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 2023\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 | |-----------------------------------------------------------------------------|