# V. AISC 360-05 Built up I E.2

## References

1. Steel Construction Manual, Version 13.0, American Institute of Steel Construction, 2005
2. Design Examples, Version 13.0, American Institute of Steel Construction, 2005, Example E.2, pp.E-10 - E-13

## Details

From reference (2):

Verify that a built-up, ASTM A572 grade 50, column with PL1in.×8in. flanges and a PL1/4in.×15in. 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

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.

$KLry=1.0(15.0)(12)2.08=86.5$
 (Eq. E3-4)

Slenderness

Check for slender flanges and then determine the unstiffened element (flange) reduction factor.

 $kc=4h/tw=415.0/0.25=0.516$ (Table B4.1b note a)

0.35 < kc < 0.76

Flange slenderness:

$λ=bt=4.01.0=4.0$

The limiting flange slenderness ratio, λr:

 $λr=0.64kcEFy=0.640.516(29,000)50=11.1>λ$ (Table B4.1a, case 2)

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:

$λ=ht=15.00.25=60.0$

The limiting web slenderness ratio, λr:

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

Thus, the web is slender.

 $Qa=AeAg$ (Eq. E7-16)
where
 Ae = the effective area based on the reduced effective width, be be = $1.92tEf[1−0.34(b/t)Ef]≤b$ (Eq. E7-17) $f$ = Fcr calculated based on Q = 1.0 Fcr = because $KLr=86.5<4.71EQFy=4.7129,0001.0(50)=113$
$Qa=19.119.8=0.965$
$Q=QsQa=1.0×0.965=0.965$
$KLr=86.5<4.71EQFy=4.7129,0000.965(50)=115$

Nominal Compressive Strength

 (Eq E7-1)

The available compressive strength:

LRFD:

ASD:

Table 1. Comparison of results
ϕcPn (kips) [LRFD] 508 513 1.0%
Pnc (kips) [ASD] 338 341 0.9%

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-05 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
19.75 17 0.25 8 1 1095.65 85.3529 5.41146 4.25 10.6667 8 1
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
END DEFINE MATERIAL
CONSTANTS
MATERIAL STEEL ALL
MEMBER PROPERTY AMERICAN
1 UPTABLE 2 I
UNIT FEET KIP
SUPPORTS
1 PINNED
2 FIXED BUT FY MX MY MZ
2 FY -70
2 FY -210
UNIT INCHES KIP
1 1.2 2 1.6
1 1.0 2 1.0
PERFORM ANALYSIS
PARAMETER 1
CODE AISC UNIFIED 2005
FU 65 ALL
FYLD 50 ALL
METHOD LRFD
TRACK 2 ALL
STP 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2005
FU 65 ALL
FYLD 50 ALL
METHOD ASD
STP 2 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH


                       STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
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     11.22    T.B4.1-4     |
|                Slender        60.00     N/A     36.33    T.B4.1-10    |
| Flexure     :  Compact         4.00     9.27    19.90    T.B4.1-2     |
|                Compact        60.00    91.69   139.00    T.B4.1-9     |
STAAD PLANE                                              -- PAGE NO.    4
STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
********************************************
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      Sec. E1       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     8.00   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-360-05-LRFD)   v3.3a
********************************************
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                   |
|-----------------------------------------------------------------------|
59. PARAMETER 2
60. CODE AISC UNIFIED 2005
61. FU 65 ALL
62. FYLD 50 ALL
63. METHOD ASD
64. STP 2 ALL
65. TRACK 2 ALL
66. CHECK CODE ALL
STEEL DESIGN
STAAD PLANE                                              -- PAGE NO.    6
STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
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     11.22    T.B4.1-4     |
|                Slender        60.00     N/A     36.33    T.B4.1-10    |
| Flexure     :  Compact         4.00     9.27    19.90    T.B4.1-2     |
|                Compact        60.00    91.69   139.00    T.B4.1-9     |
STAAD PLANE                                              -- PAGE NO.    7
STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
********************************************
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      Sec. E1       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     8.00   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-360-05-ASD)   v3.3a
********************************************
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                   |
|-----------------------------------------------------------------------|