# V. AISC 360-05 Built Up I E 12

## 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.12, pp.E-44 - E-47

## Details

From reference (2):

Compute the available strength of a built-up compression member with a length of 14 ft. The ends are pinned. The outside flange is PL3/4×5, the inside flange is PL3/4×8, and the web is PL3/8×10½. Material is ASTM A572 Grade 50.

## Validation

Material Properties

Fy = 50 ksi

Fu = 65 ksi

Section Properties

Built-up section properties (ignoring fillet welds):

where $y¯$ is measured from the bottom of the outside flange.

From Eq. 3.4 in Reference 3:

Distance between flange centroids:

Due to symmetry about the y-axis, the shear center lies on the y axis (x0 = 0). The distance from the centroid to the shear center can be calculated by finding the shear center from outside flange plus one-half the outside flange and then subtracting the centroid distance from that same reference point.

$H=1−x02+y02r¯02=1−0+(2.55)233.8=0.808$

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.

$KyLry=1.0(14.0)(12)1.71=98.2$
 (Eq. E4-8)
 (Eq. E4-9)
 (Eq. E4-5)

Nominal Compressive Strength

 (Eq E7-2)
 (Eq E7-1)

The available compressive strength:

LRFD:

ASD:

ϕcPn (kips) [LRFD] 279 278 negligible
Pnc (kips) [ASD] 186 185 negligible

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 12.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 06-Feb-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 14 0;
MEMBER INCIDENCES
1 1 2;
START USER TABLE
TABLE 1
UNIT INCHES KIP
WIDE FLANGE
I
13.6875 12 0.375 8 0.75 333.426 39.8586 2.0127 4.5 6.5 5 0.75
END
UNIT FEET KIP
DEFINE MATERIAL START
ISOTROPIC STEEL
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
ISOTROPIC STEEL_36_KSI
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 5184 FU 8352 RY 1.5 RT 1.2
END DEFINE MATERIAL
UNIT INCHES KIP
MEMBER PROPERTY AMERICAN
1 UPTABLE 1 I
CONSTANTS
MATERIAL STEEL_36_KSI ALL
UNIT FEET KIP
SUPPORTS
1 PINNED
2 FIXED BUT FY MX MZ
2 FY -20
2 FY -40
1 1.2 2 1.6
1 1.0 2 1.0
PERFORM ANALYSIS
UNIT INCHES KIP
PARAMETER 1
CODE AISC UNIFIED 2005
METHOD LRFD
STP 2 ALL
FU 65 ALL
FYLD 50 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2005
METHOD ASD
STP 2 ALL
FU 65 ALL
FYLD 50 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            0.316         3
88.00 C          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     98.449  L/C  :     3                |
| Allowable Slenderness Ratio :    200.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.316(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H1-1a                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   8.800E+01(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:   6.500E+00     Ayy:   4.500E+00     Cw:  7.947E+02              |
| Szz:   4.815E+01     Syy:   9.965E+00                                 |
| Izz:   3.334E+02     Iyy:   3.986E+01     Ix:  2.013E+00              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          50.000   Fu:          65.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:       168.000                                   |
| 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     5.33     N/A     13.40    T.B4.1-4     |
|                Non-Slender    28.00     N/A     35.88    T.B4.1-10    |
| Flexure     :  Compact         5.33     9.15    23.84    T.B4.1-2     |
|                Compact        23.17   127.82   137.27    T.B4.1-11    |
STAAD SPACE                                              -- 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   6.16E+02   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   6.67E+02   0.000      Eq. D2-2      3     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    8.80E+01   5.66E+02   0.156      Sec. E1       3     0.00 |
| Min Buck    8.80E+01   3.03E+02   0.290      Eq. E3-1      3     0.00 |
| Flexural                                                              |
| Tor Buck    8.80E+01   2.78E+02   0.316      Eq. E4-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.37E+01    34.04   4.59E+01   2.47E+02   6.29E+02        |
| Min Buck    1.37E+01    98.45   2.46E+01   2.95E+01   3.37E+02        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    1.37E+01   2.26E+01   3.09E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   1.76E+02   0.000      Eq. G2-1      3     0.00 |
| Local-Y     0.00E+00   1.22E+02   0.000      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     6.50E+00     1.00     1.20    10.67   1.95E+02            |
| Local-Y     4.50E+00     1.00     5.00    28.00   1.35E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   2.78E+03   0.000      Sec. F4.2     3     0.00 |
| Minor       0.00E+00   7.17E+02   0.000      Eq. F6-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       3.09E+03   0.00E+00                                       |
| Minor       7.97E+02   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   2.30E+03   0.000      Eq. F4-2      3     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       2.56E+03   0.00E+00    1.00    60.83   343.65   168.00    |
STAAD SPACE                                              -- PAGE NO.    5
STAAD.PRO CODE CHECKING - (AISC-360-05-LRFD)   v3.3a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-COMPRESSION FLANGE YIELDING                         |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             0.00E+00   2.78E+03   0.000      Eq. F4-1      3     0.00 |
| Intermediate   Mn        Rpc                                          |
|             3.09E+03   1.28E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.316      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         2.30E+03   0.00E+00   2.78E+02                   |
|                      7.17E+02   0.00E+00   8.80E+01                   |
| Flexure Tens         2.30E+03   0.00E+00   6.16E+02                   |
|                      7.17E+02   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
68. PARAMETER 2
69. CODE AISC UNIFIED 2005
70. METHOD ASD
71. STP 2 ALL
72. FU 65 ALL
73. FYLD 50 ALL
74. TRACK 2 ALL
75. CHECK CODE ALL
STEEL DESIGN
STAAD SPACE                                              -- 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            0.324         4
60.00 C          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     98.449  L/C  :     4                |
| Allowable Slenderness Ratio :    200.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     0.324(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H1-1a                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   6.000E+01(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:   6.500E+00     Ayy:   4.500E+00     Cw:  7.947E+02              |
| Szz:   4.815E+01     Syy:   9.965E+00                                 |
| Izz:   3.334E+02     Iyy:   3.986E+01     Ix:  2.013E+00              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          50.000   Fu:          65.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:       168.000                                   |
| 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     5.33     N/A     13.40    T.B4.1-4     |
|                Non-Slender    28.00     N/A     35.88    T.B4.1-10    |
| Flexure     :  Compact         5.33     9.15    23.84    T.B4.1-2     |
|                Compact        23.17   127.82   137.27    T.B4.1-11    |
STAAD SPACE                                              -- 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   4.10E+02   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   4.45E+02   0.000      Eq. D2-2      4     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    6.00E+01   3.77E+02   0.159      Sec. E1       4     0.00 |
| Min Buck    6.00E+01   2.02E+02   0.297      Eq. E3-1      4     0.00 |
| Flexural                                                              |
| Tor Buck    6.00E+01   1.85E+02   0.324      Eq. E4-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.37E+01    34.04   4.59E+01   2.47E+02   6.29E+02        |
| Min Buck    1.37E+01    98.45   2.46E+01   2.95E+01   3.37E+02        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    1.37E+01   2.26E+01   3.09E+02                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   1.17E+02   0.000      Eq. G2-1      4     0.00 |
| Local-Y     0.00E+00   8.08E+01   0.000      Eq. G2-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     6.50E+00     1.00     1.20    10.67   1.95E+02            |
| Local-Y     4.50E+00     1.00     5.00    28.00   1.35E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   1.85E+03   0.000      Sec. F4.2     4     0.00 |
| Minor       0.00E+00   4.77E+02   0.000      Eq. F6-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       3.09E+03   0.00E+00                                       |
| Minor       7.97E+02   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   1.53E+03   0.000      Eq. F4-2      4     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       2.56E+03   0.00E+00    1.00    60.83   343.65   168.00    |
STAAD SPACE                                              -- PAGE NO.    8
STAAD.PRO CODE CHECKING - ( AISC-360-05-ASD)   v3.3a
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-COMPRESSION FLANGE YIELDING                         |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             0.00E+00   1.85E+03   0.000      Eq. F4-1      4     0.00 |
| Intermediate   Mn        Rpc                                          |
|             3.09E+03   1.28E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.324      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         1.53E+03   0.00E+00   1.85E+02                   |
|                      4.77E+02   0.00E+00   6.00E+01                   |
| Flexure Tens         1.53E+03   0.00E+00   4.10E+02                   |
|                      4.77E+02   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|