V. AISC 360-10 Pipe E.11

Verify the compressive strength of a pipe section braced at the midpoint in the Y-Y direction per the LRFD and ADS methods of the AISC 360-10 codes.

References

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.11, pp. E-54 - E-56

Details

From reference (2):

Select an ASTM A53 Grade B Pipe compression member with a length of 30 ft to support a dead load of 35 kips and live load of 105 kips in axial compression. The column is pin-connected at the ends in both axes and braced at the midpoint in the y-y direction.

Validation

Ultimate load:

P_{u} = 1.2 (35 kips) + 1.6 (105 kips) = 210 kips

Service load:

P_{a} = 35 kips + 105 kips = 140 kips

Per Table C-A-7.1 in Reference 1, K = 1.0 for pinned-pinned columns.

{(\frac{K L}{r})}_{x} = \frac{1.0 \times 30 \times 12}{3.68} = 97.8

{(\frac{K L}{r})}_{y} = \frac{1.0 \times 15 \times 12}{3.68} = 48.9

So buckling about the x-x axis governs. For 35 ksi, no pipe sections are slender per Table 4-6 in Reference 1.

{(\frac{K L}{r})}_{\max} = 97.8 < 4.71 \sqrt{\frac{E}{F_{y}}} = 4.71 \sqrt{\frac{29, 000}{35}} = 136

The critical stress

F_{e} = \frac{π^{2} E}{{(\frac{K L}{r})}^{2}} = \frac{π^{2} 29, 000}{{(97.8)}^{2}} = 29.9 ksi

(Eq. E3-4)

Nominal Compressive Strength

F_{c r} = ({0.658}^{F_{y} / F_{e}}) F_{y} = 0.804 [{0.658}^{35 / 29.9}] 35 = 21.4 ksi

(Eq E7-2)

P_{n} = F_{c r} A_{g} = 21.4 (11.5) = 246 kips

(Eq E7-1)

The available compressive strength:

LRFD: $ϕ_{c} P_{n} = 0.90 (246) = 221 kips$

ASD: $P_{n} / Ω_{c} = \frac{246}{1.67} = 147 kips$

Results

Result Type	Reference	STAAD.Pro	Difference	Comments
ϕ_cP_n (kips) [LRFD]	221	219	negligible
P_n/Ω_c (kips) [ASD]	147	145	negligible

STAAD.Pro Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC 360-10 Pipe E.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 05-Feb-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 30 0;
MEMBER INCIDENCES
1 1 2;
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_50_KSI
E 4.176e+06
POISSON 0.3
DENSITY 0.489024
ALPHA 6.5e-06
DAMP 0.03
TYPE STEEL
STRENGTH FY 7200 FU 8928 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
MEMBER PROPERTY AMERICAN
1 TABLE ST PIPS100
CONSTANTS
MATERIAL STEEL_36_KSI ALL
SUPPORTS
1 PINNED
2 FIXED BUT FY MX MZ
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
JOINT LOAD
2 FY -35
LOAD 2 LOADTYPE None  TITLE LOAD CASE 2
JOINT LOAD
2 FY -105
LOAD COMB 3 LRFD
1 1.2 2 1.6 
LOAD COMB 4 ASD
1 1.0 2 1.0 
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
UNIT INCHES KIP
LOAD LIST 3
PARAMETER 1
CODE AISC UNIFIED 2010
FU 60 ALL
FYLD 35 ALL
LY 180 ALL
METHOD LRFD
TRACK 2 ALL
CHECK CODE ALL
LOAD LIST 4
PARAMETER 2
CODE AISC UNIFIED 2010
FU 60 ALL
FYLD 35 ALL
LY 180 ALL
METHOD ASD
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD.Pro 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   PIPS100                  (AISC SECTIONS)
                           PASS   Eq. H1-1a            0.961         3
                      210.00 C          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     99.349  L/C  :     3                |
| Allowable Slenderness Ratio :    200.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      3    Ratio     :     0.961(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H1-1a                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   2.100E+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:   5.926E+00     Ayy:   5.926E+00     Cw:  0.000E+00              |
| Szz:   2.809E+01     Syy:   2.809E+01                                 |
| Izz:   1.510E+02     Iyy:   1.510E+02     Ix:  3.020E+02              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          35.000   Fu:          60.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:       360.000                                   |
| 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    31.62     N/A     91.14    T.B4.1(a)-9  |
|                Non-Slender    31.62     N/A     91.14    T.B4.1(a)-9  |
| Flexure     :  Compact        31.62    58.00   256.86    T.B4.1(b)-20 |
|                Compact        31.62    58.00   256.86    T.B4.1(b)-20 |
      STAAD SPACE                                              -- PAGE NO.    7
                       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   3.62E+02   0.000      Eq. D2-1      3     0.00 |
| Rupture     0.00E+00   5.18E+02   0.000      Eq. D2-2      3     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    2.10E+02   2.19E+02   0.961      Eq. E3-1      3     0.00 |
| Min Buck    2.10E+02   3.19E+02   0.658      Eq. E3-1      3     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.15E+01    99.35   2.11E+01   2.90E+01   2.43E+02        |
| Min Buck    1.15E+01    49.67   3.08E+01   1.16E+02   3.55E+02        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   1.09E+02   0.000      Eq. G6-1      3     0.00 |
| Local-Y     0.00E+00   1.09E+02   0.000      Eq. G6-1      3     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.15E+01     0.00     0.00     0.00   1.21E+02            |
| Local-Y     1.15E+01     0.00     0.00     0.00   1.21E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION                                                     |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             0.00E+00   1.09E+03   0.000      Eq. H3-1      3     0.00 |
| Intermediate Fcr        Tn                                            |
|             2.10E+01   1.22E+03                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   1.16E+03   0.000      Eq. F8-1      3     0.00 |
| Minor       0.00E+00   1.16E+03   0.000      Eq. F8-1      3     0.00 |
| Intermediate   Mn        My                                           |
| Major       1.29E+03   0.00E+00                                       |
| Minor       1.29E+03   0.00E+00                                       |
      STAAD SPACE                                              -- PAGE NO.    8
                       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          0.961      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         1.16E+03   0.00E+00   2.19E+02                   |
|                      1.16E+03   0.00E+00   2.10E+02                   |
| Flexure Tens         1.16E+03   0.00E+00   3.62E+02                   |
|                      1.16E+03   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|
    66. LOAD LIST 4
    67. PARAMETER 2
    68. CODE AISC UNIFIED 2010
    69. FU 60 ALL
    70. FYLD 35 ALL
    71. LY 180 ALL
    72. METHOD ASD
    73. TRACK 2 ALL
    74. CHECK CODE ALL
 STEEL DESIGN    
   WARNING: For member#      1 the profile has been selected from HSS Rect/Round (non A1085)/Pipe 
            tables of AISC database. Weld type is considered to be Elect-resist-weld.
            Thickness is already reduced from the table. Further reductions will not be done.
      STAAD SPACE                                              -- PAGE NO.    9
                       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   PIPS100                  (AISC SECTIONS)
                           PASS   Eq. H1-1a            0.963         4
                      140.00 C          0.00           0.00        0.00
|-----------------------------------------------------------------------|
| SLENDERNESS                                                           |
| Actual Slenderness Ratio    :     99.349  L/C  :     4                |
| Allowable Slenderness Ratio :    200.000  LOC  :     0.00             |
|-----------------------------------------------------------------------|
| STRENGTH CHECKS                                                       |
| Critical L/C  :      4    Ratio     :     0.963(PASS)                 |
|          Loc  :    0.00   Condition :   Eq. H1-1a                     |
|-----------------------------------------------------------------------|
| DESIGN FORCES                                                         |
| Fx:   1.400E+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:   5.926E+00     Ayy:   5.926E+00     Cw:  0.000E+00              |
| Szz:   2.809E+01     Syy:   2.809E+01                                 |
| Izz:   1.510E+02     Iyy:   1.510E+02     Ix:  3.020E+02              |
|-----------------------------------------------------------------------|
| MATERIAL PROPERTIES                                                   |
| Fyld:          35.000   Fu:          60.000                           |
|-----------------------------------------------------------------------|
| Actual Member Length:       360.000                                   |
| 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    31.62     N/A     91.14    T.B4.1(a)-9  |
|                Non-Slender    31.62     N/A     91.14    T.B4.1(a)-9  |
| Flexure     :  Compact        31.62    58.00   256.86    T.B4.1(b)-20 |
|                Compact        31.62    58.00   256.86    T.B4.1(b)-20 |
      STAAD SPACE                                              -- PAGE NO.   10
                       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   2.41E+02   0.000      Eq. D2-1      4     0.00 |
| Rupture     0.00E+00   3.45E+02   0.000      Eq. D2-2      4     0.00 |
|-----------------------------------------------------------------------|
| CHECK FOR AXIAL COMPRESSION                                           |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Maj Buck    1.40E+02   1.45E+02   0.963      Eq. E3-1      4     0.00 |
| Min Buck    1.40E+02   2.12E+02   0.659      Eq. E3-1      4     0.00 |
| Intermediate                                                          |
| Results     Eff Area     KL/r      Fcr        Fe         Pn           |
| Maj Buck    1.15E+01    99.35   2.11E+01   2.90E+01   2.43E+02        |
| Min Buck    1.15E+01    49.67   3.08E+01   1.16E+02   3.55E+02        |
|-----------------------------------------------------------------------|
| CHECK FOR SHEAR                                                       |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Local-Z     0.00E+00   7.23E+01   0.000      Eq. G6-1      4     0.00 |
| Local-Y     0.00E+00   7.23E+01   0.000      Eq. G6-1      4     0.00 |
| Intermediate                                                          |
| Results        Aw        Cv       Kv      h/tw      Vn                |
| Local-Z     1.15E+01     0.00     0.00     0.00   1.21E+02            |
| Local-Y     1.15E+01     0.00     0.00     0.00   1.21E+02            |
|-----------------------------------------------------------------------|
| CHECK FOR TORSION                                                     |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
|             0.00E+00   7.28E+02   0.000      Eq. H3-1      4     0.00 |
| Intermediate Fcr        Tn                                            |
|             2.10E+01   1.22E+03                                       |
|-----------------------------------------------------------------------|
| CHECK FOR BENDING-YIELDING                                            |
|                                                                       |
|              FORCE     CAPACITY   RATIO      CRITERIA     L/C    LOC  |
| Major       0.00E+00   7.73E+02   0.000      Eq. F8-1      4     0.00 |
| Minor       0.00E+00   7.73E+02   0.000      Eq. F8-1      4     0.00 |
| Intermediate   Mn        My                                           |
| Major       1.29E+03   0.00E+00                                       |
| Minor       1.29E+03   0.00E+00                                       |
      STAAD SPACE                                              -- PAGE NO.   11
                       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          0.963      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         7.73E+02   0.00E+00   1.45E+02                   |
|                      7.73E+02   0.00E+00   1.40E+02                   |
| Flexure Tens         7.73E+02   0.00E+00   2.41E+02                   |
|                      7.73E+02   0.00E+00   0.00E+00                   |
|-----------------------------------------------------------------------|