Axial Capacities of Eccentrically Loaded Equal-Leg Single Angles - Comparisons of Various Design Methods
Axial Capacities of Eccentrically Loaded Equal-Leg Single Angles - Comparisons of Various Design Methods
Axial Capacities of Eccentrically Loaded Equal-Leg Single Angles - Comparisons of Various Design Methods
ABSTRACT
For most structural engineers, the design of an eccentrically loaded single angle without lateral restraint along its length was considered to
be a formidable task prior to the publication of the 2005 AISC Specification for Structural Steel Buildings. According to Section E5 of the
2005 Specification, the effects of eccentricity on single-angle members are permitted to be neglected by using the effective slenderness ratio
as specified, provided that members are loaded at the ends in compression through the same leg; members are attached by welding or by
a minimum of two-bolt connections; there are no intermediate transverse loads; the leg length ratio is less than 1.7, if angles are connected
through the shorter leg; and the modified KL/r is less than or equal to 200.
Table 4-12 of the 13th edition AISC Steel Construction Manual provided the available strengths in axial compression of eccentrically loaded
single angles, with the assumption that the compressive force is applied at the geometric y-y axis at a distance of 0.75t from the back of the
connected leg, where t is the angle thickness. Table 4-12 has been revised in the 14th edition AISC Steel Construction Manual. The new table
corrects some numerical errors in the calculations and moves the compressive force to the midpoint of the connected leg. The values of the
axial compressive design strength in Table 4-12 are developed on the basis of bending about the principal axes w-w and z-z.
Keywords: eccentrically loaded single angles, design tables.
INTRODUCTION
ingle angles are commonly used as secondary bracing members for bridges and other structures, as web
members for small or medium-sized truss structures, and in
latticed structures, such as transmission towers. In structural
analysis, single-angle members are always treated as truss
members that can take only axial loads, either in tension
or in compression. However, because single angles are connected to gusset plates through one leg using welding or
bolting, the members are subjected to both axial and flexural demands resulting from the eccentric connection. Although the single angle is the most basic shape of hot-rolled
steel sections, its behavior under eccentric force is complex
and difficult to predict due to the fact that its geometric axes
do not align with its principal axes. Therefore, the design
method for predicting the axial strength of single angles
evolves with the better understanding of its behavior, and it
is evident in specification revisions over the years.
A design example of eccentrically loaded equal-leg single
angles was presented in the 1st edition AISC Manual of
Steel Construction, LRFD (AISC, 1986). However, there
was not a specification specifically for single angles. The
YuWen Li, P.E., Principal Structural Engineer, Gannett Fleming, Inc., Audubon,
PA. E-mail: yli@gfnet.com
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(a)
(b)
Fig. 1. Welded connection.
(a)
(b)
Fig. 2. Bolted connection.
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Eccentricity
As previously discussed, an end connection through one leg
creates the eccentricity for the applied axial load that induces the end moment and, therefore, affects the load carrying capacity of either the connection or the member, or
both. The effect of connection eccentricity is a function of
connection and member stiffness, the proper eccentricity
should be assumed when computing the axial capacity of
single angles. Blodgett (1966) concluded that if the gusset
plate is very flexible and offers no restraining action at the
end of the member, the moment due to connection eccentricity must be resisted by the member, not by the connection.
DESIGN EXAMPLES
Four methods are presented here to illustrate the design procedures involved with the eccentrically loaded single angle.
Equation and section references in these examples refer to
the 2010 AISC Specification.
Fig. 3. Eccentricity.
ENGINEERING JOURNAL / FOURTH QUARTER / 2012 / 133
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KL
L
= 72 + 0.75 = 72 + 0.75(58.5) = 116
r
rx
E
29, 000
= 0.45
= 12.8
Fy
36
Method 1
Fig. 4. Method 1.
L
K
Fy
E
Ag
b
t
rx
rz
KL/r
c
c
= 72 in.
= 1.0
= 36 ksi
= 29,000 ksi
= 2.86 in.2
= 4.0 in.
= 0.375 in.
= 1.230 in.
= 0.779 in.
200
= 0.90
= 1.67
Solution
Check the required radius of gyration, r min:
rmin = KL/200 = 1.0(72)/200
= 0.360 in
0.360 in. < rz = 0.779 in. OK
Determine the effective slenderness ratio, KL/r. For
2 E
KL
r
2 (29, 000)
1162
= 21.2 ksi
E
29, 000
= 4.71
= 134
QFy
1.0(36)
Fcr = Q 0.658 Fe
Fy
1.0(36 )
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Fcr = Q 0.658 Fe Fy
1
.
0
(
36
)
Method 2
L44a, connected to one leg, axial load is applied at the
middle thickness of the gusset plate. The angle is designed
on the basis of geometric axis (x-x) bending. See Figure 5.
t1
Ix
Sx
y
Sx(A,B)
ex
b
= 1.5t = b in.
= 4.32 in.4
= 1.50 in.3
= 1.13 in.
= Ix/ y = 3.82 in.3
= 0.75t + y = 1.41 in.
= 0.90
KL KL
72
=
=
= 92.4 200, OK
r
rz
0.779
Determine the reduction factor Q, for unstiffened element from Section E7.1(c):
Same as Method 1, Q = Qs = 1.0
2
0.66 Eb 4 tCb
Lb t
Me =
1 + 0.78
+ 1
Lb2
b2
2 E
KL
r
2 (29, 000)
92.42
= 33.5 ksi
E
29, 000
= 4.71
= 134
QFy
1.0(36)
722
72(0.375)
1 + 0.78
+ 1
42
= 991 kip-in
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My
M y 1.5 M y
M n = 1.92 1.17
Me
43.2
= 1.92 1.17
(443.2)
991
EI*
= 0.8bEIx
B1x =
2 EI *
( K1L )2
[1.0(72)] 2
= 191b
Cm
191b
1.0
=
=
1 Pr Pe1x 1 1.0( Pr ) 191b 191b Pr
191b
Mrx = B1x ( ex Pr ) =
( ex Pr )
191b Pr
frbx ( A, B)
fra
+
Fca Fcbx ( A, B)
191b ( ex Pr ) 1
Solving the previous equation, Pr = 22.5 kips.
Apply Equation H2-1 at point C:
frbx (C )
where
fra = required axial stress
frbx(A,B), frbx(C) = required flexure stresses
(Equation A-8-5)
( K1L )2
Point C:
fra frbx (C )
1.0
Fca Fcbx (C )
2 EI *
fra frbx ( A, B)
+
1.0
Fca Fcbx ( A, B)
Cm = 1.0 (conservative)
Pe1x =
fra frbx
+
1.0
Fca Fcbx
Cm
1.0 (Equation A-8-3)
1 Pr / Pe1x
Pe1x =
B1x =
fra
P / 2 .86
= r
20.7
Fca Fcbx (C )
191b (ex Pr ) 1
191b Pr 1.50
38.9
1.0
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Method 3
L44a, connected to one leg, axial load is applied at midpoint of angle leg and mid-thickness of gusset plate. The
angle is designed on the basis of principal axes (w-w, z-z)
bending. See Figure 6.
Fig. 6. Method 3.
= 1.5t = b in.
= 4.32 in.4
= 4.32 in.4
= 1.613 in.
= 0.382 in.
= Ag(rz)2 =1.74 in.4
= Ix + Iy Iz = 6.90 in.4
= I A = 1.55 in.4
t1
Ix
Iy
ew
ez
Iz
Iw
r w
M yw
M nw = 1.92 1.17
Me
92.2
= 1.92 1.17
92.2 138
417
= 126 138
Solution
Same as Method 2.
= 126 kip-in.
M yw 1.5 M yw
2. Calculate the angle flexural strength about major principal axis, bMnw.
3. Calculate the angle flexural strength about minor principal axis, bMnz.
Points A and C:
Point B
Points A and C
Cw( A,C ) = sin 45(b + t / 2) Cw( B)
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where
B1w, B1z = multiplier to account for P- effect based
on Section 8.2 of Appendix 8
Cm
1.0
1 Pr / Pe1
B1 =
Cm = 1.0 (conservative)
Pe1 =
1.0
Fca Fcbw( A) Fcbz( A)
fra frbz( B)
+
1.0
Fca Fcbz( B)
1.0
Fca Fcbw(C ) Fcbz (C )
= 4(Pr/Py)[1 (Pr/Py)]
=
B1z =
=
Mrw = B1w(ewPr)
Mrz = B1z(ezPr)
[1.0(72)] 2
2 EI z*
( K1L )2
[1.0(72)] 2
Cm
1.0
=
1 Pr / Pe1w 1 1.0 ( Pr ) / 305b
305b
305b Pr
Cm
1.0
=
1 Pr / Pe1z 1 1.0 ( Pr ) / 76.7b
76.7b
76.7b Pr
where
fra = required axial stress
( K1L )2
= 76.7b kips
B1w =
2 EI w*
= 305b kips
Pe1z =
(Equation A-8-5)
( K1L )2
Pe1w =
2 EI *
= 0.8bEI
EI*
(Equation A-8-3)
305b
Mrw = B1w (ew Pr ) =
(ew Pr )
305b Pr
76.7b
Mrz = B1z (ez Pr ) =
76.7b Pr
(ez Pr )
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=
Fca Fcbw( A) Fcbz( A)
305b (ew Pr )
2 .56
305b Pr
Pr / 2.86
+
44.4
20.7
76.7b (ez Pr )
1.27
76.7b Pr
41.3
1.0
Fig. 7. Method 4.
76.7b (ez Pr )
1.09
Pr / 2.86 76.7b Pr
=
+
1.0
20.7
48.6
All calculations are the same as Method 3, except for replacing values of ez and ew in Method 3 with the values provided
in this method.
Apply Equation H2-1 at point A, solve for Pr = 46.7 kips
Apply Equation H2-1 at point B, solve for Pr = 22.8 kips
Apply Equation H2-1 at point C, solve for Pr = 39.0 kips
305b (ew Pr )
2.56
305b Pr
Pr / 2.86
44.4
20.66
76.7b (ez Pr )
1.27
76.7b Pr
41.3
Solution
Determine the design compressive strength, cPn and the allowable compressive strength, Pn /c:
=
Fca Fcbw( A) Fcbz( A)
= 0.998 in.
= 0.998 in.
fra frbz( B)
+
Fca Fcbz( B)
ew
ez
1.0
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Pn/
Method 1
45.69
30.40
Method 2
22.54
15.00
3a
33.49
22.28
Method 3b
35.17
23.40
Method
a
b
35.2
23.2
Method 4
22.76
15.14
EI* = 0.8bEI
EI* = EI
5. As discussed in the design consideration section, because the slight eccentricity between the neutral axis of
the single angle and the center of gravity of the weld
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350
Method 1
330
Method 2
Method 3 (0.8bEI)
310
Method 3 (EI)
290
Method 4
270
250
230
210
190
170
150
130
110
90
70
50
6
10
12
14
16
18
20
22
24
26
160
Method 1
150
Method 2
Method 3 (0.8bEI)
140
Method 3 (EI)
Method 4
130
120
110
100
90
80
70
60
50
40
30
20
6
10
12
14
16
18
20
22
24
26
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60
Method 1
Method 2
55
Method 3 (0.8bEI)
Method 3 (EI)
50
Method 4
Table 4-12 (AISC, 2011)
45
10
22
Method 1
Method 2
20
Method 3 (0.8bEI)
Method 3 (EI)
18
Method 4
Table 4-12 (AISC, 2011)
Table 4-12 (AISC, 2005)
16
14
12
10
8
6
4
2
2
10
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(Method 1) are due to the presumptions that the significant bending and rotational restraints are provided by
the end connections; in other words, if another method
(Method 2, 3 or 4) is used to evaluate the available
compressive strength of the single angles, the reduced
unbraced lengths (effective length factor, K) and eccentricities due to the end restraints should be considered
to avoid overly conservative results, as described in
Commentary sectionE5 of the 2010 AISC Specification.
However, this could pose some challenges when the design is based on a particular code, where the unbraced
length reduction factor is limited to 1.0, as discussed in
design considerations of single angles in compression.
DESIGN TABLES
Design tables for the axial compressive design strength of
eccentrically loaded equal-leg single angles (grades 36 and
50) are prepared based on previously discussed Methods1,
3 and 4. The format of the tables follows the format of Table4-12 of the 14th edition AISC Manual.
Design Table 1: Axial compressive design strength of
equal-leg angles based on Method1, see Method1.
Design Table 2: Axial compressive design strength of
equal-leg angles based on Method3, assuming the axial load
is applied at mid-point of the connected leg and mid-thickness of the gusset plate. Angles are designed on the basis of
principal axes (w-w, z-z) bending. See Method3.
Design Table 3: Axial compressive design strength of
equal-leg angles based on Method 4, assuming the axial
load is applied at geometric axis y-y and mid-thickness of
the gusset plate. Angles are designed on the basis of principal axes (ww, z-z) bending. See Method4.
Design Table 4: Axial compressive design strength of
equal-leg angles based on Method4, assuming the axial load
is applied at geometric axis y-y, and mid-thickness of the
connected leg. Angles are designed on the basis of principal
axes (w-w, z-z) bending.
Design Tables 3 and 4 are integrated such that identical
angle sizes appear in adjacent tables for ease of comparison.
REFERENCES
AASHTO (2004), LRFD Bridge Design Specifications,
3rdEdition, American Association of State Highway and
Transportation Offices, Washington, D.C.
AASHTO (2007), LRFD Bridge Design Specifications,
4thEdition, American Association of State Highway and
Transportation Offices, Washington, D.C.
AISC (1986), Manual of Steel Construction, Load and Resistance Factor Design, 1stEdition, American Institute of
Steel Construction, Chicago, IL.
AISC (1989), Steel Construction Manual, Allowable Stress
Design, 9th Edition, American Institute of Steel Construction, Chicago, IL.
AISC (1993), Specification for Load and Resistance Factor
Design of Single Angle Members, American Institute of
Steel Construction, Chicago, IL.
AISC (1994), Manual of Steel Construction, Load and Resistance Factor Design, 2nd Edition, American Institute
of Steel Construction, Chicago, IL.
AISC (2001), Manual of Steel Construction, Load and Resistance Factor Design, 3rdEdition, American Institute
of Steel Construction, Chicago, IL.
AISC (2005a), Specification for Structural Steel Buildings,
American Institute of Steel Construction, Chicago, IL.
AISC (2005b), Steel Construction Manual, 13th Edition,
American Institute of Steel Construction, Chicago, IL.
AISC (2010), Specification for Structural Steel Buildings,
American Institute of Steel Construction, Chicago, IL.
AISC (2011), Steel Construction Manual, 14th Edition,
American Institute of Steel Construction, Chicago, IL.
Blodgett, O.W. (1966), Design of Welded Structures, The
James F. Lincoln Arc Welding Foundation, Cleveland,
OH.
Lutz, L.A. (2006), Evaluating Single-Angle Compression
Struts Using an Effective Slenderness Approach,
Engineering Journal, AISC, Fourth Quarter, 2006,
pp.241246.
Sakla, S.S. (2001), Tables for the Design Strength of Eccentrically-Loaded Single Angle Struts, Engineering
Journal, AISC, Third Quarter, 2001, pp.127136.
Walker, W.W. (1991), Table for Equal Single Angles in
Compression, Engineering Journal, AISC, Second
Quarter, 1991, pp.6568.
Woolcock, S.T. and Kitipornchai, S. (1986), Design of Single-Angle Web Struts in Trusses, Journal of Structural
Engineering, ASCE, Vol.112, No.6, pp.13271345.
Zureick, A. (1993), Design Strength of Concentrically
Loaded Single Angle Struts, Engineering Journal,
AISC, First Quarter, 1993, pp.1730.
131-168_EJ4Q_2012_2010-30R.indd 143
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Shape
11/8
lb/ft
56.9
Design
6
7
8
9
10
11
12
13
14
15
16
18
20
22
24
26
6
7
8
9
10
11
12
13
14
15
16
18
20
22
24
26
51.0
5 8c
45.0
9 16c
3 4
7 8
38.9
1 2c,
32.7
29.6
26.4
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
227
218
210
201
193
185
177
169
161
153
145
133
122
112
103
95.4
340
328
315
303
290
278
265
253
241
230
218
200
183
168
155
143
204
196
189
182
174
167
159
152
145
138
131
121
111
102
93.9
86.9
307
295
284
273
262
251
240
229
218
208
198
182
167
153
141
131
180
173
167
160
154
147
141
135
129
122
117
108
98.9
90.9
83.8
77.5
271
261
251
241
231
222
212
203
193
184
175
162
149
137
126
117
131
127
122
117
113
108
103
98.8
94.4
90.0
85.7
80.1
73.4
67.5
62.2
57.6
197
190
183
176
169
162
155
149
142
135
129
120
110
101
94
86.6
116
112
108
104
100
96.5
92.6
88.7
84.9
81.1
77.4
72.8
66.8
61.5
56.7
52.5
175
169
163
157
151
145
139
133
128
122
116
109
100
92.4
85.2
78.9
101
97.8
94.5
91.2
87.9
84.6
81.3
78.1
74.9
71.7
68.6
64.7
59.8
54.9
50.7
46.9
152
147
142
137
132
127
122
117
113
108
103
97.3
89.9
82.6
76.2
70.5
Fy = 36 ksi
156
234
150
226
144
217
139
209
133
200
128
192
122
184
117
176
111
168
106
160
101
152
93.9
141
86.0
129
79.1
119
72.9
110
67.5
101
Fy = 50 ksi
Design
Unbraced Length between Work Points, L (ft)
1/
1 8
262
249
236
223
210
197
185
174
163
154
145
133
122
112
103
95.4
394
374
354
334
315
297
278
261
246
232
219
200
183
168
155
143
236
224
212
201
190
178
167
157
148
139
132
121
111
102
93.9
86.9
355
337
319
302
285
268
252
236
222
210
198
182
167
153
141
131
209
198
188
178
168
158
148
139
131
124
117
108
98.9
90.9
83.8
77.5
5 8c
314
181
298
172
282
163
267
154
252
145
238
137
223
129
210
121
197
114
186
107
176
101
162
93.9
149
86.0
137
79.1
126
72.9
117
67.5
Properties
9 16c,
3 4
7 8
271
258
244
231
219
206
193
182
171
161
152
141
129
119
110
101
149
142
135
128
122
115
109
103
96.6
91.1
86.1
80.1
73.4
67.5
62.2
57.6
224
213
203
193
183
173
164
154
145
137
129
120
110
101
93.6
86.6
132
126
121
115
109
104
98.3
93.0
87.7
82.7
78.2
73.0
66.8
61.5
56.7
52.5
199
190
181
173
164
156
148
140
132
124
118
110
100
92.4
85.2
78.9
1 2c,
115
110
105
101
96.0
91.4
87.0
82.6
78.3
74.0
69.9
65.2
59.8
54.9
50.7
46.9
172
165
158
151
144
137
131
124
118
111
105
98.0
89.8
82.6
76.2
70.5
Ag (in.2)
16.8
15.1
13.3
11.5
9.69
8.77
7.84
z (in.)
1.56
1.56
1.57
1.57
1.58
1.58
1.59
ASD
LRFD
c = 1.67
c = 0.9
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate L/rz equal to or greater than 120, 140 and 200, respectively.
*Method 1.
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Shape
lb/ft
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
33.1
5 8
28.7
24.2
7 16c
9 16
1 2
21.9
19.6
17.3
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
152
144
137
129
122
115
108
101
94.0
83.2
74.2
66.5
59.9
54.3
49.5
45.2
228
217
206
195
184
173
162
152
141
125
111
99.9
90.1
81.6
74.3
68.0
135
128
122
115
109
103
96.3
90.3
84.4
75.1
66.9
60.0
54.1
49.0
44.6
40.8
203
193
183
173
164
154
145
136
127
113
101
90.2
81.3
73.7
67.1
61.4
117
111
106
100
94.7
89.3
83.9
78.6
73.5
65.7
58.5
52.5
47.4
42.9
39.1
35.8
176
167
159
151
142
134
126
118
111
98.7
88.0
78.9
71.2
64.5
58.8
53.7
Fy = 36 ksi
98.9
149
94.2
142
89.5
135
84.8
128
80.2
121
75.7
114
71.2
107
66.8
100
62.5
94.0
56.3
84.6
50.2
75.4
45.0
67.7
40.6
61.0
36.8
55.4
33.5
50.4
30.7
46.1
89.5
85.3
81.1
76.9
72.8
68.7
64.6
60.7
56.8
51.3
45.8
41.1
37.1
33.6
30.6
28.0
135
128
122
116
109
103
97.1
91.2
85.4
77.2
68.8
61.7
55.7
50.5
46.0
42.1
80.2
76.4
72.7
68.9
65.2
61.6
58.0
54.5
51.0
46.3
41.3
37.1
33.4
30.3
27.6
25.3
120
115
109
104
98.1
92.6
87.2
81.9
76.7
69.6
62.1
55.7
50.3
45.6
41.5
38.0
69.5
66.3
63.2
60.0
56.9
53.8
50.7
47.7
44.8
40.8
36.4
32.6
29.4
26.7
24.3
22.3
104
99.7
94.9
90.2
85.5
80.8
76.2
71.7
67.3
61.3
54.7
49.0
44.3
40.1
36.6
33.5
Fy = 50 ksi
Design
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
3 4
7 8
37.4
Design
1
177
165
154
142
131
120
111
102
94.1
83.2
74.2
66.5
59.9
54.3
49.5
45.2
266
248
231
214
197
181
166
153
141
125
111
99.9
90.1
81.6
74.3
68.0
157
147
137
127
117
108
98.9
91.3
84.5
75.1
66.9
60.0
54.1
49.0
44.6
40.8
3 4
7 8
237
221
206
191
176
162
149
137
127
113
101
90.2
81.3
73.7
67.1
61.4
137
128
119
110
102
93.7
86.2
79.6
73.7
65.7
58.5
52.5
47.4
42.9
39.1
35.8
206
116
192
108
179
101
166
93.5
153
86.5
141
79.6
130
73.3
120
67.7
111
62.7
98.7
56.3
88.0
50.2
78.9
45.0
71.2
40.6
64.5
36.8
58.8
33.5
53.7
30.7
Properties
1 2c
5 8
174
163
151
141
130
120
110
102
94.3
84.6
75.4
67.7
61.0
55.4
50.4
46.1
105
98.0
91.3
84.9
78.5
72.3
66.6
61.5
57.0
51.3
45.8
41.1
37.1
33.6
30.6
28.0
7 16c,
9 16
157
147
137
128
118
109
100
92.5
85.7
77.2
68.8
61.7
55.7
50.5
46.0
42.1
92.4
86.7
81.0
75.5
70.2
65.0
59.8
55.3
51.3
46.3
41.3
37.1
33.4
30.3
27.6
25.3
139
130
122
114
105
97.7
89.9
83.1
77.1
69.6
62.1
55.7
50.3
45.6
41.5
38.0
/
79.3
74.7
70.1
65.6
61.2
56.9
52.7
48.7
45.1
40.8
36.4
32.6
29.4
26.7
24.3
22.3
119
112
105
98.6
92.0
85.5
79.2
73.2
67.8
61.3
54.7
49.0
44.3
40.1
36.6
33.5
Ag (in.2)
11.0
9.75
8.46
7.13
6.45
5.77
5.08
z (in.)
1.17
1.17
1.17
1.17
1.18
1.18
1.18
ASD
LRFD
c = 1.67
c = 0.9
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate L/rz equal to or greater than 120, 140 and 200, respectively.
*Method 1.
131-168_EJ4Q_2012_2010-30R.indd 145
10/11/12 4:53 PM
Shape
lb/ft
27.2
Design
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
5 8
23.6
20.0
3 8c
1 2
16.2
5 16c,
7 16
14.3
12.3
10.4
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
125
119
112
106
99.5
93.1
86.7
80.5
74.4
68.3
59.0
51.5
45.3
40.2
35.9
32.3
188
179
169
159
150
140
130
121
112
103
88.7
77.4
68.1
60.4
54.0
48.5
109
104
98.2
92.6
87.0
81.4
75.9
70.5
65.2
60.1
52.0
45.4
40.0
35.5
31.7
28.5
164
156
148
139
131
122
114
106
98.0
90.4
78.2
68.3
60.1
53.3
47.6
42.8
92.4
87.8
83.2
78.5
73.9
69.2
64.6
60.1
55.7
51.4
44.9
39.2
34.5
30.6
27.4
24.6
139
132
125
118
111
104
97.1
90.3
83.7
77.2
67.5
58.9
51.9
46.0
41.1
37.0
Fy = 36 ksi
75.0
113
71.4
107
67.6
102
63.9
96.0
60.1
90.3
56.3
84.7
52.6
79.1
49.0
73.6
45.4
68.2
41.9
63.0
36.8
55.3
32.1
48.3
28.3
42.6
25.1
37.8
22.5
33.8
20.2
30.3
66.1
62.9
59.7
56.4
53.0
49.8
46.5
43.3
40.2
37.1
32.8
28.6
25.2
22.4
20.0
18.0
99.4
94.6
89.7
84.7
79.7
74.8
69.9
65.1
60.4
55.8
49.2
43.0
37.9
33.6
30.1
27.0
56.5
53.9
51.1
48.4
45.6
42.8
40.1
37.4
34.8
32.2
28.6
25.0
22.0
19.6
17.5
15.7
85.0
81.0
76.9
72.7
68.5
64.4
60.3
56.2
52.3
48.4
43.0
37.6
33.1
29.4
26.3
23.6
45.2
43.2
41.2
39.1
37.0
35.0
32.9
30.9
28.9
26.9
24.3
21.2
18.7
16.6
14.9
13.4
67.9
64.9
61.9
58.8
55.7
52.6
49.5
46.4
43.4
40.5
36.5
31.9
28.1
25.0
22.3
20.1
Fy = 50 ksi
Design
Unbraced Length between Work Points, L (ft)
3 4
7 8
153
143
132
122
112
102
92.1
83.1
75.3
68.3
59.0
51.5
45.3
40.2
35.9
32.3
3 4
7 8
231
215
199
183
168
153
138
125
113
103
88.7
77.4
68.1
60.4
54.0
48.5
134
125
116
107
97.7
89.1
80.7
72.9
66.1
60.2
52.0
45.4
40.0
35.5
31.7
28.5
201
188
174
160
147
134
121
110
99.3
90.5
78.2
68.3
60.1
53.3
47.6
42.8
113
106
98.0
90.4
83.0
75.9
68.9
62.2
56.5
51.5
44.9
39.2
34.5
30.6
27.4
24.6
7 16c
5 8
1 2
170
92.0
159
85.9
147
79.7
136
73.6
125
67.6
114
61.8
104
56.2
93.5
50.8
84.9
46.1
77.4
42.1
67.5
36.8
58.9
32.1
51.9
28.3
46.0
25.1
41.1
22.5
37.0
20.2
Properties
138
129
120
111
102
92.9
84.5
76.3
69.3
63.2
55.3
48.3
42.6
37.8
33.8
30.3
80.2
75.0
69.7
64.5
59.4
54.5
49.7
45.0
40.9
37.3
32.8
28.6
25.2
22.4
20.0
18.0
121
113
105
97.0
89.3
81.8
74.6
67.6
61.4
56.0
49.2
43.0
37.9
33.6
30.1
27.0
3 8c,
66.9
62.8
58.7
54.6
50.6
46.6
42.8
39.1
35.5
32.4
28.6
25.0
22.0
19.6
17.5
15.7
101
94.4
88.2
82.1
76.0
70.1
64.3
58.8
53.4
48.7
43.0
37.6
33.1
29.4
26.3
23.6
5 16c,
/
53.1
50.2
47.2
44.2
41.3
38.4
35.5
32.7
30.1
27.4
24.3
21.2
18.7
16.6
14.9
13.4
79.8
75.4
70.9
66.5
62.0
57.6
53.4
49.2
45.2
41.2
36.5
31.9
28.1
25.0
22.3
20.1
Ag (in.2)
8.00
6.98
5.90
4.79
4.22
3.65
3.07
z (in.)
0.971
0.972
0.975
0.980
0.983
0.986
0.990
ASD
LRFD
c = 1.67
c = 0.9
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate L/rz equal to or greater than 120, 140 and 200, respectively.
*Method 1.
131-168_EJ4Q_2012_2010-30R.indd 146
10/11/12 4:53 PM
Shape
lb/ft
18.5
Design
2
2.5
3
3.5
4
4.5
5
5.5
6
7
8
9
10
11
12
13
2
2.5
3
3.5
4
4.5
5
5.5
6
7
8
9
10
11
12
13
1 2
15.7
12.8
5 16c
7 16
3 8
11.3
9.8
1 4c,
8.2
6.6
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
78.5
75.8
73.0
70.2
67.4
64.7
61.9
59.2
56.5
51.3
45.8
38.1
32.3
27.7
24.0
118
114
110
106
101
97.2
93.1
89.0
84.9
77.0
68.8
57.3
48.5
41.6
36.1
66.7
64.4
62.1
59.8
57.5
55.2
52.9
50.6
48.3
43.9
39.7
33.2
28.1
24.1
20.9
100
96.8
93.3
89.9
86.4
82.9
79.5
76.0
72.7
66.0
59.7
49.9
42.3
36.2
31.4
54.3
52.5
50.6
48.7
46.9
45.0
43.2
41.3
39.5
35.9
32.5
27.3
23.2
19.9
17.3
81.7
78.9
76.1
73.3
70.4
67.6
64.9
62.1
59.4
54.0
48.9
41.1
34.8
29.9
25.9
Fy = 36 ksi
47.9
71.9
46.2
69.5
44.6
67.1
43.0
64.6
41.4
62.2
39.7
59.7
38.1
57.3
36.5
54.9
34.9
52.5
31.8
47.8
28.8
43.3
24.4
36.6
20.7
31.1
17.7
26.7
15.4
23.1
41.5
40.1
38.7
37.3
35.9
34.5
33.1
31.8
30.4
27.7
25.1
21.4
18.1
15.6
13.5
62.4
60.3
58.2
56.1
54.0
51.9
49.8
47.7
45.7
41.7
37.8
32.2
27.3
23.4
20.3
34.8
33.7
32.5
31.4
30.2
29.0
27.9
26.7
25.6
23.4
21.2
18.2
15.4
13.2
11.5
10.0
52.3
50.6
48.9
47.1
45.4
43.6
41.9
40.2
38.5
35.1
31.9
27.3
23.2
19.9
17.3
15.1
26.5
25.7
24.9
24.1
23.3
22.5
21.7
20.9
20.1
18.5
16.9
14.8
12.6
10.8
9.4
8.1
39.8
38.6
37.4
36.2
35.0
33.8
32.6
31.4
30.2
27.8
25.5
22.3
18.9
16.2
14.1
12.2
Fy = 50 ksi
Design
Unbraced Length between Work Points, L (ft)
5 8
3 4
93.3
88.8
84.3
79.9
75.5
71.3
67.1
63.0
59.0
52.0
45.7
38.1
32.3
27.7
24.0
5 8
3 4
140
133
127
120
114
107
101
94.6
88.6
78.2
68.8
57.3
48.5
41.6
36.1
79.4
75.6
71.8
68.1
64.5
60.9
57.4
54.0
50.6
44.7
39.8
33.2
28.1
24.1
20.9
1 2
119
114
108
102
96.9
91.6
86.3
81.2
76.1
67.2
59.8
49.9
42.3
36.2
31.4
64.7
61.6
58.6
55.6
52.7
49.8
47.0
44.2
41.4
36.6
32.6
27.3
23.2
19.9
17.3
97.2
92.6
88.1
83.6
79.2
74.8
70.6
66.4
62.3
55.0
49.0
41.1
34.8
29.9
25.9
57.0
54.3
51.7
49.1
46.5
44.0
41.5
39.1
36.7
32.4
28.9
24.4
20.7
17.7
15.4
5 16c
7 16
3 8
85.7
81.7
77.7
73.8
69.9
66.1
62.4
58.8
55.2
48.8
43.4
36.6
31.1
26.7
23.1
49.5
47.2
44.9
42.7
40.5
38.3
36.2
34.1
32.0
28.3
25.2
21.4
18.1
15.6
13.5
74.3
70.9
67.5
64.1
60.8
57.5
54.3
51.2
48.1
42.6
37.9
32.2
27.3
23.4
20.3
40.3
38.6
36.8
35.1
33.4
31.8
30.1
28.5
27.0
23.9
21.3
18.2
15.4
13.2
11.5
10.0
60.6
58.0
55.4
52.8
50.3
47.8
45.3
42.9
40.5
36.0
32.1
27.3
23.2
19.9
17.3
15.1
1 4c,
30.6
29.4
28.3
27.1
25.9
24.8
23.7
22.6
21.5
19.3
17.3
14.8
12.6
10.8
9.4
8.1
46.0
44.2
42.5
40.7
39.0
37.3
35.6
33.9
32.3
29.1
26.0
22.2
18.9
16.2
14.1
12.2
Properties
(in.2)
5.43
4.61
3.75
3.30
2.86
2.40
1.93
z (in.)
0.774
0.774
0.776
0.777
0.779
0.781
0.783
ASD
LRFD
c = 1.67
c = 0.9
Ag
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate L/rz equal to or greater than 120, 140 and 200, respectively.
*Method 1.
131-168_EJ4Q_2012_2010-30R.indd 147
10/11/12 4:53 PM
Shape
lb/ft
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
9
10
11
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
9
10
11
9.80
1 4c
3 8
5 16
8.50
7.20
5.80
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
46.1
44.2
42.4
40.5
38.7
36.8
35.0
33.2
31.4
29.7
28.0
25.2
22.8
18.9
16.0
13.7
69.3
66.5
63.7
60.9
58.1
55.3
52.6
49.9
47.2
44.6
42.1
37.9
34.3
28.5
24.0
20.5
41.1
39.4
37.8
36.1
34.5
32.9
31.3
29.7
28.1
26.6
25.1
22.8
20.6
17.1
14.4
12.3
61.7
59.3
56.8
54.3
51.8
49.4
47.0
44.6
42.3
40.0
37.7
34.2
31.0
25.7
21.7
18.5
Fy = 36 ksi
35.6
53.5
34.2
51.4
32.8
49.2
31.4
47.1
29.9
45.0
28.6
42.9
27.2
40.8
25.8
38.8
24.5
36.8
23.2
34.8
21.9
32.9
20.0
30.0
18.1
27.2
15.0
22.6
12.7
19.0
10.8
16.3
29.9
28.8
27.6
26.4
25.2
24.1
22.9
21.8
20.7
19.6
18.5
17.0
15.4
12.8
10.8
9.2
45.0
43.2
41.5
39.7
37.9
36.2
34.5
32.8
31.1
29.4
27.8
25.6
23.2
19.2
16.2
13.9
23.8
22.9
22.0
21.1
20.2
19.3
18.4
17.6
16.7
15.9
15.0
14.0
12.7
10.5
8.9
7.6
35.7
34.4
33.0
31.7
30.4
29.0
27.7
26.4
25.1
23.8
22.6
21.0
19.0
15.8
13.3
11.4
Fy = 50 ksi
Design
Unbraced Length between Work Points, L (ft)
7 16
11.1
Design
1 2
54.4
51.4
48.4
45.5
42.6
39.8
37.0
34.4
32.1
29.9
28.0
25.2
22.8
18.9
16.0
13.7
7 16
1 2
81.8
77.3
72.8
68.3
64.0
59.8
55.7
51.7
48.2
45.0
42.1
37.9
34.3
28.5
24.0
20.5
48.5
45.8
43.2
40.6
38.1
35.6
33.2
30.8
28.7
26.9
25.1
22.8
20.6
17.1
14.4
12.3
72.9
42.0
68.9
39.8
64.9
37.5
61.0
35.3
57.2
33.1
53.5
31.0
49.8
28.9
46.3
26.9
43.2
25.1
40.4
23.4
37.8
21.9
34.2
20.0
31.0
18.1
25.7
15.0
21.7
12.7
18.5
10.8
Properties
1 4c
3 8
5 16
63.2
59.8
56.4
53.0
49.7
46.6
43.5
40.4
37.7
35.2
33.0
30.0
27.2
22.6
19.0
16.3
35.2
33.3
31.5
29.6
27.9
26.1
24.4
22.7
21.2
19.8
18.6
17.0
15.4
12.8
10.8
9.2
52.9
50.1
47.3
44.6
41.9
39.3
36.7
34.2
31.9
29.8
27.9
25.6
23.2
19.2
16.2
13.9
27.3
26.0
24.7
23.4
22.2
20.9
19.7
18.5
17.3
16.2
15.2
14.0
12.7
10.5
8.9
7.6
41.1
39.1
37.1
35.2
33.3
31.4
29.6
27.8
26.0
24.3
22.8
21.0
19.0
15.8
13.3
11.4
Ag (in.2)
3.25
2.89
2.50
2.10
1.70
z (in.)
0.679
0.681
0.683
0.685
0.688
ASD
LRFD
c = 1.67
c = 0.9
131-168_EJ4Q_2012_2010-30R.indd 148
10/11/12 4:53 PM
Shape
lb/ft
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
3 8
8.30
7.20
3 16c,
5 16
6.10
1 4
4.90
3.71
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
38.1
36.2
34.3
32.5
30.7
28.9
27.1
25.3
23.6
20.9
18.6
16.7
15.0
13.6
12.4
11.3
57.2
54.4
51.6
48.8
46.1
43.4
40.7
38.1
35.5
31.4
28.0
25.1
22.6
20.5
18.7
17.1
33.6
31.9
30.3
28.7
27.1
25.5
24.0
22.5
21.0
18.6
16.6
14.9
13.4
12.2
11.1
10.1
50.5
48.0
45.6
43.1
40.7
38.4
36.0
33.8
31.5
28.0
25.0
22.4
20.2
18.3
16.7
15.2
29.2
27.8
26.4
25.0
23.6
22.3
20.9
19.6
18.3
16.4
14.6
13.1
11.8
10.7
9.8
8.9
Fy = 36 ksi
43.9
24.7
41.8
23.5
39.7
22.3
37.6
21.2
35.5
20.0
33.5
18.9
31.4
17.7
29.5
16.7
27.6
15.6
24.6
14.0
21.9
12.5
19.7
11.2
17.8
10.1
16.1
9.2
14.7
8.3
13.4
7.6
37.1
35.3
33.6
31.8
30.1
28.4
26.7
25.0
23.4
21.1
18.8
16.8
15.2
13.8
12.5
11.5
20.0
19.1
18.1
17.2
16.3
15.3
14.4
13.6
12.7
11.5
10.2
9.2
8.3
7.5
6.8
6.3
30.0
28.6
27.2
25.8
24.4
23.0
21.7
20.4
19.1
17.3
15.4
13.8
12.5
11.3
10.3
9.4
14.4
13.8
13.1
12.5
11.9
11.3
10.7
10.1
9.5
8.8
7.8
7.0
6.4
5.8
5.2
4.8
21.6
20.7
19.8
18.8
17.9
17.0
16.1
15.2
14.3
13.2
11.8
10.6
9.5
8.7
7.9
7.2
Fy = 50 ksi
Design
Unbraced Length between Work Points, L (ft)
7 16
9.40
Design
1 2
44.4
41.4
38.5
35.7
32.9
30.2
27.7
25.6
23.6
20.9
18.6
16.7
15.0
13.6
12.4
11.3
7 16
1 2
66.8
62.3
57.9
53.6
49.5
45.4
41.7
38.5
35.5
31.4
28.0
25.1
22.6
20.5
18.7
17.1
39.2
36.6
34.1
31.6
29.1
26.8
24.6
22.7
21.0
18.6
16.6
14.9
13.4
12.2
11.1
10.1
3 8
58.9
55.0
51.2
47.4
43.8
40.2
37.0
34.1
31.6
28.0
25.0
22.4
20.2
18.3
16.7
15.2
34.1
51.3
31.9
47.9
29.7
44.6
27.5
41.4
25.4
38.2
23.4
35.1
21.5
32.3
19.9
29.8
18.4
27.6
16.4
24.6
14.6
21.9
13.1
19.7
11.8
17.8
10.7
16.1
9.8
14.7
8.9
13.4
Properties
28.9
27.0
25.1
23.3
21.6
19.8
18.3
16.9
15.6
14.0
12.5
11.2
10.1
9.2
8.3
7.6
3 16c
5 16
1 4
43.4
40.5
37.8
35.1
32.4
29.8
27.5
25.4
23.5
21.1
18.8
16.8
15.2
13.8
12.5
11.5
23.0
21.6
20.2
18.8
17.5
16.2
14.9
13.8
12.7
11.5
10.2
9.2
8.3
7.5
6.8
6.3
34.6
32.5
30.3
28.3
26.3
24.3
22.4
20.7
19.2
17.3
15.4
13.8
12.5
11.3
10.3
9.4
16.4
15.5
14.6
13.8
12.9
12.1
11.3
10.5
9.7
8.8
7.8
7.0
6.4
5.8
5.2
4.8
24.6
23.3
22.0
20.7
19.4
18.2
16.9
15.7
14.6
13.2
11.8
10.6
9.5
8.7
7.9
7.2
Ag (in.2)
2.76
2.43
2.11
1.78
1.44
1.09
z (in.)
0.580
0.580
0.581
0.583
0.585
0.586
ASD
LRFD
c = 1.67
c = 0.9
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate L/rz equal to or greater than 120, 140 and 200, respectively.
*Method 1.
131-168_EJ4Q_2012_2010-30R.indd 149
10/11/12 4:53 PM
Shape
11/8
lb/ft
56.9
Design
6
7
8
9
10
11
12
13
14
15
16
18
20
22
24
26
6
7
8
9
10
11
12
13
14
15
16
18
20
22
24
26
51.0
5 8c
45.0
9 16c
3 4
7 8
38.9
1 2c,
32.7
29.6
26.4
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
153
147
140
133
125
118
110
103
96.1
89.5
83.1
71.3
61.3
53.3
46.7
41.2
230
221
210
199
188
177
166
155
144
134
125
107
92.2
80.1
70.1
61.9
147
140
133
126
119
112
104
97.4
90.6
84.1
78.0
66.6
57.1
49.5
43.2
38.1
220
211
201
190
179
168
157
146
136
126
117
100
85.8
74.3
65.0
57.2
139.7
133.5
126.8
119.9
112.7
105.5
98.5
91.7
85.1
78.9
73.0
62.1
53.0
45.8
39.9
35.0
210
201
191
180
169
159
148
138
128
119
110
93.3
79.7
68.8
59.9
52.7
Fy = 36 ksi
131
196
125
187
118
178
112
168
105
157
97.7
147
91.0
137
84.4
127
78.2
117
72.2
109
66.6
100
56.4
84.8
47.9
72.1
41.2
61.9
35.8
53.8
31.4
47.1
119
114
108
102
95.3
88.9
82.6
76.5
70.6
65.1
60.0
50.5
42.7
36.6
31.7
27.7
180
171
162
153
143
134
124
115
106
97.9
90.1
75.9
64.2
55.0
47.6
41.6
103
99.9
96.9
93.7
87.9
82.1
76.3
70.7
65.4
60.3
55.5
46.8
39.5
33.8
29.2
25.5
155
150
146
141
132
123
115
106
98.2
90.6
83.4
70.4
59.4
50.8
43.9
38.3
85.9
83.1
80.3
77.5
74.8
72.2
69.9
65.0
60.2
55.6
51.2
43.3
36.6
31.2
26.9
23.5
129
125
121
116
112
109
105
97.7
90.4
83.5
77.0
65.1
55.0
46.9
40.5
35.3
Fy = 50 ksi
Design
1/
1 8
203
192
180
167
155
144
132
121
111
102
92.7
78.2
66.7
57.5
50.1
44.0
305
288
270
252
234
216
199
182
167
153
139
117
100
86.4
75.2
66.1
194
183
171
159
147
136
125
114
104
95.0
86.5
72.6
61.8
53.1
46.2
40.5
292
275
257
239
221
204
187
171
157
143
130
109
92.8
79.9
69.4
60.8
185
174
162
150
139
128
117
107
97.4
88.5
80.5
67.2
57.0
48.9
42.4
37.1
5 8c
277
172
261
162
244
151
226
139
209
128
192
118
176
107
161
97.8
146
88.8
133
80.5
121
72.9
101
60.6
85.6
51.2
73.5
43.8
63.7
37.8
55.7
33.0
Properties
9 16c,
3 4
7 8
259
243
227
210
193
177
161
147
133
121
110
91.1
76.9
65.8
56.8
49.6
153
144
134
124
114
105
95.9
87.4
79.4
72.0
65.2
54.0
45.4
38.6
33.3
29.0
230
216
201
187
172
158
144
131
119
108
98.0
81.1
68.2
58.1
50.1
43.6
130
125
120
114
105
96.7
88.5
80.7
73.3
66.6
60.4
49.8
41.8
35.6
30.6
26.6
195
188
181
172
158
145
133
121
110
100
90.7
74.9
62.8
53.4
46.0
40.0
1 2c,
104
102
98.6
94.3
90.2
86.3
81.0
74.1
67.5
61.4
55.8
46.1
38.6
32.8
28.2
24.5
157
154
148
142
136
130
122
111
101
92.3
83.9
69.2
58.0
49.2
42.3
36.8
Ag (in.2)
16.8
15.1
13.3
11.5
9.69
8.77
7.84
z (in.)
1.56
1.56
1.57
1.57
1.58
1.58
1.59
ASD
LRFD
c = 1.67
c = 0.9
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate KL/rz equal to or greater than 120, 140 and 200, respectively.
*Method 3 (flexural rigidity El* = 0.8bEl).
131-168_EJ4Q_2012_2010-30R.indd 150
10/11/12 4:53 PM
Shape
lb/ft
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
33.1
5 8
28.7
24.2
7 16c
9 16
1 2
21.9
19.6
17.3
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
92.1
87.5
82.5
77.1
71.5
66.0
60.6
55.4
50.5
45.9
41.5
37.8
34.5
31.6
29.0
26.8
138
132
124
116
108
99.2
91.1
83.3
75.9
68.9
62.4
56.8
51.8
47.5
43.6
40.2
89.5
84.9
79.8
74.2
68.6
63.1
57.7
52.5
47.6
43.1
38.9
35.2
32.1
29.3
26.9
24.7
135
128
120
112
103
94.8
86.7
78.9
71.6
64.8
58.4
53.0
48.2
44.0
40.4
37.1
84.4
79.9
74.9
69.4
64.0
58.6
53.3
48.4
43.7
39.4
35.4
32.0
29.0
26.5
24.2
22.2
127
120
113
104
96.1
88.0
80.1
72.7
65.7
59.2
53.2
48.1
43.7
39.8
36.4
33.4
Fy = 36 ksi
78.6
118
74.2
112
69.3
104
64.0
96.3
58.7
88.3
53.5
80.4
48.5
72.9
43.8
65.8
39.4
59.2
35.4
53.1
31.7
47.6
28.5
42.8
25.8
38.7
23.4
35.2
21.4
32.1
19.6
29.4
74.6
70.4
65.8
60.7
55.7
50.7
45.9
41.4
37.2
33.3
29.8
26.8
24.2
22.0
20.0
18.3
112
106
98.8
91.3
83.7
76.2
69.0
62.2
55.9
50.1
44.8
40.3
36.4
33.0
30.1
27.6
71.1
67.1
62.5
57.6
52.7
47.8
43.2
38.8
34.8
31.1
27.7
24.9
22.4
20.3
18.5
16.9
107
101
93.9
86.6
79.2
71.9
64.9
58.3
52.3
46.7
41.7
37.4
33.7
30.5
27.8
25.4
62.7
60.4
56.8
52.4
47.9
43.5
39.2
35.2
31.5
28.2
25.1
22.5
20.2
18.3
16.6
15.2
94.3
90.7
85.4
78.7
72.0
65.4
59.0
53.0
47.4
42.4
37.7
33.8
30.4
27.5
25.0
22.8
Fy = 50 ksi
Design
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
3 4
7 8
37.4
Design
1
123
115
107
97.4
88.4
79.8
71.6
64.0
56.9
50.9
45.8
41.4
37.6
34.3
31.4
28.8
186
173
160
146
133
120
108
96.1
85.5
76.5
68.8
62.2
56.5
51.5
47.1
43.3
120
112
103
93.4
84.3
75.7
67.6
60.1
53.2
47.5
42.5
38.3
34.7
31.6
28.8
26.4
3 4
7 8
180
168
154
140
127
114
102
90.3
80.0
71.3
63.9
57.6
52.2
47.5
43.3
39.7
113
105
95.9
87.0
78.2
69.9
62.1
54.9
48.5
43.1
38.5
34.6
31.3
28.4
25.9
23.7
170
105
157
96.9
144
88.4
131
79.8
118
71.3
105
63.3
93.3
56.0
82.6
49.3
72.9
43.3
64.7
38.3
57.9
34.1
52.0
30.6
47.0
27.5
42.6
24.9
38.9
22.7
35.6
20.7
Properties
1 2c
5 8
158
146
133
120
107
95.2
84.1
74.1
65.1
57.6
51.3
45.9
41.4
37.5
34.1
31.1
99.5
92.0
83.9
75.6
67.5
59.9
52.9
46.5
40.8
36.0
32.0
28.7
25.8
23.3
21.2
19.3
7 16c,
9 16
150
138
126
114
101
90.0
79.5
69.9
61.3
54.1
48.1
43.1
38.8
35.1
31.9
29.1
92.9
85.9
78.4
70.6
63.0
55.9
49.3
43.3
37.9
33.4
29.6
26.4
23.7
21.4
19.5
17.7
140
129
118
106
94.8
83.9
74.0
65.1
57.0
50.2
44.5
39.7
35.7
32.2
29.2
26.6
/
79.8
76.0
70.3
63.5
56.8
50.4
44.5
39.2
34.3
30.2
26.7
23.8
21.4
19.3
17.5
15.9
120
114
106
95.5
85.4
75.8
66.9
58.8
51.6
45.3
40.1
35.8
32.1
29.0
26.2
23.9
Ag (in.2)
11.0
9.75
8.46
7.13
6.45
5.77
5.08
z (in.)
1.17
1.17
1.17
1.17
1.18
1.18
1.18
ASD
LRFD
c = 1.67
c = 0.9
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate KL/rz equal to or greater than 120, 140 and 200, respectively.
*Method 3 (flexural rigidity El* = 0.8bEl).
131-168_EJ4Q_2012_2010-30R.indd 151
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Shape
lb/ft
27.2
Design
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
5 8
23.6
20.0
3 8c
1 2
16.2
5 16c,
7 16
14.3
12.3
10.4
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
71.3
69.5
66.7
63.0
58.8
54.1
49.4
44.7
40.3
36.1
32.1
28.6
25.5
23.0
20.8
18.9
107.2
104.4
100.2
94.7
88.3
81.3
74.3
67.3
60.5
54.2
48.2
42.9
38.4
34.5
31.2
28.3
68.2
66.3
63.5
59.8
55.6
51.0
46.4
41.8
37.5
33.4
29.6
26.2
23.4
21.0
18.9
17.1
102.5
99.7
95.4
89.9
83.6
76.7
69.7
62.8
56.3
50.2
44.5
39.4
35.1
31.5
28.4
25.7
65.1
63.3
60.4
56.8
52.5
48.0
43.3
38.8
34.6
30.6
27.0
23.8
21.1
18.9
16.9
15.3
97.9
95.1
90.8
85.3
78.9
72.1
65.1
58.4
52.0
46.0
40.6
35.8
31.8
28.4
25.5
23.0
Fy = 36 ksi
60.2
90.5
58.5
87.9
55.7
83.8
52.2
78.5
48.1
72.3
43.7
65.7
39.3
59.1
35.0
52.6
31.0
46.5
27.2
41.0
23.9
35.9
20.9
31.5
18.5
27.8
16.4
24.7
14.7
22.1
13.2
19.9
55.9
54.2
51.7
48.4
44.5
40.4
36.3
32.2
28.4
25.0
21.8
19.1
16.8
14.9
13.3
12.0
84.0
81.5
77.7
72.8
66.9
60.8
54.5
48.4
42.7
37.5
32.8
28.7
25.3
22.4
20.0
18.0
46.3
45.9
45.3
43.7
41.3
37.4
33.5
29.7
26.1
22.9
20.0
17.4
15.3
13.5
12.0
10.8
69.6
69.0
68.0
65.7
62.0
56.2
50.3
44.6
39.2
34.4
30.0
26.1
22.9
20.3
18.1
16.2
35.3
35.0
34.4
33.0
31.2
29.5
27.8
25.9
22.8
20.0
17.5
15.3
13.4
11.8
10.5
9.4
53.1
52.6
51.7
49.6
46.9
44.3
41.8
38.9
34.3
30.1
26.4
23.0
20.1
17.8
15.8
14.1
Fy = 50 ksi
Design
3 4
7 8
98.7
95.3
90.0
83.4
75.9
68.2
60.6
53.4
46.7
40.6
35.6
31.5
28.0
25.0
22.5
20.3
3 4
7 8
148.4
143.2
135.2
125.3
114.0
102.4
91.0
80.3
70.2
61.1
53.5
47.3
42.0
37.6
33.8
30.5
94.3
90.9
85.6
79.0
71.6
64.0
56.5
49.5
43.1
37.4
32.6
28.7
25.4
22.7
20.3
18.3
141.7
136.6
128.6
118.8
107.6
96.1
85.0
74.4
64.8
56.1
49.0
43.1
38.2
34.1
30.5
27.5
90.1
86.6
81.3
74.7
67.3
59.7
52.4
45.6
39.4
33.9
29.5
25.8
22.8
20.2
18.1
16.3
7 16c
5 8
1 2
135.4 83.3
130.2 80.0
122.3 74.9
112.2 68.5
101.1 61.4
89.8
54.2
78.8
47.2
68.5
40.7
59.3
35.0
51.0
29.9
44.3
25.8
38.8
22.5
34.2
19.7
30.4
17.5
27.2
15.6
24.4
14.0
Properties
125.2
120.3
112.6
103.0
92.3
81.4
70.9
61.2
52.6
44.9
38.8
33.8
29.7
26.3
23.4
21.0
76.4
73.4
68.7
62.9
56.3
49.7
43.2
37.3
32.0
27.3
23.5
20.4
17.9
15.8
14.1
12.6
114.8
110.2
103.3
94.5
84.7
74.7
64.9
56.0
48.0
41.0
35.3
30.7
26.9
23.8
21.2
18.9
3 8c,
61.1
60.4
58.6
55.2
51.1
45.2
39.3
33.9
29.1
24.9
21.3
18.5
16.1
14.2
12.6
11.3
91.9
90.7
88.1
83.0
76.8
67.9
59.1
51.0
43.8
37.4
32.0
27.7
24.2
21.4
19.0
17.0
5 16c,
/
43.1
42.5
41.6
40.3
38.4
35.7
33.2
29.5
25.5
21.8
18.7
16.1
14.1
12.4
11.0
9.8
64.8
63.9
62.5
60.6
57.7
53.7
50.0
44.4
38.3
32.8
28.1
24.3
21.2
18.6
16.5
14.7
Ag (in.2)
8.00
6.98
5.90
4.79
4.22
3.65
3.07
z (in.)
0.971
0.972
0.975
0.980
0.983
0.986
0.990
ASD
LRFD
c = 1.67
c = 0.9
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate KL/rz equal to or greater than 120, 140 and 200, respectively.
*Method 3 (flexural rigidity El* = 0.8bEl).
131-168_EJ4Q_2012_2010-30R.indd 152
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Shape
lb/ft
18.5
Design
2
2.5
3
3.5
4
4.5
5
5.5
6
7
8
9
10
11
12
13
2
2.5
3
3.5
4
4.5
5
5.5
6
7
8
9
10
11
12
13
1 2
15.7
12.8
5 16c
7 16
3 8
11.3
9.8
1 4c,
8.2
6.6
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
43.5
42.3
40.9
39.3
37.6
35.9
34.1
32.2
30.4
26.8
23.4
20.3
17.6
15.5
13.6
65.4
63.5
61.4
59.1
56.6
53.9
51.2
48.4
45.6
40.3
35.2
30.5
26.5
23.2
20.5
42.1
40.8
39.4
37.7
36.0
34.2
32.3
30.4
28.6
25.0
21.6
18.6
16.1
14.0
12.3
63.2
61.4
59.2
56.7
54.1
51.4
48.6
45.7
42.9
37.5
32.5
28.0
24.1
21.0
18.5
38.9
37.6
36.2
34.6
32.9
31.1
29.3
27.5
25.7
22.3
19.2
16.4
14.0
12.2
10.6
58.4
56.5
54.4
52.0
49.5
46.8
44.1
41.3
38.6
33.5
28.8
24.6
21.1
18.3
16.0
Fy = 36 ksi
37.2
55.9
36.0
54.0
34.5
51.9
33.0
49.6
31.3
47.1
29.6
44.4
27.8
41.7
26.0
39.0
24.2
36.4
20.9
31.4
17.9
26.8
15.2
22.8
12.9
19.5
11.2
16.8
9.7
14.6
34.6
33.4
32.1
30.6
29.0
27.4
25.6
23.9
22.3
19.1
16.3
13.8
11.7
10.1
8.7
52.0
50.3
48.3
46.0
43.6
41.1
38.5
36.0
33.5
28.7
24.5
20.7
17.6
15.1
13.1
31.3
30.2
29.0
27.6
26.1
24.6
23.0
21.5
19.9
17.0
14.4
12.1
10.3
8.8
7.6
6.7
47.0
45.4
43.6
41.5
39.3
37.0
34.6
32.3
30.0
25.6
21.7
18.3
15.5
13.2
11.5
10.0
22.0
21.7
21.2
20.5
19.8
19.1
18.5
17.9
17.0
14.6
12.4
10.4
8.8
7.5
6.5
5.6
33.0
32.6
31.9
30.8
29.8
28.8
27.8
26.8
25.6
21.9
18.6
15.7
13.2
11.3
9.7
8.5
Fy = 50 ksi
Design
5 8
3 4
59.2
57.0
54.4
51.7
48.8
45.7
42.7
39.7
36.8
31.4
26.5
22.6
19.5
16.9
14.8
5 8
3 4
89.0
85.7
81.8
77.7
73.3
68.7
64.2
59.7
55.4
47.2
39.9
34.0
29.2
25.4
22.3
57.2
54.9
52.3
49.4
46.4
43.3
40.2
37.2
34.3
29.0
24.2
20.5
17.5
15.2
13.2
1 2
86.0
82.5
78.5
74.2
69.7
65.0
60.4
55.9
51.6
43.5
36.4
30.8
26.4
22.8
19.9
52.8
50.5
47.9
45.1
42.2
39.2
36.2
33.4
30.6
25.6
21.3
17.8
15.2
13.1
11.3
79.3
75.9
72.0
67.8
63.4
58.9
54.5
50.2
46.1
38.5
31.9
26.8
22.8
19.6
17.1
50.4
48.2
45.7
42.9
40.0
37.0
34.2
31.4
28.7
23.8
19.7
16.4
13.9
11.9
10.3
5 16c
7 16
3 8
75.8
72.5
68.6
64.5
60.1
55.7
51.3
47.1
43.1
35.8
29.5
24.7
20.9
17.9
15.5
46.9
44.8
42.4
39.7
37.0
34.2
31.4
28.8
26.3
21.7
17.8
14.8
12.5
10.7
9.2
70.5
67.3
63.7
59.7
55.6
51.4
47.3
43.3
39.5
32.6
26.8
22.3
18.8
16.1
13.9
40.9
39.1
37.1
34.8
32.4
30.0
27.7
25.3
23.1
19.1
15.7
13.0
10.9
9.3
8.0
7.0
61.4
58.8
55.7
52.3
48.8
45.2
41.6
38.1
34.8
28.7
23.6
19.5
16.4
14.0
12.1
10.5
1 4c,
26.6
26.2
25.7
25.2
24.3
23.3
22.3
21.4
19.7
16.3
13.5
11.1
9.3
7.9
6.8
5.9
40.0
39.4
38.7
37.9
36.6
35.0
33.5
32.2
29.6
24.5
20.2
16.6
13.9
11.8
10.2
8.8
Properties
(in.2)
5.44
4.61
3.75
3.30
2.86
2.40
1.93
z (in.)
0.774
0.774
0.776
0.777
0.779
0.781
0.783
ASD
LRFD
c = 1.67
c = 0.9
Ag
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate KL/rz equal to or greater than 120, 140 and 200, respectively.
*Method 3 (flexural rigidity El* = 0.8bEl).
131-168_EJ4Q_2012_2010-30R.indd 153
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Shape
lb/ft
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
9
10
11
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
9
10
11
9.80
1 4c
3 8
5 16
8.50
7.20
5.80
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
31.1
29.9
28.5
27.0
25.4
23.7
22.0
20.4
18.9
17.4
16.0
14.6
13.4
11.3
9.7
8.3
46.8
45.0
42.8
40.5
38.1
35.6
33.1
30.7
28.4
26.1
24.0
22.0
20.1
17.0
14.5
12.5
29.6
28.4
27.0
25.5
23.9
22.3
20.7
19.2
17.7
16.2
14.9
13.6
12.4
10.4
8.9
7.7
44.4
42.6
40.6
38.3
36.0
33.6
31.2
28.8
26.5
24.4
22.4
20.5
18.7
15.7
13.4
11.5
Fy = 36 ksi
28.4
42.6
27.2
40.8
25.8
38.8
24.3
36.5
22.7
34.2
21.1
31.8
19.6
29.4
18.0
27.1
16.5
24.9
15.1
22.8
13.8
20.8
12.6
19.0
11.5
17.2
9.6
14.4
8.1
12.2
7.0
10.5
25.9
24.7
23.5
22.1
20.6
19.1
17.6
16.2
14.8
13.5
12.3
11.2
10.2
8.4
7.1
6.1
38.9
37.2
35.3
33.2
31.0
28.7
26.5
24.4
22.3
20.4
18.5
16.8
15.3
12.7
10.7
9.2
20.7
20.2
19.5
18.8
18.0
16.7
15.4
14.1
12.9
11.8
10.7
9.7
8.8
7.3
6.1
5.2
31.0
30.3
29.3
28.3
27.1
25.1
23.2
21.3
19.4
17.7
16.1
14.6
13.2
10.9
9.2
7.8
Fy = 50 ksi
Design
7 16
11.1
Design
1 2
42.0
39.8
37.3
34.6
31.9
29.3
26.7
24.2
21.9
19.8
17.8
16.1
14.6
12.2
10.4
8.9
7 16
1 2
63.2
59.8
56.1
52.1
48.0
44.0
40.1
36.4
32.9
29.7
26.7
24.2
22.0
18.4
15.6
13.4
39.9
37.7
35.3
32.7
30.1
27.5
25.0
22.6
20.4
18.4
16.5
14.9
13.5
11.3
9.5
8.2
59.9
38.2
56.7
36.0
53.0
33.6
49.1
31.0
45.2
28.4
41.3
25.9
37.5
23.4
34.0
21.1
30.7
19.0
27.6
17.0
24.8
15.2
22.4
13.7
20.3
12.4
16.9
10.3
14.3
8.6
12.3
7.4
Properties
1 4c
3 8
5 16
57.4
54.2
50.5
46.6
42.7
38.9
35.2
31.7
28.5
25.5
22.9
20.6
18.6
15.4
13.0
11.1
34.6
32.6
30.4
28.0
25.6
23.2
21.0
18.8
16.9
15.1
13.5
12.1
10.9
9.0
7.5
6.4
52.0
49.0
45.7
42.1
38.4
34.9
31.5
28.3
25.4
22.7
20.2
18.1
16.4
13.5
11.3
9.6
26.4
25.6
24.5
23.4
21.9
19.9
18.0
16.2
14.6
13.0
11.6
10.4
9.3
7.7
6.4
5.4
39.7
38.4
36.8
35.2
32.9
30.0
27.1
24.4
21.9
19.6
17.5
15.6
14.0
11.5
9.6
8.2
Ag (in.2)
3.25
2.89
2.50
2.10
1.70
z (in.)
0.679
0.681
0.683
0.685
0.688
ASD
LRFD
c = 1.67
c = 0.9
131-168_EJ4Q_2012_2010-30R.indd 154
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Shape
lb/ft
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
3 8
8.30
7.20
3 16c,
5 16
6.10
1 4
4.90
3.71
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
22.9
21.8
20.5
19.2
17.8
16.4
15.0
13.7
12.5
11.3
10.3
9.3
8.5
7.8
7.2
6.6
34.5
32.8
30.9
28.8
26.7
24.6
22.6
20.6
18.8
17.1
15.4
14.0
12.8
11.7
10.8
9.9
22.0
20.9
19.6
18.2
16.8
15.5
14.1
12.9
11.7
10.5
9.5
8.6
7.8
7.2
6.6
6.0
33.1
31.4
29.4
27.4
25.3
23.2
21.2
19.3
17.5
15.8
14.3
12.9
11.8
10.8
9.9
9.1
21.0
19.9
18.6
17.2
15.9
14.5
13.2
12.0
10.8
9.7
8.7
7.9
7.2
6.5
6.0
5.5
Fy = 36 ksi
31.5
19.5
29.8
18.4
27.9
17.2
25.9
15.9
23.8
14.6
21.8
13.3
19.8
12.0
18.0
10.9
16.2
9.8
14.6
8.8
13.1
7.8
11.9
7.1
10.8
6.4
9.8
5.8
9.0
5.3
8.2
4.9
29.3
27.7
25.9
23.9
21.9
20.0
18.1
16.3
14.7
13.2
11.8
10.6
9.6
8.7
8.0
7.3
17.5
16.5
15.4
14.1
12.9
11.7
10.6
9.5
8.5
7.6
6.8
6.1
5.5
5.0
4.5
4.1
26.3
24.8
23.1
21.3
19.4
17.6
15.9
14.3
12.8
11.4
10.2
9.1
8.2
7.5
6.8
6.2
12.3
11.8
11.2
10.7
10.3
9.5
8.6
7.7
6.9
6.2
5.5
4.9
4.4
4.0
3.6
3.3
18.4
17.7
16.9
16.1
15.4
14.3
12.9
11.6
10.4
9.3
8.3
7.4
6.6
6.0
5.4
5.0
Fy = 50 ksi
Design
7 16
9.40
Design
1 2
30.8
28.7
26.5
24.2
22.0
19.8
17.7
15.8
14.1
12.6
11.3
10.2
9.3
8.5
7.7
7.1
7 16
1 2
46.2
43.2
39.8
36.4
33.0
29.7
26.7
23.8
21.1
18.9
17.0
15.4
14.0
12.7
11.6
10.7
29.4
27.4
25.2
22.9
20.7
18.5
16.5
14.7
13.0
11.6
10.4
9.4
8.5
7.7
7.1
6.5
3 8
44.3
41.2
37.8
34.4
31.1
27.9
24.9
22.1
19.6
17.4
15.6
14.1
12.8
11.6
10.6
9.7
28.0
42.1
26.0
39.1
23.8
35.8
21.5
32.4
19.4
29.1
17.3
26.0
15.3
23.0
13.6
20.4
12.0
18.0
10.6
16.0
9.5
14.3
8.5
12.8
7.7
11.6
7.0
10.5
6.4
9.6
5.8
8.8
Properties
26.0
24.1
21.9
19.8
17.7
15.7
13.9
12.2
10.7
9.5
8.5
7.6
6.8
6.2
5.6
5.1
3 16c
5 16
1 4
39.1
36.2
33.0
29.7
26.6
23.6
20.9
18.4
16.1
14.3
12.7
11.4
10.3
9.3
8.4
7.7
22.9
21.1
19.2
17.3
15.5
13.7
12.1
10.6
9.3
8.2
7.2
6.5
5.8
5.2
4.8
4.3
34.4
31.8
28.9
26.0
23.2
20.6
18.1
15.9
13.9
12.3
10.9
9.7
8.7
7.9
7.2
6.5
14.8
14.4
13.8
13.0
12.4
11.0
9.7
8.6
7.5
6.6
5.8
5.2
4.6
4.2
3.8
3.4
22.2
21.7
20.8
19.6
18.6
16.5
14.6
12.9
11.3
9.9
8.8
7.8
7.0
6.3
5.7
5.2
Ag (in.2)
2.76
2.43
2.11
1.78
1.44
1.09
z (in.)
0.580
0.580
0.581
0.583
0.585
0.586
ASD
LRFD
c = 1.67
c = 0.9
131-168_EJ4Q_2012_2010-30R.indd 155
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Shape
11/8
lb/ft
56.9
Design
6
7
8
9
10
11
12
13
14
15
16
18
20
22
24
26
6
7
8
9
10
11
12
13
14
15
16
18
20
22
24
26
51.0
5 8c
45.0
9 16c
3 4
7 8
38.9
1 2c,
32.7
29.6
26.4
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
104
101
97.3
93.3
89.1
84.9
80.6
76.3
72.1
67.9
63.9
56.2
49.4
43.6
38.8
34.7
157
152
146
140
134
128
121
115
108
102
96.1
84.4
74.2
65.6
58.4
52.2
97.7
94.4
90.8
86.9
83.0
78.9
74.9
70.8
66.8
62.9
59.0
51.8
45.4
40.1
35.6
31.8
147
142
136
131
125
119
113
106
100
94.5
88.8
77.8
68.2
60.2
53.5
47.8
90.4
87.3
83.9
80.3
76.6
72.8
68.9
65.1
61.3
57.7
54.1
47.4
41.5
36.5
32.4
28.9
136
131
126
121
115
109
104
97.8
92.2
86.7
81.4
71.2
62.3
54.9
48.7
43.4
Fy = 36 ksi
82.1
123
79.1
119
75.9
114
72.6
109
69.1
104
65.6
98.6
62.0
93.2
58.5
87.9
55.0
82.7
51.7
77.6
48.4
72.8
42.2
63.5
36.9
55.4
32.4
48.7
28.7
43.1
25.5
38.4
72.5
69.9
67.0
64.0
60.9
57.7
54.5
51.4
48.3
45.3
42.4
37.0
32.2
28.2
25.0
22.2
109
105
101
96.2
91.5
86.8
81.9
77.2
72.6
68.1
63.8
55.6
48.4
42.4
37.5
33.4
66.1
63.7
61.1
58.4
55.6
52.7
49.8
46.9
44.1
41.4
38.8
33.9
29.5
25.8
22.8
20.3
99.3
95.8
91.9
87.8
83.5
79.2
74.8
70.5
66.3
62.3
58.3
50.9
44.3
38.8
34.3
30.5
59.6
57.5
55.2
52.8
50.3
47.8
45.2
42.6
40.2
37.7
35.4
31.0
27.0
23.6
20.8
18.5
89.6
86.4
83.0
79.4
75.6
71.8
67.9
64.1
60.4
56.7
53.2
46.6
40.5
35.5
31.3
27.8
Fy = 50 ksi
Design
1/
1 8
140
134
127
120
113
106
99.3
92.6
86.0
79.7
73.8
63.6
55.3
48.4
42.8
38.0
210
201
191
181
170
160
149
139
129
120
111
95.6
83.1
72.8
64.3
57.1
131
125
118
112
105
98.5
92.0
85.6
79.4
73.5
67.9
58.4
50.7
44.3
39.1
34.7
196
188
178
168
158
148
138
129
119
110
102
87.8
76.2
66.6
58.7
52.1
121
115
109
103
96.8
90.6
84.5
78.5
72.8
67.3
62.1
53.3
46.1
40.3
35.5
31.4
5 8c
182
110
173
104
164
98.8
155
93.0
146
87.1
136
81.4
127
75.7
118
70.3
109
65.0
101
60.0
93.3
55.3
80.1
47.3
69.4
40.9
60.6
35.6
53.3
31.3
47.2
27.7
Properties
9 16c,
3 4
7 8
165
157
148
140
131
122
114
106
97.8
90.2
83.1
71.1
61.4
53.5
47.0
41.6
94.9
90.5
85.7
80.8
75.7
70.8
65.9
61.3
56.8
52.5
48.3
41.3
35.6
31.0
27.2
24.0
143
136
129
121
114
106
99.1
92.1
85.3
78.8
72.7
62.0
53.5
46.5
40.8
36.1
/
86.1
82.1
77.9
73.5
68.9
64.5
60.1
55.9
51.8
48.0
44.3
37.7
32.5
28.3
24.8
21.9
129
123
117
110
104
96.9
90.4
84.0
77.9
72.1
66.5
56.7
48.9
42.5
37.2
32.9
1 2c,
77.2
73.8
70.1
66.2
62.3
58.4
54.5
50.8
47.2
43.7
40.5
34.5
29.7
25.8
22.6
20.0
116
111
105
99.5
93.6
87.7
81.9
76.3
70.9
65.7
60.8
51.9
44.6
38.8
34.0
30.0
Ag (in.2)
16.8
15.1
13.3
11.5
9.69
8.77
7.84
z (in.)
1.56
1.56
1.57
1.57
1.58
1.58
1.59
ASD
LRFD
c = 1.67
c = 0.9
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate L/rz equal to or greater than 120, 140 and 200, respectively.
*Method 4 (flexural rigidity El* = 0.8bEl).
131-168_EJ4Q_2012_2010-30R.indd 156
10/11/12 4:53 PM
Shape
lb/ft
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
33.1
5 8
28.7
24.2
7 16c
9 16
1 2
21.9
19.6
17.3
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
64.9
62.4
59.5
56.4
53.1
49.7
46.4
43.1
39.8
36.7
33.7
31.0
28.6
26.5
24.5
22.8
97.6
93.8
89.5
84.8
79.9
74.8
69.7
64.7
59.8
55.1
50.6
46.6
43.0
39.8
36.9
34.3
61.2
58.7
55.9
52.8
49.6
46.3
43.1
39.9
36.8
33.8
31.0
28.5
26.2
24.2
22.4
20.8
92.0
88.2
84.0
79.4
74.6
69.7
64.8
60.0
55.3
50.9
46.6
42.8
39.4
36.4
33.7
31.3
55.9
53.6
50.9
48.0
45.0
42.0
38.9
36.0
33.1
30.4
27.8
25.5
23.4
21.6
20.0
18.5
84.1
80.5
76.5
72.2
67.6
63.1
58.5
54.1
49.8
45.6
41.7
38.3
35.2
32.4
30.0
27.8
Fy = 36 ksi
50.0
75.2
47.8
71.9
45.4
68.2
42.7
64.2
39.9
60.0
37.1
55.8
34.3
51.6
31.7
47.6
29.1
43.7
26.6
40.0
24.3
36.5
22.2
33.4
20.4
30.6
18.7
28.2
17.3
26.0
16.0
24.1
46.6
44.6
42.2
39.8
37.1
34.5
32.0
29.4
27.0
24.7
22.6
20.6
18.9
17.4
16.1
14.9
70.0
67.0
63.5
59.8
55.8
51.9
48.0
44.3
40.6
37.2
33.9
31.0
28.4
26.2
24.1
22.3
43.4
41.4
39.2
36.9
34.4
31.9
29.5
27.1
24.8
22.7
20.7
18.9
17.3
15.9
14.6
13.5
65.2
62.3
58.9
55.4
51.7
48.0
44.3
40.7
37.3
34.1
31.1
28.4
26.0
23.9
22.0
20.3
38.7
37.0
35.0
32.9
30.7
28.5
26.3
24.2
22.2
20.3
18.4
16.8
15.4
14.1
13.0
12.0
58.2
55.6
52.6
49.4
46.1
42.8
39.5
36.4
33.3
30.4
27.7
25.3
23.2
21.3
19.6
18.1
Fy = 50 ksi
Design
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
3 4
7 8
37.4
Design
1
87.7
83.1
78.1
72.6
67.1
61.6
56.3
51.1
46.2
42.0
38.2
34.9
32.0
29.4
27.2
25.1
132
125
117
109
101
92.6
84.6
76.8
69.5
63.1
57.4
52.5
48.1
44.3
40.8
37.8
82.5
78.0
73.1
67.8
62.4
57.2
52.0
47.1
42.5
38.5
35.0
31.9
29.2
26.8
24.7
22.8
3 4
7 8
124
117
110
102
93.8
85.9
78.2
70.9
63.9
57.9
52.6
48.0
43.9
40.3
37.1
34.3
75.4
71.1
66.4
61.5
56.5
51.6
46.8
42.3
38.1
34.4
31.2
28.4
26.0
23.8
21.9
20.2
113
67.3
107
63.4
99.9
59.1
92.4
54.5
84.9
49.9
77.5
45.4
70.4
41.1
63.6
37.1
57.2
33.3
51.7
30.0
46.9
27.1
42.7
24.7
39.0
22.5
35.8
20.6
32.9
18.9
30.4
17.4
Properties
1 2c
5 8
101
95.3
88.8
81.9
75.0
68.3
61.8
55.7
50.0
45.1
40.8
37.1
33.8
31.0
28.5
26.2
62.8
59.0
54.9
50.7
46.4
42.3
38.3
34.5
30.9
27.9
25.2
22.9
20.9
19.1
17.5
16.2
7 16c,
9 16
94.4
88.7
82.6
76.2
69.8
63.5
57.5
51.8
46.5
41.9
37.9
34.4
31.4
28.7
26.4
24.3
57.6
54.2
50.4
46.5
42.6
38.7
35.1
31.6
28.3
25.5
23.0
20.9
19.0
17.4
16.0
14.7
86.6
81.5
75.8
69.9
64.0
58.2
52.7
47.5
42.6
38.3
34.6
31.4
28.6
26.1
24.0
22.1
/
50.9
47.9
44.7
41.2
37.8
34.4
31.2
28.1
25.3
22.7
20.5
18.6
16.9
15.5
14.2
13.0
76.5
72.0
67.1
61.9
56.8
51.7
46.9
42.3
38.0
34.1
30.8
27.9
25.4
23.2
21.3
19.6
Ag (in.2)
11.0
9.75
8.46
7.13
6.45
5.77
5.08
z (in.)
1.17
1.17
1.17
1.17
1.18
1.18
1.18
ASD
LRFD
c = 1.67
c = 0.9
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate L/rz equal to or greater than 120, 140 and 200, respectively.
*Method 4 (flexural rigidity El* = 0.8bEl).
131-168_EJ4Q_2012_2010-30R.indd 157
10/11/12 4:53 PM
Shape
lb/ft
27.2
Design
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
5 8
23.6
20.0
3 8c
1 2
16.2
5 16c,
7 16
14.3
12.3
10.4
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
50.0
48.9
47.4
45.3
42.8
40.1
37.2
34.3
31.4
28.6
25.9
23.4
21.2
19.3
17.7
16.2
75.1
73.6
71.2
68.0
64.4
60.3
56.0
51.6
47.2
43.0
39.0
35.2
31.9
29.1
26.5
24.3
46.0
45.1
43.5
41.6
39.2
36.7
34.0
31.2
28.5
25.9
23.4
21.1
19.1
17.4
15.8
14.5
69.2
67.7
65.5
62.5
59.0
55.1
51.0
46.9
42.9
39.0
35.2
31.7
28.7
26.1
23.8
21.8
42.1
41.2
39.8
37.9
35.6
33.2
30.6
28.1
25.6
23.2
20.8
18.7
16.9
15.3
13.9
12.7
63.3
61.9
59.7
56.9
53.6
49.9
46.0
42.2
38.4
34.8
31.3
28.2
25.4
23.0
21.0
19.1
Fy = 36 ksi
37.2
55.9
36.3
54.6
35.0
52.6
33.3
50.0
31.2
46.9
29.0
43.6
26.7
40.1
24.4
36.6
22.1
33.2
20.0
30.0
17.9
26.9
16.1
24.1
14.4
21.7
13.1
19.6
11.9
17.8
10.8
16.2
33.6
32.8
31.6
30.0
28.2
26.1
24.0
21.9
19.9
17.9
16.1
14.4
12.9
11.7
10.6
9.7
50.5
49.4
47.5
45.1
42.3
39.3
36.1
32.9
29.9
26.9
24.2
21.6
19.5
17.6
15.9
14.5
30.4
29.7
28.5
27.1
25.4
23.5
21.6
19.7
17.8
16.1
14.4
12.9
11.5
10.4
9.4
8.6
45.7
44.6
42.9
40.7
38.2
35.4
32.5
29.6
26.8
24.1
21.6
19.3
17.3
15.6
14.2
12.9
25.7
25.1
24.2
23.0
21.6
20.0
18.4
16.8
15.3
13.8
12.4
11.1
9.9
9.0
8.1
7.4
38.6
37.7
36.4
34.6
32.5
30.1
27.7
25.3
23.0
20.7
18.6
16.7
14.9
13.5
12.2
11.1
Fy = 50 ksi
Design
3 4
7 8
69.2
67.3
64.3
60.5
56.1
51.4
46.7
42.0
37.5
33.3
29.6
26.5
23.9
21.5
19.6
17.8
3 4
7 8
104
101
96.6
90.9
84.4
77.3
70.1
63.1
56.3
50.0
44.5
39.9
35.8
32.4
29.4
26.8
63.8
61.9
59.1
55.5
51.3
46.9
42.4
38.1
33.9
30.0
26.6
23.8
21.4
19.3
17.5
15.9
95.9
93.1
88.8
83.4
77.1
70.5
63.8
57.2
50.9
45.1
40.0
35.8
32.1
29.0
26.2
23.9
58.3
56.6
53.9
50.4
46.5
42.3
38.1
34.1
30.2
26.6
23.6
21.0
18.8
16.9
15.3
13.9
7 16c
5 8
1 2
87.7
51.5
85.1
49.9
81.0
47.4
75.8
44.2
69.8
40.6
63.6
36.8
57.3
33.0
51.2
29.4
45.4
26.0
40.0
22.8
35.4
20.1
31.5
17.9
28.3
16.0
25.4
14.3
23.0
12.9
20.9
11.7
Properties
77.4
75.0
71.2
66.5
61.0
55.3
49.7
44.2
39.1
34.3
30.2
26.9
24.0
21.5
19.4
17.6
46.2
44.7
42.5
39.7
36.4
33.0
29.6
26.4
23.3
20.5
18.0
16.0
14.3
12.8
11.6
10.5
69.4
67.3
63.9
59.6
54.7
49.6
44.6
39.7
35.1
30.8
27.1
24.1
21.5
19.3
17.4
15.8
3 8c,
41.0
39.7
37.7
35.2
32.4
29.4
26.4
23.5
20.8
18.3
16.1
14.2
12.7
11.4
10.2
9.3
61.6
59.7
56.7
53.0
48.7
44.2
39.7
35.3
31.3
27.5
24.2
21.4
19.1
17.1
15.4
13.9
5 16c,
/
34.2
33.2
31.7
29.7
27.4
24.9
22.5
20.1
17.9
15.8
13.9
12.3
10.9
9.8
8.8
8.0
51.5
50.0
47.6
44.6
41.1
37.5
33.8
30.2
26.8
23.7
20.8
18.4
16.4
14.7
13.2
12.0
Ag (in.2)
8.00
6.98
5.90
4.79
4.22
3.65
3.07
z (in.)
0.971
0.972
0.975
0.980
0.983
0.986
0.990
ASD
LRFD
c = 1.67
c = 0.9
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate L/rz equal to or greater than 120, 140 and 200, respectively.
*Method 4 (flexural rigidity El* = 0.8bEl).
131-168_EJ4Q_2012_2010-30R.indd 158
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Shape
lb/ft
18.5
Design
2
2.5
3
3.5
4
4.5
5
5.5
6
7
8
9
10
11
12
13
2
2.5
3
3.5
4
4.5
5
5.5
6
7
8
9
10
11
12
13
1 2
15.7
12.8
5 16c
7 16
3 8
11.3
9.8
1 4c,
8.2
6.6
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
31.3
30.6
29.8
28.9
27.9
26.8
25.7
24.6
23.4
21.1
18.8
16.6
14.7
13.1
11.7
47.0
46.0
44.8
43.4
41.9
40.3
38.6
36.9
35.2
31.7
28.3
25.0
22.1
19.7
17.6
28.9
28.2
27.4
26.5
25.5
24.5
23.4
22.3
21.2
19.0
16.9
14.9
13.1
11.6
10.3
43.4
42.4
41.2
39.9
38.4
36.8
35.2
33.6
31.9
28.6
25.4
22.3
19.7
17.4
15.5
25.4
24.8
24.1
23.2
22.3
21.4
20.4
19.4
18.4
16.4
14.5
12.7
11.2
9.8
8.7
38.2
37.3
36.2
34.9
33.6
32.2
30.7
29.2
27.7
24.7
21.8
19.1
16.8
14.8
13.1
Fy = 36 ksi
23.5
35.3
22.9
34.4
22.2
33.4
21.4
32.2
20.6
30.9
19.7
29.6
18.8
28.2
17.8
26.8
16.9
25.4
15.0
22.5
13.2
19.9
11.5
17.4
10.1
15.2
8.9
13.4
7.9
11.9
21.3
20.7
20.1
19.3
18.6
17.7
16.9
16.0
15.1
13.4
11.8
10.3
9.0
7.9
7.0
32.0
31.1
30.2
29.1
27.9
26.7
25.4
24.1
22.8
20.2
17.8
15.5
13.5
11.9
10.5
18.7
18.2
17.6
16.9
16.2
15.5
14.7
14.0
13.2
11.7
10.2
8.9
7.8
6.8
6.0
5.4
28.1
27.3
26.4
25.5
24.4
23.3
22.1
21.0
19.8
17.5
15.4
13.4
11.7
10.2
9.0
8.1
15.4
15.0
14.5
14.0
13.4
12.8
12.2
11.6
10.9
9.7
8.5
7.4
6.5
5.7
5.0
4.4
23.1
22.5
21.8
21.0
20.2
19.3
18.3
17.4
16.4
14.6
12.8
11.2
9.7
8.5
7.5
6.7
Fy = 50 ksi
Design
5 8
3 4
42.8
41.5
40.0
38.4
36.6
34.7
32.9
30.9
29.0
25.4
21.9
19.0
16.6
14.6
13.0
5 8
3 4
64.3
62.4
60.1
57.7
55.0
52.2
49.4
46.5
43.6
38.1
32.9
28.6
25.0
22.0
19.5
39.5
38.2
36.7
35.1
33.4
31.6
29.8
28.0
26.2
22.7
19.5
16.9
14.7
12.9
11.4
1 2
59.3
57.4
55.2
52.8
50.2
47.6
44.8
42.1
39.4
34.2
29.3
25.3
22.1
19.4
17.1
34.7
33.5
32.2
30.7
29.2
27.5
25.9
24.2
22.6
19.5
16.7
14.4
12.5
10.9
9.6
52.2
50.4
48.4
46.2
43.8
41.4
38.9
36.4
34.0
29.3
25.1
21.6
18.7
16.4
14.4
32.1
31.0
29.7
28.3
26.8
25.3
23.7
22.2
20.6
17.8
15.1
13.0
11.2
9.8
8.6
5 16c
7 16
3 8
48.2
46.5
44.6
42.5
40.3
38.0
35.6
33.3
31.0
26.7
22.7
19.5
16.9
14.8
13.0
29.0
28.0
26.8
25.5
24.1
22.7
21.3
19.9
18.5
15.9
13.5
11.5
10.0
8.7
7.6
43.6
42.0
40.3
38.3
36.3
34.2
32.0
29.9
27.8
23.9
20.3
17.4
15.0
13.1
11.5
24.9
24.0
23.0
21.9
20.7
19.5
18.3
17.1
15.9
13.7
11.7
10.0
8.6
7.5
6.6
5.8
37.4
36.1
34.6
32.9
31.2
29.4
27.5
25.7
24.0
20.6
17.5
15.0
12.9
11.2
9.9
8.7
1 4c,
20.3
19.6
18.8
17.9
17.0
16.1
15.1
14.1
13.2
11.4
9.7
8.3
7.1
6.2
5.4
4.8
30.5
29.4
28.3
27.0
25.6
24.1
22.7
21.2
19.8
17.1
14.6
12.4
10.7
9.3
8.1
7.2
Properties
(in.2)
5.43
4.61
3.75
3.30
2.86
2.40
1.93
z (in.)
0.774
0.774
0.776
0.777
0.779
0.781
0.783
ASD
LRFD
c = 1.67
c = 0.9
Ag
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate L/rz equal to or greater than 120, 140 and 200, respectively.
*Method 4 (flexural rigidity El* = 0.8bEl).
131-168_EJ4Q_2012_2010-30R.indd 159
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Shape
lb/ft
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
9
10
11
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
9
10
11
9.80
1 4c
3 8
5 16
8.50
7.20
5.80
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
21.0
20.4
19.6
18.8
17.9
17.0
16.0
15.1
14.1
13.2
12.3
11.4
10.6
9.2
8.0
7.0
31.6
30.6
29.5
28.3
26.9
25.5
24.1
22.7
21.2
19.8
18.5
17.2
15.9
13.8
12.0
10.5
19.4
18.8
18.1
17.3
16.5
15.6
14.7
13.8
12.9
12.1
11.2
10.4
9.7
8.3
7.2
6.3
29.1
28.2
27.2
26.0
24.7
23.4
22.1
20.7
19.4
18.1
16.9
15.7
14.5
12.5
10.9
9.5
Fy = 36 ksi
17.9
26.9
17.3
26.1
16.7
25.0
15.9
23.9
15.1
22.7
14.3
21.5
13.4
20.2
12.6
18.9
11.8
17.7
11.0
16.5
10.2
15.3
9.5
14.2
8.7
13.1
7.5
11.3
6.5
9.8
5.7
8.5
15.8
15.3
14.6
14.0
13.3
12.5
11.8
11.0
10.3
9.6
8.9
8.2
7.6
6.5
5.6
4.9
23.7
22.9
22.0
21.0
19.9
18.8
17.7
16.5
15.4
14.4
13.3
12.3
11.4
9.8
8.4
7.4
13.3
12.9
12.4
11.8
11.2
10.6
9.9
9.3
8.7
8.0
7.5
6.9
6.4
5.4
4.7
4.1
20.1
19.4
18.6
17.7
16.8
15.9
14.9
13.9
13.0
12.1
11.2
10.4
9.6
8.2
7.1
6.1
Fy = 50 ksi
Design
7 16
11.1
Design
1 2
28.6
27.4
26.0
24.6
23.0
21.5
19.9
18.4
16.9
15.5
14.2
13.0
12.0
10.2
8.8
7.7
7 16
1 2
43.0
41.2
39.1
36.9
34.6
32.2
29.9
27.6
25.4
23.3
21.3
19.6
18.0
15.4
13.2
11.5
26.3
25.2
23.9
22.6
21.1
19.7
18.2
16.8
15.5
14.1
12.9
11.8
10.9
9.3
8.0
6.9
39.6
24.3
37.9
23.2
36.0
22.0
33.9
20.7
31.7
19.3
29.5
18.0
27.4
16.6
25.3
15.3
23.2
14.0
21.3
12.8
19.4
11.7
17.8
10.7
16.4
9.8
14.0
8.3
12.0
7.1
10.4
6.2
Properties
1 4c
3 8
5 16
36.6
34.9
33.1
31.1
29.1
27.0
24.9
23.0
21.1
19.2
17.5
16.0
14.7
12.5
10.7
9.3
21.3
20.4
19.3
18.1
16.9
15.7
14.5
13.3
12.2
11.1
10.1
9.2
8.5
7.2
6.1
5.3
32.1
30.6
29.0
27.2
25.4
23.5
21.7
20.0
18.3
16.7
15.2
13.9
12.7
10.8
9.2
8.0
17.6
16.9
16.0
15.0
14.0
13.0
12.1
11.1
10.2
9.3
8.5
7.8
7.1
6.0
5.1
4.4
26.5
25.3
24.0
22.6
21.1
19.6
18.1
16.7
15.3
14.0
12.8
11.7
10.7
9.0
7.7
6.7
Ag (in.2)
3.25
2.89
2.50
2.10
1.70
z (in.)
0.679
0.681
0.683
0.685
0.688
ASD
LRFD
c = 1.67
c = 0.9
131-168_EJ4Q_2012_2010-30R.indd 160
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Shape
lb/ft
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
3 8
8.30
7.20
3 16c,
5 16
6.10
1 4
4.90
3.71
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
16.2
15.5
14.8
14.0
13.2
12.3
11.5
10.7
9.9
9.1
8.3
7.7
7.1
6.5
6.1
5.6
24.3
23.3
22.2
21.1
19.8
18.6
17.3
16.0
14.8
13.6
12.5
11.5
10.6
9.8
9.1
8.5
15.0
14.4
13.7
13.0
12.2
11.4
10.6
9.8
9.0
8.3
7.6
7.0
6.4
5.9
5.5
5.1
22.6
21.7
20.6
19.5
18.3
17.1
15.9
14.7
13.6
12.4
11.4
10.5
9.6
8.9
8.3
7.7
13.9
13.3
12.6
11.9
11.1
10.4
9.6
8.9
8.2
7.5
6.8
6.3
5.8
5.3
4.9
4.6
Fy = 36 ksi
20.9
12.4
20.0
11.9
19.0
11.2
17.9
10.6
16.7
9.9
15.6
9.2
14.5
8.5
13.4
7.8
12.3
7.2
11.3
6.6
10.3
6.0
9.4
5.5
8.7
5.0
8.0
4.6
7.4
4.3
6.9
4.0
18.6
17.8
16.9
15.9
14.9
13.8
12.8
11.8
10.8
9.9
9.0
8.3
7.6
7.0
6.4
6.0
10.6
10.1
9.6
9.0
8.4
7.8
7.2
6.6
6.1
5.5
5.0
4.6
4.2
3.9
3.6
3.3
16.0
15.3
14.4
13.6
12.7
11.7
10.8
10.0
9.1
8.3
7.6
6.9
6.4
5.8
5.4
5.0
8.3
7.9
7.5
7.1
6.6
6.1
5.7
5.2
4.8
4.4
4.0
3.6
3.3
3.0
2.8
2.6
12.5
11.9
11.3
10.6
9.9
9.2
8.5
7.8
7.2
6.6
6.0
5.4
5.0
4.6
4.2
3.9
Fy = 50 ksi
Design
7 16
9.40
Design
1 2
21.8
20.7
19.4
18.0
16.6
15.3
13.9
12.6
11.4
10.4
9.4
8.6
7.9
7.3
6.7
6.2
7 16
1 2
32.8
31.1
29.1
27.1
25.0
23.0
20.9
19.0
17.2
15.6
14.2
13.0
11.9
10.9
10.1
9.3
20.3
19.2
17.9
16.6
15.3
14.0
12.8
11.5
10.4
9.4
8.6
7.8
7.2
6.6
6.0
5.6
3 8
30.5
28.8
27.0
25.0
23.0
21.1
19.2
17.4
15.6
14.2
12.9
11.7
10.8
9.9
9.1
8.4
18.7
28.1
17.6
26.5
16.5
24.7
15.2
22.9
14.0
21.0
12.7
19.2
11.6
17.4
10.4
15.7
9.4
14.1
8.5
12.8
7.7
11.6
7.0
10.5
6.4
9.6
5.9
8.8
5.4
8.1
5.0
7.5
Properties
16.7
15.7
14.6
13.5
12.4
11.3
10.2
9.2
8.2
7.4
6.7
6.1
5.6
5.1
4.7
4.3
3 16c
5 16
1 4
25.1
23.6
22.0
20.3
18.6
16.9
15.3
13.8
12.4
11.2
10.1
9.2
8.4
7.7
7.0
6.5
14.1
13.3
12.4
11.4
10.4
9.5
8.6
7.7
6.9
6.2
5.6
5.1
4.7
4.3
3.9
3.6
21.2
20.0
18.6
17.1
15.7
14.2
12.9
11.6
10.4
9.4
8.5
7.7
7.0
6.4
5.9
5.4
10.8
10.2
9.5
8.8
8.1
7.4
6.7
6.0
5.4
4.9
4.4
4.0
3.6
3.3
3.0
2.8
16.3
15.3
14.3
13.2
12.1
11.1
10.1
9.1
8.2
7.3
6.6
6.0
5.5
5.0
4.6
4.2
Ag (in.2)
2.76
2.43
2.11
1.78
1.44
1.09
z (in.)
0.580
0.580
0.581
0.583
0.585
0.586
ASD
LRFD
c = 1.67
c = 0.9
131-168_EJ4Q_2012_2010-30R.indd 161
10/11/12 4:53 PM
Shape
lb/ft
6
7
8
9
10
11
12
13
14
15
16
18
20
22
24
26
6
7
8
9
10
11
12
13
14
15
16
18
20
22
24
26
51.0
5 8c
45.0
9 16c
3 4
7 8
38.9
1 2c,
32.7
29.6
26.4
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
145
139
133
126
119
112
106
98.8
92.3
86.1
80.1
68.9
59.5
51.8
45.5
40.2
218
209
200
190
179
169
159
149
139
129
120
104
89.4
77.9
68.4
60.5
131
125
120
114
108
101
95.1
89.0
83.2
77.5
72.1
62.1
53.6
46.6
41.0
36.2
197
189
180
171
162
152
143
134
125
117
108
93.3
80.5
70.1
61.6
54.4
117
112
107
102
96.1
90.5
85.0
79.6
74.4
69.4
64.6
55.6
48.0
41.7
36.6
32.4
176
169
161
153
145
136
128
120
112
104
97.1
83.6
72.1
62.7
55.1
48.7
Fy = 36 ksi
102
154
98.1
147
93.6
141
88.9
134
84.1
126
79.1
119
74.3
112
69.5
105
64.9
97.6
60.5
91.0
56.3
84.6
48.4
72.8
41.8
62.8
36.3
54.6
31.9
47.9
28.2
42.3
87.2
83.7
79.9
75.9
71.8
67.6
63.4
59.4
55.5
51.8
48.2
41.5
35.7
31.1
27.3
24.1
131
126
120
114
108
102
95.4
89.3
83.4
77.8
72.4
62.3
53.7
46.7
41.0
36.2
77.9
74.8
71.5
68.0
64.3
60.7
57.0
53.5
50.0
46.7
43.5
37.6
32.4
28.2
24.7
21.8
117
112
107
102
96.7
91.2
85.7
80.4
75.2
70.2
65.4
56.5
48.7
42.3
37.1
32.8
68.7
66.1
63.3
60.3
57.2
54.1
50.9
47.9
44.8
41.9
39.2
34.0
29.3
25.5
22.4
19.8
103
99.4
95.1
90.7
86.0
81.3
76.6
71.9
67.4
63.0
58.9
51.1
44.1
38.3
33.6
29.7
Fy = 50 ksi
Design
56.9
Design
11/8
1/
1 8
193
182
171
160
149
138
127
117
107
98.2
89.8
75.9
65.0
56.1
49.0
43.1
290
274
257
240
223
207
191
176
161
148
135
114
97.6
84.4
73.6
64.8
174
164
154
144
134
124
114
105
96.6
88.4
80.9
68.4
58.5
50.5
44.1
38.8
261
247
232
216
201
186
172
158
145
133
122
103
87.9
75.9
66.3
58.3
155
147
138
129
120
111
102
94.2
86.5
79.2
72.4
61.2
52.3
45.2
39.4
34.7
5 8c
233
136
221
128
207
121
194
113
180
105
167
96.8
154
89.3
142
82.2
130
75.4
119
69.0
109
63.1
92.0
53.3
78.6
45.5
67.9
39.3
59.3
34.3
52.1
30.1
Properties
9 16c,
3 4
7 8
204
193
181
169
157
146
134
123
113
104
94.8
80.1
68.4
59.1
51.5
45.3
113
107
101
94.5
88.1
81.8
75.6
69.8
64.2
59.0
54.0
45.6
38.9
33.6
29.3
25.8
170
161
152
142
132
123
114
105
96.5
88.6
81.2
68.5
58.5
50.5
44.0
38.7
101
95.6
90.2
84.6
78.9
73.4
68.0
62.8
57.9
53.3
48.9
41.3
35.3
30.4
26.5
23.3
151
144
136
127
119
110
102
94.5
87.1
80.1
73.5
62.1
53.0
45.8
39.9
35.1
1 2c,
88.4
84.2
79.6
74.9
70.1
65.4
60.8
56.3
52.1
48.0
44.2
37.4
31.9
27.6
24.0
21.1
133
127
120
113
105
98.3
91.3
84.6
78.2
72.2
66.5
56.2
48.0
41.4
36.1
31.7
Ag (in.2)
16.8
15.1
13.3
11.5
9.69
8.77
7.84
z (in.)
1.56
1.56
1.57
1.57
1.58
1.58
1.59
ASD
LRFD
c = 1.67
c = 0.9
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate L/rz equal to or greater than 120, 140 and 200, respectively.
*Method 4, except the axial load is applied at mid-thickness of connected leg.
131-168_EJ4Q_2012_2010-30R.indd 162
10/11/12 4:53 PM
Shape
lb/ft
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
33.1
5 8
28.7
24.2
7 16c
9 16
1 2
21.9
19.6
17.3
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
95.9
91.1
85.8
80.0
74.1
68.3
62.6
57.1
51.9
47.1
42.6
38.7
35.2
32.2
29.6
27.3
144
137
129
120
111
103
94.0
85.8
78.1
70.8
64.0
58.1
53.0
48.5
44.5
41.0
86.2
81.9
77.0
71.8
66.5
61.2
56.0
51.1
46.5
42.1
38.1
34.5
31.5
28.8
26.4
24.3
130
123
116
108
99.9
92.0
84.2
76.8
69.8
63.3
57.2
51.9
47.3
43.2
39.7
36.5
75.2
71.4
67.1
62.6
57.9
53.3
48.8
44.5
40.5
36.6
33.1
30.0
27.4
25.0
23.0
21.1
113
107
101
94.1
87.1
80.1
73.4
66.9
60.8
55.1
49.8
45.2
41.1
37.6
34.5
31.8
Fy = 36 ksi
64.1
96.4
60.9
91.5
57.2
86.0
53.3
80.1
49.3
74.1
45.4
68.2
41.5
62.4
37.8
56.9
34.4
51.7
31.1
46.8
28.1
42.2
25.5
38.3
23.2
34.9
21.2
31.9
19.5
29.3
17.9
26.9
58.3
55.4
52.1
48.6
45.0
41.4
37.9
34.6
31.5
28.5
25.8
23.4
21.3
19.5
17.9
16.4
87.6
83.3
78.3
73.0
67.6
62.3
57.0
52.0
47.3
42.9
38.8
35.2
32.0
29.3
26.9
24.7
52.9
50.3
47.3
44.0
40.8
37.5
34.3
31.3
28.4
25.8
23.3
21.1
19.2
17.5
16.1
14.8
79.6
75.6
71.0
66.2
61.3
56.4
51.6
47.0
42.7
38.7
35.0
31.7
28.8
26.4
24.2
22.3
46.1
43.8
41.2
38.4
35.6
32.8
30.1
27.4
25.0
22.6
20.5
18.6
16.9
15.4
14.2
13.0
69.2
65.8
61.9
57.8
53.5
49.3
45.2
41.3
37.5
34.0
30.8
27.9
25.4
23.2
21.3
19.6
Fy = 50 ksi
Design
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
3 4
7 8
37.4
Design
1
129
120
111
101
91.4
82.2
73.6
65.6
58.3
52.1
46.8
42.2
38.3
34.9
31.9
29.2
193
180
166
152
137
124
111
98.6
87.6
78.3
70.3
63.5
57.5
52.4
47.9
44.0
116
108
99.2
90.5
81.9
73.6
65.9
58.7
52.1
46.5
41.7
37.7
34.1
31.1
28.4
26.1
3 4
7 8
174
162
149
136
123
111
99.0
88.2
78.3
69.9
62.7
56.6
51.3
46.7
42.7
39.2
101
93.9
86.5
78.8
71.3
64.1
57.4
51.1
45.3
40.5
36.3
32.8
29.7
27.0
24.7
22.7
151
85.9
141
80.1
130
73.7
119
67.1
107
60.7
96.4
54.5
86.2
48.8
76.7
43.4
68.1
38.5
60.8
34.3
54.6
30.8
49.2
27.8
44.6
25.2
40.6
22.9
37.1
20.9
34.1
19.2
Properties
1 2c
5 8
129
120
111
101
91.2
82.0
73.3
65.2
57.8
51.6
46.3
41.7
37.8
34.4
31.4
28.8
78.1
72.9
67.1
61.3
55.5
49.9
44.6
39.8
35.3
31.5
28.3
25.5
23.1
21.0
19.2
17.6
7 16c,
9 16
117
110
101
92.1
83.3
75.0
67.1
59.8
53.0
47.3
42.5
38.3
34.7
31.6
28.9
26.5
69.9
65.3
60.2
55.0
49.8
44.9
40.2
35.8
31.8
28.4
25.5
23.0
20.8
18.9
17.3
15.8
105
98.1
90.4
82.6
74.9
67.4
60.4
53.9
47.9
42.7
38.3
34.5
31.3
28.4
26.0
23.8
/
60.1
56.3
52.0
47.7
43.3
39.1
35.2
31.4
28.0
25.0
22.4
20.2
18.3
16.7
15.2
13.9
90.3
84.6
78.2
71.6
65.1
58.8
52.8
47.3
42.1
37.6
33.7
30.4
27.5
25.0
22.9
21.0
Ag (in.2)
11.0
9.75
8.46
7.13
6.45
5.77
5.08
z (in.)
1.17
1.17
1.17
1.17
1.18
1.18
1.18
ASD
LRFD
c = 1.67
c = 0.9
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate L/rz equal to or greater than 120, 140 and 200, respectively.
*Method 4, except the axial load is applied at mid-thickness of connected leg.
131-168_EJ4Q_2012_2010-30R.indd 163
10/11/12 4:53 PM
Shape
lb/ft
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
5 8
23.6
20.0
3 8c
1 2
16.2
5 16c,
7 16
14.3
12.3
10.4
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
76.6
74.6
71.5
67.4
62.7
57.5
52.3
47.2
42.3
37.8
33.5
29.7
26.5
23.8
21.4
19.4
115
112
107
101
94.2
86.5
78.6
71.0
63.6
56.8
50.3
44.6
39.8
35.7
32.2
29.2
66.8
65.0
62.2
58.7
54.6
50.1
45.6
41.2
36.9
32.9
29.2
25.9
23.1
20.8
18.7
17.0
100
97.7
93.5
88.2
82.1
75.4
68.6
61.9
55.5
49.5
43.9
39.0
34.8
31.2
28.1
25.5
57.5
56.0
53.6
50.6
47.0
43.1
39.2
35.4
31.7
28.3
25.1
22.2
19.8
17.8
16.0
14.5
86.5
84.2
80.6
76.0
70.7
64.9
59.0
53.2
47.7
42.5
37.7
33.4
29.8
26.7
24.1
21.8
Fy = 36 ksi
47.8
71.8
46.5
69.9
44.5
66.9
42.0
63.1
39.0
58.6
35.8
53.8
32.5
48.9
29.3
44.1
26.3
39.5
23.4
35.2
20.8
31.2
18.4
27.7
16.4
24.7
14.7
22.1
13.3
19.9
12.0
18.0
41.9
40.8
39.1
36.9
34.3
31.5
28.6
25.8
23.2
20.7
18.4
16.3
14.5
13.0
11.7
10.6
63.0
61.3
58.8
55.4
51.6
47.3
43.1
38.8
34.8
31.1
27.6
24.4
21.8
19.5
17.6
15.9
36.7
35.7
34.2
32.3
30.0
27.6
25.1
22.7
20.3
18.1
16.1
14.3
12.7
11.4
10.3
9.3
55.1
53.6
51.4
48.5
45.1
41.5
37.7
34.1
30.5
27.3
24.2
21.4
19.1
17.1
15.4
14.0
29.9
29.2
28.0
26.5
24.8
22.8
20.9
18.9
17.0
15.3
13.6
12.1
10.8
9.7
8.7
7.9
44.9
43.8
42.1
39.9
37.2
34.3
31.4
28.4
25.6
23.0
20.5
18.2
16.2
14.5
13.1
11.8
Fy = 50 ksi
Design
3 4
27.2
Design
7 8
106
102
96.4
89.0
80.7
72.2
63.9
56.0
48.8
42.3
37.0
32.5
28.8
25.7
23.1
20.8
3 4
7 8
159
154
145
134
121
108
96.0
84.2
73.3
63.6
55.6
48.9
43.4
38.7
34.7
31.3
92.3
89.0
83.9
77.5
70.3
62.9
55.7
48.8
42.6
36.9
32.3
28.4
25.2
22.5
20.2
18.2
139
134
126
117
106
94.6
83.7
73.4
64.0
55.5
48.5
42.7
37.9
33.8
30.3
27.3
79.6
76.7
72.3
66.8
60.5
54.1
47.9
42.0
36.6
31.7
27.7
24.3
21.6
19.2
17.3
15.6
7 16c
5 8
1 2
120
66.1
115
63.7
109
60.0
100
55.4
90.9
50.2
81.3
44.9
71.9
39.7
63.1
34.8
54.9
30.3
47.6
26.2
41.6
22.9
36.6
20.1
32.4
17.8
28.9
15.9
25.9
14.2
23.4
12.8
Properties
99.3
95.7
90.2
83.3
75.5
67.5
59.6
52.3
45.5
39.4
34.4
30.2
26.8
23.9
21.4
19.3
57.5
55.4
52.3
48.4
43.9
39.3
34.8
30.6
26.7
23.2
20.2
17.8
15.7
14.0
12.6
11.4
86.4
83.3
78.6
72.7
66.0
59.1
52.4
46.0
40.1
34.8
30.4
26.7
23.7
21.1
18.9
17.1
3 8c,
49.1
47.5
44.9
41.6
37.9
34.1
30.3
26.7
23.4
20.3
17.7
15.6
13.8
12.3
11.0
9.9
73.8
71.3
67.4
62.6
57.0
51.2
45.5
40.1
35.1
30.6
26.6
23.4
20.7
18.5
16.6
14.9
5 16c,
/
39.6
38.4
36.4
34.0
31.1
28.1
25.2
22.3
19.7
17.2
15.0
13.2
11.7
10.4
9.4
8.4
59.5
57.7
54.8
51.0
46.8
42.3
37.8
33.5
29.5
25.9
22.6
19.9
17.6
15.7
14.1
12.7
Ag (in.2)
8.00
6.98
5.90
4.79
4.22
3.65
3.07
z (in.)
0.971
0.972
0.975
0.980
0.983
0.986
0.990
ASD
LRFD
c = 1.67
c = 0.9
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate KL/rz equal to or greater than 120, 140 and 200, respectively.
*Method 4, except that the axial load is applied at mid-thickness of connected leg.
131-168_EJ4Q_2012_2010-30R.indd 164
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Shape
lb/ft
18.5
Design
2
2.5
3
3.5
4
4.5
5
5.5
6
7
8
9
10
11
12
13
2
2.5
3
3.5
4
4.5
5
5.5
6
7
8
9
10
11
12
13
1 2
15.7
12.8
5 16c
7 16
3 8
11.3
9.8
1 4c,
8.2
6.6
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
48.9
47.5
45.8
43.9
41.9
39.8
37.7
35.5
33.3
29.1
25.3
21.8
18.8
16.4
14.4
73.6
71.4
68.8
66.0
63.0
59.8
56.6
53.3
50.1
43.8
38.0
32.7
28.3
24.6
21.6
42.1
40.8
39.4
37.8
36.0
34.2
32.3
30.4
28.6
25.0
21.6
18.6
16.1
14.0
12.3
63.3
61.4
59.2
56.8
54.1
51.4
48.6
45.7
42.9
37.5
32.5
28.0
24.1
21.0
18.5
34.5
33.5
32.3
30.9
29.5
28.0
26.5
24.9
23.4
20.5
17.7
15.3
13.2
11.5
10.1
51.8
50.3
48.5
46.5
44.3
42.1
39.8
37.5
35.2
30.7
26.7
22.9
19.8
17.2
15.1
Fy = 36 ksi
30.8
46.3
29.8
44.8
28.8
43.2
27.6
41.4
26.3
39.5
25.0
37.5
23.6
35.5
22.2
33.4
20.8
31.3
18.2
27.4
15.8
23.7
13.6
20.4
11.7
17.6
10.2
15.3
8.9
13.4
26.8
26.0
25.1
24.0
22.9
21.8
20.6
19.3
18.2
15.9
13.8
11.8
10.2
8.9
7.8
40.3
39.1
37.7
36.1
34.4
32.7
30.9
29.1
27.3
23.9
20.7
17.8
15.3
13.3
11.7
22.6
22.0
21.2
20.3
19.4
18.4
17.4
16.4
15.4
13.4
11.6
10.0
8.6
7.5
6.6
5.8
34.0
33.0
31.8
30.5
29.1
27.6
26.1
24.6
23.1
20.2
17.5
15.0
13.0
11.3
9.9
8.7
17.9
17.3
16.8
16.1
15.4
14.7
13.9
13.1
12.3
10.8
9.4
8.2
7.0
6.1
5.4
4.7
26.8
26.1
25.2
24.2
23.1
22.0
20.9
19.7
18.5
16.3
14.2
12.3
10.6
9.2
8.1
7.1
Fy = 50 ksi
Design
5 8
3 4
66.5
63.9
60.8
57.5
54.0
50.4
46.9
43.4
40.1
33.9
28.4
24.0
20.6
17.8
15.5
5 8
3 4
100
96.0
91.4
86.4
81.2
75.8
70.5
65.3
60.3
50.9
42.6
36.1
30.9
26.7
23.3
57.3
54.9
52.3
49.4
46.4
43.3
40.2
37.2
34.3
29.0
24.3
20.5
17.5
15.2
13.2
1 2
86.1
82.6
78.6
74.3
69.7
65.1
60.5
56.0
51.6
43.6
36.5
30.8
26.4
22.8
19.9
46.9
45.0
42.8
40.5
38.0
35.5
33.0
30.5
28.1
23.7
19.9
16.8
14.4
12.4
10.8
70.5
67.6
64.4
60.8
57.1
53.3
49.5
45.8
42.3
35.7
29.9
25.2
21.6
18.7
16.3
41.8
40.1
38.2
36.1
33.9
31.6
29.3
27.1
25.0
21.1
17.7
14.9
12.7
11.0
9.6
5 16c
7 16
3 8
62.9
60.3
57.4
54.2
50.9
47.5
44.1
40.8
37.6
31.7
26.5
22.4
19.2
16.5
14.4
36.4
35.0
33.3
31.4
29.5
27.5
25.6
23.7
21.8
18.4
15.4
13.0
11.1
9.6
8.4
54.8
52.5
50.0
47.2
44.4
41.4
38.4
35.6
32.8
27.7
23.1
19.5
16.7
14.4
12.6
30.0
28.8
27.5
26.0
24.5
22.9
21.3
19.8
18.3
15.5
13.0
11.0
9.4
8.1
7.1
6.2
45.1
43.3
41.3
39.1
36.8
34.4
32.1
29.7
27.5
23.3
19.6
16.5
14.1
12.2
10.6
9.3
1 4c,
23.4
22.5
21.5
20.5
19.3
18.2
17.0
15.8
14.7
12.5
10.6
9.0
7.7
6.6
5.8
5.1
35.1
33.8
32.4
30.8
29.1
27.3
25.5
23.8
22.1
18.8
16.0
13.5
11.5
9.9
8.7
7.6
Properties
(in.2)
5.44
4.61
3.75
3.30
2.86
2.40
1.93
z (in.)
0.774
0.774
0.776
0.777
0.779
0.781
0.783
ASD
LRFD
c = 1.67
c = 0.9
Ag
Shape is slender for compression. f Shape exceeds compact limit for flexure.
Notes: Heavy lines indicate KL/rz equal to or greater than 120, 140 and 200, respectively.
*Method 4, except that the axial load is applied at mid-thickness of connected leg.
131-168_EJ4Q_2012_2010-30R.indd 165
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Shape
lb/ft
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
9
10
11
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
9
10
11
9.80
1 4c
3 8
5 16
8.50
7.20
5.80
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
29.6
28.5
27.2
25.7
24.2
22.7
21.2
19.6
18.2
16.8
15.4
14.2
13.0
11.0
9.4
8.1
44.5
42.8
40.8
38.7
36.4
34.1
31.8
29.5
27.3
25.2
23.2
21.3
19.5
16.5
14.2
12.2
26.2
25.2
24.1
22.8
21.5
20.2
18.8
17.5
16.2
14.9
13.7
12.6
11.6
9.8
8.4
7.3
39.4
37.9
36.2
34.3
32.3
30.3
28.2
26.2
24.3
22.4
20.7
19.0
17.4
14.7
12.6
10.9
Fy = 36 ksi
23.2
34.9
22.3
33.6
21.3
32.0
20.2
30.4
19.0
28.6
17.8
26.8
16.6
25.0
15.4
23.2
14.3
21.4
13.2
19.8
12.1
18.2
11.1
16.7
10.2
15.3
8.6
13.0
7.4
11.1
6.4
9.6
19.6
18.9
18.0
17.1
16.1
15.1
14.0
13.0
12.1
11.1
10.3
9.4
8.6
7.3
6.2
5.4
29.5
28.4
27.1
25.7
24.2
22.6
21.1
19.6
18.1
16.7
15.4
14.2
13.0
11.0
9.4
8.1
15.9
15.3
14.6
13.8
13.1
12.2
11.4
10.6
9.8
9.1
8.4
7.7
7.1
6.0
5.1
4.4
23.8
22.9
21.9
20.8
19.6
18.4
17.2
16.0
14.8
13.7
12.6
11.6
10.6
9.0
7.7
6.6
Fy = 50 ksi
Design
7 16
11.1
Design
1 2
40.0
37.9
35.6
33.1
30.6
28.1
25.7
23.4
21.2
19.2
17.3
15.7
14.3
12.0
10.2
8.7
7 16
1 2
60.1
57.0
53.5
49.8
46.0
42.2
38.6
35.1
31.9
28.8
26.0
23.6
21.5
18.0
15.3
13.1
35.5
33.6
31.6
29.4
27.2
25.0
22.8
20.8
18.9
17.1
15.4
14.0
12.7
10.7
9.1
7.8
53.3
31.4
50.6
29.8
47.5
28.0
44.2
26.0
40.9
24.0
37.5
22.1
34.3
20.2
31.3
18.3
28.4
16.6
25.6
15.0
23.2
13.6
21.0
12.3
19.1
11.2
16.0
9.4
13.6
8.0
11.7
6.8
Properties
1 4c
3 8
5 16
47.2
44.7
42.0
39.1
36.1
33.1
30.3
27.6
25.0
22.6
20.4
18.5
16.8
14.1
12.0
10.3
26.4
25.0
23.5
21.9
20.2
18.6
17.0
15.5
14.1
12.7
11.5
10.4
9.5
7.9
6.7
5.8
39.7
37.6
35.4
32.9
30.4
28.0
25.6
23.3
21.1
19.1
17.2
15.6
14.2
11.9
10.1
8.7
20.8
19.8
18.7
17.5
16.2
15.0
13.7
12.6
11.4
10.4
9.4
8.5
7.8
6.5
5.5
4.7
31.3
29.8
28.1
26.3
24.4
22.5
20.6
18.9
17.2
15.6
14.2
12.8
11.7
9.8
8.3
7.1
Ag (in.2)
3.25
2.89
2.50
2.10
1.70
z (in.)
0.679
0.681
0.683
0.685
0.688
ASD
LRFD
c = 1.67
c = 0.9
Notes: Heavy lines indicate L/rz equal to or greater than 120, 140 and 200,
respectively.
*Method 4, except that the axial load is applied at mid-thickness of connected
leg.
131-168_EJ4Q_2012_2010-30R.indd 166
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Shape
lb/ft
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
3 8
8.30
7.20
3 16c,
5 16
6.10
1 4
4.90
3.71
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
Pn /c
cPn
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
ASD
LRFD
23.9
22.7
21.3
19.9
18.4
16.9
15.5
14.1
12.9
11.6
10.5
9.6
8.7
8.0
7.3
6.7
35.9
34.1
32.1
29.9
27.7
25.5
23.3
21.3
19.3
17.5
15.8
14.4
13.1
12.0
11.0
10.1
21.2
20.2
18.9
17.7
16.3
15.0
13.8
12.5
11.4
10.3
9.3
8.5
7.7
7.0
6.5
6.0
31.9
30.3
28.5
26.5
24.5
22.6
20.7
18.8
17.1
15.5
14.0
12.7
11.6
10.6
9.7
8.9
18.7
17.7
16.7
15.5
14.3
13.2
12.1
11.0
10.0
9.0
8.2
7.4
6.7
6.2
5.7
5.2
Fy = 36 ksi
28.1
15.9
26.6
15.1
25.0
14.2
23.3
13.2
21.6
12.2
19.8
11.2
18.1
10.3
16.5
9.4
15.0
8.5
13.6
7.7
12.3
7.0
11.1
6.3
10.1
5.8
9.3
5.3
8.5
4.8
7.8
4.4
23.9
22.7
21.3
19.9
18.4
16.9
15.5
14.1
12.8
11.6
10.5
9.5
8.6
7.9
7.2
6.7
13.0
12.3
11.6
10.8
10.0
9.2
8.4
7.7
7.0
6.3
5.7
5.2
4.7
4.3
3.9
3.6
19.5
18.5
17.4
16.2
15.0
13.8
12.6
11.5
10.5
9.5
8.5
7.8
7.1
6.5
5.9
5.4
9.6
9.1
8.6
8.1
7.5
6.9
6.3
5.8
5.3
4.8
4.4
3.9
3.6
3.3
3.0
2.8
14.4
13.7
13.0
12.1
11.2
10.4
9.5
8.7
7.9
7.2
6.5
5.9
5.4
4.9
4.5
4.2
Fy = 50 ksi
Design
7 16
9.40
Design
1 2
32.0
29.9
27.5
25.1
22.7
20.4
18.2
16.2
14.4
12.9
11.6
10.4
9.5
8.6
7.9
7.2
7 16
1 2
48.1
44.9
41.3
37.7
34.1
30.6
27.4
24.4
21.7
19.3
17.4
15.7
14.2
12.9
11.8
10.9
28.4
26.5
24.4
22.2
20.1
18.1
16.2
14.4
12.7
11.4
10.2
9.2
8.4
7.6
7.0
6.4
3 8
42.7
39.8
36.7
33.4
30.2
27.2
24.3
21.6
19.2
17.1
15.4
13.9
12.6
11.4
10.5
9.6
25.0
37.6
23.3
35.0
21.4
32.2
19.5
29.3
17.6
26.5
15.9
23.8
14.2
21.3
12.6
18.9
11.2
16.8
10.0
15.0
9.0
13.5
8.1
12.1
7.3
11.0
6.7
10.0
6.1
9.1
5.6
8.4
Properties
21.3
19.9
18.3
16.6
15.0
13.5
12.1
10.7
9.5
8.5
7.6
6.9
6.2
5.7
5.2
4.8
3 16c
5 16
1 4
32.0
29.9
27.5
25.0
22.6
20.3
18.2
16.1
14.3
12.8
11.5
10.3
9.4
8.5
7.8
7.1
17.1
16.0
14.8
13.5
12.2
11.0
9.8
8.8
7.8
6.9
6.2
5.6
5.1
4.6
4.2
3.9
25.8
24.1
22.2
20.2
18.3
16.5
14.8
13.2
11.7
10.4
9.4
8.4
7.6
7.0
6.4
5.8
12.4
11.7
10.8
10.0
9.1
8.2
7.4
6.7
6.0
5.3
4.8
4.3
3.9
3.5
3.2
3.0
18.7
17.6
16.3
15.0
13.6
12.4
11.1
10.0
8.9
8.0
7.2
6.4
5.8
5.3
4.9
4.4
Ag (in.2)
2.76
2.43
2.11
1.78
1.44
1.09
z (in.)
0.580
0.580
0.581
0.583
0.585
0.586
ASD
LRFD
c = 1.67
c = 0.9
hape is slender for compression. f Shape exceeds compact limit for flexure.
S
Notes:Heavy lines indicate L/rz equal to or greater than 120, 140 and 200, respectively.
*Method 4, except that the axial load is applied at mid-thickness of connected leg.
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131-168_EJ4Q_2012_2010-30R.indd 168
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