V. AISC N690 1984 W Shaped
Verify the design of a wide-flange section used for a cantilever beam using the AISC N690 1984 code.
Details
The beam is a 10 ft cantilever with a 12.5 kip concentrated load at the free end.
The member is a W16X40 section with Grade A36 steel.
Validation
Maximum shear force (constant shear): V = 12.5 kips
Maximum moment (at fixed end): M = 12.5 kips × 120 in = 1,500 in·kips
Slenderness Ratio
(KL/r)z = Slenderness Ratio along Z-Axis = 18.11
(KL/r)y = Slenderness Ratio along Y-Axis = 76.68
Maximum Slenderness Ratio = 76.68 < 240 (Hence OK)
Bending
Allowable Bending Stress About Major Axis (Z Axis)
bf/2tf = 6.862 < 65/√(Fy)
Thus, allowable bending tensile stress = Fbtz = 0.66×Fy = 23.76 ksi
Actual bending stress About Major Axis
fbtz = MzD / 2×Iz = 23.2 ksi
Stress ratio = 23.2 ksi / 23.76 kis = 0.975
Shear
Allowable Shear Stress
Fv = 0.4×Fy = 14.4 ksi
Actual Shear Stress
Vy = D×tw = 4.8 in2
fv = Fy/Vy = 2.6 ksi
Stress ratio = fv/Fv = 0.18
Results
| Parameter | Hand Calculation | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Slenderness ratio | 76.68 | 76.68 | none | |
| Allowable bending stress (ksi) | 23.8 | 23.8 | none | |
| Actual bending stress (ksi) | 23.2 | 23.2 | none | |
| Critical stress ratio | 0.975 | 0.975 | none | |
| Allowable shear stress (ksi) | 14.4 | 14.4 | none | |
| Actual shear stress (ksi) | 2.60 | 2.56 | 1.5% | |
| Shear stress ratio | 0.180 | 0.178 | 1.1% |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC N690 1984 W Shaped.std is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 18-Jun-18
END JOB INFORMATION
SET SHEAR
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 10 0 0;
MEMBER INCIDENCES
1 1 2;
MEMBER PROPERTY AMERICAN
1 TABLE ST W16X40
UNIT INCHES KIP
DEFINE MATERIAL START
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
END DEFINE MATERIAL
UNIT FEET KIP
CONSTANTS
MATERIAL STEEL_36_KSI ALL
SUPPORTS
1 FIXED
LOAD 1
JOINT LOAD
2 FY 12.5
PERFORM ANALYSIS
UNIT INCHES KIP
PARAMETER 1
CODE AISC N690 1984
MAIN 2 ALL
FYLD 36 ALL
UNB 72 ALL
UNT 72 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD Output
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 W16X40 (AISC SECTIONS) PASS Q1.6-Eqn 2 0.975 1 0.00 T 0.00 -1500.00 0.00 |-----------------------------------------------------------------------------| | SLENDERNESS CHECK: ACTUAL RATIO: 76.68 ALLOWABLE RATIO: 240.00 | | ALLOWABLE STRESSES: (UNIT - KIP INCH) | | AXIAL: 1.49E+01 FCZ: 2.38E+01 FCY: 2.70E+01 FTZ: 2.38E+01 FTY: 2.70E+01 | | SHEAR: 1.44E+01 | | ACTUAL STRESSES: (UNIT - KIP INCH) | | AXIAL: 0.00E+00 FBZ: 2.32E+01 FBY: 0.00E+00 SHEAR: 2.56E+00 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES: (UNIT - INCH) | | AXX: 11.80 AYY: 4.88 AZZ: 7.07 RZZ: 6.63 RYY: 1.56 | | SZZ: 64.75 SYY: 8.26 | |-----------------------------------------------------------------------------| | PARAMETER: (UNIT - KIP INCH) | | KL/R-Z: 18.11 KL/R-Y: 76.68 UNL: 72.0 CMZ: 0.85 CMY: 0.85 | | CB: 1.00 FYLD: 36.00 FU: 58.02 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 0.000 1 0.00E+00 - - - - | | COMPRESSION 0.000 1 0.00E+00 - - - - | | COMP&BEND 0.975 1 0.00E+00 - - 1.50E+03 0.00E+00 | | TEN&BEND 0.000 1 0.00E+00 - - 1.50E+03 0.00E+00 | | SHEAR-Y 0.178 1 - 1.25E+01 - - - | | SHEAR-Z 0.000 1 - - 0.00E+00 - - | |-----------------------------------------------------------------------------|