V. AISC 360-10 Angle F.11A

Verify the available flexural strength of a single angle member per the AISC 360-10 code.

References

American Institute of Steel Construction. 2010 Steel Construction Manual. Fourteenth Edition. AISC: Chicago, IL.
American Institute of Steel Construction. 2011. Design Examples, Version 14.0. AISC:Chicago, IL. Example Example F.11A, pp. F47-F49

Details

From reference (2):

Select an ASTM A36 single angle with a simple span of 6 ft. The vertical leg of the single angle is up and the toe is in compression. The vertical loads are a uniform dead load of 0.05 kip/ft and a uniform live load of 0.15 kip/ft. There are no horizontal loads. There is no deflection limit for this angle. The angle is braced at the end points only. Assume bending about the geometric x-x axis and that there is no lateral-torsional restraint.

Note: The angle section is given a beta angle as the geometrical axis and principal axis are different. In STAAD.Pro the calculation is done with reference with the principal axis, but in AISC 360-10 Code geometrical axis is used calculating the capacities of the section.

Validation

Ultimate moment:

w_{u} = 1.2 (0.05 k/ft) + 1.6 (0.15 k/ft) = 0.30 k/ft

M_{u} = \frac{0.30 {(6)}^{2}}{8} = 1.35 ft·k

Service moment:

w_{a} = 0.05 k/ft + 0.15 k/ft = 0.20 k/ft

M_{a} = \frac{0.2 {(6)}^{2}}{8} = 0.90 ft·k

Try an L4×4×1/4, which has a section modulus, S_x = 1.03 in³.

The yield strength, F_y = 36 ksi

The nominal flexural strength for the flexural yielding limit state:

M_{n} = 1.5 M_{y} = 1.5 F_{y} S_{x} = 1.5 \times 36 \times 1.03 = 55.6 in⋅k

(F10-1)

The yield moment for a single angle bent about its geometric axis with no lateral-torsional restraint:

M_{y} = 0.8 F_{y} S_{x} = 0.8 \times 36 \times 1.03 = 29.7 in⋅k

Determine M_e:

M_{e} = \frac{0.66 E b^{4} t C_{b}}{{L_{b}}^{2}} [\sqrt{1 + 0.78 {(\frac{L_{b} t}{b^{2}})}^{2}} - 1]

(F10-6a)

where

C_b

1.14 from Ref. 1, Table 3-1

M_{e} = \frac{0.66 (29, 000) {(4.0)}^{4} (1 / 4) 1.14}{{(6 \times 12)}^{2}} [\sqrt{1 + 0.78 {(\frac{6 \times 12 (1 / 4)}{{(4.0)}^{2}})}^{2}} - 1] = 110 in⋅k > M_{y}

M_{n} = (1.92 - 1.17 \sqrt{\frac{M_{y}}{M_{e}}}) M_{y} \leq 1.5 M_{y}

(F10-3)

M_{n} = (1.92 - 1.17 \sqrt{\frac{29.7}{110}}) 29.7 = 39.0 in⋅k \leq 1.5 (29.7) = 44.6 in⋅k

Leg local buckling

Leg slenderness ratio: $λ = \frac{b}{t} = \frac{4.0}{1 / 4} = 16.0$

Determine the compact and slender leg ratio limits from Table B4.1b:

λ_{p} = 0.54 \sqrt{\frac{E}{F_{y}}} = 0.54 \sqrt{\frac{29,000}{36}} = 15.3

λ_{r} = 0.91 \sqrt{\frac{E}{F_{y}}} = 0.91 \sqrt{\frac{29,000}{36}} = 25.8

λ_p < λ < λ_r; thus, the leg is non-compact in flexure.

M_{n} = F_{y} S_{c} [2.43 - 1.72 (\frac{b}{t}) \sqrt{\frac{F_{y}}{E}}]

(F10-3)

where

S_c

0.80S_x = 0.80 × 1.03 = 0..824 in³

M_{n} = 36 \times 0.824 [2.43 - 1.72 (16.0) \sqrt{\frac{36}{29, 000}}] = 43.3 in⋅k

The lateral-torsional buckling limit state governs.

M_{n} = 43.3 in⋅k = 3.25 ft⋅k

The available flexural strength:

LRFD: $ϕ_{b} M_{n} = 0.90 (3.25) = 2.93 ft-k$

ASD: $M_{n} / Ω_{b} = \frac{3.25}{1.67} = 1.95 ft-k$

Results

Result Type	Reference	STAAD.Pro	Difference	Comments
LTB ϕ_bM_n (ft·k) [LRFD]	2.93	2.96	negligible
LTB M_n/Ω_b (ft·k) [ASD]	1.95	1.97	negligible

STAAD.Pro Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-10 Angle F.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 06-Mar-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 6 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST L40404
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED BUT MZ
2 FIXED BUT FX MZ
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GZ 0.25
LOAD 2 LOADTYPE None  TITLE LOAD CASE 2
MEMBER LOAD
1 UNI GZ 0.2
LOAD COMB 3 COMBINATION LOAD CASE 3
1 1.2 2 1.6 
LOAD COMB 4 COMBINATION LOAD CASE 4
1 1.0 2 1.0 
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2010
METHOD LRFD
FU 8352 ALL
FYLD 5184 ALL
CB 1.14 ALL
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2010
METHOD ASD
FU 8352 ALL
FYLD 5184 ALL
CB 1.14 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD.Pro Output

                       STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
                       ********************************************
 ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
       1 ST   L40404                   (AISC SECTIONS)
                           PASS   Sec. F1              0.444         3
                        0.00           -1.86           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     91.954  L/C  :     3                |
| Allowable Slenderness Ratio :    300.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.444(PASS)                 |
|          Loc  :    0.00   Condition :   Sec. F1                       |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   0.000E+00(  ) Fy:   0.000E+00     Fz:  -1.860E+00               |
| Mx:   0.000E+00     My:  -1.860E+00     Mz:   0.000E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   1.000E+00     Ayy:   1.000E+00     Cw:  5.051E-02              |
| Szz:   7.837E-01     Syy:   1.719E+00                                 |
| Izz:   1.183E+00     Iyy:   4.895E+00     Ix:  4.021E-02              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        5183.999   Fu:        8351.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:         6.000                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    1.00 NSF:    1.00 SLF:    1.00 CSP:   12.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Slender        16.00     N/A     12.77    T.B4.1(a)-3  |
|                  N/A           N/A      N/A      N/A      N/A         |
| Flexure     :  Non-Compact    16.00    15.33    25.83    T.B4.1(b)-12 |
|                  N/A           N/A      N/A      N/A      N/A         |
      STAAD SPACE                                              -- PAGE NO.    7
                       STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
                       ********************************************
 ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   6.25E+01   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   8.40E+01   0.000      Eq. D2-2      3     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Min Buck    0.00E+00   3.33E+01   0.000      Eq. E7-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Min Buck    1.34E-02   105.90   2.76E+03   3.68E+03   3.70E+01        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     1.86E+00   1.94E+01   0.096      Eq. G2-1      3     0.00 |
| Local-Y     0.00E+00   1.94E+01   0.000      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     6.94E-03     1.00     1.20    16.00   2.16E+01            |
| Local-Y     6.94E-03     1.00     1.20    16.00   2.16E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.86E+00   6.96E+00   0.267      Eq. F10-1     3     0.00 |
| Minor       0.00E+00   3.17E+00   0.000      Eq. F10-1     3     0.00 |
| Intermediate   Mn        My                                           |
| Major       7.74E+00   5.16E+00                                       |
| Minor       3.53E+00   2.35E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.86E+00   5.97E+00   0.311      Eq. F10-3     3     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       6.64E+00   1.76E+01    1.14     0.00     0.00     6.00    |
      STAAD SPACE                                              -- PAGE NO.    8
                       STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
                       ********************************************
 ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LEG LOCAL BUCKLING                                  |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.86E+00   6.78E+00   0.274      Eq. F10-7     3     0.00 |
| Intermediate   Mn        Me                                           |
| Major       7.53E+00   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR AND NORMAL STRESS INTERACTION                         |
|                                                                       |
|              STRESS     RATIO      CRITERIA     L/C    LOC            |
| Shear       2.80E+03    0.096      Eq. H3-8      3     0.00           |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.311      Eq. H2-1      3     0.00             |
| Flexure Tens          0.311      Eq. H2-1      3     0.00             |
| Intermediate         frbw /     frbz /     fra /                      |
|                      Fcbw       Fcbz       Fca                        |
| Flexure Comp         1.87E+03   0.00E+00   0.00E+00                   |
|                      6.00E+03   7.00E+03   2.48E+03                   |
| Flexure Tens         1.87E+03   0.00E+00   0.00E+00                   |
|                      6.00E+03   7.00E+03   4.67E+03                   |
  GEOMETRIC AXIS DESIGN
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.32E+00   4.24E+00   0.310      Eq. F10-1     3     0.00 |
| Minor       1.32E+00   4.24E+00   0.310      Eq. F10-1     3     0.00 |
| Intermediate   Mn        My                                           |
| Major       4.71E+00   3.14E+00                                       |
| Minor       4.71E+00   3.14E+00                                       |
      STAAD SPACE                                              -- PAGE NO.    9
                       STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
                       ********************************************
 ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.32E+00   2.96E+00   0.444      Eq. F10-3     3     0.00 |
| Minor       1.32E+00   3.39E+00   0.388      Eq. F10-3     3     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       3.29E+00   9.20E+00    1.14     0.00     0.00     6.00    |
| Minor       3.77E+00   5.41E+01    1.14     0.00     0.00     6.00    |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LEG LOCAL BUCKLING                                  |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.32E+00   3.30E+00   0.398      Eq. F10-7     3     0.00 |
| Minor      -6.58E-01   3.30E+00   0.199      Eq. F10-7     3     3.00 |
| Intermediate   Mn        Me                                           |
| Major       3.67E+00   0.00E+00                                       |
| Minor       3.67E+00   0.00E+00                                       |
|-----------------------------------------------------------------------|
    49. LOAD LIST 4
    50. PARAMETER 2
    51. CODE AISC UNIFIED 2010
    52. METHOD ASD
    53. FU 8352 ALL
    54. FYLD 5184 ALL
    55. CB 1.14 ALL
    56. TRACK 2 ALL
    57. CHECK CODE ALL
 STEEL DESIGN    
      STAAD SPACE                                              -- PAGE NO.   10
                       STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
                       ********************************************
 ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
       1 ST   L40404                   (AISC SECTIONS)
                           PASS   Sec. F1              0.485         4
                        0.00           -1.35           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     91.954  L/C  :     4                |
| Allowable Slenderness Ratio :    300.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     0.485(PASS)                 |
|          Loc  :    0.00   Condition :   Sec. F1                       |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   0.000E+00(  ) Fy:   0.000E+00     Fz:  -1.350E+00               |
| Mx:   0.000E+00     My:  -1.350E+00     Mz:   0.000E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   1.000E+00     Ayy:   1.000E+00     Cw:  5.051E-02              |
| Szz:   7.837E-01     Syy:   1.719E+00                                 |
| Izz:   1.183E+00     Iyy:   4.895E+00     Ix:  4.021E-02              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:        5183.999   Fu:        8351.999                           |
|-----------------------------------------------------------------------|
| Actual Member Length:         6.000                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    1.00 NSF:    1.00 SLF:    1.00 CSP:   12.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Slender        16.00     N/A     12.77    T.B4.1(a)-3  |
|                  N/A           N/A      N/A      N/A      N/A         |
| Flexure     :  Non-Compact    16.00    15.33    25.83    T.B4.1(b)-12 |
|                  N/A           N/A      N/A      N/A      N/A         |
      STAAD SPACE                                              -- PAGE NO.   11
                       STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
                       ********************************************
 ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   4.16E+01   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   5.60E+01   0.000      Eq. D2-2      4     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Min Buck    0.00E+00   2.21E+01   0.000      Eq. E7-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Min Buck    1.34E-02   105.90   2.76E+03   3.68E+03   3.70E+01        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     1.35E+00   1.29E+01   0.104      Eq. G2-1      4     0.00 |
| Local-Y     0.00E+00   1.29E+01   0.000      Eq. G2-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     6.94E-03     1.00     1.20    16.00   2.16E+01            |
| Local-Y     6.94E-03     1.00     1.20    16.00   2.16E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.35E+00   4.63E+00   0.291      Eq. F10-1     4     0.00 |
| Minor       0.00E+00   2.11E+00   0.000      Eq. F10-1     4     0.00 |
| Intermediate   Mn        My                                           |
| Major       7.74E+00   5.16E+00                                       |
| Minor       3.53E+00   2.35E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.35E+00   3.97E+00   0.340      Eq. F10-3     4     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       6.64E+00   1.76E+01    1.14     0.00     0.00     6.00    |
      STAAD SPACE                                              -- PAGE NO.   12
                       STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
                       ********************************************
 ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LEG LOCAL BUCKLING                                  |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       1.35E+00   4.51E+00   0.299      Eq. F10-7     4     0.00 |
| Intermediate   Mn        Me                                           |
| Major       7.53E+00   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR AND NORMAL STRESS INTERACTION                         |
|                                                                       |
|              STRESS     RATIO      CRITERIA     L/C    LOC            |
| Shear       1.86E+03    0.104      Eq. H3-8      4     0.00           |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.340      Eq. H2-1      4     0.00             |
| Flexure Tens          0.340      Eq. H2-1      4     0.00             |
| Intermediate         frbw /     frbz /     fra /                      |
|                      Fcbw       Fcbz       Fca                        |
| Flexure Comp         1.36E+03   0.00E+00   0.00E+00                   |
|                      3.99E+03   4.66E+03   1.65E+03                   |
| Flexure Tens         1.36E+03   0.00E+00   0.00E+00                   |
|                      3.99E+03   4.66E+03   3.10E+03                   |
  GEOMETRIC AXIS DESIGN
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       9.55E-01   2.82E+00   0.338      Eq. F10-1     4     0.00 |
| Minor       9.55E-01   2.82E+00   0.338      Eq. F10-1     4     0.00 |
| Intermediate   Mn        My                                           |
| Major       4.71E+00   3.14E+00                                       |
| Minor       4.71E+00   3.14E+00                                       |
      STAAD SPACE                                              -- PAGE NO.   13
                       STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
                       ********************************************
 ALL UNITS ARE - KIP  FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       9.55E-01   1.97E+00   0.485      Eq. F10-3     4     0.00 |
| Minor       9.55E-01   2.26E+00   0.423      Eq. F10-3     4     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       3.29E+00   9.20E+00    1.14     0.00     0.00     6.00    |
| Minor       3.77E+00   5.41E+01    1.14     0.00     0.00     6.00    |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LEG LOCAL BUCKLING                                  |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       9.55E-01   2.20E+00   0.434      Eq. F10-7     4     0.00 |
| Minor      -4.77E-01   2.20E+00   0.217      Eq. F10-7     4     3.00 |
| Intermediate   Mn        Me                                           |
| Major       3.67E+00   0.00E+00                                       |
| Minor       3.67E+00   0.00E+00                                       |
|-----------------------------------------------------------------------|