Discussion
Steel Column Bending Amplification Factor
Paper presented by WILLIAM Y. LIU (April, 1965, Issue)
Figure 1
Cm
Values of—.
Discussion by ALFRED SCHEINER
-—^ for Category A (C = 0.85).
\'-*j
M R . LIU'S curves for the column bending amplification
factor provide a useful tool for the designer by reducing
the number of calculations required for column design
under the AISC Specification.
Some time ago, in connection with my work on the
design of the 24-story residential structure, St. Paul's
Towers, Oakland, Calif., I prepared a set of tables to
eliminate the need for repeatedly calculating the amplification factors in this building, which had 30 different
types of columns checked at eight different stories for
three different loads, requiring over 500 calculations of
the column formulas.
Figures 1 and 2, tabulations (to slide rule accuracy)
for use in formula (7a), may be preferred to curves by
some designers, particularly for use in the region where
M r . Liu's curves tend to converge. T h e tables are identified by the categories used in Table CI.6.1.1 of the Commentary on the A I S C Specification. Figure 1 covers
Category A, and provides values of Cm/{\ —
fa/F'e),
the same case covered by M r . Liu's curves. Figure 2
covers Categories B and C, and provides values of
(1 — fa/F'e),
the denominator of the amplification
factor. These values may be used with values of Cm =
(0.4 M1/M2 + 0.6) and Cm = (1 + +fJF'e)9 Categories
B and C respectively.
{See Table C1.6.1.1 in Commentary on AISC Specification)
Figure 2
Values of I 1 — ^ - ) for Categories B and C
For Category B, Cm = (o.4 ^
+
0.6);
for Category C, Cm = ( 1 + $ j± J
(See Table CI.6.1.1 in Commentary on AISC Specification)
Alfred Scheiner is Senior Engineer, Victor Gruen Associates, Los
Angeles, Calif.
146
AISC
ENGINEERING
JOURNAL
Kh
\.
>v
Tb
/ 0 ( k s i ) \ 20
25
30
35
3
4
5
6
7
.855
.86
.86
.865
.87
.86
.865
.87
.87
.875
.865
.87
.875
.88
.885
.87
.88
.89
.90
.90
8
9
10
11
12
.87
.87
.87
.875
.875
.88
.885
.89
.89
.895
.89
.90
.905
.91
.915
.91
.92
.93
.94
.95
13
14
15
16
17
.88
.88
.885
.89
.89
.90
.905
.91
.91
.915
.92
.93
.935
.94
.95
.96
.96
.97
.98
.99
18
19
20
21
22
.895
.90
.90
.90
.905
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.925
.93
.935
.94
.955
.96
.97
.975
.98
23
24
25
26
27
28
.905
.91
.91
.915
.915
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.94
.945
.95
.955
.96
.965
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.995
1.000
1.010
1.015
1.020
fa (ksi) N ^ 20
40
.88
89
90
91
92
45
.89
.90
.91
.93
.94
60
50
55
.90
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.96
.91 .92 .93 .94 .96 .98
.93 .94 .96 .98 1.00 1.03
.95 .97 .99 1.02 1.05 1.08
.97 1.00 1.02 1.06 1.10 1.15
.99 1.02 1.06 1.10 1.15 1.21
65
70
75
80
85
90
95
100
105
110
115
120
1.00
1.05
1.12
1.20
1.29
1.02
1.09
1.17
1.26
1.37
1.04
1.12
1.22
1.34
1.47
1.06
1.16
1.28
1.42
1.61
1.09
1.21
1.35
1.53
1.76
1.12
1.26
1.43
1.66
1.97
1.16
1.32
1.52
1.82
2.24
1.20
1.39
1.65
2.02
2.63
1.50
1.66
1.86
2.11
2.43
1.65
1.87
2.15
2.54
3.09
1.83
2.14
2.58
3.24
4.36
2.08 2.42 2.92 3.71
2.54 3.15 4.20
3.26 4.48
4.52
93 .95 .98
94 .97 1.00
95 .99 1.02
97 1.00 1.04
98 1.02 1.06
1.01
1.04
1.07
1.10
1.12
1.05
1.09
1.12
1.16
1.20
1.10
1.14
1.19
1.24
1.29
1.15
1.21
1.27
1.33
1.40
1.21
1.29
1.36
1.45
1.56
1.29
1.38
1.49
1.61
1.75
1.39
1.51
1.65
1.82
2.03
1
1
1
1
99
00
01
02
04
1.03
1.05
1.07
1.08
1.11
1.09
1.11
1.14
1.16
1.19
1.15
1.19
1.22
1.26
1.30
1.24
1.28
1.33
1.38
1.44
1.35
1.41
1.48
1.55
1.64
1.48
1.57
1.67
1.79
1.92
1.67
1.80
1.96
2.14
2.36
1.92
2.12
2.40
2.72
3.15
2.30 2.88 3.98
2.64 3.54
3.12 4.59
3.78
4.85
1.00
1.01
1.02
1.03
1.04
1
1
1
1
1
05
07
08
10
11
1.12
1.15
1.17
1.19
1.21
1.22
1.25
1.28
1.31
1.35
1.34
1.38
1.43
1.48
1.54
1.51
1.58
1.65
1.73
1.82
1.73
1.85
1.97
2.10
2.25
2.08
2.27
2.48
2.74
3.09
2.68 3.73
3.01 4.60
3.47
4.09
5.00
1.05
1.06
1.07
1.08
1.09
1.10
1
1
1
1
1
1
13
14
16
18
20
21
1.24
1.26
1.29
1.31
1.34
1.37
1.38
1.42
1.46
1.50
1.55
1.60
1.60
1.66
1.72
1.80
1.88
1.97
1.92
2.02
2.15
2.29
2.45
2.64
2.45 3.50
2.66 4.02
2.91 4.77
3.20
3.62
4.11
Figure 1
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
.757
.676
.595
.514
.433
.734
.645
.556
.467
.380
.710
.614
.517
.420
.323
3
4
5
6
7
.992
.989
.987
.984
.981
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.983
.979
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.976
.970
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.661
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.819
.758
.698
.636
.577
.800
.732
.665
.598
.531
.778
.704
.630
.557
.484
8
9
10
11
12
.979
.976
.973
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.968
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.962
.958
.954
.950
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.945
.940
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.882
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.878
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.738
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.639
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.564
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.565
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.464
.397
.330
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.409 .352 .290 .229
.335 .270 .202
.261 .190
.188
13
14
15
16
17
.965
.962
.960
.957
.954
.946
.941
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.933
.929
.922
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.910
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.475
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.472
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.396
.360
.442
.400
.355
.312
.270
.370 .295 .214
.322 .240 .152
.272 .185
.225
.175
18
19
20
21
22
.952
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.943
.941
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.920
.916
.912
.908
.891
.885
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.844
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.807
.796
.786
.775
.764
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.742
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.648
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.634
.615
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.575
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.564
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.515
.492
.467
.490
.461
.433
.405
.377
.408
.375
.342
.310
.275
.320 .228
.282 .185
.245
.208
.170
23
24
25
26
27
28
.938
.935
.933
.930
.927
.925
.904
.900
.895
.891
.887
.883
.861
.855
.849
.843
.837
.831
.811
.802
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.778
.770
.753
.743
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.721
.710
.700
.687
.674
.660
.647
.633
.620
.614
.598
.581
.565
.547
.530
.533
.514
.493
.474
.452
.431
.444
.420
.395
.371
.347
.322
.347 .243
.320 .211
.292 .178
.265
.235
.207
Figure 2
147
O C T O B E R / 1965