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
- a 10 kip axial tension force,
- a 10 kip axial compression force,
- 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
- 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:
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:
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):
(Eq. Q1.6-1b) |
Combined Bending and Axial Compression
Interaction per Cl Q1.6 in load case 4 (compression + bending):
(Eq. Q1.6-2) |
Shear
Actual shear (at supports):
Shear area (calculated as per Gere & Timoshenko reference):
where= | ||
= |
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
Parameter | Hand Calculation | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
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 |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\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
LOAD 1 TENSION ONLY
JOINT LOAD
2 FX 10
LOAD 2 COMPRESSION ONLY
JOINT LOAD
2 FX -10
LOAD 3 TENSION+BENDING
SELFWEIGHT Y -1
MEMBER LOAD
1 UNI GY -0.3
JOINT LOAD
2 FX 10
MEMBER LOAD
1 UNI GZ 0.3
LOAD 4 COMPRESSION+BENDING
SELFWEIGHT Y -1
MEMBER LOAD
1 UNI GY -0.3
JOINT LOAD
2 FX -10
MEMBER LOAD
1 UNI GZ 0.3
PERFORM ANALYSIS PRINT LOAD DATA
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 Output
STAAD SPACE -- PAGE NO. 6 STAAD.PRO CODE CHECKING - ( AISC N690 1984) v1.0 ******************************************** ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ 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: 2.02 AZZ: 2.02 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 - - | |-----------------------------------------------------------------------------|