V. AISC 360-05 Tension
Verify the tensile yield strength and tensile rupture strength of an I section using both the LRFD and ASD methods per the AISC 360-05 code.
Reference
- Design Examples, Version 13.0, American Institute of Steel Construction, 2005, page D-2. Example D.1
- Steel Construction Manual, Version 13.0, American Institute of Steel Construction, 2005
Details
Verify the member Tensile Yield strength and Tensile Rupture Strength by both LRFD and ASD with the bolted end connection of a I Section (W8X21) using the LRFD and ASD method
Steel Gr. ASTM A992.
The connection consists of 2 rows of 4- 3/4"Ø bolts in each flange (16 bolts total) in standard holes. The holes are spaced evenly at 3" on center, with a 1-1/4" edge to center at the end of the flange in line with the tensile force.
Validation
ASTM A992: Fy = 50 ksi, Fu = 65 ksi
- Ag = 6.16 in2
- bf = 5.27 in
- tf = 0.400 in
- d = 8.28 in
- ry = 1.26 in
- y = 0.831 in (for a WT4X10.5)
Calculate the required tensile strength.
LRFD
ASD
Check the tensile yield strength limit state using tabulated values per Table 5-1 in ref. 2:
Check the available tensile rupture strength at the end connection. The tabulated values are for Ae/Ag ≥ 0.75. Verify this assumption is applicable.
Calculate U as the larger of the values from Table D3.1 case 2 or case 7 (ref. 2).
Case 7
Use U = 0.908
Calculate the net area at the bolted connection:
Calculate the effective area:
Therefore, the tabulated values for rupture do not apply. Calculate the rupture strength:
LRFD
ASD
Results
Parameter | Hand Calculation | STAAD.Pro | Difference | Comments | |
---|---|---|---|---|---|
ϕtPn (kips) [LRFD] | Yield | 277 | 277 | none | |
Rupture | 211 | 211 | none | ||
Pn/Ωt (kips) [ASD] | Yield | 184 | 184 | none | |
Rupture | 141 | 141 | none |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\US\AISC\AISC 360-05 Tension.STD is typically installed with the program.
STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 27-Aug-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 25 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
ISOTROPIC STEEL_50_KSI
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 7200 FU 8928 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE ST W8X21
CONSTANTS
MATERIAL STEEL_50_KSI ALL
SUPPORTS
2 PINNED
1 FIXED BUT FY MZ
LOAD 1 DEAD LOAD
JOINT LOAD
1 FY -30
LOAD 2 LIVE LOAD
JOINT LOAD
1 FY -90
LOAD COMB 3 SERVICE LOAD
1 1.0 2 1.0
LOAD COMB 4 ULTIMATE LOAD
1 1.2 2 1.6
PERFORM ANALYSIS
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2005
METHOD ASD
FYLD 7200 ALL
FU 9360 ALL
NSF 0.773 ALL
SLF 0.908 ALL
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2005
METHOD LRFD
TRACK 2 ALL
NSF 0.773 ALL
SLF 0.908 ALL
FU 9360 ALL
FYLD 7200 ALL
CHECK CODE ALL
FINISH
STAAD Output
STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD) v3.3a
********************************************
ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted)
MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/
FX MY MZ LOCATION
=======================================================================
1 ST W8X21 (AISC SECTIONS)
PASS Eq. H1-1a 0.854 3
120.00 T 0.00 0.00 0.00
|-----------------------------------------------------------------------|
| SLENDERNESS |
| Actual Slenderness Ratio : 238.212 L/C : 3 |
| Allowable Slenderness Ratio : 300.000 LOC : 0.00 |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS |
| Critical L/C : 3 Ratio : 0.854(PASS) |
| Loc : 0.00 Condition : Eq. H1-1a |
|-----------------------------------------------------------------------|
| DESIGN FORCES |
| Fx: 1.200E+02(T ) Fy: 0.000E+00 Fz: 0.000E+00 |
| Mx: 0.000E+00 My: 0.000E+00 Mz: 0.000E+00 |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES (UNIT: INCH) |
| Azz: 4.216E+00 Ayy: 2.070E+00 Cw: 1.517E+02 |
| Szz: 1.819E+01 Syy: 3.708E+00 |
| Izz: 7.530E+01 Iyy: 9.770E+00 Ix: 2.820E-01 |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES |
| Fyld: 7199.999 Fu: 9359.999 |
|-----------------------------------------------------------------------|
| Actual Member Length: 25.000 |
| Design Parameters |
| Kz: 1.00 Ky: 1.00 NSF: 0.77 SLF: 0.91 CSP: 12.00 |
|-----------------------------------------------------------------------|
| SECTION CLASS UNSTIFFENED / λ λp λr CASE |
| STIFFENED |
| Compression : Non-Slender 6.59 N/A 13.49 T.B4.1-3 |
| Non-Slender 27.52 N/A 35.88 T.B4.1-10 |
| Flexure : Compact 6.59 9.15 24.08 T.B4.1-1 |
| Compact 27.52 90.55 137.27 T.B4.1-9 |
STAAD PLANE -- PAGE NO. 4
STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD) v3.3a
********************************************
ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Yield 1.20E+02 1.84E+02 0.651 Eq. D2-1 3 0.00 |
| Rupture 1.20E+02 1.41E+02 0.854 Eq. D2-2 3 0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Maj Buck 0.00E+00 1.08E+02 0.000 Sec. E1 3 0.00 |
| Min Buck 0.00E+00 1.63E+01 0.000 Eq. E3-1 3 0.00 |
| Flexural |
| Tor Buck 0.00E+00 1.13E+02 0.000 Eq. E4-1 3 0.00 |
| Intermediate |
| Results Eff Area KL/r Fcr Fe Pn |
| Maj Buck 4.28E-02 85.81 4.20E+03 5.60E+03 1.80E+02 |
| Min Buck 4.28E-02 238.21 6.37E+02 7.26E+02 2.72E+01 |
| Flexural Ag Fcr Pn |
| Tor Buck 4.28E-02 4.41E+03 1.89E+02 |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Local-Z -0.00E+00 7.57E+01 0.000 Eq. G2-1 3 0.00 |
| Local-Y 0.00E+00 4.14E+01 0.000 Eq. G2-1 3 0.00 |
| Intermediate |
| Results Aw Cv Kv h/tw Vn |
| Local-Z 2.93E-02 1.00 1.20 6.59 1.26E+02 |
| Local-Y 1.44E-02 1.00 0.00 27.52 6.21E+01 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 5.09E+01 0.000 Eq. F2-1 3 0.00 |
| Minor 0.00E+00 1.42E+01 0.000 Eq. F6-1 3 0.00 |
| Intermediate Mn My |
| Major 8.50E+01 0.00E+00 |
| Minor 2.37E+01 0.00E+00 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 1.68E+01 0.000 Eq. F2-3 3 0.00 |
| Intermediate Mn Me Cb Lp Lr Lb |
| Major 2.80E+01 0.00E+00 1.00 4.45 14.75 25.00 |
STAAD PLANE -- PAGE NO. 5
STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD) v3.3a
********************************************
ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION |
| RATIO CRITERIA L/C LOC |
| Flexure Comp 0.000 Eq. H1-1b 3 0.00 |
| Flexure Tens 0.854 Eq. H1-1a 3 0.00 |
| Intermediate Mcx Mrx Pc |
| Mcy Mry Pr |
| Flexure Comp 1.68E+01 -0.00E+00 1.63E+01 |
| 1.42E+01 0.00E+00 0.00E+00 |
| Flexure Tens 1.68E+01 -0.00E+00 1.41E+02 |
| 1.42E+01 0.00E+00 1.20E+02 |
|-----------------------------------------------------------------------|
55. LOAD LIST 4
56. PARAMETER 2
57. CODE AISC UNIFIED 2005
58. METHOD LRFD
59. TRACK 2 ALL
60. NSF 0.773 ALL
61. SLF 0.908 ALL
62. FU 9360 ALL
63. FYLD 7200 ALL
64. CHECK CODE ALL
STEEL DESIGN
STAAD PLANE -- PAGE NO. 6
STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD) v3.3a
********************************************
ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted)
MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/
FX MY MZ LOCATION
=======================================================================
1 ST W8X21 (AISC SECTIONS)
PASS Eq. H1-1a 0.854 4
180.00 T 0.00 0.00 0.00
|-----------------------------------------------------------------------|
| SLENDERNESS |
| Actual Slenderness Ratio : 238.212 L/C : 4 |
| Allowable Slenderness Ratio : 300.000 LOC : 0.00 |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS |
| Critical L/C : 4 Ratio : 0.854(PASS) |
| Loc : 0.00 Condition : Eq. H1-1a |
|-----------------------------------------------------------------------|
| DESIGN FORCES |
| Fx: 1.800E+02(T ) Fy: 0.000E+00 Fz: 0.000E+00 |
| Mx: 0.000E+00 My: 0.000E+00 Mz: 0.000E+00 |
|-----------------------------------------------------------------------|
| SECTION PROPERTIES (UNIT: INCH) |
| Azz: 4.216E+00 Ayy: 2.070E+00 Cw: 1.517E+02 |
| Szz: 1.819E+01 Syy: 3.708E+00 |
| Izz: 7.530E+01 Iyy: 9.770E+00 Ix: 2.820E-01 |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES |
| Fyld: 7199.999 Fu: 9359.999 |
|-----------------------------------------------------------------------|
| Actual Member Length: 25.000 |
| Design Parameters |
| Kz: 1.00 Ky: 1.00 NSF: 0.77 SLF: 0.91 CSP: 12.00 |
|-----------------------------------------------------------------------|
| SECTION CLASS UNSTIFFENED / λ λp λr CASE |
| STIFFENED |
| Compression : Non-Slender 6.59 N/A 13.49 T.B4.1-3 |
| Non-Slender 27.52 N/A 35.88 T.B4.1-10 |
| Flexure : Compact 6.59 9.15 24.08 T.B4.1-1 |
| Compact 27.52 90.55 137.27 T.B4.1-9 |
STAAD PLANE -- PAGE NO. 7
STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD) v3.3a
********************************************
ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Yield 1.80E+02 2.77E+02 0.649 Eq. D2-1 4 0.00 |
| Rupture 1.80E+02 2.11E+02 0.854 Eq. D2-2 4 0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Maj Buck 0.00E+00 1.62E+02 0.000 Sec. E1 4 0.00 |
| Min Buck 0.00E+00 2.45E+01 0.000 Eq. E3-1 4 0.00 |
| Flexural |
| Tor Buck 0.00E+00 1.70E+02 0.000 Eq. E4-1 4 0.00 |
| Intermediate |
| Results Eff Area KL/r Fcr Fe Pn |
| Maj Buck 4.28E-02 85.81 4.20E+03 5.60E+03 1.80E+02 |
| Min Buck 4.28E-02 238.21 6.37E+02 7.26E+02 2.72E+01 |
| Flexural Ag Fcr Pn |
| Tor Buck 4.28E-02 4.41E+03 1.89E+02 |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Local-Z -0.00E+00 1.14E+02 0.000 Eq. G2-1 4 0.00 |
| Local-Y 0.00E+00 6.21E+01 0.000 Eq. G2-1 4 0.00 |
| Intermediate |
| Results Aw Cv Kv h/tw Vn |
| Local-Z 2.93E-02 1.00 1.20 6.59 1.26E+02 |
| Local-Y 1.44E-02 1.00 0.00 27.52 6.21E+01 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 7.65E+01 0.000 Eq. F2-1 4 0.00 |
| Minor 0.00E+00 2.13E+01 0.000 Eq. F6-1 4 0.00 |
| Intermediate Mn My |
| Major 8.50E+01 0.00E+00 |
| Minor 2.37E+01 0.00E+00 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 2.52E+01 0.000 Eq. F2-3 4 0.00 |
| Intermediate Mn Me Cb Lp Lr Lb |
| Major 2.80E+01 0.00E+00 1.00 4.45 14.75 25.00 |
STAAD PLANE -- PAGE NO. 8
STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD) v3.3a
********************************************
ALL UNITS ARE - KIP FEET (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION |
| RATIO CRITERIA L/C LOC |
| Flexure Comp 0.000 Eq. H1-1b 4 0.00 |
| Flexure Tens 0.854 Eq. H1-1a 4 0.00 |
| Intermediate Mcx Mrx Pc |
| Mcy Mry Pr |
| Flexure Comp 2.52E+01 -0.00E+00 2.45E+01 |
| 2.13E+01 0.00E+00 0.00E+00 |
| Flexure Tens 2.52E+01 -0.00E+00 2.11E+02 |
| 2.13E+01 0.00E+00 1.80E+02 |
|-----------------------------------------------------------------------|