V. AISI 2016 SHS section

Determine the flexural Strength and axial strength of a square hollow section according to AISI S100 2016 Specification using both LRFD and ASD methods.

Details

The member is a simply-supported, 10 ft span. The member is subject to a transverse uniform dead load of 100 lbs/ft. Additionally, the member is subject to a 7,500 lb axial dead load and a 37,500 lb axial live load. The section used is a HSS 6x6x0.125. The beam-column is not subject to moment or axial loading due to lateral translation of the structure.

Section Properties

Depth of section, d = 6 in
Width of section, b = 6 in
Thickness, t = 0.125 in
Area, A = 2.7 in²
Moment of inertia, I_zz = 15.5 in⁴
Section modulus, Z_zz = 5.167 in³
Radius of gyration of cross-section: $r_{x} = \sqrt{\frac{I_{x}}{A}} = 2.393 in.$
Torsion constant, J = 23.63 in⁴

Material Properties

E = 29,500 ksi
G = 11,300 ksi
F_y = 46 ksi
F_u = 58 ksi

Design Forces

ASD: M_z = 15 in·k, P = 45 kip
LRFD M_uz = 1.2 (15) = 18 in·k, P_u = 1.2 ( 7.5) + 1.6 (37.5) = 69 kip

Validation

Axial Compressive Strength

Nominal Flexural Buckling Stress

\frac{K_{x} \times L_{x}}{r_{x}} = \frac{K_{y} \times L_{y}}{r_{y}} = \frac{1.0 \times 120}{2.393} = 50.15

F_{cre} = \frac{π^{2} \times E}{{(K \times L / r)}^{2}} = \frac{π^{2} \times 29,500}{{(50.15)}^{2}} = 115.8 ksi

λ_{c} = \sqrt{\frac{F_{y}}{F_{cre}}} = \sqrt{\frac{46}{115.8}} = 0.630 < 1.5

F_{n} = {0.658}^{{λ_{c}}^{2}} \times F_{y} = {0.658}^{{(0.630)}^{2}} \times 46 = 38.95 ksi

P_{n} = A \times F_{n} = 2.7 \times 38.95 = 105.2 kips

Allowable nominal axial strength (ASD):

\frac{P_{n}}{Ω_{c}} = \frac{105.2}{1.80} = 58.43 kips

Design nominal axial strength (LRFD):

ϕ_{c} \times P_{n} = 0.85 \times 105.2 = 89.40 kips

Nominal Sectional Flexural Strength

According to Eq. F2.1.4-1 in the specification, the minimum unbraced length of a closed box member subject to lateral-torsional buckling, L_u , is calculated as:

L_{u} = \frac{0.36 \times C_{b} \times π}{F_{y} \times S_{f}} \sqrt{E G J I_{y}} = 138 ft

Since L_u > 10 ft, global buckling does not need to be considered and F_n = F_y = 46 ksi

M_y = S_f × F_n = 5.167 × 46 = 237.7 ksi

Allowable nominal axial strength (ASD):

\frac{M_{y}}{Ω_{b}} = \frac{237.7}{1.67} = 142.3 in·kips

Design nominal axial strength (LRFD):

ϕ_{b} \times M_{y} = 0.90 \times 237.79 = 213.9 in·kips

Governing strength ratio:

LRFD: 18 / 213.9 = 0.084

ASD: 15 / 142.3 = 0.105

Table 1. Comparison of results
Result Type	Reference	STAAD.Pro	Difference
Design local axial strength, LRFD $ϕ_{c} P_{n}$ (kips)	89.40	89.434	negligible
Allowable local axial strength, ASD $\frac{P_{n}}{Ω_{c}}$ (kips)	58.43	58.454	negligible
Design section flexural strength, LRFD $ϕ_{b} M_{y}$ (in·kips)	213.9	213.91	negligible
Allowable section flexural strength, ASD $\frac{M_{y}}{Ω_{b}}$ (in·kips)	142.3	142.315	negligible
Strength ratio in major sectional bending (LRFD)	0.084	0.084	none
Strength ratio in major sectional bending (ASD)	0.105	0.105	none

STAAD.Pro Input File

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISI\AISI 2016 SHS section.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 31-Mar-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 10 0;
MEMBER INCIDENCES
1 1 2;
START USER TABLE
TABLE 1
UNIT INCHES KIP
TUBE
HS6X6X18
2.913 6 6 0.125 16.688 16.688 25.3 4.413 4.413
END
UNIT INCHES KIP
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29500
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 HSST6X6X0.125
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FY MX MZ
LOAD 1 LOADTYPE Dead  TITLE DL
MEMBER LOAD
1 CON GY -7.5 0
1 CON GY 7.5 120
1 UNI GX 0.00833
LOAD 2 LOADTYPE Live  TITLE LL
MEMBER LOAD
1 CON GY -37.5 0
1 CON GY 37.5 120
LOAD COMB 3 LRFD 1.2 D+1.6 L
1 1.2 2 1.6 
LOAD COMB 4 ASD D + L
1 1.0 2 1.0 
PERFORM ANALYSIS
LOAD LIST 3
PARAMETER 1
CODE AISI 2016
METHOD LRFD
TRACK 2 ALL
FYLD 46 ALL
FU 58 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 1
CODE AISI 2016
METHOD ASD
TRACK 2 ALL
FYLD 46 ALL
FU 58 ALL
CHECK CODE ALL
FINISH

STAAD.Pro Output

            STAAD.Pro CODE CHECKING - (AISI S100-16) [LRFD] (v1.0)
           ********************************************************
ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.)
|-----------------------------------------------------------------------------|
|  MEMBER:     1     SECTION:ST  HSST6X6X0.125   LEN:  120.000     LOC:  60.000 |
| STATUS: PASS       RATIO:  0.701             REF: Eq. H1.1-1    LC:      3  |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Location:   60.000  Criteria:   Eq. H1.1-1           LC:           3       |
|  Fx:(T)      -69.000       Fy:         0.000          Fz:       0.000       |
|  Mx:           0.000       My:         0.000          Mz:     -17.993       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                                         |
|  Ag:         2.70000       Az:     1.33818            Ay:     1.33818       |
|  Cz:         0.00000       Cy:     0.00000                                  |
|  Iz:        15.50000       Iy:    15.50000             J:    23.63067       |
|  Sz:         5.16667       Sy:     5.16667                                  |
|  Rz:         2.39598       Ry:     2.39598            Cw:     0.00000       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                              |
|  Fy:    46.000        Fu:    58.000      E:  29500.000       G:  11300.000  |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES:                                                          |
|  Member Length:   120.000   Lz:   120.000   Ly:   120.000   Lb:       0.000 |
| DESIGN PARAMETERS:                                                          |
|  Kz:   1.000    Ky:   1.000    NSF:  1.000                                  |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS:                                                       |
|-----------------------------------------------------------------------------|
|  LC :     3   Actual :   50.084   Allowable :  200.000   Ratio :   0.250    |
|-----------------------------------------------------------------------------|
|  Section Dimension Check      |    Ratio     |    Limit     |     Status    |
|-----------------------------------------------------------------------------|
|  Width To Thickness Ratio     |     49.724   |    500.000   |      PASS     |
|  Web Depth To Thickness Ratio |     49.724   |    200.000   |      PASS     |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.    4
            STAAD.Pro CODE CHECKING - (AISI S100-16) [LRFD] (v1.0)
           ********************************************************
ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.)
|                                              - MEMBER:       1 (Contd.....) |
|                                                                             |
|-----------------------------------------------------------------------------|
| Limit States       | Load# |Location|  Demand  | Capacity |Ratio| Reference |
|--------------------|-------|--------|----------|----------|-----|-----------|
| Tension            |     3 |  10.00 |  -69.000 |  111.780 |0.617|Sec. D2    |
|   Yielding         |     3 |  10.00 |  -69.000 |  111.780 |0.617|Sec. D2    |
|   Rupture          |     3 |  10.00 |  -69.000 |  117.450 |0.587|Sec. D3    |
| Compression        |   -   |   -    |     -    |   73.089 |  -  |Sec. E3    |
|   Local Comp       |   -   |   -    |     -    |   73.089 |  -  |Sec. E3    |
|   Axial Comp       |   -   |   -    |     -    |   89.434 |  -  |Sec. E2    |
| Bending            |     3 |  60.00 |  -17.993 |  185.281 |0.097|Sec. F3    |
|   Major Local Bend |     3 |  60.00 |  -17.993 |  185.281 |0.097|Sec. F3    |
|   Minor Local Bend |   -   |   -    |     -    |  185.281 |  -  |Sec. F3    |
|   Major Sectional  |     3 |  60.00 |  -17.993 |  213.900 |0.084|Sec. F2    |
|   Minor Sectional  |   -   |   -    |     -    |  213.900 |  -  |Sec. F2    |
| Shear              |     3 | 120.00 |   -0.600 |   35.087 |0.017|Sec. G2    |
|   Major Shear (Z)  |   -   |   -    |     -    |   35.087 |  -  |Sec. G2    |
|   Minor Shear (Y)  |     3 | 120.00 |   -0.600 |   35.087 |0.017|Sec. G2    |
| Interaction        |     3 |  60.00 |     -    |     -    |0.701|Eq. H1.1-1 |
|   (Bend+Ten) Int1  |     3 |  60.00 |     -    |     -    |0.701|Eq. H1.1-1 |
|   (Bend+Comp)      |     3 |  60.00 |     -    |     -    |0.097|Eq. H1.2-1 |
|   (Bend+Shear) Z   |     3 |  60.00 |     -    |     -    |0.097|Sec. H2    |
|-----------------------------------------------------------------------------|
    58. LOAD LIST 4
    59. PARAMETER 1
    60. CODE AISI 2016
    61. METHOD ASD
    62. TRACK 2 ALL
    63. FYLD 46 ALL
    64. FU 58 ALL
    65. CHECK CODE ALL
 STEEL DESIGN    
      STAAD SPACE                                              -- PAGE NO.    5
            STAAD.Pro CODE CHECKING - (AISI S100-16) [ASD ] (v1.0)
           ********************************************************
ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.)
|-----------------------------------------------------------------------------|
|  MEMBER:     1     SECTION:ST  HSST6X6X0.125   LEN:  120.000     LOC:  60.000 |
| STATUS: PASS       RATIO:  0.710             REF: Eq. H1.1-1    LC:      4  |
|-----------------------------------------------------------------------------|
| DESIGN FORCES:                                                              |
|  Location:   60.000  Criteria:   Eq. H1.1-1           LC:           4       |
|  Fx:(T)      -45.000       Fy:         0.000          Fz:       0.000       |
|  Mx:           0.000       My:         0.000          Mz:     -14.994       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES:                                                         |
|  Ag:         2.70000       Az:     1.33818            Ay:     1.33818       |
|  Cz:         0.00000       Cy:     0.00000                                  |
|  Iz:        15.50000       Iy:    15.50000             J:    23.63067       |
|  Sz:         5.16667       Sy:     5.16667                                  |
|  Rz:         2.39598       Ry:     2.39598            Cw:     0.00000       |
|-----------------------------------------------------------------------------|
| MATERIAL INFO:                                                              |
|  Fy:    46.000        Fu:    58.000      E:  29500.000       G:  11300.000  |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES:                                                          |
|  Member Length:   120.000   Lz:   120.000   Ly:   120.000   Lb:       0.000 |
| DESIGN PARAMETERS:                                                          |
|  Kz:   1.000    Ky:   1.000    NSF:  1.000                                  |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS:                                                       |
|-----------------------------------------------------------------------------|
|  LC :     4   Actual :   50.084   Allowable :  200.000   Ratio :   0.250    |
|-----------------------------------------------------------------------------|
|  Section Dimension Check      |    Ratio     |    Limit     |     Status    |
|-----------------------------------------------------------------------------|
|  Width To Thickness Ratio     |     49.724   |    500.000   |      PASS     |
|  Web Depth To Thickness Ratio |     49.724   |    200.000   |      PASS     |
|-----------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.    6
            STAAD.Pro CODE CHECKING - (AISI S100-16) [ASD ] (v1.0)
           ********************************************************
ALL UNITS ARE IN "INCH" AND "KIP " (U.N.O.)
|                                              - MEMBER:       1 (Contd.....) |
|                                                                             |
|-----------------------------------------------------------------------------|
| Limit States       | Load# |Location|  Demand  | Capacity |Ratio| Reference |
|--------------------|-------|--------|----------|----------|-----|-----------|
| Tension            |     4 |  10.00 |  -45.000 |   74.371 |0.605|Sec. D2    |
|   Yielding         |     4 |  10.00 |  -45.000 |   74.371 |0.605|Sec. D2    |
|   Rupture          |     4 |  10.00 |  -45.000 |   78.300 |0.575|Sec. D3    |
| Compression        |   -   |   -    |     -    |   47.770 |  -  |Sec. E3    |
|   Local Comp       |   -   |   -    |     -    |   47.770 |  -  |Sec. E3    |
|   Axial Comp       |   -   |   -    |     -    |   58.454 |  -  |Sec. E2    |
| Bending            |     4 |  60.00 |  -14.994 |  123.274 |0.122|Sec. F3    |
|   Major Local Bend |     4 |  60.00 |  -14.994 |  123.274 |0.122|Sec. F3    |
|   Minor Local Bend |   -   |   -    |     -    |  123.274 |  -  |Sec. F3    |
|   Major Sectional  |     4 |  60.00 |  -14.994 |  142.315 |0.105|Sec. F2    |
|   Minor Sectional  |   -   |   -    |     -    |  142.315 |  -  |Sec. F2    |
| Shear              |     4 | 120.00 |   -0.500 |   23.084 |0.022|Sec. G2    |
|   Major Shear (Z)  |   -   |   -    |     -    |   23.084 |  -  |Sec. G2    |
|   Minor Shear (Y)  |     4 | 120.00 |   -0.500 |   23.084 |0.022|Sec. G2    |
| Interaction        |     4 |  60.00 |     -    |     -    |0.710|Eq. H1.1-1 |
|   (Bend+Ten) Int1  |     4 |  60.00 |     -    |     -    |0.710|Eq. H1.1-1 |
|   (Bend+Comp)      |     4 |  60.00 |     -    |     -    |0.122|Eq. H1.2-1 |
|   (Bend+Shear) Z   |     4 |  60.00 |     -    |     -    |0.122|Sec. H2    |
|-----------------------------------------------------------------------------|