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, Izz = 15.5 in4
- Section modulus, Zzz = 5.167 in3
- Radius of gyration of cross-section:
- Torsion constant, J = 23.63 in4
Material Properties
- E = 29,500 ksi
- G = 11,300 ksi
- Fy = 46 ksi
- Fu = 58 ksi
Design Forces
- ASD: Mz = 15 in·k, P = 45 kip
- LRFD Muz = 1.2 (15) = 18 in·k, Pu = 1.2 ( 7.5) + 1.6 (37.5) = 69 kip
Validation
Axial Compressive Strength
Nominal Flexural Buckling Stress
Allowable nominal axial strength (ASD):
Design nominal axial strength (LRFD):
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, Lu , is calculated as:
Since Lu > 10 ft, global buckling does not need to be considered and Fn = Fy = 46 ksi
My = Sf × Fn = 5.167 × 46 = 237.7 ksi
Allowable nominal axial strength (ASD):
Design nominal axial strength (LRFD):
Governing strength ratio:
LRFD: 18 / 213.9 = 0.084
ASD: 15 / 142.3 = 0.105
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Design local axial strength, LRFD (kips) | 89.40 | 89.434 | negligible | |
| Allowable local axial strength, ASD (kips) | 58.43 | 58.454 | negligible | |
| Design section flexural strength, LRFD (in·kips) | 213.9 | 213.91 | negligible | |
| Allowable section flexural strength, ASD (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 2024\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. 5
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. 6
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. 7
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 |
|-----------------------------------------------------------------------------|