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.
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
Assume a W8X21 section:
- 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
Pu = 1.2(30 kips) + 1.6(90 kips) = 180 kips
ASD
Pa = 30 kips + 90 kips = 120 kips
Check the tensile yield strength limit state using tabulated values per Table 5-1 in ref. 2:
ϕtPn = 277 kips > 180 kips
Pn/Ωt = 184 kips > 120 kips
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 2 - Check as two WT shapes:
where
| U = 1 - x/l = 1 - 0.831 in / 9.0 in = 0.908 |
| = | ||
| = |
Case 7
bf = 5.27 in < 2/3d = 2/3(8.28 in) = 5.52 in; U = 0.85
Use U = 0.908
Calculate the net area at the bolted connection:
An = Ag - 4(Øh + 1/16 in)tf = 6.16 in2 - 4×(13/16 in + 1/16 in)(0.400 in) = 4.76 in2
Calculate the effective area:
Ae = AnU = 4.76 in2 × 0.908 = 4.32 in2
Ae/Ag = 4.32 in2/ 6.16 in2 = 0.701 < 0.75
Therefore, the tabulated values for rupture do not apply. Calculate the rupture strength:
Pn = FuAe = 65 ksi (4.32 in2) = 281 kips
LRFD
ϕtPn = 0.75(281 kips) = 211 kips > 180 kips
ASD
Pn/Ωt = 281 kips/2.00 = 141 kips > 120 kips
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\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 | |-----------------------------------------------------------------------|