V. AISC 360-10 Built up I E.3
Verify the compressive strength of a built-up I section with slender flanges per the LRFD and ASD methods of the AISC 360-10 code.
References
- American Institute of Steel Construction. 2010. Steel Construction Manual. Fourteenth Edition. AISC: Chicago, IL.
-
American Institute of Steel Construction. 2011. Design Examples, Version 14.0. AISC:Chicago, IL. Example E.3, pp. E-16 - E-20
- Seaburg, Paul A. and Charles J. Carter. 1997. Design Guide 9: Torsional Analysis of Structural Steel members. AISC: Chicago, IL.
Details
From reference (2):
Determine if a built-up, ASTM A572 Grade 50 column with PL3/8 in. × 102 in. flanges and a PL1/4 in. × 74 in. web has sufficient available strength to carry a dead load of 40 kips and a live load of 120 kips in axial compression. The column’s unbraced length is 15.0 ft in both axes and the ends are pinned.
Validation
Ultimate load:
Service load:
Section Properties
Built-up section properties (ignoring fillet welds):
From the User Note in Section E4 of Reference 1:
From Eq. 3.4 in Reference 3:
Slenderness
Check for slender web and then determine the stiffened element (web) reduction factor.
Web slenderness:
The limiting web slenderness ratio, λr :
Thus, the web is not slender and there is no reduction (i.e., Qa 1.0)
Check for slender flanges and then determine the unstiffened element (flange) reduction factor.
0.35 < kc < 0.76, OK.
Flange slenderness:
The limiting flange slenderness ratio, λr :
Thus, the flanges are slender.
Elastic Flexural Buckling Stress
Per Table C-A-7.1 in Reference 1, K = 1.0 for pinned-pinned columns. Since the unbraced length is the same both directions, by inspection the y-y axis governs.
Nominal Compressive Strength
The available compressive strength:
LRFD:
ASD:
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
ϕcPn (kips) [LRFD] | 312 | 314 | negligible | |
Pn/Ωc (kips) [ASD] | 208 | 209 | negligible | |
Slenderness ratio | 65.9 | 65.86 | negligible |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\US\AISC\AISC 360-10 Built up I E.3.STD is typically installed with the program.
STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 31-Oct-12
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 15 0;
MEMBER INCIDENCES
1 1 2;
START USER TABLE
TABLE 2
UNIT INCHES KIP
WIDE FLANGE
I
9.6875 8 0.25 10.5 0.375 122.496 72.361 0.406901 2 5.25 10.5 0.375
END
UNIT INCHES KIP
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29732.7
POISSON 0.3
DENSITY 0.000283
ALPHA 1.2e-05
DAMP 0.03
TYPE STEEL
STRENGTH FY 50 FU 65 RY 1.5 RT 1.2
ISOTROPIC STEEL_36_KSI
E 29000
POISSON 0.3
DENSITY 0.000283
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 36 FU 58 RY 1.5 RT 1.2
END DEFINE MATERIAL
CONSTANTS
MATERIAL STEEL_36_KSI ALL
MEMBER PROPERTY AMERICAN
1 UPTABLE 2 I
UNIT FEET KIP
SUPPORTS
1 PINNED
2 FIXED BUT FY MX MY MZ
LOAD 1 LOADTYPE Dead TITLE LOAD CASE 1
JOINT LOAD
2 FY -40
LOAD 2 LOADTYPE Live TITLE LOAD CASE 2
JOINT LOAD
2 FY -120
UNIT INCHES KIP
LOAD COMB 3 LRFD
1 1.2 2 1.6
LOAD COMB 4 ASD
1 1.0 2 1.0
PERFORM ANALYSIS
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2010
FU 65 ALL
FYLD 50 ALL
METHOD LRFD
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2010
FU 65 ALL
FYLD 50 ALL
METHOD ASD
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD) v1.4a
********************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted)
MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/
FX MY MZ LOCATION
=======================================================================
1 ST I (UPT)
PASS Eq. H1-1a 0.764 3
240.00 C 0.00 0.00 0.00
|-----------------------------------------------------------------------|
| SLENDERNESS |
| Actual Slenderness Ratio : 65.861 L/C : 3 |
| Allowable Slenderness Ratio : 200.000 LOC : 0.00 |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS |
| Critical L/C : 3 Ratio : 0.764(PASS) |
| Loc : 0.00 Condition : Eq. H1-1a |
|-----------------------------------------------------------------------|
| DESIGN FORCES |
| Fx: 2.400E+02(C ) 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: 5.250E+00 Ayy: 2.000E+00 Cw: 1.052E+03 |
| Szz: 3.062E+01 Syy: 1.378E+01 |
| Izz: 1.225E+02 Iyy: 7.236E+01 Ix: 4.069E-01 |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES |
| Fyld: 50.000 Fu: 65.000 |
|-----------------------------------------------------------------------|
| Actual Member Length: 180.000 |
| Design Parameters |
| Kz: 1.00 Ky: 1.00 NSF: 1.00 SLF: 1.00 CSP: 12.00 |
|-----------------------------------------------------------------------|
| SECTION CLASS UNSTIFFENED / λ λp λr CASE |
| STIFFENED |
| Compression : Slender 14.00 N/A 13.49 T.B4.1(a)-1 |
| Non-Slender 29.00 N/A 35.88 T.B4.1(a)-5 |
| Flexure : Non-Compact 14.00 9.15 24.08 T.B4.1(b)-10 |
| Compact 29.00 90.55 137.27 T.B4.1(b)-15 |
STAAD PLANE -- PAGE NO. 4
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD) v1.4a
********************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Yield 0.00E+00 4.36E+02 0.000 Eq. D2-1 3 0.00 |
| Rupture 0.00E+00 4.72E+02 0.000 Eq. D2-2 3 0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Maj Buck 2.40E+02 3.57E+02 0.672 Eq. E7-1 3 0.00 |
| Min Buck 2.40E+02 3.14E+02 0.764 Eq. E7-1 3 0.00 |
| Flexural |
| Tor Buck 2.40E+02 3.21E+02 0.747 Eq. E7-1 3 0.00 |
| Intermediate |
| Results Eff Area KL/r Fcr Fe Pn |
| Maj Buck 9.69E+00 50.62 4.09E+01 1.12E+02 3.97E+02 |
| Min Buck 9.69E+00 65.86 3.60E+01 6.60E+01 3.49E+02 |
| Flexural Ag Fcr Pn |
| Tor Buck 9.69E+00 3.68E+01 3.57E+02 |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Local-Z -0.00E+00 1.42E+02 0.000 Eq. G2-1 3 0.00 |
| Local-Y 0.00E+00 6.00E+01 0.000 Eq. G2-1 3 0.00 |
| Intermediate |
| Results Aw Cv Kv h/tw Vn |
| Local-Z 5.25E+00 1.00 1.20 14.00 1.58E+02 |
| Local-Y 2.00E+00 1.00 0.00 29.00 6.00E+01 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 1.50E+03 0.000 Eq. F2-1 3 0.00 |
| Minor 0.00E+00 9.35E+02 0.000 Eq. F6-1 3 0.00 |
| Intermediate Mn My |
| Major 1.67E+03 0.00E+00 |
| Minor 1.04E+03 0.00E+00 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 1.36E+03 0.000 Eq. F2-2 3 0.00 |
| Intermediate Mn Me Cb Lp Lr Lb |
| Major 1.51E+03 0.00E+00 1.00 115.84 354.09 180.00 |
STAAD PLANE -- PAGE NO. 5
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD) v1.4a
********************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-FLANGE LOCAL BUCKLING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 1.33E+03 0.000 Eq. F3-1 3 0.00 |
| Minor 0.00E+00 7.73E+02 0.000 Eq. F6-2 3 0.00 |
| Intermediate Mn Fcr |
| Major 1.47E+03 0.00E+00 |
| Minor 8.58E+02 0.00E+00 |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION |
| RATIO CRITERIA L/C LOC |
| Flexure Comp 0.764 Eq. H1-1a 3 0.00 |
| Flexure Tens 0.000 Eq. H1-1b 3 0.00 |
| Intermediate Mcx Mrx Pc |
| Mcy Mry Pr |
| Flexure Comp 1.33E+03 -0.00E+00 3.14E+02 |
| 7.73E+02 0.00E+00 2.40E+02 |
| Flexure Tens 1.33E+03 -0.00E+00 4.36E+02 |
| 7.73E+02 0.00E+00 0.00E+00 |
|-----------------------------------------------------------------------|
65. LOAD LIST 4
66. PARAMETER 2
67. CODE AISC UNIFIED 2010
68. FU 65 ALL
69. FYLD 50 ALL
70. METHOD ASD
71. TRACK 2 ALL
72. CHECK CODE ALL
STEEL DESIGN
STAAD PLANE -- PAGE NO. 6
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD) v1.4a
********************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted)
MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/
FX MY MZ LOCATION
=======================================================================
1 ST I (UPT)
PASS Eq. H1-1a 0.765 4
160.00 C 0.00 0.00 0.00
|-----------------------------------------------------------------------|
| SLENDERNESS |
| Actual Slenderness Ratio : 65.861 L/C : 4 |
| Allowable Slenderness Ratio : 200.000 LOC : 0.00 |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS |
| Critical L/C : 4 Ratio : 0.765(PASS) |
| Loc : 0.00 Condition : Eq. H1-1a |
|-----------------------------------------------------------------------|
| DESIGN FORCES |
| Fx: 1.600E+02(C ) 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: 5.250E+00 Ayy: 2.000E+00 Cw: 1.052E+03 |
| Szz: 3.062E+01 Syy: 1.378E+01 |
| Izz: 1.225E+02 Iyy: 7.236E+01 Ix: 4.069E-01 |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES |
| Fyld: 50.000 Fu: 65.000 |
|-----------------------------------------------------------------------|
| Actual Member Length: 180.000 |
| Design Parameters |
| Kz: 1.00 Ky: 1.00 NSF: 1.00 SLF: 1.00 CSP: 12.00 |
|-----------------------------------------------------------------------|
| SECTION CLASS UNSTIFFENED / λ λp λr CASE |
| STIFFENED |
| Compression : Slender 14.00 N/A 13.49 T.B4.1(a)-1 |
| Non-Slender 29.00 N/A 35.88 T.B4.1(a)-5 |
| Flexure : Non-Compact 14.00 9.15 24.08 T.B4.1(b)-10 |
| Compact 29.00 90.55 137.27 T.B4.1(b)-15 |
STAAD PLANE -- PAGE NO. 7
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD) v1.4a
********************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL TENSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Yield 0.00E+00 2.90E+02 0.000 Eq. D2-1 4 0.00 |
| Rupture 0.00E+00 3.15E+02 0.000 Eq. D2-2 4 0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Maj Buck 1.60E+02 2.38E+02 0.674 Eq. E7-1 4 0.00 |
| Min Buck 1.60E+02 2.09E+02 0.765 Eq. E7-1 4 0.00 |
| Flexural |
| Tor Buck 1.60E+02 2.14E+02 0.749 Eq. E7-1 4 0.00 |
| Intermediate |
| Results Eff Area KL/r Fcr Fe Pn |
| Maj Buck 9.69E+00 50.62 4.09E+01 1.12E+02 3.97E+02 |
| Min Buck 9.69E+00 65.86 3.60E+01 6.60E+01 3.49E+02 |
| Flexural Ag Fcr Pn |
| Tor Buck 9.69E+00 3.68E+01 3.57E+02 |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Local-Z -0.00E+00 9.43E+01 0.000 Eq. G2-1 4 0.00 |
| Local-Y 0.00E+00 4.00E+01 0.000 Eq. G2-1 4 0.00 |
| Intermediate |
| Results Aw Cv Kv h/tw Vn |
| Local-Z 5.25E+00 1.00 1.20 14.00 1.58E+02 |
| Local-Y 2.00E+00 1.00 0.00 29.00 6.00E+01 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 9.97E+02 0.000 Eq. F2-1 4 0.00 |
| Minor 0.00E+00 6.22E+02 0.000 Eq. F6-1 4 0.00 |
| Intermediate Mn My |
| Major 1.67E+03 0.00E+00 |
| Minor 1.04E+03 0.00E+00 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 9.02E+02 0.000 Eq. F2-2 4 0.00 |
| Intermediate Mn Me Cb Lp Lr Lb |
| Major 1.51E+03 0.00E+00 1.00 115.84 354.09 180.00 |
STAAD PLANE -- PAGE NO. 8
STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD) v1.4a
********************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-FLANGE LOCAL BUCKLING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 8.82E+02 0.000 Eq. F3-1 4 0.00 |
| Minor 0.00E+00 5.14E+02 0.000 Eq. F6-2 4 0.00 |
| Intermediate Mn Fcr |
| Major 1.47E+03 0.00E+00 |
| Minor 8.58E+02 0.00E+00 |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION |
| RATIO CRITERIA L/C LOC |
| Flexure Comp 0.765 Eq. H1-1a 4 0.00 |
| Flexure Tens 0.000 Eq. H1-1b 4 0.00 |
| Intermediate Mcx Mrx Pc |
| Mcy Mry Pr |
| Flexure Comp 8.82E+02 -0.00E+00 2.09E+02 |
| 5.14E+02 0.00E+00 1.60E+02 |
| Flexure Tens 8.82E+02 -0.00E+00 2.90E+02 |
| 5.14E+02 0.00E+00 0.00E+00 |
|-----------------------------------------------------------------------|