V. AISC 360-05 UPT Pipe Section
Verify the axial compression capacity, flexure capacity, and interaction ratio of a tapered I section member per both the LRFD and ASD methods of the AISC 360-05 code.
Details
A 5' × 5' portal frame consists of W12x72 columns and a UPT pipe member for the beam. The pipe outer diameter, D, is 10" and the thickness, t, is 0.25".
- E = 29,000 ksi
- Fy = 50 ksi
Validation
Design Forces
Section Properties
- Inner diameter, d = 10 - 2×0.25 = 9.5 in.
- Area,
- Shear area, Ay = Ax= Ag / 2 = 3.83 in2
- Moment of inertia,
- Elastic section modulus,
- Radius of gyration,
- Plastic section modulus,
- HSS Torsional constant,
Section Classification
Flange in compression
Per Table 4.1a Case 9, , therefore flanges are non-slender for compression.
Web in compression
Per Table 4.1a, Case 9, , therefore the web is non-slender for compression.
Flexure classification:
Per Table 4.1b, Case 20, , therefore flange is compact for bending.
Compression Capacity
Effective slenderness ratio:
Elastic buckling stress:
(Eq. E3-4) |
Critical buckling stress:
(Eq. E3-2) |
Nominal buckling strength:
Pn = Ag× Fcr = 7.66 × 48.91 = 374.5 kips | (Eq. E3-1) |
- The ultimate compression capacity (LRFD) = ϕcPn = 0.9 × 374.5 = 337.0 kips
- The allowable compression capacity (ASD) = Pn/Ωc = 374.5 / 1.67 = 224.3 kips
Calculate Shear Capacity
Critical stress is the minimum of Fcr1, Fcr2, and Fcr3:
So, Fcr = 30 ksi.
The nominal shear strength:
Vn = Fcr × Ax = 30 × 3.83 = 114.9 kips
The axial capacity:- The ultimate shear capacity (LRFD) = ϕvVn = 0.9 × 114.9 = 103.4 kips
- The allowable shear capacity (ASD) = Vn/Ωv = 114.9 / 1.67 = 68.78 kips
Calculate Bending Capacity
Bending capacity in plastic yielding (compact section):
My = Fy × Zx = 50 × 23.77 = 1,189 in·kips | (Eq F8-1) |
- The ultimate bending capacity (LRFD) = ϕbMy = 0.9 × 1,189 = 1,070 in·kips
- The allowable bending capacity (ASD) = My/Ωb = 1,189 / 1.67 = 711.7 in·kips
Interaction Ratio for Bending and Compression
Check the interaction ratio for Load Case 1:
So use Eq. H1-1b for both methods: .
Calculate Torsion Capacity
Critical stress is the minimum of Fcr1, Fcr2, and Fcr3. From shear calculations, Fcr = 30 ksi.
The nominal shear strength:
Tn = Fcr × C = 30 × 37.33 = 1,120 in·kips
The axial capacity:- The ultimate torsional capacity (LRFD) = ϕTTn = 0.9 × 1,120 = 1,008 in·kips
- The allowable torsional capacity (ASD) = Tn/ΩT = 114.9 / 1.67 = 670.6 in·kips
Results
Result Type | Reference | STAAD.Pro | Difference | Comments | |
---|---|---|---|---|---|
LRFD | Compression capacity (kips) | 337 | 337 | none | |
Bending capacity (in·kips) | 1,070 | 1,070 | none | ||
Shear capacity (kips) | 103.4 | 103 | negligible | ||
Interaction ratio | 0.578 | 0.578 | none | ||
Torsional capacity (in·kips) | 1,008 | 1,010 | negligible | ||
ASD | Compression capacity (kips) | 224.3 | 224.3 | none | |
Bending capacity (in·kips) | 711.7 | 712 | negligible | ||
Shear capacity (kips) | 68.78 | 68.8 | negligible | ||
Interaction ratio | 0.869 | 0.869 | none | ||
Torsional capacity (in·kips) | 670.6 | 671 | negligible |
STAAD.Pro Input
The following design parameters are used:
- The welded pipe member is specified using STP 2
- Shear lag factor, U for tension rupture capacity is specified by SLF 0.8
The remaining parameters all use their default values.
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-05 UPT Pipe Section.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 13-Apr-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT INCHES KIP
JOINT COORDINATES
1 0 0 0; 2 0 60 0; 3 60 60 0; 4 60 0 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4;
START USER TABLE
TABLE 1
UNIT INCHES KIP
PIPE
PIPE
10 9.5 0 0
END
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29000
POISSON 0.3
DENSITY 0.000283
ALPHA 6.5e-06
DAMP 0.03
G 11200
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 3 TABLE ST W12X72
MEMBER PROPERTY
2 UPTABLE 1 PIPE
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 4 FIXED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
2 UNI GY -2.25
LOAD 2 LOADTYPE None TITLE LOAD CASE 2
JOINT LOAD
2 FX 50 FZ 25
LOAD 3 LOADTYPE None TITLE LOAD CASE 3
MEMBER LOAD
2 CMOM GX 0.75
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
PARAMETER 1
CODE AISC UNIFIED 2005
SLF 0.8 MEMB 2
FYLD 50 ALL
FU 60 ALL
METHOD LRFD
STP 2 MEMB 2
TRACK 2 MEMB 2
CHECK CODE MEMB 2
PARAMETER 2
CODE AISC UNIFIED 2005
SLF 0.8 MEMB 2
FYLD 50 ALL
FU 60 ALL
METHOD ASD
STP 2 MEMB 2
TRACK 2 MEMB 2
CHECK CODE MEMB 2
FINISH
STAAD.Pro Output
STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD) v3.3a ******************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= 2 ST PIPE (UPT) PASS Sec. G1 0.653 1 11.75 C 0.00 599.60 0.00 |-----------------------------------------------------------------------| | SLENDERNESS | | Actual Slenderness Ratio : 17.400 L/C : 1 | | Allowable Slenderness Ratio : 200.000 LOC : 0.00 | |-----------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 1 Ratio : 0.653(PASS) | | Loc : 0.00 Condition : Sec. G1 | |-----------------------------------------------------------------------| | DESIGN FORCES | | Fx: 1.175E+01(C ) Fy: 6.750E+01 Fz: 0.000E+00 | | Mx: 0.000E+00 My: 0.000E+00 Mz: 5.996E+02 | |-----------------------------------------------------------------------| | SECTION PROPERTIES (UNIT: INCH) | | Azz: 3.829E+00 Ayy: 3.829E+00 Cw: 0.000E+00 | | Szz: 1.821E+01 Syy: 1.821E+01 | | Izz: 9.105E+01 Iyy: 9.105E+01 Ix: 1.821E+02 | |-----------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 50.000 Fu: 60.000 | |-----------------------------------------------------------------------| | Actual Member Length: 60.000 | | Design Parameters | | Kz: 1.00 Ky: 1.00 NSF: 1.00 SLF: 0.80 CSP: 12.00 | |-----------------------------------------------------------------------| | SECTION CLASS UNSTIFFENED / λ λp λr CASE | | STIFFENED | | Compression : Non-Slender 40.00 N/A 63.80 T.B4.1-15a | | Non-Slender 40.00 N/A 63.80 T.B4.1-15a | | Flexure : Compact 40.00 40.60 179.80 T.B4.1-15b | | Compact 40.00 40.60 179.80 T.B4.1-15b | STAAD SPACE -- PAGE NO. 7 STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD) v3.3a ******************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted) |-----------------------------------------------------------------------| | CHECK FOR AXIAL TENSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Yield 0.00E+00 3.45E+02 0.000 Eq. D2-1 1 0.00 | | Rupture 0.00E+00 2.76E+02 0.000 Eq. D2-2 1 0.00 | |-----------------------------------------------------------------------| | CHECK FOR AXIAL COMPRESSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Maj Buck 2.43E+01 3.37E+02 0.072 Sec. E1 2 0.00 | | Min Buck 2.43E+01 3.37E+02 0.072 Eq. E3-1 2 0.00 | | Intermediate | | Results Eff Area KL/r Fcr Fe Pn | | Maj Buck 7.66E+00 17.40 4.89E+01 9.45E+02 3.74E+02 | | Min Buck 7.66E+00 17.40 4.89E+01 9.45E+02 3.74E+02 | |-----------------------------------------------------------------------| | CHECK FOR SHEAR | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Local-Z -6.96E-02 1.03E+02 0.001 Eq. G6-1 2 0.00 | | Local-Y 6.75E+01 1.03E+02 0.653 Eq. G6-1 1 0.00 | | Intermediate | | Results Aw Cv Kv h/tw Vn | | Local-Z 7.66E+00 0.00 0.00 0.00 1.15E+02 | | Local-Y 7.66E+00 0.00 0.00 0.00 1.15E+02 | |-----------------------------------------------------------------------| | CHECK FOR TORSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | 1.56E+02 1.01E+03 0.155 Eq. H3-1 2 0.00 | | Intermediate Fcr Tn | | 3.00E+01 1.12E+03 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-YIELDING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major -6.00E+02 1.07E+03 0.561 Eq. F8-1 1 0.00 | | Minor -2.09E+00 1.07E+03 0.002 Eq. F8-1 2 0.00 | | Intermediate Mn My | | Major 1.19E+03 0.00E+00 | | Minor 1.19E+03 0.00E+00 | STAAD SPACE -- PAGE NO. 8 STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD) v3.3a ******************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted) |-----------------------------------------------------------------------| | CHECK FOR FLEXURE TENS/COMP INTERACTION | | RATIO CRITERIA L/C LOC | | Flexure Comp 0.578 Eq. H1-1b 1 0.00 | | Flexure Tens 0.561 Eq. H1-1b 1 0.00 | | Intermediate Mcx / Mrx / Pc / | | Mcy Mry Pr | | Flexure Comp 1.07E+03 -6.00E+02 3.37E+02 | | 1.07E+03 0.00E+00 1.17E+01 | | Flexure Tens 1.07E+03 -6.00E+02 2.76E+02 | | 1.07E+03 0.00E+00 0.00E+00 | |-----------------------------------------------------------------------| 57. PARAMETER 2 58. CODE AISC UNIFIED 2005 59. SLF 0.8 MEMB 2 60. FYLD 50 ALL 61. FU 60 ALL 62. METHOD ASD 63. STP 2 MEMB 2 64. TRACK 2 MEMB 2 65. CHECK CODE MEMB 2 STEEL DESIGN WARNING: For member# 2 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. 9 STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD) v3.3a ******************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= 2 ST PIPE (UPT) PASS Sec. G1 0.981 1 11.75 C 0.00 599.60 0.00 |-----------------------------------------------------------------------| | SLENDERNESS | | Actual Slenderness Ratio : 17.400 L/C : 1 | | Allowable Slenderness Ratio : 200.000 LOC : 0.00 | |-----------------------------------------------------------------------| | STRENGTH CHECKS | | Critical L/C : 1 Ratio : 0.981(PASS) | | Loc : 0.00 Condition : Sec. G1 | |-----------------------------------------------------------------------| | DESIGN FORCES | | Fx: 1.175E+01(C ) Fy: 6.750E+01 Fz: 0.000E+00 | | Mx: 0.000E+00 My: 0.000E+00 Mz: 5.996E+02 | |-----------------------------------------------------------------------| | SECTION PROPERTIES (UNIT: INCH) | | Azz: 3.829E+00 Ayy: 3.829E+00 Cw: 0.000E+00 | | Szz: 1.821E+01 Syy: 1.821E+01 | | Izz: 9.105E+01 Iyy: 9.105E+01 Ix: 1.821E+02 | |-----------------------------------------------------------------------| | MATERIAL PROPERTIES | | Fyld: 50.000 Fu: 60.000 | |-----------------------------------------------------------------------| | Actual Member Length: 60.000 | | Design Parameters | | Kz: 1.00 Ky: 1.00 NSF: 1.00 SLF: 0.80 CSP: 12.00 | |-----------------------------------------------------------------------| | SECTION CLASS UNSTIFFENED / λ λp λr CASE | | STIFFENED | | Compression : Non-Slender 40.00 N/A 63.80 T.B4.1-15a | | Non-Slender 40.00 N/A 63.80 T.B4.1-15a | | Flexure : Compact 40.00 40.60 179.80 T.B4.1-15b | | Compact 40.00 40.60 179.80 T.B4.1-15b | STAAD SPACE -- PAGE NO. 10 STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD) v3.3a ******************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted) |-----------------------------------------------------------------------| | CHECK FOR AXIAL TENSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Yield 0.00E+00 2.29E+02 0.000 Eq. D2-1 1 0.00 | | Rupture 0.00E+00 1.84E+02 0.000 Eq. D2-2 1 0.00 | |-----------------------------------------------------------------------| | CHECK FOR AXIAL COMPRESSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Maj Buck 2.43E+01 2.24E+02 0.108 Sec. E1 2 0.00 | | Min Buck 2.43E+01 2.24E+02 0.108 Eq. E3-1 2 0.00 | | Intermediate | | Results Eff Area KL/r Fcr Fe Pn | | Maj Buck 7.66E+00 17.40 4.89E+01 9.45E+02 3.74E+02 | | Min Buck 7.66E+00 17.40 4.89E+01 9.45E+02 3.74E+02 | |-----------------------------------------------------------------------| | CHECK FOR SHEAR | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Local-Z -6.96E-02 6.88E+01 0.001 Eq. G6-1 2 0.00 | | Local-Y 6.75E+01 6.88E+01 0.981 Eq. G6-1 1 0.00 | | Intermediate | | Results Aw Cv Kv h/tw Vn | | Local-Z 7.66E+00 0.00 0.00 0.00 1.15E+02 | | Local-Y 7.66E+00 0.00 0.00 0.00 1.15E+02 | |-----------------------------------------------------------------------| | CHECK FOR TORSION | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | 1.56E+02 6.71E+02 0.233 Eq. H3-1 2 0.00 | | Intermediate Fcr Tn | | 3.00E+01 1.12E+03 | |-----------------------------------------------------------------------| | CHECK FOR BENDING-YIELDING | | | | FORCE CAPACITY RATIO CRITERIA L/C LOC | | Major -6.00E+02 7.12E+02 0.843 Eq. F8-1 1 0.00 | | Minor -2.09E+00 7.12E+02 0.003 Eq. F8-1 2 0.00 | | Intermediate Mn My | | Major 1.19E+03 0.00E+00 | | Minor 1.19E+03 0.00E+00 | STAAD SPACE -- PAGE NO. 11 STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD) v3.3a ******************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted) |-----------------------------------------------------------------------| | CHECK FOR FLEXURE TENS/COMP INTERACTION | | RATIO CRITERIA L/C LOC | | Flexure Comp 0.869 Eq. H1-1b 1 0.00 | | Flexure Tens 0.843 Eq. H1-1b 1 0.00 | | Intermediate Mcx / Mrx / Pc / | | Mcy Mry Pr | | Flexure Comp 7.12E+02 3.58E+02 2.24E+02 | | 7.12E+02 -2.09E+00 2.43E+01 | | Flexure Tens 7.12E+02 3.58E+02 1.84E+02 | | 7.12E+02 -2.09E+00 0.00E+00 | |-----------------------------------------------------------------------| | CHECK FOR FLEXURE TENS/COMP TORSION SHEAR INTERACTION | | RATIO CRITERIA L/C LOC | | Flx Tor Comp Shr 0.775 Eq. H3-6 2 0.00 | | Flx Tor Tens Shr 0.667 Eq. H3-6 2 0.00 | | Intermediate Mcx / Mcy / Mrx / Mry / | | Vcx / Vcy / Vrx / Vry / | | Tc Tr Pc Pr | | Flx Tor Comp Shr 7.12E+02 7.12E+02 3.58E+02 -2.09E+00 | | 6.88E+01 6.88E+01 -6.96E-02 -1.18E+01 | | 6.71E+02 1.56E+02 2.24E+02 2.43E+01 | | Flx Tor Tens Shr 7.12E+02 7.12E+02 3.58E+02 -2.09E+00 | | 6.88E+01 6.88E+01 -6.96E-02 -1.18E+01 | | 6.71E+02 1.56E+02 1.84E+02 0.00E+00 | |-----------------------------------------------------------------------|