# 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

1. American Institute of Steel Construction. 2010. Steel Construction Manual. Fourteenth Edition. AISC: Chicago, IL.
2. American Institute of Steel Construction. 2011. Design Examples, Version 14.0. AISC:Chicago, IL. Example E.3, pp. E-16 - E-20

3. 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

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:

$λ=ht=7.250.25=29.0$

The limiting web slenderness ratio, λr:

 $λr=1.49EFy=1.4929,00050=35.9>λ$ (Table B4.1a, case 5)

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.

 $kc=4h/tw=47.25/0.25=0.743$ (Table B4.1b note a)

0.35 < kc < 0.76, OK.

Flange slenderness:

$λ=bt=5.250.375=14.0$

The limiting flange slenderness ratio, λr:

 $λr=0.64kcEFy=0.640.743(29,000)50=13.3<λ$ (Table B4.1a, case 2)

Thus, the flanges are slender.

$0.64kcEFy=13.3
 $Qs=1.415−0.65(bt)FykcE=1.415−0.65(14.0)500.743(29,000)=0.977$ (Eq. E7-8)
$Q=QsQa=0.977(1.0)=0.977$

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.

$KyLry=1.0(15.0)(12)2.73=65.9$
 (Eq. E3-4)

Nominal Compressive Strength

$KLr=65.9<4.71EQFy=4.7129,0000.977(50)=115$
 (Eq E7-2)
 (Eq E7-1)

The available compressive strength:

LRFD:

ASD:

## Results

ϕcPn (kips) [LRFD] 312 314 negligible
Pnc (kips) [ASD] 208 209 negligible
Slenderness ratio 65.9 65.86 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-10 Built up I E.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
2 FY -40
2 FY -120
UNIT INCHES KIP
1 1.2 2 1.6
1 1.0 2 1.0
PERFORM ANALYSIS
PARAMETER 1
CODE AISC UNIFIED 2010
FU 65 ALL
FYLD 50 ALL
METHOD LRFD
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2010
FU 65 ALL
FYLD 50 ALL
METHOD ASD
TRACK 2 ALL
CHECK CODE ALL
FINISH


                       STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD)   v1.4a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
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                   |
|-----------------------------------------------------------------------|
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)
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                   |
|-----------------------------------------------------------------------|