# V. AISC 360-05 Double L E.6

## 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.6, pp.E-26 - E-30

## Details

From reference (2):

Determine if a 2L5×3×1/4 LLBB (3/4-in. separation) strut with a length of 8 ft and pinned ends has sufficient available strength to support a dead load of 10 kips and live load of 30 kips in axial compression. Also, calculate the required number of fully tightened or welded intermediate connectors.

## Validation

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

$λ=bt=5.00.25=20.0$

The limiting slenderness ratio, λr:

 $λr=0.45EFy=0.4529,00036=12.8<λ$ (Table B4.1a, case 3)

Thus, the outstanding legs are slender.

Check for slender web and then determine the stiffened element (web) reduction factor.

$0.45EFy=12.8
 $Qs=1.34−0.76(bt)FyE=1.34−0.76(20.0)3629,000=0.804$ (Eq. E7-11)
$Q=QsQa=0.804(1.0)=0.804$
$Fcr=Q(0.658QFy/Fe)Fy$
where
 Fe = $(Fey+Fez2H)[1−1−4FeyFezH(Fey+Fez)2]$ (Eq E4-5) Ki = 0.5 for angles back-to-back ri = rz = 0.652 in; the radius of gyration for a single angle a = 32 in spacing between connectors (using the bolts at 1/3 points from Reference 2) $(KyLry)m$ = $(KLr)02+(Kiari)2=(1.0×961.33)2+(0.5×320.652)2=76.3$ for Fey = Fez =

Thus,

Nominal Compressive Strength

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

The available compressive strength:

LRFD:

ASD:

ϕcPn (kips) [LRFD] 64.3 63.8 negligible
Pnc (kips) [ASD] 42.8 42.4 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-05 Double L E.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 5-Dec-12
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 8 0; 2 0 0 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY AMERICAN
1 TABLE LD L50304 SP 0.0625
UNIT INCHES KIP
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 29000
POISSON 0.3
ISOTROPIC STEEL
E 29000
POISSON 0.3
DENSITY 0.000283
ALPHA 6e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 36 FU 58 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
ISOTROPIC STEEL_50_KSI
E 29000
POISSON 0.3
DENSITY 0.000283
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 50 FU 62 RY 1.5 RT 1.2
END DEFINE MATERIAL
UNIT FEET KIP
CONSTANTS
MATERIAL STEEL_50_KSI ALL
SUPPORTS
2 PINNED
1 FIXED BUT FY MX MZ
1 FY -10
1 FY -30
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
FU 58 ALL
FYLD 36 ALL
CSPACING 32 ALL
TRACK 2 ALL
CHECK CODE ALL
PARAMETER 2
CODE AISC UNIFIED 2005
METHOD ASD
FU 58 ALL
FYLD 36 ALL
CSPACING 32 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 LD   L50304                   (AISC SECTIONS)
PASS   Eq. H2-1             0.945         3
60.00 C          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     78.939  L/C  :     3                |
| Allowable Slenderness Ratio :    200.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.945(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H2-1                      |
|-----------------------------------------------------------------------|
| 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:   1.500E+00     Ayy:   1.250E+00     Cw:  0.000E+00              |
| Szz:   3.055E+00     Syy:   2.075E+00                                 |
| Izz:   1.022E+01     Iyy:   7.003E+00     Ix:  8.083E-02              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          36.000   Fu:          58.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        96.000                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    1.00 NSF:    1.00 SLF:    1.00 CSP:   32.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Slender        20.00     N/A     12.77    T.B4.1-5     |
|                  N/A           N/A      N/A      N/A      N/A         |
| Flexure     :  Non-Compact    20.00    15.33    25.83    T.B4.1-6     |
|                  N/A           N/A      N/A      N/A      N/A         |
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   1.26E+02   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   1.69E+02   0.000      Eq. D2-2      3     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    6.00E+01   8.72E+01   0.688      Sec. E1       3     0.00 |
| Min Buck    6.00E+01   8.09E+01   0.742      Eq. E7-1      3     0.00 |
| Flexural                                                              |
| Tor Buck    6.00E+01   6.35E+01   0.945      Eq. E7-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    3.88E+00    59.15   2.50E+01   8.18E+01   9.69E+01        |
| Min Buck    3.88E+00    72.59   2.32E+01   5.43E+01   8.99E+01        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    3.88E+00   1.82E+01   7.05E+01                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   2.92E+01   0.000      Eq. G2-1      3     0.00 |
| Local-Y     0.00E+00   2.43E+01   0.000      Eq. G2-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.50E+00     1.00     1.20    12.00   3.24E+01            |
| Local-Y     1.25E+00     1.00     1.20    20.00   2.70E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   1.58E+02   0.000      Eq. F9-1      3     0.00 |
| Minor       0.00E+00   1.08E+02   0.000      Eq. F6-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       1.76E+02   0.00E+00                                       |
| Minor       1.20E+02   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   1.04E+03   0.000      Eq. F9-4      3     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       1.16E+03   0.00E+00    1.00     0.00     0.00    96.00    |
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 FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.945      Eq. H2-1      3     0.00             |
| Flexure Tens          0.000      Eq. H2-1      3     0.00             |
| Intermediate         frbw /     frbz /     fra /                      |
|                      Fcbw       Fcbz       Fca                        |
| Flexure Comp         0.00E+00   0.00E+00   1.55E+01                   |
|                      5.18E+01   5.18E+01   1.64E+01                   |
| Flexure Tens         0.00E+00   0.00E+00   0.00E+00                   |
|                      2.57E+01   5.18E+01   3.24E+01                   |
|-----------------------------------------------------------------------|
71. PARAMETER 2
72. CODE AISC UNIFIED 2005
73. METHOD ASD
74. FU 58 ALL
75. FYLD 36 ALL
76. CSPACING 32 ALL
77. TRACK 2 ALL
78. 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 LD   L50304                   (AISC SECTIONS)
PASS   Eq. H2-1             0.947         4
40.00 C          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     78.939  L/C  :     4                |
| Allowable Slenderness Ratio :    200.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     0.947(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H2-1                      |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   4.000E+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:   1.500E+00     Ayy:   1.250E+00     Cw:  0.000E+00              |
| Szz:   3.055E+00     Syy:   2.075E+00                                 |
| Izz:   1.022E+01     Iyy:   7.003E+00     Ix:  8.083E-02              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          36.000   Fu:          58.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:        96.000                                   |
| Design Parameters                                                     |
| Kz:    1.00 Ky:    1.00 NSF:    1.00 SLF:    1.00 CSP:   32.00        |
|-----------------------------------------------------------------------|
| SECTION CLASS  UNSTIFFENED /     λ       λp      λr        CASE       |
|                STIFFENED                                              |
| Compression :  Slender        20.00     N/A     12.77    T.B4.1-5     |
|                  N/A           N/A      N/A      N/A      N/A         |
| Flexure     :  Non-Compact    20.00    15.33    25.83    T.B4.1-6     |
|                  N/A           N/A      N/A      N/A      N/A         |
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   8.36E+01   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   1.13E+02   0.000      Eq. D2-2      4     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    4.00E+01   5.80E+01   0.689      Sec. E1       4     0.00 |
| Min Buck    4.00E+01   5.38E+01   0.743      Eq. E7-1      4     0.00 |
| Flexural                                                              |
| Tor Buck    4.00E+01   4.22E+01   0.947      Eq. E7-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    3.88E+00    59.15   2.50E+01   8.18E+01   9.69E+01        |
| Min Buck    3.88E+00    72.59   2.32E+01   5.43E+01   8.99E+01        |
| Flexural       Ag       Fcr        Pn                                 |
| Tor Buck    3.88E+00   1.82E+01   7.05E+01                            |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   1.94E+01   0.000      Eq. G2-1      4     0.00 |
| Local-Y     0.00E+00   1.62E+01   0.000      Eq. G2-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.50E+00     1.00     1.20    12.00   3.24E+01            |
| Local-Y     1.25E+00     1.00     1.20    20.00   2.70E+01            |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   1.05E+02   0.000      Eq. F9-1      4     0.00 |
| Minor       0.00E+00   7.16E+01   0.000      Eq. F6-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       1.76E+02   0.00E+00                                       |
| Minor       1.20E+02   0.00E+00                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-LATERAL TORSIONAL BUCKLING                          |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   6.93E+02   0.000      Eq. F9-4      4     0.00 |
| Intermediate   Mn        Me        Cb      Lp       Lr       Lb       |
| Major       1.16E+03   0.00E+00    1.00     0.00     0.00    96.00    |
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 FLEXURE TENS/COMP INTERACTION                               |
|                       RATIO      CRITERIA    L/C     LOC              |
| Flexure Comp          0.947      Eq. H2-1      4     0.00             |
| Flexure Tens          0.000      Eq. H2-1      4     0.00             |
| Intermediate         frbw /     frbz /     fra /                      |
|                      Fcbw       Fcbz       Fca                        |
| Flexure Comp         0.00E+00   0.00E+00   1.03E+01                   |
|                      3.45E+01   3.45E+01   1.09E+01                   |
| Flexure Tens         0.00E+00   0.00E+00   0.00E+00                   |
|                      1.71E+01   3.45E+01   2.16E+01                   |
|-----------------------------------------------------------------------|