V. AISC 360-10 - E-2
Reference
- 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.2, pp. E-11 - E-15
Problem
From the reference:
Verify that a built-up, ASTM A572 Grade 50 column with PL 1 in. × 8 in. flanges and a PL 4 in. × 15 in. web is sufficient to carry a dead load of 70 kips and live load of 210 kips in axial compression. The column length is 15 ft and the ends are pinned in both axes.
Validation
Ultimate load:
Service load:
Section Properties
Built-up section properties (ignoring fillet welds):
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.
Slenderness
Check for slender flanges and then determine the unstiffened element (flange) reduction factor.
0.35 < kc < 0.76
Flange slenderness:
The limiting flange slenderness ratio, λr :
Thus, the flanges are not slender and there is no reduction (Qs = 1.0).
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 slender.
Nominal Compressive Strength
The available compressive strength:
LRFD:
ASD:
Comparison
Result Type | Reference | STAAD.Pro | Difference |
---|---|---|---|
ϕcPn (kips) [LRFD] | 508 | 513 | 1.0% |
Pn/Ωc (kips) [ASD] | 338 | 341 | 0.9% |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\US\AISC\AISC 360-10 E-2.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 1
*UNIT INCHES KIP
*ISECTION
*I1
*17 0.25 17 8 1 8 1 0 0 0
TABLE 2
UNIT INCHES KIP
WIDE FLANGE
I
19.75 17 0.25 8 1 1095.65 85.3529 5.41146 4.25 10.6667 8 1
END
UNIT inch KIP
DEFINE MATERIAL START
ISOTROPIC STEEL
E 29732.7
POISSON 0.3
DENSITY 0.000283
ALPHA 1.2e-005
DAMP 0.03
TYPE STEEL
STRENGTH FY 50 FU 65 RY 1.5 RT 1.2
END DEFINE MATERIAL
UNIT INCHES KIP
CONSTANTS
MATERIAL STEEL 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 -70
LOAD 2 LOADTYPE Live TITLE LOAD CASE 2
JOINT LOAD
2 FY -210
UNIT INCHES KIP
LOAD COMB 3 COMBINATION LOAD CASE 3
1 1.2 2 1.6
LOAD COMB 4 COMBINATION LOAD CASE 4
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 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 0.819 3
420.00 C 0.00 0.00 0.00
|-----------------------------------------------------------------------|
| SLENDERNESS |
| Actual Slenderness Ratio : 86.586 L/C : 3 |
| Allowable Slenderness Ratio : 200.000 LOC : 0.00 |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS |
| Critical L/C : 3 Ratio : 0.819(PASS) |
| Loc : 0.00 Condition : Eq. H1-1a |
|-----------------------------------------------------------------------|
| DESIGN FORCES |
| Fx: 4.200E+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: 1.067E+01 Ayy: 4.250E+00 Cw: 5.461E+03 |
| Szz: 1.289E+02 Syy: 2.134E+01 |
| Izz: 1.096E+03 Iyy: 8.535E+01 Ix: 5.411E+00 |
|-----------------------------------------------------------------------|
| 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 : Non-Slender 4.00 N/A 13.66 T.B4.1(a)-1 |
| Slender 60.00 N/A 36.33 T.B4.1(a)-5 |
| Flexure : Compact 4.00 9.27 24.39 T.B4.1(b)-10 |
| Compact 60.00 91.69 139.00 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 8.89E+02 0.000 Eq. D2-1 3 0.00 |
| Rupture 0.00E+00 9.63E+02 0.000 Eq. D2-2 3 0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Maj Buck 4.20E+02 8.03E+02 0.523 Eq. E7-1 3 0.00 |
| Min Buck 4.20E+02 5.13E+02 0.819 Eq. E7-1 3 0.00 |
| Flexural |
| Tor Buck 4.20E+02 6.84E+02 0.614 Eq. E7-1 3 0.00 |
| Intermediate |
| Results Eff Area KL/r Fcr Fe Pn |
| Maj Buck 1.86E+01 24.17 4.52E+01 5.02E+02 8.93E+02 |
| Min Buck 1.91E+01 86.59 2.89E+01 3.91E+01 5.70E+02 |
| Flexural Ag Fcr Pn |
| Tor Buck 1.88E+01 3.85E+01 7.60E+02 |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Local-Z -0.00E+00 2.88E+02 0.000 Eq. G2-1 3 0.00 |
| Local-Y 0.00E+00 1.15E+02 0.000 Eq. G2-1 3 0.00 |
| Intermediate |
| Results Aw Cv Kv h/tw Vn |
| Local-Z 1.07E+01 1.00 1.20 4.00 3.20E+02 |
| Local-Y 4.25E+00 1.00 5.00 60.00 1.27E+02 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 6.39E+03 0.000 Eq. F2-1 3 0.00 |
| Minor 0.00E+00 1.45E+03 0.000 Eq. F6-1 3 0.00 |
| Intermediate Mn My |
| Major 7.10E+03 0.00E+00 |
| Minor 1.61E+03 0.00E+00 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 5.44E+03 0.000 Eq. F2-2 3 0.00 |
| Intermediate Mn Me Cb Lp Lr Lb |
| Major 6.04E+03 0.00E+00 1.00 89.22 311.02 180.00 |
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 FLEXURE TENS/COMP INTERACTION |
| RATIO CRITERIA L/C LOC |
| Flexure Comp 0.819 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 5.44E+03 -0.00E+00 5.13E+02 |
| 1.45E+03 0.00E+00 4.20E+02 |
| Flexure Tens 5.44E+03 -0.00E+00 8.89E+02 |
| 1.45E+03 0.00E+00 0.00E+00 |
|-----------------------------------------------------------------------|
63. LOAD LIST 4
64. PARAMETER 2
65. CODE AISC UNIFIED 2010
66. FU 65 ALL
67. FYLD 50 ALL
68. METHOD ASD
69. TRACK 2 ALL
70. 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 0.820 4
280.00 C 0.00 0.00 0.00
|-----------------------------------------------------------------------|
| SLENDERNESS |
| Actual Slenderness Ratio : 86.586 L/C : 4 |
| Allowable Slenderness Ratio : 200.000 LOC : 0.00 |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS |
| Critical L/C : 4 Ratio : 0.820(PASS) |
| Loc : 0.00 Condition : Eq. H1-1a |
|-----------------------------------------------------------------------|
| DESIGN FORCES |
| Fx: 2.800E+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: 1.067E+01 Ayy: 4.250E+00 Cw: 5.461E+03 |
| Szz: 1.289E+02 Syy: 2.134E+01 |
| Izz: 1.096E+03 Iyy: 8.535E+01 Ix: 5.411E+00 |
|-----------------------------------------------------------------------|
| 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 : Non-Slender 4.00 N/A 13.66 T.B4.1(a)-1 |
| Slender 60.00 N/A 36.33 T.B4.1(a)-5 |
| Flexure : Compact 4.00 9.27 24.39 T.B4.1(b)-10 |
| Compact 60.00 91.69 139.00 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 5.91E+02 0.000 Eq. D2-1 4 0.00 |
| Rupture 0.00E+00 6.42E+02 0.000 Eq. D2-2 4 0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Maj Buck 2.80E+02 5.35E+02 0.524 Eq. E7-1 4 0.00 |
| Min Buck 2.80E+02 3.41E+02 0.820 Eq. E7-1 4 0.00 |
| Flexural |
| Tor Buck 2.80E+02 4.55E+02 0.615 Eq. E7-1 4 0.00 |
| Intermediate |
| Results Eff Area KL/r Fcr Fe Pn |
| Maj Buck 1.86E+01 24.17 4.52E+01 5.02E+02 8.93E+02 |
| Min Buck 1.91E+01 86.59 2.89E+01 3.91E+01 5.70E+02 |
| Flexural Ag Fcr Pn |
| Tor Buck 1.88E+01 3.85E+01 7.60E+02 |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Local-Z -0.00E+00 1.92E+02 0.000 Eq. G2-1 4 0.00 |
| Local-Y 0.00E+00 7.63E+01 0.000 Eq. G2-1 4 0.00 |
| Intermediate |
| Results Aw Cv Kv h/tw Vn |
| Local-Z 1.07E+01 1.00 1.20 4.00 3.20E+02 |
| Local-Y 4.25E+00 1.00 5.00 60.00 1.27E+02 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 4.25E+03 0.000 Eq. F2-1 4 0.00 |
| Minor 0.00E+00 9.65E+02 0.000 Eq. F6-1 4 0.00 |
| Intermediate Mn My |
| Major 7.10E+03 0.00E+00 |
| Minor 1.61E+03 0.00E+00 |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING |
| |
| FORCE CAPACITY RATIO CRITERIA L/C LOC |
| Major -0.00E+00 3.62E+03 0.000 Eq. F2-2 4 0.00 |
| Intermediate Mn Me Cb Lp Lr Lb |
| Major 6.04E+03 0.00E+00 1.00 89.22 311.02 180.00 |
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 FLEXURE TENS/COMP INTERACTION |
| RATIO CRITERIA L/C LOC |
| Flexure Comp 0.820 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 3.62E+03 -0.00E+00 3.41E+02 |
| 9.65E+02 0.00E+00 2.80E+02 |
| Flexure Tens 3.62E+03 -0.00E+00 5.91E+02 |
| 9.65E+02 0.00E+00 0.00E+00 |
|-----------------------------------------------------------------------|