 # V. AISC N690 1984 Pipe Section With SLC

Verify the design of a pipe section used for a beam member per the AISC N690 1984 code.

## References

Gere, J. M. and S. P. Timoshenko. 1984. Mechanics of Materials, 2nd Edition. Boston, MA: PWS Publishers. p.238.

## Details

The 10 ft long span is a propped cantilever which is free to move axially at the fixed end. The beam is subject to the following four different load cases:
1. a 10 kip axial tension force,
2. a 10 kip axial compression force,
3. a uniformly distributed load of 0.3 kip/ft in the Global Y and Z directions, the member selfweight (acts in Global Y), and the tension load from case 1
4. a uniformly distributed load of 0.3 kip/ft in the Global Y and Z directions, the member selfweight (acts in Global Y), and the compression load from case 2

The member is Pipe 5-Sched. 40 (standard) pipe section with Grade A36 steel. The self-weight is 14.6 lbs/ft.

## Validation

Slenderness Ratio

The slenderness ratio is the same about either local z or y axes: KL/r = 120 in / 1.888 in = 63.56 < 300, OK

Axial Tension

From section Q1.5.1.1, the allowable tensile stress:

The actual tensile stress from load case 1:

Stress ratio = 2.49 / 21.6 = 0.115, hence OK.

Axial Compression

Allowable compressive stress per Cl Q1.9.2.3:

$OD t = 5.56 0.24 = 23.17 < 3,300 F y = 3,300 36 = 91.67$
$C c = 2 π 2 E F y = 126.1$

Since Kl/r < Cc, per eq. Q1.5-1, the allowable axial compressive stress:

The actual compressive stress from load case 2:

Stress ratio = 2.49 / 17.08 = 0.146, hence OK.

Bending

Section is compact per Cl Q1.5.1.4.1: $O D t = 23.17 < 3,300 F y = 91.67$

Allowable bending stress about both axes: Fb = 0.66×Fy = 23.76 ksi

Moment due to load case 3 or 4 on a propped cantilever (ref. AISC Steel Construction Manual):

Actual bending stress about the major axis:

Actual bending stress about the minor axis:

Stress ratio: 9.17 / 23.76 = 0.386, hence OK.

Combined Bending and Axial Tension

Interaction per Cl Q1.6.2 in load case 3 (tension + bending):

 $f a SFT × 0.6 F y + f b y SMY × F b y + f b z SMZ × F b z = 2.49 1.3 × 21.6 + 8.75 1.4 × 23.76 + 9.17 1.4 × 23.76 = 0.627$ (Eq. Q1.6-1b)

Combined Bending and Axial Compression

Interaction per Cl Q1.6 in load case 4 (compression + bending):

 $f a F a = 0.145 < 0.15$ (Eq. Q1.6-2)
$f a SFC × F a + f b y SMY × F b y + f b z SMZ × F b z = 2.49 1.3 × 17.08 + 8.75 1.4 × 23.76 + 9.17 1.4 × 23.76 = 0.651$

Shear

Actual shear (at supports):

Shear area (calculated as per Gere & Timoshenko reference):

$A z = π 4 r 2 4 - r 1 4 × 2 r 2 - r 1 2 3 r 2 3 - r 2 3$
where
 $r 1$ = the inner radius of the pipe = 5.56 / 2 - 0.24 = 2.54 in $r 2$ = the outer radius of the pipe = 5.56 / 2 = 2.78 in

Thus, the shear area along both axes = 2.008 in2.

The allowable shear stress:

Stress ratio in Y (minor axis): 0.98/14.4 = 0.068, hence OK.

Stress ratio in Z (major axis): 0.94/14.4 = 0.065, hence OK.

## Results

Table 1. Comparison of results
Slenderness ratio 63.56 63.55 negligible
Actual axial tensile stress (ksi) 2.49 2.49 none
Allowable axial tensile stress 21.6 21.6 none
Tensile stress ratio (LC1) 0.115 0.115 none
Actual axial compressive stress (ksi) 2.49 2.49 none
Allowable axial compressive stress 17.08 17.1 negligible
Compressive stress ratio (LC2) 0.146 0.146 none
Allowable bending stress (ksi) 23.76 23.8 negligible
Actual bending stress (ksi) 9.17 9.15 negligible
Combined axial tension and bending stress ratio (LC3) 0.627 0.625 negligible
Combined axial compression and bending stress ratio (LC4) 0.651 0.649 negligible
Allowable shear stress (ksi) 14.4 14.4 none
Actual shear stress (ksi) 0.98 0.97 negligible
Shear stress ratio in major axis 0.065 0.064 negligible
Shear stress ratio in minor axis 0.068 0.067 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC N690 1984 Pipe Section With SLC.std is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 05-Apr-19
END JOB INFORMATION
INPUT WIDTH 79
SET SHEAR
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 10 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 4.176e+006
POISSON 0.3
DENSITY 0.489024
ALPHA 1.2e-005
DAMP 0.03
END DEFINE MATERIAL
UNIT INCHES KIP
MEMBER PROPERTY AMERICAN
1 TABLE ST PIPS50
UNIT FEET KIP
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX
2 FX 10
2 FX -10
SELFWEIGHT Y -1
1 UNI GY -0.3
2 FX 10
1 UNI GZ 0.3
SELFWEIGHT Y -1
1 UNI GY -0.3
2 FX -10
1 UNI GZ 0.3
PRINT MEMBER PROPERTIES ALL
UNIT INCHES KIP
PARAMETER 1
CODE AISC N690 1984
CB 1 ALL
CMY 1 ALL
CMZ 1 ALL
FYLD 36 ALL
FU 58 ALL
KY 1 ALL
KZ 1 ALL
MAIN 200 ALL
NSF 1 ALL
RATIO 1 ALL
SMZ 1.4 ALL
SMY 1.4 ALL
SFT 1.3 ALL
SFC 1.3 ALL
TMAIN 300 ALL
TRACK 2 ALL
UNB 30 ALL
UNT 30 ALL
CT 0.75 ALL
CHECK CODE ALL
FINISH


      STAAD SPACE                                              -- PAGE NO.    6
STAAD.PRO CODE CHECKING - (  AISC N690 1984)   v1.0
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1  ST   PIPS50                   (AISC SECTIONS)
PASS      Q1.6-Eqn 2        0.651         4
10.00 C         45.00          47.04      120.00
|-----------------------------------------------------------------------------|
| SLENDERNESS CHECK:    ACTUAL RATIO:  63.55 ALLOWABLE RATIO: 200.00          |
| ALLOWABLE STRESSES:   (UNIT - KIP  INCH)                                    |
| AXIAL: 1.71E+01  FCZ: 2.38E+01  FCY: 2.38E+01  FTZ: 2.38E+01  FTY: 2.38E+01 |
| SHEAR: 1.44E+01                                                             |
| ACTUAL STRESSES: (UNIT - KIP  INCH)                                         |
| AXIAL: 2.49E+00  FBZ: 9.15E+00  FBY: 8.75E+00 SHEAR: 9.72E-01               |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES: (UNIT - INCH)                                           |
| AXX:   4.01  AYY:   2.10  AZZ:   2.10  RZZ:  1.89  RYY:  1.89               |
| SZZ:       5.14  SYY:       5.14                                            |
|-----------------------------------------------------------------------------|
| PARAMETER: (UNIT - KIP  INCH)                                               |
| KL/R-Z: 63.55   KL/R-Y: 63.55   UNL:   30.0   CMZ:  1.00   CMY:  1.00       |
| CB: 1.00   FYLD:    36.00   FU:    58.00   NET SECTION FACTOR: 1.00         |
| CT:  0.75   STEEL TYPE:  0.0                                                |
|-----------------------------------------------------------------------------|
| CRITICAL LOADS FOR EACH CLAUSE CHECK (UNITS KIP -INCH)                      |
| CLAUSE       RATIO  LOAD       FX        VY        VZ        MZ        MY   |
| TENSION      0.115    1    1.00E+01       -         -         -         -   |
| COMPRESSION  0.146    2    1.00E+01       -         -         -         -   |
| COMP&BEND    0.651    4    1.00E+01       -         -    4.70E+01 4.50E+01  |
| TEN&BEND     0.627    3    1.00E+01       -         -    4.70E+01 4.50E+01  |
| SHEAR-Y      0.067    3        -     1.96E+00       -         -         -   |
| SHEAR-Z      0.065    3        -          -    1.88E+00       -         -   |
|-----------------------------------------------------------------------------|