# V. AISC 360-10 Rect HSS E.9

Verify the compressive strength of an unbraced column with a rectangular HSS section per the LRFD and ASD methods of the AISC 360-10 code.

## References

1. American Institute of Steel Construction. 2010 Steel Construction Manual. Fourteenth Edition. AISC: Chicago, IL.
2. American Institute of Steel Construction. 2011. Design Examples, Version 14.0. AISC:Chicago, IL. Example E.9, pp. E-47 - E-49

## Details

From reference (2):

Select an ASTM A500 Grade B rectangular HSS compression member, with a length of 20 ft, to support a dead load of 85 kips and live load of 255 kips in axial compression. The base is fixed and the top is pinned.

## Validation

Slenderness

Note: The corner radius is taken as 1.5× the design wall thickness per Section B4.1b of Reference 1.
$λ=ht=12.0⁢−3(0.349)0.349=31.4$

The limiting slenderness ratio, λr:

 $λr=1.40EFy=1.4029,00046=35.2>λ$ (Table B4.1a, case 3)

Thus, the section does not contain slender elements.

Per Table C-A-7.1 in Reference 1, K = 0.8 for fixed-pinned columns. Since the unbraced length is the same both directions, by inspection the y-y axis governs.

$KyLry=0.8(20)(12)4.01=47.9<4.71EFy=4.7129,00046=118$
 (Eq. E3-4)
 (Eq. E3-2)

Nominal Compressive Strength

 (Eq E7-1)

The available compressive strength:

LRFD:

ASD:

## Results

ϕcPn (kips) [LRFD] 518 518 none
Pnc (kips) [ASD] 344 345 negligible

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

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 05-Feb-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT INCHES KIP
JOINT COORDINATES
1 0 0 0; 2 0 240 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29000
POISSON 0.3
DENSITY 0.000283
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 HSST12X10X0.375
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
2 FIXED BUT FY MX MZ
2 FY -85
2 FY -255
1 1.2 2 1.6
1 1.0 2 1.0
PERFORM ANALYSIS
PARAMETER 1
CODE AISC UNIFIED 2010
KX 0.8 ALL
KY 0.8 ALL
METHOD LRFD
TRACK 2 ALL
KZ 0.8 ALL
FU 58 ALL
FYLD 46 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2010
KX 0.8 ALL
KY 0.8 ALL
KZ 0.8 ALL
FU 58 ALL
FYLD 46 ALL
METHOD ASD
TRACK 2 ALL
CHECK CODE ALL
FINISH


                       STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1 ST   HSST12X10X0.375          (AISC SECTIONS)
PASS   Eq. H1-1a            0.985         3
510.00 C          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     47.959  L/C  :     3                |
| Allowable Slenderness Ratio :    200.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.985(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H1-1a                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   5.100E+02(C ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:   0.000E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   6.249E+00     Ayy:   7.645E+00     Cw:  0.000E+00              |
| Szz:   5.167E+01     Syy:   4.680E+01                                 |
| Izz:   3.100E+02     Iyy:   2.340E+02     Ix:  4.210E+02              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          46.000   Fu:          58.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:       240.000                                   |
| Design Parameters                                                     |
| Kz:    0.80 Ky:    0.80 NSF:    1.00 SLF:    1.00 CSP:   12.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Non-Slender     0.00     N/A      0.00      N/A        |
|                Non-Slender    31.38     N/A     35.15    T.B4.1(a)-6  |
| Flexure     :  Compact        25.65    28.12    35.15    T.B4.1(b)-17 |
|                Compact        31.38    60.76   143.12    T.B4.1(b)-19 |
STAAD SPACE                                              -- PAGE NO.    4
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   6.04E+02   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   6.35E+02   0.000      Eq. D2-2      3     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    5.10E+02   5.38E+02   0.948      Eq. E3-1      3     0.00 |
| Min Buck    5.10E+02   5.18E+02   0.985      Eq. E3-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.46E+01    41.67   4.09E+01   1.65E+02   5.98E+02        |
| Min Buck    1.46E+01    47.96   3.94E+01   1.24E+02   5.75E+02        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   1.55E+02   0.000      Eq. G2-1      3     0.00 |
| Local-Y     0.00E+00   1.90E+02   0.000      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     6.25E+00     1.00     5.00    25.65   1.72E+02            |
| Local-Y     7.65E+00     1.00     5.00    31.38   2.11E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION                                                     |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             0.00E+00   1.94E+03   0.000      Eq. H3-1      3     0.00 |
| Intermediate Fcr        Tn                                            |
|             2.76E+01   2.16E+03                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   2.53E+03   0.000      Eq. F7-1      3     0.00 |
| Minor       0.00E+00   2.24E+03   0.000      Eq. F7-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       2.81E+03   0.00E+00                                       |
| Minor       2.48E+03   0.00E+00                                       |
STAAD SPACE                                              -- PAGE NO.    5
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-FLANGE LOCAL BUCKLING                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Minor       0.00E+00   2.10E+03   0.000      Eq. F7-2      3     0.00 |
| Intermediate   Mn        Fcr                                          |
| Minor       2.33E+03   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.985      Eq. H1-1a     3     0.00             |
| Flexure Tens          0.000      Eq. H1-1b     3     0.00             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         2.53E+03   0.00E+00   5.18E+02                   |
|                      2.10E+03   0.00E+00   5.10E+02                   |
| Flexure Tens         2.53E+03   0.00E+00   6.04E+02                   |
|                      2.10E+03   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
51. PARAMETER 2
52. CODE AISC UNIFIED 2010
53. KX 0.8 ALL
54. KY 0.8 ALL
55. KZ 0.8 ALL
56. FU 58 ALL
57. FYLD 46 ALL
58. METHOD ASD
59. TRACK 2 ALL
60. CHECK CODE ALL
STEEL DESIGN
WARNING: For member#      1 the profile has been selected from HSS Rect/Round (non A1085)/Pipe
tables of AISC database. Weld type is considered to be Elect-resist-weld.
Thickness is already reduced from the table. Further reductions will not be done.
STAAD SPACE                                              -- PAGE NO.    6
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1 ST   HSST12X10X0.375          (AISC SECTIONS)
PASS   Eq. H1-1a            0.987         4
340.00 C          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     47.959  L/C  :     4                |
| Allowable Slenderness Ratio :    200.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     0.987(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H1-1a                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   3.400E+02(C ) Fy:   0.000E+00     Fz:   0.000E+00               |
| Mx:   0.000E+00     My:   0.000E+00     Mz:   0.000E+00               |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES  (UNIT: INCH)                                      |
| Azz:   6.249E+00     Ayy:   7.645E+00     Cw:  0.000E+00              |
| Szz:   5.167E+01     Syy:   4.680E+01                                 |
| Izz:   3.100E+02     Iyy:   2.340E+02     Ix:  4.210E+02              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          46.000   Fu:          58.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:       240.000                                   |
| Design Parameters                                                     |
| Kz:    0.80 Ky:    0.80 NSF:    1.00 SLF:    1.00 CSP:   12.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Non-Slender     0.00     N/A      0.00      N/A        |
|                Non-Slender    31.38     N/A     35.15    T.B4.1(a)-6  |
| Flexure     :  Compact        25.65    28.12    35.15    T.B4.1(b)-17 |
|                Compact        31.38    60.76   143.12    T.B4.1(b)-19 |
STAAD SPACE                                              -- PAGE NO.    7
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION                                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Yield       0.00E+00   4.02E+02   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   4.23E+02   0.000      Eq. D2-2      4     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    3.40E+02   3.58E+02   0.950      Eq. E3-1      4     0.00 |
| Min Buck    3.40E+02   3.45E+02   0.987      Eq. E3-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.46E+01    41.67   4.09E+01   1.65E+02   5.98E+02        |
| Min Buck    1.46E+01    47.96   3.94E+01   1.24E+02   5.75E+02        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   1.03E+02   0.000      Eq. G2-1      4     0.00 |
| Local-Y     0.00E+00   1.26E+02   0.000      Eq. G2-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     6.25E+00     1.00     5.00    25.65   1.72E+02            |
| Local-Y     7.65E+00     1.00     5.00    31.38   2.11E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION                                                     |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             0.00E+00   1.29E+03   0.000      Eq. H3-1      4     0.00 |
| Intermediate Fcr        Tn                                            |
|             2.76E+01   2.16E+03                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   1.68E+03   0.000      Eq. F7-1      4     0.00 |
| Minor       0.00E+00   1.49E+03   0.000      Eq. F7-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       2.81E+03   0.00E+00                                       |
| Minor       2.48E+03   0.00E+00                                       |
STAAD SPACE                                              -- PAGE NO.    8
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-FLANGE LOCAL BUCKLING                               |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Minor       0.00E+00   1.40E+03   0.000      Eq. F7-2      4     0.00 |
| Intermediate   Mn        Fcr                                          |
| Minor       2.33E+03   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.987      Eq. H1-1a     4     0.00             |
| Flexure Tens          0.000      Eq. H1-1b     4     0.00             |
| Intermediate         Mcx /      Mrx /      Pc /                       |
|                      Mcy        Mry        Pr                         |
| Flexure Comp         1.68E+03   0.00E+00   3.45E+02                   |
|                      1.40E+03   0.00E+00   3.40E+02                   |
| Flexure Tens         1.68E+03   0.00E+00   4.02E+02                   |
|                      1.40E+03   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|