designed as if the yield stress is F_y = 36 ksi.

3. W-shapes have formerly been specified in A36; current practice in the U.S. is to use A992 with F_y = 50 ksi.

4. In wood fastener design, the dowel bearing strength of connector plates, F_e equals 1.5F_u (for A36 hot-rolled steel) and 1.375F_u (for A653 GR 33 cold-formed steel). These values are 1.6 times less than those permitted in steel structures so that they can be used in yield limit equations for wood members that have load duration adjustments (adjustments that may be as high as 1.6 for wind or seismic).

5. HSS can also be specified by ASTM A1085 and A1065, which follow somewhat different rules and are not considered in this text.

Table A-4.2: Steel allowable stresses and available strengths

Type of structural action	Allowable stress¹ (same units as F_y or F_u)	Available strength limit states (with safety factor, Ω)⁴
Tension	F_t^gross = 0.60F_y (yielding) F_t^net = 0.50F_u (rupture)
Compression	See Tables A-4.11 through A-4.14 (analysis) or A-4.10 (design)
Bending², assuming laterally braced, compact section	F_b = 0.60F_y (used with plastic section modulus, Z_x) or F_b = 0.66F_y (used with elastic section modulus, S_x)	The available strength method has no official limit state for the elastic moment
Shear³	F_v = 0.40F_y

Notes:

1. Allowable stresses, although no longer officially sanctioned by the American Institute of Steel Construction, result in the same values that are obtained when considering available strength, except in the case of bending. For bending, the limit state defined by the elastic moment, formerly the basis of allowable stress design, is no longer applicable, although it can still be used with somewhat conservative results for laterally-braced, compact sections. On the other hand, an allowable stress equation can be formulated based on the plastic section modulus that is equivalent to the available strength equation for laterally-braced, compact sections.

2. The allowable stress for bending, 0.66F_b, used with the elastic section modulus, S_x, gives a generally conservative value compared with using Ω = 1.67 and the plastic section modulus, Z_x. To reconcile these two different safety factors, it is necessary to approximate the ratio of Z_x/S_x, which varies depending upon the cross section. This ratio can be taken conservatively as 1.1 for W shapes; therefore, Z_x = 1.1S_x, and the allowable moment, M_p /Ω = F_yZ_x/Ω = 1.1F_yS_x/Ω = 1.1F_yS_x/1.67 = 0.66F_bS_x, which corresponds to the assumptions used for an allowable bending stress.

3. Both the allowable stress and available strength values for shear assume I-shape symbol -shaped rolled members meeting the slenderness criteria for beam webs. For beam webs that do not meet slenderness criteria for shear, a reduced allowable shear stress, F_v = 0.36F_y, is used. This is equivalent to using an increased allowable strength design safety factor, Ω = 1.67, and applies to the following W-shapes: W12 × 14, W16 × 26, W24 × 55, W30 × 90, W33 × 118, W36 × 135, W40 × 149, and W44 × 230. For the rectangular HSS listed in Appendix Table A-4.6, the reduced shear stress, F_v = 0.36F_y, is also used, with a web area, A_w, equal to 2ht (where t is the wall thickness of the web and h can be assumed to equal the nominal depth minus 3t). The value for the coefficient C_v is equal to 1.0 for all W-shapes, and is not included in the shear equations. For cross sections with very thin webs, this coefficient needs to be considered.

4. In these equations for various limit states, the subscript a refers to the available strength of the cross section, that is, the strength that is considered safe. The subscript n refers to the nominal strength of the cross section, that is, the actual limit state of the material. In other words, P_a is equivalent to the maximum tension force that the cross section can safely sustain; M_a is equivalent to the maximum bending moment that the cross section can safely sustain; and V_a is equivalent to the maximum shear force that the cross section can safely sustain.

Table A-4.3: Dimensions and properties of steel W sections⁵

Designa- tion	A (in²)	d (in.)	t_w (in.)	b_f (in.)	t_f (in.)	S_x (in³)	Z_x (in³)	I_x (in⁴)	I_y (in⁴)	r_y (in.)

W4 × 13	3.83	4.16	0.280	4.06	0.345	5.46	6.28	11.3	3.86	1.00
W5 × 16 W5 × 19	4.71 5.56	5.01 5.15	0.240 0.270	5.00 5.03	0.360 0.430	8.55 10.2	9.63 11.6	21.4 26.3	7.51 9.13	1.26 1.28
W6 × 8.5² W6 × 92 W6 × 12 W6 × 16	2.52 2.68 3.55 4.74	5.83 5.90 6.03 6.28	0.170 0.170 0.230 0.260	3.94 3.94 4.00 4.03	0.195 0.215 0.280 0.405	5.10 5.56 7.31 10.2	5.73 6.23 8.30 11.7	14.9 16.4 22.1 32.1	1.99 2.20 2.99 4.43	0.890 0.905 0.918 0.967
W6 × 15¹ W6 × 20 W6 × 25	4.43 5.87 7.34	5.99 6.20 6.38	0.230 0.260 0.320	5.99 6.02 6.08	0.260 0.365 0.455	9.72 13.4 16.7	10.8 14.9 18.9	29.1 41.4 53.4	9.32 13.3 17.1	1.45 1.50 1.52
W8 × 10^2,4 W8 × 13 W8 × 15	2.96 3.84 4.44	7.89 7.99 8.11	0.170 0.230 0.245	3.94 4.00 4.02	0.205 0.255 0.315	7.81 9.91 11.8	8.87 11.4 13.6	30.8 39.6 48.0	2.09 2.73 3.41	0.841 0.843 0.876
W8 × 18 W8 × 21	5.26 6.16	8.14 8.28	0.230 0.250	5.250 5.270	0.330 0.400	15.2 18.2	17.0 20.4	61.9 75.3	7.97 9.77	1.23 1.26
W8 × 24 W8 × 28	7.08 8.25	7.93 8.06	0.245 0.285	6.50 6.54	0.400 0.465	20.9 24.3	23.1 27.2	82.7 98.0	18.3 21.7	1.61 1.62
W8 × 31² W8 × 35 W8 × 40 W8 × 48 W8 × 58 W8 × 67	9.13 10.3 11.7 14.1 17.1 19.7	8.00 8.12 8.25 8.50 8.75 9.00	0.285 0.310 0.360 0.400 0.510 0.570	8.00 8.02 8.07 8.11 8.22 8.28	0.435 0.495 0.560 0.685 0.810 0.935	27.5 31.2 35.5 43.2 52.0 60.4	30.4 34.7 39.8 49.0 59.8 70.1	110 127 146 184 228 272	37.1 42.6 49.1 60.9 75.1 88.6	2.02 2.03 2.04 2.08 2.10 2.12
W10 × 12^2,4 W10 × 154 W10 × 174 W10 × 19	3.54 4.41 4.99 5.62	9.87 10.0 10.1 10.2	0.190 0.230 0.240 0.250	3.96 4.00 4.01 4.02	0.210 0.270 0.330 0.395	10.9 13.8 16.2 18.8	12.6 16.0 18.7 21.6	53.8 68.9 81.9 96.3	2.18 2.89 3.56 4.29	0.785 0.810 0.845 0.874
W10 × 22⁴ W10 × 26 W10 × 30	6.49 7.61 8.84	10.2 10.3 10.5	0.240 0.260 0.300	5.75 5.77 5.81	0.360 0.440 0.510	23.2 27.9 32.4	26.0 31.3 36.6	118 144 170	11.4 14.1 16.7	1.33 1.36 1.37
W10 × 33 W10 × 39 W10 × 45	9.71 11.5 13.3	9.73 9.92 10.10	0.290 0.315 0.350	7.96 7.99 8.02	0.435 0.530 0.620	35.0 42.1 49.1	38.8 46.8 54.9	171 209 248	36.6 45.0 53.4	1.94 1.98 2.01
W10 × 49 W10 × 54 W10 × 60 W10 × 68 W10 × 77 W10 × 88 W10 × 100 W10 × 112	14.4 15.8 17.7 19.9 22.7 26.0 29.3 32.9	10.0 10.1 10.2 10.4 10.6 10.8 11.1 11.4	0.340 0.370 0.420 0.470 0.530 0.605 0.680 0.755	10.0 10.0 10.1 10.1 10.2 10.3 10.3 10.4	0.560 0.615 0.680 0.770 0.870 0.990 1.120 1.250	54.6 60.0 66.7 75.7 85.9 98.5 112 126	60.4 66.6 74.6 85.3 97.6 113 130 147	272 303 341 394 455 534 623 716	93.4 103 116 134 154 179 207 236	2.54 2.56 2.57 2.59 2.60 2.63 2.65 2.68
W12 × 14^3,4 W12 × 16⁴ W12 × 19⁴ W12 × 22⁴	4.16 4.71 5.57 6.48	11.9 12.0 12.2 12.3	0.200 0.220 0.235 0.260	3.97 3.99 4.01 4.03	0.225 0.265 0.350 0.425	14.9 17.1 21.3 25.4	17.4 20.1 24.7 29.3	88.6 103 130 156	2.36 2.82 3.76 4.66	0.753 0.773 0.822 0.848
Designa- tion	A (in²)	d (in.)	t_w (in.)	b_f (in.)	t_f (in.)	S_x (in³)	Z_x (in³)	I_x (in⁴)	I_y (in⁴)	r_y (in.)
W12 × 26⁴ W12 × 30⁴ W12 × 35⁴	7.65 8.79 10.3	12.2 12.3 12.5	0.230 0.260 0.300	6.49 6.52 6.56	0.380 0.440 0.520	33.4 38.6 45.6	37.2 43.1 51.2	204 238 285	17.3 20.3 24.5	1.51 1.52 1.54
W12 × 40 W12 × 45 W12 × 50	11.7 13.1 14.6	11.9 12.1 12.2	0.295 0.335 0.370	8.01 8.05 8.08	0.515 0.575 0.640	51.5 57.7 64.2	57.0 64.2 71.9	307 348 391	44.1 50.0 56.3	1.94 1.95 1.96
W12 × 53 W12 × 58	15.6 17.0	12.1 12.2	0.345 0.360	10.0 10.0	0.575 0.640	70.6 78.0	77.9 86.4	425 475	95.8 107	2.48 2.51
W12 × 65² W12 × 72 W12 × 79 W12 × 87 W12 × 96 W12 × 106 W12 × 120 W12 × 136 W12 × 152 W12 × 170 W12 × 190 W12 × 210 W12 × 230 W12 × 252 W12 × 279 W12 × 305 W12 × 336	19.1 21.1 23.2 25.6 28.2 31.2 35.2 39.9 44.7 50.0 56.0 61.8 67.7 74.1 81.9 89.5 98.9	12.1 12.3 12.4 12.5 12.7 12.9 13.1 13.4 13.7 14.0 14.4 14.7 15.1 15.4 15.9 16.3 16.8	0.390 0.430 0.470 0.515 0.550 0.610 0.710 0.790 0.870 0.960 1.06 1.18 1.29 1.40 1.53 1.63 1.78	12.0 12.0 12.1 12.1 12.2 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 13.0 13.1 13.2 13.4	0.605 0.670 0.735 0.810 0.900 0.990 1.11 1.25 1.40 1.56 1.74 1.90 2.07 2.25 2.47 2.71 2.96	87.9 97.4 107 118 131 145 163 186 209 235 263 292 321 353 393 435 483	96.8 108 119 132 147 164 186 214 243 275 311 348 386 428 481 537 603	533 597 662 740 833 933 1070 1240 1430 1650 1890 2140 2420 2720 3110 3550 4060	174 195 216 241 270 301 345 398 454 517 589 664 742 828 937 1050 1190	3.02 3.04 3.05 3.07 3.09 3.11 3.13 3.16 3.19 3.22 3.25 3.28 3.31 3.34 3.38 3.42 3.47
W14 × 22⁴ W14 × 26⁴	6.49 7.69	13.7 13.9	0.230 0.255	5.00 5.03	0.335 0.420	29.0 35.3	33.2 40.2	199 245	7.00 8.91	1.04 1.08
W14 × 30⁴ W14 × 34⁴ W14 × 38⁴	8.85 10.0 11.2	13.8 14.0 14.1	0.270 0.285 0.310	6.73 6.75 6.77	0.385 0.455 0.515	42.0 48.6 54.6	47.3 54.6 61.5	291 340 385	19.6 23.3 26.7	1.49 1.53 1.55
W14 × 43⁴ W14 × 48 W14 × 53	12.6 14.1 15.6	13.7 13.8 13.9	0.305 0.340 0.370	8.00 8.03 8.06	0.530 0.595 0.660	62.6 70.2 77.8	69.6 78.4 87.1	428 484 541	45.2 51.4 57.7	1.89 1.91 1.92
W14 × 61 W14 × 68 W14 × 74 W14 × 82	17.9 20.0 21.8 24.0	13.9 14.0 14.2 14.3	0.375 0.415 0.450 0.510	10.0 10.0 10.1 10.1	0.645 0.720 0.785 0.855	92.1 103 112 123	102 115 126 139	640 722 795 881	107 121 134 148	2.45 2.46 2.48 2.48
W14 × 90² W14 × 99² W14 × 109 W14 × 120 W14 × 132	26.5 29.1 32.0 35.3 38.8	14.0 14.2 14.3 14.5 14.7	0.440 0.485 0.525 0.590 0.645	14.5 14.6 14.6 14.7 14.7	0.710 0.780 0.860 0.940 1.03	143 157 173 190 209	157 173 192 212 234	999 1110 1240 1380 1530	362 402 447 495 548	3.70 3.71 3.73 3.74 3.76
Designa- tion	A (in²)	d (in.)	t_w (in.)	b_f (in.)	t_f (in.)	S_x (in³)	Z_x (in³)	I_x (in⁴)	I_y (in⁴)	r_y (in.)
W14 × 145 W14 × 159 W14 × 176 W14 × 193 W14 × 211 W14 × 233 W14 × 257 W14 × 283 W14 × 311 W14 × 342 W14 × 370 W14 × 398 W14 × 426 W14 × 455 W14 × 500 W14 × 550 W14 × 605 W14 × 665 W14 × 730 W14 × 808 W14 × 873	42.7 46.7 51.8 56.8 62.0 68.5 75.6 83.3 91.4 101 109 117 125 134 147 162 178 196 215 238 257	14.8 15.0 15.2 15.5 15.7 16.0 16.4 16.7 17.1 17.5 17.9 18.3 18.7 19.0 19.6 20.2 20.9 21.6 22.4 22.8 23.6	0.680 0.745 0.830 0.890 0.980 1.07 1.18 1.29 1.41 1.54 1.66 1.77 1.88 2.02 2.19 2.38 2.60 2.83 3.07 3.74 3.94	15.5 15.6 15.7 15.7 15.8 15.9 16.0 16.1 16.2 16.4 16.5 16.6 16.7 16.8 17.0 17.2 17.4 17.7 17.9 18.6 18.8	1.09 1.19 1.31 1.44 1.56 1.72 1.89 2.07 2.26 2.47 2.66 2.85 3.04 3.21 3.50 3.82 4.16 4.52 4.91 5.12 5.51	232 254 281 310 338 375 415 459 506 558 607 656 706 756 838 931 1040 1150 1280 1390 1530	260 287 320 355 390 436 487 542 603 672 736 801 869 936 1050 1180 1320 1480 1660 1830 2030	1710 1900 2140 2400 2660 3010 3400 3840 4330 4900 5440 6000 6600 7190 8210 9430 10800 12400 14300 15900 18100	677 748 838 931 1030 1150 1290 1440 1610 1810 1990 2170 2360 2560 2880 3250 3680 4170 4720 5550 6170	3.98 4.00 4.02 4.05 4.07 4.10 4.13 4.17 4.20 4.24 4.27 4.31 4.34 4.38 4.43 4.49 4.55 4.62 4.69 4.83 4.90
W16 × 26^3,4 W16 × 31⁴	7.68 9.13	15.7 15.9	0.250 0.275	5.50 5.53	0.345 0.440	38.4 47.2	44.2 54.0	301 375	9.59 12.4	1.12 1.17
W16 × 36⁴ W16 × 40⁴ W16 × 45⁴ W16 × 50⁴ W16 × 57	10.6 11.8 13.3 14.7 16.8	15.9 16.0 16.1 16.3 16.4	0.295 0.305 0.345 0.380 0.430	6.99 7.00 7.04 7.07 7.12	0.430 0.505 0.565 0.630 0.715	56.5 64.7 72.7 81.0 92.2	64.0 73.0 82.3 92.0 105	448 518 586 659 758	24.5 28.9 32.8 37.2 43.1	1.52 1.57 1.57 1.59 1.60
W16 × 67⁴ W16 × 77 W16 × 89 W16 × 100	19.6 22.6 26.2 29.4	16.3 16.5 16.8 17.0	16.3 16.5 16.8 17.0	10.2 10.3 10.4 10.4	0.665 0.760 0.875 0.985	117 134 155 175	130 150 175 198	954 1110 1300 1490	119 138 163 186	2.46 2.47 2.49 2.51
W18 × 35⁴ W18 × 40⁴ W18 × 46⁴	10.3 11.8 13.5	17.7 17.9 18.1	0.300 0.315 0.360	6.00 6.02 6.06	0.425 0.525 0.605	57.6 68.4 78.8	66.5 78.4 90.7	510 612 712	15.3 19.1 22.5	1.22 1.27 1.29
W18 × 50⁴ W18 × 55⁴ W18 × 60⁴ W18 × 65 W18 × 71	14.7 16.2 17.6 19.1 20.9	18.0 18.1 18.2 18.4 18.5	0.355 0.390 0.415 0.450 0.495	7.50 7.53 7.56 7.59 7.64	0.570 0.630 0.695 0.750 0.810	88.9 98.3 108 117 127	101 112 123 133 146	800 890 984 1070 1170	40.1 44.9 50.1 54.8 60.3	1.65 1.67 1.68 1.69 1.70
W18 × 76⁴ W18 × 86 W18 × 97 W18 × 106 W18 × 119 W18 × 130 W18 × 143 W18 × 158 W18 × 175 W18 × 192 W18 × 211 W18 × 234 W18 × 258 W18 × 283 W18 × 311	22.3 25.3 28.5 31.1 35.1 38.3 42.0 46.3 51.4 56.2 62.3 68.8 76.0 83.3 91.6	18.2 18.4 18.6 18.7 19.0 19.3 19.5 19.7 20.0 20.4 20.7 21.1 21.5 21.9 22.3	0.425 0.480 0.535 0.590 0.655 0.670 0.730 0.810 0.890 0.960 1.06 1.16 1.28 1.40 1.52	11.0 11.1 11.1 11.2 11.3 11.2 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 12.0	0.680 0.770 0.870 0.940 1.06 1.20 1.32 1.44 1.59 1.75 1.91 2.11 2.30 2.50 2.74	146 166 188 204 231 256 282 310 344 380 419 466 514 565 624	163 186 211 230 262 290 322 356 398 442 490 549 611 676 754	1330 1530 1750 1910 2190 2460 2750 3060 3450 3870 4330 4900 5510 6170 6970	152 175 201 220 253 278 311 347 391 440 493 558 628 704 795	2.61 2.63 2.65 2.66 2.69 2.70 2.72 2.74 2.76 2.79 2.82 2.85 2.88 2.91 2.95
Designa- tion	A (in²)	d (in.)	t_w (in.)	b_f (in.)	t_f (in.)	S_x (in³)	Z_x (in³)	I_x (in⁴)	I_y (in⁴)	r_y (in.)
W21 × 44⁴ W21 × 50⁴ W21 × 57⁴	13.0 14.7 16.7	20.7 20.8 21.1	0.350 0.380 0.405	6.50 6.53 6.56	0.450 0.535 0.650	81.6 94.5 111	95.4 110 129	843 984 1170	20.7 24.9 30.6	1.26 1.30 1.35
W21 × 48^2,4 W21 × 55⁴ W21 × 62⁴ W21 × 68⁴ W21 × 73⁴ W21 × 83⁴ W21 × 93	14.1 16.2 18.3 20.0 21.5 24.4 27.3	20.6 20.8 21.0 21.1 21.2 21.4 21.6	0.350 0.375 0.400 0.430 0.455 0.515 0.580	8.14 8.22 8.24 8.27 8.30 8.36 8.42	0.430 0.522 0.615 0.685 0.740 0.835 0.930	93.0 110 127 140 151 171 192	107 126 144 160 172 196 221	959 1140 1330 1480 1600 1830 2070	38.7 48.4 57.5 64.7 70.6 81.4 92.9	1.66 1.73 1.77 1.80 1.81 1.83 1.84
W21 × 101⁴ W21 × 111 W21 × 122 W21 × 132 W21 × 147 W21 × 166 W21 × 182 W21 × 201 W21 × 223 W21 × 248 W21 × 275	29.8 32.6 35.9 38.8 43.2 48.8 53.6 59.3 66.5 73.8 81.8	21.4 21.5 21.7 21.8 22.1 22.5 22.7 23.0 23.4 23.7 24.1	0.500 0.550 0.600 0.650 0.720 0.750 0.830 0.910 1.00 1.10 1.22	12.3 12.3 12.4 12.4 12.5 12.4 12.5 12.6 12.7 12.8 12.9	0.800 0.875 0.960 1.04 1.15 1.36 1.48 1.63 1.79 1.99 2.19	227 249 273 295 329 380 417 461 520 576 638	253 279 307 333 373 432 476 530 601 671 749	2420 2670 2960 3220 3630 4280 4730 5310 6080 6830 7690	248 274 305 333 376 435 483 542 614 699 787	2.89 2.90 2.92 2.93 2.95 2.99 3.00 3.02 3.04 3.08 3.10
W24 × 55^3,4 W24 × 62⁴	16.2 18.2	23.6 23.7	0.395 0.430	7.01 7.04	0.505 0.590	114 131	134 153	1350 1550	29.1 34.5	1.34 1.38
W24 × 68⁴ W24 × 76⁴ W24 × 84⁴ W24 × 94⁴ W24 × 103⁴	20.1 22.4 24.7 27.7 30.3	23.7 23.9 24.1 24.3 24.5	0.415 0.440 0.470 0.515 0.550	8.97 8.99 9.02 9.07 9.00	0.585 0.680 0.770 0.875 0.980	154 176 196 222 245	177 200 224 254 280	1830 2100 2370 2700 3000	70.4 82.5 94.4 109 119	1.87 1.92 1.95 1.98 1.99
W24 × 104⁴ W24 × 117⁴ W24 × 131 W24 × 146 W24 × 162 W24 × 176 W24 × 192 W24 × 207 W24 × 229 W24 × 250 W24 × 279 W24 × 306 W24 × 335 W24 × 370	30.7 34.4 38.6 43.0 47.8 51.7 56.5 60.7 67.2 73.5 81.9 89.7 98.3 109	24.1 24.3 24.5 24.7 25.0 25.2 25.5 25.7 26.0 26.3 26.7 27.1 27.5 28.0	0.500 0.550 0.605 0.650 0.705 0.750 0.810 0.870 0.960 1.04 1.16 1.26 1.38 1.52	12.8 12.8 12.9 12.9 13.0 12.9 13.0 13.0 13.1 13.2 13.3 13.4 13.5 13.7	0.750 0.850 0.960 1.09 1.22 1.34 1.46 1.57 1.73 1.89 2.09 2.28 2.48 2.72	258 291 329 371 414 450 491 531 588 644 718 789 864 957	289 327 370 418 468 511 559 606 675 744 835 922 1020 1130	3100 3540 4020 4580 5170 5680 6260 6820 7650 8490 9600 10700 11900 13400	259 297 340 391 443 479 530 578 651 724 823 919 1030 1160	2.91 2.94 2.97 3.01 3.05 3.04 3.07 3.08 3.11 3.14 3.17 3.20 3.23 3.27
W27 × 84⁴ W27 × 94⁴ W27 × 102⁴ W27 × 114⁴ W27 × 129⁴	24.7 27.6 30.0 33.6 37.8	26.7 26.9 27.1 27.3 27.6	0.460 0.490 0.515 0.570 0.610	10.0 10.0 10.0 10.1 10.0	0.640 0.745 0.830 0.930 1.10	213 243 267 299 345	244 278 305 343 395	2850 3270 3620 4080 4760	106 124 139 159 184	2.07 2.12 2.15 2.18 2.21
Designa- tion	A (in²)	d (in.)	t_w (in.)	b_f (in.)	t_f (in.)	S_x (in³)	Z_x (in³)	I_x (in⁴)	I_y (in⁴)	r_y (in.)
W27 × 146⁴ W27 × 161⁴ W27 × 178 W27 × 194 W27 × 217 W27 × 235 W27 × 258 W27 × 281 W27 × 307 W27 × 336 W27 × 368 W27 × 539	43.2 47.6 52.5 57.1 63.9 69.4 76.1 83.1 90.2 99.2 109 159	27.4 27.6 27.8 28.1 28.4 28.7 29.0 29.3 29.6 30.0 30.4 32.5	0.605 0.660 0.725 0.750 0.830 0.910 0.980 1.06 1.16 1.26 1.38 1.97	14.0 14.0 14.1 14.0 14.1 14.2 14.3 14.4 14.4 14.6 14.7 15.3	0.975 1.08 1.19 1.34 1.50 1.61 1.77 1.93 2.09 2.28 2.48 3.54	414 458 505 559 627 677 745 814 887 972 1060 1570	464 515 570 631 711 772 852 936 1030 1130 1240 1890	5660 6310 7020 7860 8910 9700 10800 11900 13100 14600 16200 25600	443 497 555 619 704 769 859 953 1050 1180 1310 2110	3.20 3.23 3.25 3.29 3.32 3.33 3.36 3.39 3.41 3.45 3.48 3.65
W30 × 90^3,4 W30 × 99⁴ W30 × 108⁴ W30 × 116⁴ W30 × 124⁴ W30 × 132⁴ W30 × 148⁴	26.3 29.0 31.7 34.2 36.5 38.8 43.6	29.5 29.7 29.8 30.0 30.2 30.3 30.7	0.470 0.520 0.545 0.565 0.585 0.615 0.650	10.4 10.5 10.5 10.5 10.5 10.5 10.5	0.610 0.670 0.760 0.850 0.930 1.00 1.18	245 269 299 329 355 380 436	283 312 346 378 408 437 500	3610 3990 4470 4930 5360 5770 6680	115 128 146 164 181 196 227	2.09 2.10 2.15 2.19 2.23 2.25 2.28
W30 × 173⁴ W30 × 191⁴ W30 × 211 W30 × 235 W30 × 261 W30 × 292 W30 × 326 W30 × 357 W30 × 391	50.9 56.1 62.3 69.3 77.0 86.0 95.9 105 115	30.4 30.7 30.9 31.3 31.6 32.0 32.4 32.8 33.2	0.655 0.710 0.775 0.830 0.930 1.02 1.14 1.24 1.36	15.0 15.0 15.1 15.1 15.2 15.3 15.4 15.5 15.6	1.07 1.19 1.32 1.50 1.65 1.85 2.05 2.24 2.44	541 600 665 748 829 930 1040 1140 1250	607 675 751 847 943 1060 1190 1320 1450	8230 9200 10300 11700 13100 14900 16800 18700 20700	598 673 757 855 959 1100 1240 1390 1550	3.42 3.46 3.49 3.51 3.53 3.58 3.60 3.64 3.67
W33 × 118^3,4 W33 × 130⁴ W33 × 141⁴ W33 × 152⁴ W33 × 169⁴	34.7 38.3 41.5 44.9 49.5	32.9 33.1 33.3 33.5 33.8	0.550 0.580 0.605 0.635 0.670	11.5 11.5 11.5 11.6 11.5	0.740 0.855 0.960 1.06 1.22	359 406 448 487 549	415 467 514 559 629	5900 6710 7450 8160 9290	187 218 246 273 310	2.32 2.39 2.43 2.47 2.50
W33 × 201⁴ W33 × 221⁴ W33 × 241⁴ W33 × 263 W33 × 291 W33 × 318 W33 × 354 W33 × 387	59.1 65.3 71.1 77.4 85.6 93.7 104 114	33.7 33.9 34.2 34.5 34.8 35.2 35.6 36.0	0.715 0.775 0.830 0.870 0.960 1.04 1.16 1.26	15.7 15.8 15.9 15.8 15.9 16.0 16.1 16.2	1.15 1.28 1.40 1.57 1.73 1.89 2.09 2.28	686 759 831 919 1020 1110 1240 1350	773 857 940 1040 1160 1270 1420 1560	11600 12900 14200 15900 17700 19500 22000 24300	749 840 933 1040 1160 1290 1460 1620	3.56 3.59 3.62 3.66 3.68 3.71 3.74 3.77
W36 × 135^3,4 W36 × 150⁴ W36 × 160⁴ W36 × 170⁴ W36 × 182⁴ W36 × 194⁴ W36 × 210⁴ W36 × 232⁴ W36 × 256	39.9 44.3 47.0 50.0 53.6 57.0 61.9 68.0 75.3	35.6 35.9 36.0 36.2 36.3 36.5 36.7 37.1 37.4	0.600 0.625 0.650 0.680 0.725 0.765 0.830 0.870 0.960	12.0 12.0 12.0 12.0 12.1 12.1 12.2 12.1 12.2	0.790 0.940 1.02 1.10 1.18 1.26 1.36 1.57 1.73	439 504 542 581 623 664 719 809 895	509 581 624 668 718 767 833 936 1040	7800 9040 9760 10500 11300 12100 13200 15000 16800	225 270 295 320 347 375 411 468 528	2.38 2.47 2.50 2.53 2.55 2.56 2.58 2.62 2.65
Designa- tion	A (in²)	d (in.)	t_w (in.)	b_f (in.)	t_f (in.)	S_x (in³)	Z_x (in³)	I_x (in⁴)	I_y (in⁴)	r_y (in.)
W36 × 231⁴ W36 × 247⁴ W36 × 262⁴ W36 × 282⁴ W36 × 302 W36 × 330 W36 × 361 W36 × 395 W36 × 441 W36 × 487 W36 × 529 W36 × 652 W36 × 723 W36 × 802 W36 × 853 W36 × 925	68.2 72.5 77.2 82.9 89.0 96.9 106 116 130 143 156 192 213 236 251 272	36.5 36.7 36.9 37.1 37.3 37.7 38.0 38.4 38.9 39.3 39.8 41.1 41.8 42.6 43.1 43.1	0.760 0.800 0.840 0.885 0.945 1.02 1.12 1.22 1.36 1.50 1.61 1.97 2.17 2.38 2.52 3.02	16.5 16.5 16.6 16.6 16.7 16.6 16.7 16.8 17.0 17.1 17.2 17.6 17.8 18.0 18.2 18.6	1.26 1.35 1.44 1.57 1.68 1.85 2.01 2.20 2.44 2.68 2.91 3.54 3.90 4.29 4.53 4.53	854 913 972 1050 1130 1240 1350 1490 1650 1830 1990 2460 2740 3040 3250 3390	963 1030 1100 1190 1280 1410 1550 1710 1910 2130 2330 2910 3270 3660 3920 4130	15600 16700 17900 19600 21100 23300 25700 28500 32100 36000 39600 50600 57300 64800 70000 73000	940 1010 1090 1200 1300 1420 1570 1750 1990 2250 2490 3230 3700 4210 4600 4940	3.71 3.74 3.76 3.80 3.82 3.83 3.85 3.88 3.92 3.96 4.00 4.10 4.17 4.22 4.28 4.26
W40 × 149^3,4 W40 × 167⁴ W40 × 183⁴ W40 × 211⁴ W40 × 235⁴ W40 × 264 W40 × 278 W40 × 294 W40 × 327 W40 × 331 W40 × 392	43.8 49.3 53.3 62.1 69.1 77.4 82.3 86.2 95.9 97.7 116	38.2 38.6 39.0 39.4 39.7 40.0 40.2 40.4 40.8 40.8 41.6	0.630 0.650 0.650 0.750 0.830 0.960 1.03 1.06 1.18 1.22 1.42	11.8 11.8 11.8 11.8 11.9 11.9 12.0 12.0 12.1 12.2 12.4	0.830 1.03 1.20 1.42 1.58 1.73 1.81 1.93 2.13 2.13 2.52	513 600 675 786 875 971 1020 1080 1200 1210 1440	598 693 774 906 1010 1130 1190 1270 1410 1430 1710	9800 11600 13200 15500 17400 19400 20500 21900 24500 24700 29900	229 283 331 390 444 493 521 562 640 644 803	2.29 2.40 2.49 2.51 2.54 2.52 2.52 2.55 2.58 2.57 2.64
W40 × 199⁴ W40 × 215⁴ W40 × 249⁴ W40 × 277⁴ W40 × 297⁴ W40 × 324 W40 × 362 W40 × 372 W40 × 397 W40 × 431 W40 × 503 W40 × 593 W40 × 655	58.8 63.5 73.5 81.5 87.3 95.3 106 110 117 127 148 174 193	38.7 39.0 39.4 39.7 39.8 40.2 40.6 40.6 41.0 41.3 42.1 43.0 43.6	0.650 0.650 0.750 0.830 0.930 1.00 1.12 1.16 1.22 1.34 1.54 1.79 1.97	15.8 15.8 15.8 15.8 15.8 15.9 16.0 16.1 16.1 16.2 16.4 16.7 16.9	1.07 1.22 1.42 1.58 1.65 1.81 2.01 2.05 2.20 2.36 2.76 3.23 3.54	770 859 993 1100 1170 1280 1420 1460 1560 1690 1980 2340 2590	869 964 1120 1250 1330 1460 1640 1680 1800 1960 2320 2760 3080	14900 16700 19600 21900 23200 25600 28900 29600 32000 34800 41600 50400 56500	695 796 926 1040 1090 1220 1380 1420 1540 1690 2040 2520 2870	3.45 3.54 3.55 3.58 3.54 3.58 3.60 3.60 3.64 3.65 3.72 3.80 3.86
W44 × 230^3,4 W44 × 262⁴ W44 × 290⁴ W44 × 335⁴	67.8 77.2 85.4 98.5	42.9 43.3 43.6 44.0	0.710 0.785 0.865 1.03	15.8 15.8 15.8 15.9	1.22 1.42 1.58 1.77	971 1110 1240 1410	1100 1270 1410 1620	20800 24100 27000 31100	796 923 1040 1200	3.43 3.47 3.49 3.49

Notes:

1. Section not compact for steel with F_y = 36 ksi or F_y = 50 ksi.

2. Section compact for steel with F_y = 36 ksi, but not compact for steel with F_y = 50 ksi.

3. Section webs do not meet slenderness criteria for shear for which the allowable stress can be taken as F_v = 0.4F_y; instead, use a reduced allowable shear stress, F_v = 0.36Fy.

4. Section is slender for compression with F_y = 50 ksi.

5. W-shapes are grouped together with common inner roller dimensions (i.e., web "lengths" excluding fillets)

Table A-4.4: Dimensions and properties of steel C and MC channels

Designation	A (in²)	d (in.)	t_w (in.)	b_f (in.)	x (in.)	I_x (in⁴)	I_y (in⁴)

C3 × 3.5	1.09	3.00	0.132	1.37	0.443	1.57	0.169
C3 × 4.1	1.20	3.00	0.170	1.41	0.437	1.65	0.191
C3 × 5	1.47	3.00	0.258	1.50	0.439	1.85	0.241
C3 × 6	1.76	3.00	0.356	1.60	0.455	2.07	0.300
C4 × 4.5	1.38	4.00	0.125	1.58	0.493	3.65	0.289
C4 × 5.4	1.58	4.00	0.184	1.58	0.457	3.85	0.312
C4 × 6.25	1.77	4.00	0.247	1.65	0.435	4.00	0.345
C4 × 7.25	2.13	4.00	0.321	1.72	0.459	4.58	0.425
C5 × 6.7	1.97	5.00	0.190	1.75	0.484	7.48	0.470
C5 × 9	2.64	5.00	0.325	1.89	0.478	8.89	0.624
C6 × 8.2	2.39	6.00	0.200	1.92	0.512	13.1	0.687
C6 × 10.5	3.08	6.00	0.314	2.03	0.500	15.1	0.860
C6 × 13	3.81	6.00	0.437	2.16	0.514	17.3	1.05
C7 × 9.8	2.87	7.00	0.210	2.09	0.541	21.2	0.957
C7 × 12.25	3.59	7.00	0.314	2.19	0.525	24.2	1.16
C7 × 14.75	4.33	7.00	0.419	2.30	0.532	27.2	1.37
C8 × 11.5	3.37	8.00	0.220	2.26	0.572	32.5	1.31
C8 × 13.75	4.03	8.00	0.303	2.34	0.554	36.1	1.52
C8 × 18.75	5.51	8.00	0.487	2.53	0.565	43.9	1.97
C9 × 13.4	3.94	9.00	0.233	2.43	0.601	47.8	1.75
C9 × 15	4.41	9.00	0.285	2.49	0.586	51.0	1.91
C9 × 20	5.87	9.00	0.448	2.65	0.583	60.9	2.41
C10 × 15.3	4.48	10.0	0.240	2.60	0.634	67.3	2.27
C10 × 20	5.87	10.0	0.379	2.74	0.606	78.9	2.80
C10 × 25	7.34	10.0	0.526	2.89	0.617	91.1	3.34
C10 × 30	8.81	10.0	0.673	3.03	0.649	103	3.93
C12 × 20.7	6.08	12.0	0.282	2.94	0.698	129	3.86
C12 × 25	7.34	12.0	0.387	3.05	0.674	144	4.45
C12 × 30	8.81	12.0	0.510	3.17	0.674	162	5.12
C15 × 33.9	10.0	15.0	0.400	3.40	0.788	315	8.07
C15 × 40	11.8	15.0	0.520	3.52	0.778	348	9.17
C15 × 50	14.7	15.0	0.716	3.72	0.799	404	11.0

Designation	A (in²)	d (in.)	t_w (in.)	b_f (in.)	x (in.)	I_x (in⁴)	I_y (in⁴)
MC3 × 7.1	2.11	3.00	0.312	1.94	0.653	2.72	0.666
MC4 × 13.8	4.03	4.00	0.500	2.50	0.849	8.85	2.13
MC6 × 6.5	1.95	6.00	0.155	1.85	0.513	11.0	0.565
MC6 × 7	2.09	6.00	0.179	1.88	0.501	11.4	0.603
MC6 × 12	3.53	6.00	0.310	2.50	0.704	18.7	1.85
MC6 × 15.1	4.44	6.00	0.316	2.94	0.940	24.9	3.46
MC6 × 16.3	4.79	6.00	0.375	3.00	0.927	26.0	3.77
MC6 × 15.3	4.49	6.00	0.340	3.50	1.05	25.3	4.91
MC6 × 18	5.29	6.00	0.379	3.50	1.12	29.7	5.88
MC7 × 19.1	5.61	7.00	0.352	3.45	1.08	43.1	6.06
MC7 × 22.7	6.67	7.00	0.503	3.60	1.04	47.4	7.24
MC8 × 8.5	2.50	8.00	0.179	1.87	0.428	23.3	0.624
MC8 × 18.7	5.50	8.00	0.353	2.98	0.849	52.4	4.15
MC8 × 20	5.88	8.00	0.400	3.03	0.840	54.4	4.42
MC8 × 21.4	6.28	8.00	0.375	3.45	1.02	61.5	6.58
MC8 × 22.8	6.70	8.00	0.427	3.50	1.01	63.8	7.01
MC9 × 23.9	7.02	9.00	0.400	3.45	0.981	84.9	7.14
MC9 × 25.4	7.47	9.00	0.450	3.50	0.970	87.9	7.57
MC10 × 6.5¹	1.95	10.0	0.152	1.17	0.194	22.9	0.133
MC10 × 8.4¹	2.46	10.0	0.170	1.50	0.284	31.9	0.326
MC10 × 22	6.45	10.00	0.290	3.32	0.990	102	6.40
MC10 × 25	7.35	10.0	0.380	3.41	0.953	110	7.25
MC10 × 28.5	8.37	10.0	0.425	3.95	1.12	126	11.3
MC10 × 33.6	9.87	10.0	0.575	4.10	1.09	139	13.1
MC10 × 41.1	12.1	10.0	0.796	4.32	1.09	157	15.7
MC12 × 10.6¹	3.10	12.0	0.190	1.50	0.269	55.3	0.378
MC12 × 14.3	4.18	12.0	0.250	2.12	0.377	76.1	1.00
MC12 × 31	9.12	12.0	0.370	3.67	1.08	202	11.3
MC12 × 35	10.3	12.0	0.465	3.77	1.05	216	12.6
MC12 × 40	11.8	12.0	0.590	3.89	1.04	234	14.2
MC12 × 45	13.2	12.0	0.710	4.01	1.04	251	15.8
MC12 × 50	14.7	12.0	0.835	4.14	1.05	269	17.4
MC13 × 31.8	9.35	13.0	0.375	4.00	1.00	239	11.4
MC13 × 35	10.3	13.0	0.447	4.07	0.980	252	12.3
MC13 × 40	11.8	13.0	0.560	4.19	0.963	273	13.7
MC13 × 50	14.7	13.0	0.787	4.41	0.974	314	16.4
MC18 × 42.7	12.6	18.0	0.450	3.95	0.877	554	14.3
MC18 × 45.8	13.5	18.0	0.500	4.00	0.866	578	14.9
MC18 × 51.9	15.3	18.0	0.600	4.10	0.858	627	16.3
MC18 × 58	17.1	18.0	0.700	4.20	0.862	675	17.6

Note:

1. Section is slender for compression with F_y = 36 ksi.

Table A-4.5: Dimensions and properties of selected steel L angles

A. Angles with equal legs

Designation	A (in²)	d (in.)	t_w (in.)	x (in.)	I_x or I_y (in⁴)	I_z (in⁴)
L2 × 2 × ⅛^1,2	0.491	2.00	0.1250	0.534	0.189	0.0751
L2 × 2 × ¼	0.944	2.00	0.2500	0.586	0.346	0.141
L2 × 2 × 5⁄16	1.16	2.00	0.3125	0.609	0.414	0.173
L2 × 2 × ⅜	1.37	2.00	0.3750	0.632	0.476	0.203
L3 × 3 × 3⁄16^1,2	1.09	3.00	0.1875	0.812	0.948	0.374
L3 × 3 × ¼	1.44	3.00	0.2500	0.836	1.23	0.491
L3 × 3 × ⅜	2.11	3.00	0.3750	0.884	1.75	0.712
L3 × 3 × ½	2.76	3.00	0.5000	0.929	2.20	0.924
L4 × 4 × ¼^1,2	1.93	4.00	0.2500	1.08	3.00	1.18
L4 × 4 × ⅜	2.86	4.00	0.3750	1.13	4.32	1.73
L4 × 4 × ½	3.75	4.00	0.5000	1.18	5.52	2.25
L4 × 4 × ¾	5.44	4.00	0.7500	1.27	7.62	3.25
L5 × 5 × 5⁄16^1,2	3.07	5.00	0.3125	1.35	7.44	3.01
L5 × 5 × 7⁄16	4.22	5.00	0.4375	1.40	10.0	4.08
L5 × 5 × ⅝	5.90	5.00	0.6250	1.47	13.6	5.61
L5 × 5 × ⅞	8.00	5.00	0.8750	1.56	17.8	7.56
L6 × 6 × 5⁄16^1,2	3.67	6.00	0.3125	1.60	13.0	5.20
L6 × 6 × ½	5.77	6.00	0.5000	1.67	19.9	8.04
L6 × 6 × ¾	8.46	6.00	0.7500	1.77	28.1	11.6
L6 × 6 × 1	11.0	6.00	1.0000	1.86	35.4	15.0
L8 × 8 × ½^1,2	7.84	8.00	0.5000	2.17	48.8	19.7
L8 × 8 × ⅝	9.69	8.00	0.6250	2.21	59.6	24.2
L8 × 8 × ⅞	13.3	8.00	0.8750	2.31	79.7	32.7
L8 × 8 × 1⅛	16.8	8.00	1.1250	2.40	98.1	40.9

B. Angles with unequal legs

Designation	A (in²)	d (in.)	b (in.)	t_w (in.)	x (in.)	y (in.)	I_x (in⁴)	I_y (in⁴)	I_z (in⁴)	α (°)
L3 × 2 × ¼	1.20	3.00	2.00	0.2500	0.487	0.980	1.09	0.390	0.223	23.6
L3 × 2 × 5⁄16	1.48	3.00	2.00	0.3125	0.511	1.01	1.32	0.467	0.271	23.4
L3 × 2 × ⅜	1.75	3.00	2.00	0.3750	0.535	1.03	1.54	0.539	0.318	23.1
L3 × 2 × ½	2.26	3.00	2.00	0.5000	0.580	1.08	1.92	0.667	0.409	22.4
L3 × 2½ × ¼	1.32	3.00	2.50	0.2500	0.653	0.900	1.16	0.734	0.356	34.3
L3 × 2½ × 5⁄16	1.63	3.00	2.50	0.3125	0.677	0.925	1.41	0.888	0.437	34.2
L3 × 2½ × ⅜	1.93	3.00	2.50	0.3750	0.701	0.949	1.65	1.03	0.514	34.0
L3 × 2½ × ½	2.50	3.00	2.50	0.5000	0.746	0.995	2.07	1.29	0.666	33.7
L3½ × 2½ × ¼²	1.45	3.50	2.50	0.2500	0.607	1.10	1.81	0.775	0.425	26.7
L3½ × 2½ × 5⁄16	1.79	3.50	2.50	0.3125	0.632	1.13	2.20	0.937	0.518	26.6
L3½ × 2½ × ⅜	2.12	3.50	2.50	0.3750	0.655	1.15	2.56	1.09	0.608	26.3
L3-½ × 2½ × ½	2.77	3.50	2.50	0.5000	0.701	1.20	3.24	1.36	0.782	25.9
L4 × 3 × ¼^1,2	1.69	4.00	3.00	0.2500	0.725	1.22	2.75	1.33	0.691	29.2
L4 × 3 × ⅜	2.49	4.00	3.00	0.3750	0.775	1.27	3.94	1.89	1.01	28.9
L4 × 3 × ½	3.25	4.00	3.00	0.5000	0.822	1.32	5.02	2.40	1.30	28.5
L4 × 3 × ⅝	3.99	4.00	3.00	0.6250	0.867	1.37	6.01	2.85	1.59	28.1
L4 × 3½ × ¼^1,2	1.82	4.00	3.50	0.2500	0.897	1.14	2.89	2.07	0.950	37.2
L4 × 3½ × 5⁄16	2.25	4.00	3.50	0.3125	0.923	1.17	3.53	2.52	1.17	37.1
L4 × 3½ × ⅜	2.68	4.00	3.50	0.3750	0.947	1.20	4.15	2.96	1.38	37.1
L4 × 3½ × ½	3.50	4.00	3.50	0.5000	0.994	1.24	5.30	3.76	1.808	36.9
L5 × 3 × ¼^1,2	1.94	5.00	3.00	0.2500	0.648	1.64	5.09	1.41	0.825	20.4
L5 × 3 × 5⁄16^1,2	2.41	5.00	3.00	0.3125	0.673	1.67	6.24	1.72	1.01	20.2
L5 × 3 × ⅜²	2.86	5.00	3.00	0.3750	0.698	1.69	7.35	2.01	1.20	20.0
L5 × 3 × ½	3.75	5.00	3.00	0.5000	0.746	1.74	9.43	2.55	1.55	19.6
L5 × 3½ × ¼^1,2	2.07	5.00	3.50	0.2500	0.804	1.55	5.36	2.20	1.19	26.1
L5 × 3½ × ⅜²	3.05	5.00	3.50	0.3750	0.854	1.60	7.75	3.15	1.74	25.9
L5 × 3½ × ½	4.00	5.00	3.50	0.5000	0.901	1.65	9.96	4.02	2.25	25.6
L5 × 3½ × ¾	5.85	5.00	3.50	0.7500	0.993	1.74	13.9	5.52	3.22	24.9
L6 × 3½ × 5⁄16^1,2	2.89	6.00	3.50	0.3125	0.756	2.00	10.9	2.84	1.70	19.4
L6 × 3½ × ⅜^1,2	3.44	6.00	3.50	0.3750	0.781	2.02	12.9	3.33	2.00	19.2
L6 × 3½ × ½	4.50	6.00	3.50	0.5000	0.829	2.07	16.6	4.24	2.58	18.9
L6 × 4 × ⅜^1,2	3.61	6.00	4.00	0.3750	0.933	1.93	13.4	4.86	2.73	24.0
L6 × 4 × ½	4.75	6.00	4.00	0.5000	0.981	1.98	17.3	6.22	3.55	23.7
L6 × 4 × ⅝	5.86	6.00	4.00	0.6250	1.03	2.03	21.0	7.48	4.32	23.5
L6 × 4 × ⅞	8.00	6.00	4.00	0.8750	1.12	2.12	27.7	9.70	5.82	22.8
L7 × 4 × ⅜^1,2	4.00	7.00	4.00	0.3750	0.861	2.35	20.5	5.06	3.05	18.7
L7 × 4 × ½²	5.26	7.00	4.00	0.5000	0.910	2.40	26.6	6.48	3.95	18.5
L7 × 4 × ⅝	6.50	7.00	4.00	0.6250	0.958	2.45	32.4	7.79	4.80	18.2
L7 × 4 × ¾	7.74	7.00	4.00	0.7500	1.00	2.50	37.8	9.00	5.64	18.0
L8 × 4 × ½^1,2	5.80	8.00	4.00	0.5000	0.854	2.84	38.6	6.75	4.32	14.9
L8 × 4 × ⅝	7.16	8.00	4.00	0.6250	0.902	2.89	47.0	8.11	5.24	14.7
L8 × 4 × ¾	8.49	8.00	4.00	0.7500	0.949	2.94	55.0	9.37	6.13	14.4
L8 × 4 × 1	11.1	8.00	4.00	1.0000	1.04	3.03	69.7	11.6	7.87	13.9
L8 × 6 × ½^1,2	6.80	8.00	6.00	0.5000	1.46	2.46	44.4	21.7	11.5	29.1
L8 × 6 × ⅝	8.41	8.00	6.00	0.6250	1.51	2.50	54.2	26.4	14.1	29.0
L8 × 6 × ⅞	11.5	8.00	6.00	0.8750	1.60	2.60	72.4	34.9	18.9	28.6
L8 × 6 × 1	13.1	8.00	6.00	1.0000	1.65	2.65	80.9	38.8	21.3	28.5

Notes:

1. Section not compact for steel with F_y = 36 ksi.

2. Section slender for steel with F_y = 36 ksi.

Table A-4.6: Dimensions and properties of selected steel rectangular and square hollow structural sections (HSS)

Designation	A (in²)	Design wall thickness, t (in.)¹	S_x (in³)	Z_x (in³)	I_x (in⁴)	I_y (in⁴)	r_y (in.)

HSS2 × 2 × 3/16 HSS2 × 2 × 1/4	1.19 1.51	0.174 0.233	0.641 0.747	0.797 0.964	0.641 0.747	0.641 0.747	0.733 0.704
HSS2½ × 2½ × 3/16 HSS2½ × 2½ × 5/16	1.54 2.35	1.54 2.35	1.08 1.46	1.32 1.88	1.35 1.82	1.35 1.82	0.937 0.880
HSS3 × 3 × 3/16 HSS3 × 3 × 3/8	1.89 3.39	0.174 0.349	1.64 2.52	1.97 3.25	2.46 3.78	2.46 3.78	1.14 1.06
HSS3½ × 3½ × 3/16 HSS3½ × 3½ × 3/8	2.24 4.09	0.174 0.349	2.31 3.71	2.76 4.69	4.05 6.49	4.05 6.49	1.35 1.26
HSS4 × 3 × 3/16 HSS4 × 3 × 3/8	2.24 4.09	0.174 0.349	2.47 3.97	3.00 5.12	4.93 7.93	3.16 5.01	1.19 1.11
HSS4 × 4 × 1/4 HSS4 × 4 × 1/2	3.37 6.02	0.233 0.465	3.90 5.97	4.69 7.70	7.80 11.9	7.80 11.9	1.52 1.41
HSS6 × 4 × 1/4 HSS6 × 4 × 1/2	4.30 7.88	0.233 0.465	6.96 11.3	8.53 14.6	20.9 34.0	11.1 17.8	1.61 1.50
HSS6 × 6 × 1/4 HSS6 × 6 × 5/8	5.24 11.7	0.233 0.581	9.54 18.4	11.2 23.2	28.6 55.2	28.6 55.2	2.34 2.17
HSS8 × 4 × 1/4 HSS8 × 4 × 5/8	5.24 11.7	0.233 0.581	10.6 20.5	13.3 27.4	42.5 82.0	14.4 26.6	1.66 1.51
HSS8 × 8 × 1/4² HSS8 × 8 × 5/8	7.10 16.4	0.233 0.581	17.7 36.5	20.5 44.7	70.7 146	70.7 146	3.15 2.99
HSS12 × 4 × 1/4 HSS12 × 4 × 5/8	7.10 16.4	0.233 0.581	19.9 40.8	25.6 55.5	119 245	21.0 40.4	1.72 1.57
HSS12 × 8 × 1/4² HSS12 × 8 × 5/8	8.96 21.0	0.233 0.581	30.6 66.1	36.6 82.1	184 397	98.8 210	3.32 3.16
HSS12 × 12 × 1/4² HSS12 × 12 × 5/8	10.8 25.7	0.233 0.581	41.4 91.4	47.6 109	248 548	248 548	4.79 4.62
HSS16 × 4 × 5/16 HSS16 × 4 × 5/8	11.1 21.0	0.291 0.581	38.5 67.3	51.1 92.9	308 539	33.2 54.1	1.73 1.60
HSS16 × 8 × 5/16 HSS16 × 8 × 5/8	13.4 25.7	0.291 0.581	56.4 102	69.4 129	451 815	155 274	3.40 3.27
HSS16 × 12 × 5/16² HSS16 × 12 × 5/8	15.7 30.3	0.291 0.581	74.4 136	87.7 165	595 1090	384 700	4.94 4.80
HSS16 × 16 × 3/8 HSS16 × 16 × 5/8	21.5 35.0	0.349 0.581	109 171	126 200	873 1370	873 1370	6.37 6.25
HSS20 × 4 × 3/8 HSS20 × 4 × 1/2	16.0 20.9	0.349 0.465	65.7 83.8	89.3 115	657 838	47.6 58.7	1.73 1.68
HSS20 × 8 × 3/8 HSS20 × 8 × 5/8	18.7 30.3	0.349 0.581	92.6 144	117 185	926 1440	222 338	3.44 3.34
HSS20 × 12 × 3/8² HSS20 × 12 × 5/8	21.5 35.0	0.349 0.581	120 188	144 230	1200 1880	547 851	5.04 4.93

Notes:

1. The nominal wall thickness, t, in the designation for an HSS shape (for example, ½ in. or ¼ in.) is different from the "design wall thickness," t, which is tabulated for each section and which is permitted to be smaller than the nominal value.

2. Section is not compact, based on flange slenderness: use reduced nominal bending strength, M_n, as follows:

equation

Table A-4.7: Dimensions and properties of selected steel round hollow structural sections (HSS)

Designation	A (in²)	Design wall thickness, t (in.)¹	I (in⁴)	r (in.)

HSS1.660 × 0.140	0.625	0.130	0.184	0.543
HSS1.990 × 0.120 HSS1.990 × 0.188	0.624 0.943	0.111 0.174	0.251 0.355	0.634 0.613
HSS2.375 × 0.125 HSS2.375 × 0.250	0.823 1.57	0.116 0.233	0.527 0.910	0.800 0.762
HSS2.500 × 0.125 HSS2.500 × 0.250	0.869 1.66	0.116 0.233	0.619 1.08	0.844 0.806
HSS3.000 × 0.125 HSS3.000 × 0.250	1.05 2.03	0.116 0.233	1.09 1.95	1.02 0.982
HSS3.500 × 0.125 HSS3.500 × 0.313	1.23 2.93	0.116 0.291	1.77 3.81	1.20 1.14
HSS4.000 × 0.125 HSS4.000 × 0.313	1.42 3.39	0.116 0.291	2.67 5.87	1.37 1.32
HSS6.000 × 0.250 HSS6.000 × 0.500	4.22 8.09	0.233 0.465	17.6 31.2	2.04 1.96
HSS8.625 × 0.250 HSS8.625 × 0.625	6.14 14.7	0.233 0.581	54.1 119	2.97 2.85
HSS10.000 × 0.250 HSS10.000 × 0.625	7.15 17.2	0.233 0.581	85.3 191	3.45 3.34
HSS12.750 × 0.375 HSS12.750 × 0.500	13.6 17.9	0.349 0.465	262 339	4.39 4.35
HSS14.000 × 0.375 HSS14.000 × 0.625	15.0 24.5	0.349 0.581	349 552	4.83 4.75
HSS16.000 × 0.375 HSS16.000 × 0.625	17.2 28.1	0.349 0.581	526 838	5.53 5.46
HSS18.000 × 0.500	25.6	0.465	985	6.20
HSS20.000 × 0.500	28.5	0.465	1360	6.91

Note:

1. The nominal wall thickness, t, in the designation for an HSS shape (e.g., 0.500 in. or 0.250 in.) is different from the "design wall thickness," t, which is tabulated for each section and which is permitted to be smaller than the nominal value.

Table A-4.8: Dimensions and properties of selected steel pipe

Designation	A (in²)	Design wall thickness, t (in.)¹	Diameter (in.)	I (in⁴)	r (in.)

Standard weight steel pipe
Pipe 2 Std.	1.02	0.143	2.38	0.627	0.791
Pipe 2½ Std.	1.61	0.189	2.88	1.45	0.952
Pipe 3 Std.	2.07	0.201	3.50	2.85	1.17
Pipe 3½ Std.	2.50	0.211	4.00	4.52	1.34
Pipe 4 Std.	2.96	0.221	4.50	6.82	1.51
Pipe 5 Std.	4.01	0.241	5.56	14.3	1.88
Pipe 6 Std.	5.20	0.261	6.63	26.5	2.25
Pipe 8 Std.	7.85	0.300	8.63	68.1	2.95
Pipe 10 Std.	11.5	0.340	10.8	151	3.68
Pipe 12 Std.	13.7	0.349	12.8	262	4.39
Extra strong steel pipe
Pipe 2 x-Strong	1.40	0.204	2.38	0.827	0.771
Pipe 2½ x-Strong	2.10	0.257	2.88	1.83	0.930
Pipe 3 x-Strong	2.83	0.280	3.50	3.70	1.14
Pipe 3½ x-Strong	3.43	0.296	4.00	5.94	1.31
Pipe 4 x-Strong	4.14	0.315	4.50	9.12	1.48
Pipe 5 x-Strong	5.73	0.349	5.56	19.5	1.85
Pipe 6 x-Strong	7.83	0.403	6.63	38.3	2.20
Pipe 8 x-Strong	11.9	0.465	8.63	100	2.89
Pipe 10 x-Strong	15.1	0.465	10.8	199	3.64
Pipe 12 x-Strong	17.5	0.465	12.8	339	4.35
Double-extra strong steel pipe
Pipe 2 xx-Strong	2.51	0.406	2.38	1.27	0.711
Pipe 2½ xx-Strong	3.83	0.514	2.88	2.78	0.854
Pipe 3 xx-Strong	5.17	0.559	3.50	5.79	1.06
Pipe 4 xx-Strong	7.66	0.628	4.50	14.7	1.39
Pipe 5 xx-Strong	10.7	0.699	5.56	32.2	1.74
Pipe 6 xx-Strong	14.7	0.805	6.63	63.5	2.08
Pipe 8 xx-Strong	20.0	0.816	8.63	154	2.78

Table A-4.9: Shear lag coefficient, U, for bolted and welded steel connections in tension¹

Condition	Shear lag coefficient, U	Diagram
All parts of the element (e.g., web, flanges, legs) are connected by bolts or welds.	U = 1.0
Transverse welds connecting some, but not all, of the cross-sectional "parts."	U = 1.0, but the net area, A_n, is taken as only that portion of the element cross section (consisting of flanges, webs, legs, and so on) that is directly connected by the transverse welds.
Longitudinal welds connecting steel plates or other shapes.	where l = (l₁ + l₂)/2 and l₁ and l₂ are at least 4 times the weld size; and x is the distance measured from the connection plane to the centroid of the member.
Bolts connecting wide-flange (W) shapes; or M, S, HP shapes; or Tees made from any of those sections.	U = 0.90 where b_f ≥ 0.67d and flange is connected with at least 3 bolts per line. U = 0.85 where b_f < 0.67d and flange is connected with at least 3 bolts per line. U = 0.70 where only the web is connected with at least 4 bolts per line.
Bolts connecting single and double angles (L).	U = 0.80 where one leg of the angle is connected with at least 4 bolts per line. U = 0.60 where one leg of the angle is connected with 3 bolts per line. (See note 1 for angles connected with less than 3 bolts per line.)

Note:

1. The shear lag coefficient, U, for all tension members except plates and HSS, can be taken as U = 1 – x /l, where x is the distance measured from the connection plane to the centroid of the member and U is the length of the connection, measured either along the weld or measured from the first to the last bolt, in either case parallel to the direction of the tension force. For wide-flange shapes bolted through the flanges, the centroid is taken for half of the cross section, i.e., for the "tee" (WT shape), rather than for the whole W shape. Alternatively, the values for U listed in this table can be used in lieu of this equation.

Table A-4.10: Allowable axial loads^1,2,3 (kips), A992 steel wide-flange columns (F_y = 50 ksi)

Designa- tion	Effective length, KL (ft)
Designa- tion	10	12	14	16	18	20	22	24	26	28	30	32	34	36	38	40
W4 × 13	39	27	20	15	12	9	8	6	5	5	4	3	3	3	2	2
W5 × 16 W5 × 19	72 87	54 65	39 48	30 37	24 29	19 23	16 19	13 16	11 14	9 12	8 10	7 9	6 8	6 7	5 6	4 5
W6 × 9 W6 × 12 W6 × 16 W6 × 15 W6 × 20 W6 × 25	22 31 46 80 110 139	15 21 32 64 89 114	11 15 23 49 70 89	8 12 18 37 53 69	7 9 14 29 42 54	5 7 11 24 34 44	4 6 9 20 28 36	3 5 8 16 23 30	3 4 6 14 20 26	2 3 5 12 17 22	2 3 5 10 15 19	2 3 4 9 13 17	1 2 4 8 11 15	1 2 3 7 10 13	1 2 3 6 9 12	1 1 2 6 8 11
W8 × 13 W8 × 15 W8 × 18 W8 × 21 W8 × 24 W8 × 28 W8 × 31 W8 × 35 W8 × 40 W8 × 48 W8 × 58 W8 × 67	28 35 78 95 141 165 211 238 271 330 403 466	19 24 57 70 118 138 188 213 243 297 363 420	14 18 42 52 95 112 164 186 213 262 320 372	11 13 32 39 74 88 141 160 183 226 277 323	8 10 25 31 59 69 118 134 154 191 236 276	7 8 20 25 47 56 97 110 127 159 196 230	5 7 17 21 39 46 80 91 104 131 162 190	4 6 14 17 33 39 67 76 88 110 136 160	4 5 12 15 28 33 57 65 75 94 116 136	3 4 10 13 24 28 49 56 64 81 100 117	3 3 9 11 21 25 43 49 56 70 87 102	2 3 8 9 18 22 37 43 49 62 76 90	2 3 7 8 16 19 33 38 43 55 68 79	2 2 6 7 14 17 29 34 39 49 60 71	1 2 5 7 13 15 26 30 35 44 54 63	1 2 5 6 11 14 24 27 31 39 49 57
W10 × 15 W10 × 19 W10 × 26 W10 × 30 W10 × 33 W10 × 39 W10 × 45 W10 × 49 W10 × 54 W10 × 60 W10 × 68 W10 × 77 W10 × 88 W10 × 100 W10 × 112	30 44 128 151 219 263 306 366 402 451 509 581 668 755 850	20 31 100 118 194 233 273 340 375 421 475 543 625 706 797	15 22 74 88 168 203 238 313 345 387 438 500 577 653 739	11 17 57 67 142 173 204 283 313 352 398 456 527 597 676	9 13 45 53 117 144 171 254 281 316 358 410 475 539 612	7 11 36 43 95 117 140 224 248 280 318 364 423 481 548	6 9 30 35 78 97 115 195 217 244 278 319 372 424 484	5 7 25 30 66 81 97 168 187 211 241 277 323 369 423	4 6 21 25 56 69 82 143 159 180 206 236 277 317 364	3 5 18 22 48 60 71 123 137 155 177 204 239 273 314	3 4 16 19 42 52 62 107 120 135 154 177 208 238 273	2 4 14 16 37 45 54 94 105 119 136 156 183 209 240	2 3 12 14 32 40 48 83 93 105 120 138 162 185 213	2 3 11 13 29 36 43 74 83 94< 107 123 144 165 190	2 3 10 11 26 32 38 67 74 84 96 110 129 148 170	1 2 9 10 23 29 35 60 67 76 87 100 117 134 154
Designa- tion	Effective length, KL (ft)
Designa- tion	10	12	14	16	18	20	22	24	26	28	30	32	34	36	38	40
W12 × 40 W12 × 45 W12 × 50 W12 × 53 W12 × 58 W12 × 65 W12 × 72 W12 × 79 W12 × 87 W12 × 96 W12 × 106 W12 × 120 W12 × 136 W12 × 152 W12 × 170 W12 × 190 W12 × 210 W12 × 230 W12 × 252 W12 × 279 W12 × 305 W12 × 336	264 297 332 393 430 509 563 620 685 756 837 946 1075 1206 1352 1517 1677 1841 2018 2236 2448 2713	234 263 294 365 400 484 536 590 652 720 798 902 1026 1153 1293 1452 1607 1764 1936 2147 2353 2610	202 227 255 333 366 456 505 556 615 680 754 853 971 1092 1226 1379 1527 1678 1843 2046 2246 2494	171 193 216 301 331 425 471 519 575 636 706 800 912 1026 1154 1299 1440 1584 1742 1936 2128 2367	141 159 179 268 296 393 436 481 533 590 656 743 848 957 1077 1213 1347 1484 1634 1819 2001 2230	114 129 146 235 260 360 400 441 490 543 604 685 783 884 997 1125 1250 1380 1520 1696 1869 2087	94 107 120 203 226 327 363 401 446 495 551 626 717 811 915 1034 1152 1273 1405 1569 1733 1939	79 90 101 173 194 294 327 361 402 447 498 567 650 737 834 944 1052 1165 1288 1442 1595 1789	67 76 86 148 165 262 292 323 360 400 447 509 585 664 753 854 954 1058 1172 1315 1458 1639	58 66 74 127 142 231 258 286 319 355 397 453 522 594 675 767 859 954 1058 1190 1323 1491	51 57 65 111 124 201 226 250 279 312 349 399 461 527 600 683 766 853 948 1069 1191 1347	44 50 57 97 109 177 198 219 245 274 307 351 406 463 528 602 677 755 842 953 1065 1209	39 44 50 86 96 157 176 194 217 243 272 311 359 410 467 533 600 669 746 844 944 1074	35 40 45 77 86 140 157 173 194 216 242 277 320 366 417 476 535 597 665 753 842 958	31 35 40 69 77 125 140 155 174 194 218 249 287 328 374 427 480 536 597 676 756 860	28 32 36 62 69 113 127 140 157 175 196 224 259 296 338 385 433 483 539 610 682 776
Designa- tion	Effective length, KL (ft)
Designa- tion	10	12	14	16	18	20	22	24	26	28	30	32	34	36	38	40
W14 × 43³ W14 × 48 W14 × 53 W14 × 61 W14 × 68 W14 × 74 W14 × 82 W14 × 90 W14 × 99 W14 × 109 W14 × 120 W14 × 132 W14 × 145 W14 × 159 W14 × 176 W14 × 193 W14 × 211 W14 × 233 W14 × 257 W14 × 283 W14 × 311 W14 × 342 W14 × 370 W14 × 398 W14 × 426 W14 × 455 W14 × 500 W14 × 550 W14 × 605 W14 × 665 W14 × 730 W14 × 808 W14 × 873	281 316 351 449 503 550 605 734 807 888 980 1078 1196 1309 1453 1594 1741 1926 2127 2347 2577 2851 3080 3309 3539 3797 4171 4603 5065 5585 6136 6811 7364	247 278 309 416 466 510 561 710 780 859 948 1043 1161 1271 1412 1550 1693 1874 2070 2285 2511 2779 3003 3228 3453 3707 4073 4498 4952 5465 6008 6677 7223	212 239 266 380 425 466 513 682 749 826 911 1003 1122 1229 1364 1499 1638 1813 2005 2214 2434 2696 2914 3134 3354 3602 3961 4378 4823 5327 5860 6522 7060	177 201 224 342 383 421 463 651 716 789 871 960 1078 1181 1312 1442 1577 1747 1932 2135 2348 2602 2814 3029 3243 3486 3836 4243 4678 5172 5694 6348 6877	145 165 185 303 340 374 412 618 680 749 828 912 1030 1129 1255 1381 1510 1674 1853 2049 2255 2501 2706 2915 3122 3358 3698 4095 4519 5001 5512 6156 6675	117 134 150 265 298 329 362 583 641 707 782 862 979 1074 1195 1315 1439 1596 1768 1957 2155 2392 2590 2792 2992 3221 3551 3935 4348 4817 5315 5948 6456	97 110 123 229 257 285 313 546 601 664 734 810 926 1016 1131 1246 1364 1514 1678 1860 2049 2277 2467 2662 2855 3076 3394 3766 4166 4621 5105 5727 6223	82 93 104 194 219 242 267 509 560 619 685 756 871 957 1065 1174 1287 1429 1586 1759 1940 2158 2340 2527 2712 2924 3231 3590 3976 4416 4885 5494 5977	70 79 88 165 186 206 227 471 519 574 635 702 815 896 998 1101 1207 1342 1491 1656 1827 2035 2208 2388 2564 2768 3062 3407 3778 4204 4657 5252 5720	60 68 76 143 161 178 196 434 478 529 585 647 759 834 930 1028 1127 1255 1395 1551 1713 1910 2075 2246 2414 2609 2889 3220 3576 3986 4422 5002 5456	52 59 66 124 140 155 171 397 437 484 536 594 702 773 862 954 1047 1167 1298 1446 1599 1785 1940 2103 2262 2448 2715 3031 3371 3764 4184 4747 5185	— 52 58 109 123 136 150 360 398 441 488 541 647 712 795 881 968 1079 1202 1341 1485 1660 1806 1960 2111 2287 2540 2841 3165 3541 3942 4488 4910	— 46 51 96 109 121 133 326 359 399 442 491 592 653 730 809 890 994 1108 1238 1372 1536 1674 1819 1961 2127 2367 2651 2960 3317 3701 4229 4634	— 41 46 86 97 107 118 292 322 358 397 441 540 595 666 740 814 910 1017 1137 1262 1415 1544 1680 1813 1969 2195 2464 2756 3096 3461 3970 4358	— 37 41 77 87 96 106 262 289 321 356 396 488 539 604 673 741 830 928 1040 1155 1298 1417 1545 1669 1816 2028 2281 2557 2878 3224 3713 4084	— 33 37 70 78 87 96 236 261 290 322 357 441 487 545 607 669 750 841 944 1051 1184 1295 1414 1530 1667 1865 2103 2361 2665 2992 3461 3814

Notes:

1. Slenderness ratio, KL/r > 200, for table cells shown with light tone: such slender columns are permitted but not recommended.

2. Interpolation can be used to find approximate values for allowable axial loads for effective lengths not shown in the table (i.e., for odd numbers between 10 ft and 40 ft).

3. Section is "slender" for compression; values have been appropriately lowered.

Table A-4.11: Allowable stresses for A992 steel columns (F_y = 50 ksi)

KL/r F_c	KL/r F_c	KL/r F_c	KL/r F_c	KL/r F_c
1 29.9	41 26.5	81 18.5	121 10.3	161 5.80
2 29.9	42 26.3	82 18.3	122 10.1	162 5.73
3 29.9	43 26.2	83 18.1	123 9.93	163 5.66
4 29.9	44 26.0	84 17.9	124 9.77	164 5.59
5 29.9	45 25.8	85 17.7	125 9.62	165 5.52
6 29.9	46 25.6	86 17.4	126 9.46	166 5.45
7 29.8	47 25.5	87 17.2	127 9.32	167 5.39
8 29.8	48 25.3	88 17.0	128 9.17	168 5.32
9 29.8	49 25.1	89 16.8	129 9.03	169 5.26
10 29.7	50 24.9	90 16.6	130 8.89	170 5.20
11 29.7	51 24.8	91 16.3	131 8.76	171 5.14
12 29.6	52 24.6	92 16.1	132 8.62	172 5.08
13 29.6	53 24.4	93 15.9	133 8.49	173 5.02
14 29.5	54 24.2	94 15.7	134 8.37	174 4.96
15 29.5	55 24.0	95 15.5	135 8.24	175 4.91
16 29.4	56 23.8	96 15.3	136 8.12	176 4.85
17 29.3	57 23.6	97 15.0	137 8.01	177 4.80
18 29.2	58 23.4	98 14.8	138 7.89	178 4.74
19 29.2	59 23.2	99 14.6	139 7.78	179 4.69
20 29.1	60 23.0	100 14.4	140 7.67	180 4.64
21 29.0	61 22.8	101 14.2	141 7.56	181 4.59
22 28.9	62 22.6	102 14.0	142 7.45	182 4.54
23 28.8	63 22.4	103 13.8	143 7.35	183 4.49
24 28.7	64 22.2	104 13.6	144 7.25	184 4.44
25 28.6	65 22.0	105 13.4	145 7.15	185 4.39
26 28.5	66 21.8	106 13.2	146 7.05	186 4.34
27 28.4	67 21.6	107 13.0	147 6.95	186 4.34
28 28.3	68 21.4	108 12.8	148 6.86	188 4.25
29 28.2	69 21.1	109 12.6	149 6.77	189 4.21
30 28.0	70 20.9	110 12.4	150 6.68	190 4.16
31 27.9	71 20.7	111 12.2	151 6.59	191 4.12
32 27.8	72 20.5	112 12.0	152 6.50	192 4.08
33 27.6	73 20.3	113 11.8	153 6.42	193 4.03
34 27.5	74 20.1	114 11.6	154 6.34	194 3.99
35 27.4	75 19.8	115 11.4	155 6.25	195 3.95
36 27.2	76 19.6	116 11.2	156 6.17	196 3.91
37 27.1	77 19.4	117 11.0	157 6.10	197 3.87
38 26.9	78 19.2	118 10.8	158 6.02	198 3.83
39 26.8	79 19.0	119 10.6	159 5.94	199 3.79
40 26.6	80 18.8	120 10.4	160 5.87	200 3.76

Table A-4.12: Allowable stresses for A500 Grade B HSS rectangular columns (F_y = 46 ksi)

KL/r F_c	KL/r F_c	KL/r F_c	KL/r F_c	KL/r F_c
1 27.5	41 24.6	81 17.7	121 10.3	161 5.80
2 27.5	42 24.5	82 17.5	122 10.1	162 5.73
3 27.5	43 24.3	83 17.3	123 9.93	163 5.66
4 27.5	44 24.2	84 17.1	124 9.77	164 5.59
5 27.5	45 24.0	85 16.9	125 9.62	165 5.52
6 27.5	46 23.9	86 16.7	126 9.46	166 5.45
7 27.5	47 23.7	87 16.6	127 9.32	167 5.39
8 27.4	48 23.6	88 16.4	128 9.17	168 5.32
9 27.4	49 23.4	89 16.2	129 9.03	169 5.26
10 27.4	50 23.3	90 16.0	130 8.89	170 5.20
11 27.3	51 23.1	91 15.8	131 8.76	171 5.14
12 27.3	52 23.0	92 15.6	132 8.62	172 5.08
13 27.2	53 22.8	93 15.4	133 8.49	173 5.02
14 27.2	54 22.6	94 15.2	134 8.37	174 4.96
15 27.1	55 22.5	95 15.0	135 8.24	175 4.91
16 27.1	56 22.3	96 14.8	136 8.12	176 4.85
17 27.0	57 22.1	97 14.6	137 8.01	177 4.80
18 27.0	58 22.0	98 14.4	138 7.89	178 4.74
19 26.9	59 21.8	99 14.2	139 7.78	179 4.69
20 26.8	60 21.6	100 14.1	140 7.67	180 4.64
21 26.7	61 21.4	101 13.9	141 7.56	181 4.59
22 26.7	62 21.3	102 13.7	142 7.45	182 4.54
23 26.6	63 21.1	103 13.5	143 7.35	183 4.49
24 26.5	64 20.9	104 13.3	144 7.25	184 4.44
25 26.4	65 20.7	105 13.1	145 7.15	185 4.39
26 26.3	66 20.5	106 12.9	146 7.05	186 4.34
27 26.2	67 20.4	107 12.8	147 6.95	186 4.34
28 26.1	68 20.2	108 12.6	148 6.86	188 4.25
29 26.0	69 20.0	109 12.4	149 6.77	189 4.21
30 25.9	70 19.8	110 12.2	150 6.68	190 4.16
31 25.8	71 19.6	111 12.0	151 6.59	191 4.12
32 25.7	72 19.4	112 11.8	152 6.50	192 4.08
33 25.6	73 19.2	113 11.7	153 6.42	193 4.03
34 25.5	74 19.1	114 11.5	154 6.34	194 3.99
35 25.4	75 18.9	115 11.3	155 6.25	195 3.95
36 25.2	76 18.7	116 11.1	156 6.17	196 3.91
37 25.1	77 18.5	117 11.0	157 6.10	197 3.87
38 25.0	78 18.3	118 10.8	158 6.02	198 3.83
39 24.9	79 18.1	119 10.6	159 5.94	199 3.79
40 24.7	80 17.9	120 10.4	160 5.87	200 3.76

Table A-4.13: Allowable stresses for A500 Grade B HSS round columns (F_y = 42 ksi)

KL/r F_c	KL/r F_c	KL/r F_c	KL/r F_c	KL/r F_c
1 25.1	41 22.7	81 16.8	121 10.2	161 5.80
2 25.1	42 22.6	82 16.6	122 10.1	162 5.73
3 25.1	43 22.4	83 16.5	123 9.93	163 5.66
4 25.1	44 22.3	84 16.3	124 9.77	164 5.59
5 25.1	45 22.2	85 16.1	125 9.62	165 5.52
6 25.1	46 22.1	86 16.0	126 9.46	166 5.45
7 25.1	47 22.0	87 15.8	127 9.32	167 5.39
8 25.1	48 21.8	88 15.6	128 9.17	168 5.32
9 25.0	49 21.7	89 15.5	129 9.03	169 5.26
10 25.0	50 21.6	90 15.3	130 8.89	170 5.20
11 25.0	51 21.4	91 15.1	131 8.76	171 5.14
12 24.9	52 21.3	92 15.0	132 8.62	172 5.08
13 24.9	53 21.2	93 14.8	133 8.49	173 5.02
14 24.8	54 21.0	94 14.6	134 8.37	174 4.96
15 24.8	55 20.9	95 14.4	135 8.24	175 4.91
16 24.8	56 20.7	96 14.3	136 8.12	176 4.85
17 24.7	57 20.6	97 14.1	137 8.01	177 4.80
18 24.7	58 20.5	98 13.9	138 7.89	178 4.74
19 24.6	59 20.3	99 13.8	139 7.78	179 4.69
20 24.5	60 20.2	100 13.6	140 7.67	180 4.64
21 24.5	61 20.0	101 13.4	141 7.56	181 4.59
22 24.4	62 19.9	102 13.3	142 7.45	182 4.54
23 24.3	63 19.7	103 13.1	143 7.35	183 4.49
24 24.3	64 19.6	104 12.9	144 7.25	184 4.44
25 24.2	65 19.4	105 12.8	145 7.15	185 4.39
26 24.1	66 19.2	106 12.6	146 7.05	186 4.34
27 24.0	67 19.1	107 12.4	147 6.95	186 4.34
28 24.0	68 18.9	108 12.3	148 6.86	188 4.25
29 23.9	69 18.8	109 12.1	149 6.77	189 4.21
30 23.8	70 18.6	110 12.0	150 6.68	190 4.16
31 23.7	71 18.5	111 11.8	151 6.59	191 4.12
32 23.6	72 18.3	112 11.6	152 6.50	192 4.08
33 23.5	73 18.1	113 11.5	153 6.42	193 4.03
34 23.4	74 18.0	114 11.3	154 6.34	194 3.99
35 23.3	75 17.8	115 11.2	155 6.25	195 3.95
36 23.2	76 17.6	116 11.0	156 6.17	196 3.91
37 23.1	77 17.5	117 10.8	157 6.10	197 3.87
38 23.0	78 17.3	118 10.7	158 6.02	198 3.83
39 22.9	79 17.1	119 10.5	159 5.94	199 3.79
40 22.8	80 17.0	120 10.4	160 5.87	200 3.76

Table A-4.14: Allowable stresses for A36¹ steel columns (F_y = 36 ksi)

KL/r F_c	KL/r F_c	KL/r F_c	KL/r F_c	KL/r F_c
1 21.6	41 19.7	81 15.3	121 10.0	161 5.80
2 21.6	42 19.6	82 15.1	122 9.85	162 5.73
3 21.5	43 19.6	83 15.0	123 9.72	163 5.66
4 21.5	44 19.5	84 14.9	124 9.59	164 5.59
5 21.5	45 19.4	85 14.7	125 9.47	165 5.52
6 21.5	46 19.3	86 14.6	126 9.35	166 5.45
7 21.5	47 19.2	87 14.5	127 9.22	167 5.39
8 21.5	48 19.1	88 14.3	128 9.10	168 5.32
9 21.5	49 19.0	89 14.2	129 8.98	169 5.26
10 21.4	50 18.9	90 14.1	130 8.86	170 5.20
11 21.4	51 18.8	91 13.9	131 8.73	171 5.14
12 21.4	52 18.7	92 13.8	132 8.61	172 5.08
13 21.4	53 18.6	93 13.7	133 8.49	173 5.02
14 21.3	54 18.5	94 13.5	134 8.37	174 4.96
15 21.3	55 18.4	95 13.4	135 8.24	175 4.91
16 21.3	56 18.3	96 13.3	136 8.12	176 4.85
17 21.2	57 18.2	97 13.1	137 8.01	177 4.80
18 21.2	58 18.1	98 13.0	138 7.89	178 4.74
19 21.2	59 17.9	99 12.9	139 7.78	179 4.69
20 21.1	60 17.8	100 12.7	140 7.67	180 4.64
21 21.1	61 17.7	101 12.6	141 7.56	181 4.59
22 21.0	62 17.6	102 12.5	142 7.45	182 4.54
23 21.0	63 17.5	103 12.3	143 7.35	183 4.49
24 20.9	64 17.4	104 12.2	144 7.25	184 4.44
25 20.9	65 17.3	105 12.1	145 7.15	185 4.39
26 20.8	66 17.1	106 11.9	146 7.05	186 4.34
27 20.7	67 17.0	107 11.8	147 6.95	186 4.34
28 20.7	68 16.9	108 11.7	148 6.86	188 4.25
29 20.6	69 16.8	109 11.5	149 6.77	189 4.21
30 20.6	70 16.7	110 11.4	150 6.68	190 4.16
31 20.5	71 16.5	111 11.3	151 6.59	191 4.12
32 20.4	72 16.4	112 11.1	152 6.50	192 4.08
33 20.4	73 16.3	113 11.0	153 6.42	193 4.03
34 20.3	74 16.2	114 10.9	154 6.34	194 3.99
35 20.2	75 16.0	115 10.7	155 6.25	195 3.95
36 20.1	76 15.9	116 10.6	156 6.17	196 3.91
37 20.1	77 15.8	117 10.5	157 6.10	197 3.87
38 20.0	78 15.6	118 10.4	158 6.02	198 3.83
39 19.9	79 15.5	119 10.2	159 5.94	199 3.79
40 19.8	80 15.4	120 10.1	160 5.87	200 3.76

Note:

1. Steel pipe fabricated with A53 Grade B steel and F_y = 35 ksi may be analyzed using this table for F_y = 36 ksi.

Table A-4.15: Plastic section modulus (Z_x) values: lightest laterally braced steel compact shapes for bending,
F_y = 50 ksi

Shape Z_x (in³) ²L_p (ft)	Shape Z_x (in³) ²L_p (ft)	Shape Z_x (in³) ²L_p (ft)
W6 × 8.5¹ 5.59 3.14	W21 × 55 126 6.11	W40 × 211 906 8.87
W6 × 9¹ 6.23 3.20	W24 × 55 134 4.73	W40 × 215 964 12.5
W8 × 10¹ 8.77 3.14	W21 × 62 144 6.25	W44 × 230 1100 12.1
W10 × 12¹ 12.5 2.87	W24 × 62 153 4.87	W40 × 249 1120 12.5
W12 × 14 17.4 2.66	W21 × 68 160 6.36	W44 × 262 1270 12.3
W12 × 16 20.1 2.73	W24 × 68 177 6.61	W44 × 290 1410 12.3
W10 × 19 21.6 3.09	W24 × 76 200 6.78	W40 × 324 1460 12.6
W12 × 19 24.7 2.90	W24 × 84 224 6.89	W44 × 335 1620 12.3
W10 × 22 26.0 4.70	W27 × 84 244 7.31	W40 × 362 1640 12.7
W12 × 22 29.3 3.00	W30 × 90 283 7.38	W40 × 372 1680 12.7
W14 × 22 33.2 3.67	W30 × 99 312 7.42	W40 × 392 1710 9.33
W12 × 26 37.2 5.33	W30 × 108 346 7.59	W40 × 397 1800 12.9
W14 × 26 40.2 3.81	W30 × 116 378 7.74	W40 × 431 1960 12.9
W16 × 26 44.2 3.96	W33 × 118 415 8.19	W36 × 487 2130 14.0
W14 × 30 47.3 5.26	W33 × 130 467 8.44	W40 × 503 2320 13.1
W16 × 31 54.0 4.13	W36 × 135 509 8.41	W36 × 529 2330 14.1
W14 × 34 54.6 5.40	W33 × 141 514 8.58	W40 × 593 2760 13.4
W18 × 35 66.5 4.31	W40 × 149 598 8.09	W36 × 652 2910 14.5
W16 × 40 73.0 5.55	W36 × 160 624 8.83	W36 × 655 3080 13.6
W18 × 40 78.4 4.49	W40 × 167 693 8.48	W36 × 723 3270 14.7
W21 × 44 95.4 4.45	W36 × 182 718 9.01	W36 × 802 3660 14.9
W21 × 48 107 6.09	W40 × 183 774 8.80	W36 × 853 3920 15.1
W21 × 50 110 4.59	W40 × 199 869 12.2	W36 × 925 4130 15.0
W18 × 55 112 5.90

Notes:

1. Section is just out of range to qualify as compact for F_y = 50 ksi steel. Because the nominal flexural strength of the section must be reduced a small percentage to account for slenderness of the noncompact flanges, the value for plastic section modulus has been reduced by the same percentage, so that it may be used, as is, in the bending strength equation: Z_req = ΩM_max/F_y.

2. L_p, the largest unbraced length for which the section can be considered compact, is computed for F_y = 50 ksi steel. The comparable unbraced length for A36 steel is larger, and is equal to 4.16r_y (ft), where r_y is the section's radius of gyration about the y-axis (in.) — see Appendix Table A-4.3.

Table A-4.16: Available moment for A992 wide-flange (W) shapes^1,2

A. Available moments from 0 to 100 ft-kips

B. Available moments from 100 to 200 ft-kips

C. Available moments from 200 to 400 ft-kips

D. Available moments from 400 to 600 ft-kips

E. Available moments from 600 to 1000 ft-kips

F. Available moments from 1000 to 2000 ft-kips

G. Available moments from 2000 to 5000 ft-kips

H. Available moments from 5000 to 8000 ft-kips

Notes:

1. Values are based on the conservative assumption that the "lateral-torsional buckling modifier," C_b = 1.0. This conservative value of C_b = 1.0 is quite close to the actual value for simply-supported beams with equally spaced point loads of equal weight, where the beam is braced at those points only, except for the special case of a single point load at midspan, in which case C_b = 1.364. Actual values for C_b can be found for each unbraced beam segment by calculating the bending moments at the quarter-points along each segment (M_A, M_B, and M_C, with M_B being the moment at the midpoint of the segment), as well as the maximum moment, M_max, within each segment, and then inserting these values into Equation 4.13, reproduced as follows:

equation

In any case, the available moment cannot exceed M_p / Ω, the value for braced, compact sections given in Appendix Table A-4.15.

2. Solid circles represent the maximum unbraced length, L_p, for which a plastic moment can be achieved before the onset of lateral-torsional buckling; open circles represent the maximum unbraced length, L_r, for which an elastic moment can be achieved before the onset of lateral-torsional buckling (see Figure 4.24).

Table A-4.17: Maximum (actual) deflection in a beam^1,2,3

Deflection coefficient, C, for maximum (actual) deflection, Δ (in.), where Δ =

	22.46	9.33	4.49	216
	35.94	16.07	8.99	n/a
	61.34	26.27	13.31	n/a
	85.54	36.12	17.97	n/a
	n/a	n/a	n/a	576

Notes:

1. Beam diagram symbols in top row of tables represent the following conditions (from left to right): simply-supported; one end pinned and one end continuous; both ends continuous; and cantilever.

2. Units for the maximum (actual) deflection equation are as follows:

Δ = maximum (actual) deflection (in.)

C = deflection coefficient

L = span (in.): The quantity (L /12) that appears in the deflection equation is therefore the span in feet

E = modulus of elasticity (psi when load is in lb; or ksi when load is in kips)

I_x = moment of inertia about axis of bending (in⁴)

P = concentrated load or resultant of uniformly-distributed load (lb or kips)

w = uniformly-distributed load (lb/ft or kips/ft)

3. Allowable deflections (from Appendix Table A-1.3) are as follows:

For live load only (or snow or wind only), the typical basic floor beam limit is L/360 while typical roof beam limits are L/180, L/240, or L/360 (for no ceiling, nonplaster ceiling, or plaster ceiling respectively).

For total loads (combined live and dead), the typical basic floor beam limit is L/240 while typical roof beam limits are L/120, L/180, or L/240 (for no ceiling, nonplaster ceiling, or plaster ceiling respectively).

Table A-4.18: Shear capacity, or available strength, for a high-strength bolt subjected to single shear with threads excluded from shear plane (kips)

A. Bearing-type connections¹
Bolt type	Nominal bolt diameter (in.)
Bolt type	⅝	¾	⅞	1	1⅛	1¼	1⅜	1½
Group A (A325)	10.4	15.0	20.4	26.7	33.8	41.8	50.3	60.2
Group B (A490)	12.9	18.6	25.2	33.0	41.7	51.7	62.2	74.3
Group C (F3043)	—	—	—	44.4	56.2	69.5	—	—

B. Slip-critical connections (based on strength rather than serviceability)²
Bolt type	Nominal bolt diameter (in.)
Bolt type	⅝	¾	⅞	1	1⅛	1¼	1⅜	1½
Group A (A325)	4.29	6.33	8.81	11.5	12.7	16.0	19.2	23.3
Group B (A490)	5.42	7.91	11.1	14.5	18.1	23.1	27.3	33.4
Group C (F3043)	—	—	—	20.3	25.5	32.3	—	—

Notes:

1. Capacities are tabulated for single-shear connections, with bolt threads excluded from all shear planes (condition X). For double-shear, multiply values by 2; for threads included within shear planes (condition N), multiply values by 0.8. For double-shear and threads included, multiply by 2 × 0.8 = 1.6.

2. Slip-critical capacities are based on standard holes and single-shear. For double shear, multiply values by 2. Slip-critical bolts must also satisfy bearing capacity values in Appendix Table A-4.19.

Table A-4.19: Bearing capacity, or available strength, for a high-strength bolt bearing on material 1 in. thick, with clear spacing between bolts (or edge) ≥ 2 in. (kips)¹

Material being connected	Nominal bolt diameter (in.)
Material being connected	⅝	¾	⅞	1	1⅛	1¼	1⅜	1½
A36, F_u = 58 ksi	54.4	65.3	76.1	87.0	97.9	109	120	131
A992, F_u = 65 ksi	60.9	73.1	85.3	97.5	110	122	134	146

Note:

1. Capacity (available strength) is tabulated assuming that the bolt hole clear spacing (or clear spacing between bolt hole and material edge) in direction of force is no less than 2 in. For clear spacing less than 2 in., multiply capacity by L_c/ 2, where L_c is the actual clear spacing (in.). For cases where the small deformations associated with bolt bearing, at ordinary service loads, are considered to be a design issue, multiply capacity by 0.8. Where the thickness, t, of the material is other than 1 in., multiply the capacity by the thickness, t (in.). These multiplications are cumulative so that, for example, the capacity of a material with t = ⅝ in., clear spacing between bolts of 1.75 in., and consideration of bearing deformations, would be equal to the tabular value multiplied by (⅝)(1.75/2)(0.8) = (tabular value × 0.4375).

Table A-4.20: Minimum and maximum spacing and edge distance measured from bolt centerline for standard holes

A. Minimum bolt spacing (in.)
	Nominal bolt diameter (in.)
	⅝	¾	⅞	1	1⅛	1¼	1⅜	1½
Suggested	1⅞	2¼	2⅝	3	3⅜	3¾	4⅛	4½
Required	1⅔	2	2⅓	2⅔	3	3⅓	3⅔	4

B. Minimum edge distance (in.)¹
Type of edge	Nominal bolt diameter (in.)
Type of edge	⅝	¾	⅞	1	1⅛	1¼	1⅜	1½
All edges	⅞	1	1⅛	1¼	1½	1⅝	1-23/32	1⅞

C. Maximum bolt spacing and edge distance (in.)
Type of edge	Nominal bolt diameter (in.)
Type of edge	¼	⅜	½	⅝	¾	⅞	1	1⅛
Centerline spacing²	6	9	12	12	12	12	12	12
Edge distance	3	4½	6	6	6	6	6	6

Notes:

1. Minimum edge distances, measured in the direction of force, may be reduced below these values, as long as bearing capacity is appropriately reduced (see Note 1 in Appendix Table A-4.19). Bearing and tearout limits must also be met.

2. Maximum centerline spacing is measured in the direction of the applied load (longitudinally), and is valid for members not subject to corrosion, whether painted or not. For unpainted weathering steel, the maximum spacing is 7 in. or, where the thinner member is less than ½ in., 14 times that member's thickness.

Table A-4.21: Size limitations (leg size, w) for fillet welds (in.)

	T < ¼ in.	T = ¼ in.	¼ < T ≤ ½ in.	½ < T ≤ ¾ in.	¾ < T
	Thickness, T, of material being joined (in.)¹
Minimum weld size, w	1/8	1/8	3/16	1/4	5/16
Maximum weld size, w	T	3/16	T – 1/16 in.

Chapter 4 — Steel: Appendix