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".
- A uniformly distributed load of -2.25 k/in along the beam in the global Y direction.
- Lateral loads at the top of the left column of 50 kips in the global X direction and 25 kips in the global Z direction (out of plane).
- A concentrated torque of 0.75 in·kips at mid-span of the beam.
- E = 29,000 ksi
- Fy = 50 ksi
Validation
Design Forces
- Mz = 599.6 in·kips, Fy = 67.5 kips
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:
Critical buckling stress:
Nominal buckling strength:
- 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:
- 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):
- 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:
- 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 2024\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 |
|-----------------------------------------------------------------------|