Air Force Stress Manual:
Column Analysis
  1. Simple Columns
  2. Column Data
  3. Straight Line Constants
  4. Crippling of Columns
  5. Complex Columns
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Column Analysis - Constants for Straight Line Equation

This page provides constants for the straight line equation, as used in the analysis of short columns. These constants are taken from the "Stress Analysis Manual," Air Force Flight Dynamics Laboratory, October 1986. The straight line equation for the analysis of short columns is described here.

Other related chapters from the Air Force "Stress Analysis Manual" can be seen to the right.

Column Analysis
  1. Analysis of Simple Columns
  2. Column Data
  3. Constants for Straight Line Equation
  4. Crippling of Columns
  5. Analysis of Complex Columns

Table 2-3: Constants for Straight Line Equation

Extruded Rod, Bar and Shapes
Alloy and Temper Thickness, in. \(N\) (ksi) \(M\) (ksi) \(\left({L'\over \rho}\right)_{cr}\)
2014-O All 9.9 0.037 160
2014-T4 All 35.2 0.251 89
2014-T6 Up thru 0.499 61.4 0.410 50
2014-T6 0.500-0.749 67.3 0.471 48
2014-T6 0.750 and over
Area 25 sq in. max. 69.7 0.496 47
Area 25 to 32 sq in. 67.3 0.471 48
2024-O All 9.9 0.037 160
2024-T4 Up thru 0.249 43.6 0.300 65
2024-T4 0.250-0.749 44.8 0.313 64
2024-T4 0.750-1.499 50.9 0.379 60
2024-T4 1.500-2.999
Area 25 sq in. max. 58.4 0.466 56
2024-T4 3.000 and over
Area 25 sq in. max. 		58.4 0.466 56
2024-T4 1.500 and over
Area 25 thru 32 sq in. 		53.4 0.407 59
3003-O All 5.4 0.015 222
3003-H112 All 5.4 0.015 222
5454-O Up to 5.000 13.3 0.058 142
5454-H112 Up to 5.000 13.3 0.058 142
5454-H311 Up to 5.000 20.4 0.111 121
5456-O Up to 5.000 (Note 3) 21.6 0.120 111
5456-H112 Up to 5.000 (Note 3) 21.6 0.120 111
5456-H311 Up to 5.000 (Note 3) 25.3 0.153 106
6061-O All 5.4 0.015 222
6061-T4 All 15.7 0.074 128
6061-T6 All 38.3 0.202 63
6061-T62 All 28.1 0.127 74
6062-O All 5.4 0.015 222
6062-T4 All 15.7 0.074 128
6062-T6 All 38.3 0.202 63
6062-T62 All 28.1 0.127 74
6063-T42 Up thru 0.500 11.0 0.043 149
6063-T5 Up thru 0.500 17.5 0.076 103
6063-T6 Up thru 0.124 28.0 0.155 81
6063-T6 0.125-0.500 28.0 0.155 81
7075-O All 13.3 0.058 142
7075-T6 Up thru 0.249 79.3 0.602 44
7075-T6 0.250-0.499 87.8 0.859 46
7075-T6 0.500-1.499 87.8 0.859 46
7075-T6 1.500-2.499 81.7 0.629 43
7075-T6 3.000-4.499 (Note 1) 85.2 0.821 47
7075-T6 3.000-4.499 (Note 2) 79.3 0.602 44
7075-T6 4.500-5.000 (Note 3) 76.9 0.575 45
7178-T6 Up thru 0.249 86.5 0.686 42
7178-T6 0.250-2.990 (Note 3) 88.9 0.714 42
Rolled and Cold-Finished Rod and Bar
Alloy and Temper Thickness, in. \(N\) (ksi) \(M\) (ksi) \(\left({L'\over \rho}\right)_{cr}\)
EC-O All 3.2 0.006 241
EC-H12 Up to 1 in. 8.7 0.030 165
EC-H13 Up to 1 in. 13.3 0.058 142
EC-H17 Up to 1/2 in. 16.8 0.082 124
1100-O All 4.3 0.010 221
1100-F 0.375 and over 7.6 0.025 186
2011-T3 0.125-1.500 45.4 0.368 79
2011-T3 1.501-2.000 40.3 0.308 85
2011-T3 2.001-3.000 35.2 0.251 89
2011-T8 0.125-3.250 48.0 0.400 77
2014-O Up thru 8.000 9.9 0.037 160
2014-T4 Up thru 6.750 37.7 0.278 86
2014-T6 Up thru 6.750 64.7 0.543 54
2017-O Up thru 8.000 9.9 0.037 160
2017-T4 Up thru 8.000 37.7 0.278 86
2024-O Up thru 8.000 9.9 0.037 160
2024-T4 Up thru 6.500 48.0 0.400 77
3003-O All 5.4 0.015 222
3003-H12 Up thru 0.374 12.2 0.051 148
3003-H14 Up thru 0.313 16.8 0.082 124
3003-H16 Up thru 0.250 22.8 0.131 112
3003-H18 Up thru 0.204 26.5 0.164 103
5052-O All 11.0 0.043 149
5052-F 0.375 and over 12.2 0.051 148
6061-O Up thru 8.000 5.4 0.015 222
6061-T4 Up thru 8.000 18.0 0.092 128
6061-T6 Up thru 8.000 38.3 0.202 63
7075-O Up thru 8.000 12.2 0.051 148
7075-T6 Up thru 4.000 78.7 0.729 49
Standard Structural Shapes (Rolled or Extruded)
Alloy and Temper Thickness, in. \(N\) (ksi) \(M\) (ksi) \(\left({L'\over \rho}\right)_{cr}\)
2014-O All 9.9 0.037 160
2014-T4 All 35.2 0.251 89
2014-T6 All 64.7 0.543 54
5456-O All 21.6 0.120 111
5456-H112 All 21.6 0.120 111
5456-H311 All 25.3 0.153 106
6061-O All 5.4 0.015 222
6061-T4 All 15.7 0.074 128
6061-T6 All 38.3 0.202 63
6061-T62 All 28.1 0.127 74
6062-O All 5.4 0.015 222
6062-T4 All 15.7 0.074 128
6062-T6 All 38.3 0.202 63
Die Forgings
Alloy and Temper Thickness, in. \(N\) (ksi) \(M\) (ksi) \(\left({L'\over \rho}\right)_{cr}\)
1100-F Up to 4 in. 4.3 0.010 221
2014-T4 Up to 4 in. 35.2 0.251 89
2014-T6 Up to 4 in. 61.4 0.410 50
2018-T61 Up to 4 in. 48.0 0.400 77
2018-T61 Up to 4 in. 48.0 0.400 77
2018-T72 Up to 4 in. 33.9 0.237 91
3003-O All 5.4 0.015 222
3003-F All 5.4 0.015 222
4032-T6 Up to 4 in. 50.6 0.433 75
6061-T6 Up to 4 in. 38.3 0.202 63
6151-T6 Up to 4 in. 40.6 0.220 61
7075-T6 Up to 3 in. 73.3 0.535 46
7079-T6 Up to 6 in. 72.1 0.522 46
Drawn Tube
Alloy and Temper Thickness, in. \(N\) (ksi) \(M\) (ksi) \(\left({L'\over \rho}\right)_{cr}\)
2024-O All 8.7 0.030 165
2024-T3 0.018-0.500 50.6 0.433 75
3003-O All 5.4 0.015 222
3003-H12 All 12.2 0.051 148
3003-H14 All 16.8 0.082 124
3003-H16 All 22.8 0.131 112
3003-H18 All 26.5 0.164 103
Alclad 3003-O 0.014-0.500 5.4 0.015 222
Alclad 3003-H12 0.014-0.500 12.2 0.051 148
Alclad 3003-H14 0.014-0.500 16.8 0.082 124
Alclad 3003-H16 0.014-0.500 22.8 0.131 112
Alclad 3003-H18 0.014-0.500 26.5 0.164 103
5050-O All 6.5 0.019 185
5050-H34 All 20.4 0.111 121
5050-H38 All 25.3 0.153 106
5052-O All 11.0 0.043 149
5052-H34 All 26.5 0.164 103
5052-H38 All 33.9 0.237 91
6061-O All 5.4 0.015 222
6061-T4 0.025-0.500 18.0 0.092 128
6061-T6 0.025-0.500 38.3 0.202 63
6062-O All 5.4 0.015 222
6062-T4 0.025-0.500 18.0 0.092 128
6062-T6 0.025-0.500 38.3 0.202 63
6063-T83 All 32.6 0.159 69
6063-T831 All 27.0 0.120 75
6063-T832 All 38.3 0.202 63
Extruded Tube
Alloy and Temper Thickness, in. \(N\) (ksi) \(M\) (ksi) \(\left({L'\over \rho}\right)_{cr}\)
2014-O All 9.9 0.037 160
2014-T4 0.125-0.499 30.2 0.200 100
2014-T4 0.500 and over 35.2 0.251 89
2014-T6 0.125-0.499 61.4 0.410 50
2014-T6 0.500-0.749 67.3 0.471 48
2014-T6 0.750 and over --
Area 25 sq in. max. 69.7 0.496 47
Area 25 to 32 sq in. 67.3 0.471 48
2024-O All 9.9 0.037 160
2024-T4 0.499 and less 41.1 0.275 67
2024-T4 0.500-1.499 50.9 0.379 60
2024-T4 1.500 and over --
Area 25 sq in. max. 53.4 0.407 59
Area 25 to 32 sq in. 50.9 0.379 60
3003-O All 5.4 0.015 222
3003-F All 5.4 0.015 222
5154-O All 12.2 0.051 148
6061-O All 5.4 0.015 222
6061-T4 All 15.7 0.074 128
6061-T6 All 38.3 0.202 63
6062-O All 5.4 0.015 222
6062-T4 All 15.7 0.074 128
6062-T6 All 38.3 0.202 63
6063-T42 Up to 0.500 11.0 0.043 149
6063-T5 Up to 0.500 17.5 0.076 103
6063-T6 Up to 0.500 28.0 0.155 81
7075-O All 13.3 0.058 142
7075-T6 Up to 0.249 79.3 0.602 44
7075-T6 0.250-2.999 81.7 0.629 43
7178-T6 Up to 0.249 86.5 0.686 42
7178-T6 0.250-2.999 88.9 0.714 42
Pipe
Alloy and Temper Thickness, in. \(N\) (ksi) \(M\) (ksi) \(\left({L'\over \rho}\right)_{cr}\)
3003-O All 5.4 0.015 222
3003-H112 1 in. and over 6.5 0.019 185
3003-H18 Under 1 in. size 26.5 0.164 103
3003-F 1 in. and over 5.4 0.015 222
6061-T6 Under 1 in. size 38.3 0.202 63
6061-T6 1 in. and over 38.3 0.202 63
6063-T5 All 17.5 0.076 103
6063-T6 All 28.0 0.155 81
6063-T832 All 38.3 0.202 63
Sand Castings
Alloy and Temper Thickness, in. \(N\) (ksi) \(M\) (ksi) \(\left({L'\over \rho}\right)_{cr}\)
43-F The values to the right are based on tests of standard specimens individually cast. 7.6 0.025 186
122-T61 35.2 0.251 89
142-T21 15.7 0.074 128
142-T571 35.2 0.251 89
142-T77 18.0 0.092 128
195-T4 15.7 0.074 128
195-T6 24.0 0.141 107
195-T62 33.9 0.237 91
195-T7 19.2 0.101 120
214-F 11.0 0.043 149
B214-F 12.2 0.051 148
F214-F 11.0 0.043 149
220-T4 15.9 0.076 131
319-F 11.5 0.047 163
319-T6 14.4 0.065 134
355-T51 12.2 0.051 148
355-T6 14.4 0.065 134
355-T61 23.4 0.136 109
355-T7 24.2 0.143 107
355-T71 15.9 0.076 131
356-T51 11.5 0.047 163
356-T6 13.7 0.061 144
356-T7 18.8 0.098 123
356-T71 13.0 0.056 143
A612-F 14.4 0.065 134
Permanent Mold Castings
Alloy and Temper Thickness, in. \(N\) (ksi) \(M\) (ksi) \(\left({L'\over \rho}\right)_{cr}\)
43-F The values to the right are based on tests of standard specimens individually cast. 7.6 0.025 186
C113-F 24.0 0.141 107
122-T551 37.7 0.278 86
122-T65 35.2 0.251 89
F132-T5 --- --- ---
142-T571 33.9 0.237 91
142-T61 44.1 0.352 80
B195-T4 16.8 0.082 124
B195-T6 25.3 0.153 106
B195-T7 18.0 0.092 128
A214-F 14.5 0.066 135
333-F 18.0 0.092 128
333-T5 25.3 0.153 106
333-T6 29.0 0.188 100
333-T7 26.5 0.164 103
355-T51 25.3 0.153 106
355-T6 26.5 0.164 103
355-T62 44.1 0.352 80
355-T7 31.4 0.212 98
355-T71 31.4 0.212 98
C355-T61 (Note 4) 35.2 0.251 89
356-T6 25.3 0.153 106
356-T7 24.0 0.141 107
A356-T61 (Note 4) 31.4 0.212 98
C612-F 15.7 0.074 128
750-T5 8.7 0.030 165
B750-T5 --- --- ---

Notes:

  1. Area up thru 20 sq in.
  2. Area 20 thru 32 sq in.
  3. Area up thru 30 sq in.
  4. The values shown for this alloy are valid for any location in the casting.


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