V. AISC N690 1984 Tee
Verify the design of a pipe section used for a beam member per the AISC N690 1984 code.
Details
A cantilever beam is 60 in long. The beam is loaded at the free end with a 2 kip load and a uniform load of 1 kip/in along the entire length.
The member is a WT18x67.5 section with Grade A36 steel.
Validation
Maximum shear force (at support) = V = wL + P = (1 kip/in) × 60 in + 2 kip = 62 kips
Maximum moment (at support) = M = 0.5×w×L2 + P×L = 0.5 (1 kip/in)×(60 in)2 + (2 kip)×(60 in) = 1,920 in·kips
Slenderness Ratio
Slenderness Ratio along Z-Axis = (KL/r)z = 21.22
Slenderness Ratio along Y-Axis = (KL/r)y = 50.53
Maximum Slenderness Ratio = 50.53 < 300
Bending
Allowable Bending Stress About Major Axis (Z Axis)
bf/2tf = 4.65 > 65/√(FY) = 10.833
d/tw = 28.3 < 640/√(FY) = 106.67
Thus allowable bending stress is obtained by treating the section as compact.
Fb = 0.66×FY = 23.8 ksi
Actual Bending Stress
Bending Tensile Stress = fbtz =(Mz/Iz)×Ybar = 14.93 ksi < 23.8 ksi
Bending Compressive Stress = fbcz = 38.7 ksi > 23.8 ksi
Critical stress ratio = 38.7 ksi / 23.8 ksi = 1.626
Shear
Allowable Shear Stress
a = clear distance between transverse stiffeners (here taken as length) = 60 in
h = clear distance flanges of the girder = D-tf = 17.01 in
Thus, a/h = 3.527 Therefore, k = 5.34 + [4.00/ (a/h)2] = 5.65
t = tw = 0.44 inch
If Cv > 0.8, Cv = [190/(h/t)]√(k/Sy)= 78.4 which is true. Thus, the value of Cv is taken as 78.4
Allowable shear stress = Fv = (FY/2.89)Cv ≤ 0.4Fy = 14.4 ksi
Hence allowable shear =14.4ksi
Actual Shear
Vy = Dtw = 10.68 in2
fv = Fy/Vy = 5.805 ksi
Stress ratio = fv/Fv = 0.403
Allowable bending stress about minor axis, fbtz = 0.75×Fy = 27 ksi
Results
| Parameter | Hand Calculation | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Slenderness ratio | 50.53 | 50.53 | none | |
| Allowable bending stress (ksi) | 23.8 | 23.8 | none | |
| Actual bending stress (ksi) | 38.7 | 38.5 | 0.5% | |
| Critical shear ratio | 1.626 | 1.620 | 0.4% | |
| Allowable shear stress (ksi) | 14.4 | 14.4 | none | |
| Actual shear stress (ksi) | 5.81 | 5.81 | none | |
| Shear stress ratio | 0.403 | 0.403 | none |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\AISC N690 1984 Tee.std is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 03-Aug-18
END JOB INFORMATION
INPUT WIDTH 79
SET SHEAR
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 60 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.9e+007
POISSON 0.3
DENSITY 0.283
ALPHA 1.2e-005
DAMP 0.03
TYPE STEEL
STRENGTH FY 36000 FU 58000 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 TABLE T W36X135
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE Dead TITLE LOAD CASE 1
MEMBER LOAD
1 CON GY -2000 60
1 UNI GY -1000 0 60
PERFORM ANALYSIS
PARAMETER 1
CODE AISC N690 1984
CMY 1 ALL
CMZ 1 ALL
CT 0.85 ALL
FU 58000 ALL
FYLD 36000 ALL
KY 2 ALL
KZ 2 ALL
UNT 60 ALL
UNB 60 ALL
MAIN 200 ALL
NSF 0.9 ALL
RATIO 1 ALL
TMAIN 300 ALL
STYPE 0 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD Output
STAAD.PRO CODE CHECKING - ( AISC N690 1984) v1.0 ******************************************** ALL UNITS ARE - POUN INCH (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= * 1 T W36X135 (AISC SECTIONS) FAIL Q1.6-Eqn 2 1.620 1 0.00 T 0.00 1919999.75 0.00 |-----------------------------------------------------------------------------| | SLENDERNESS CHECK: ACTUAL RATIO: 50.53 ALLOWABLE RATIO: 300.00 | | ALLOWABLE STRESSES: (UNIT - POUN INCH) | | AXIAL: 1.16E+04 FCZ: 2.38E+04 FCY: 2.70E+04 FTZ: 2.38E+04 FTY: 2.70E+04 | | SHEAR: 1.44E+04 | | ACTUAL STRESSES: (UNIT - POUN INCH) | | AXIAL: 0.00E+00 FBZ: 3.85E+04 FBY: 0.00E+00 SHEAR: 5.81E+03 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES: (UNIT - INCH) | | AXX: 19.95 AYY: 10.68 AZZ: 9.48 RZZ: 5.66 RYY: 2.37 | | SZZ: 49.69 SYY: 18.75 | |-----------------------------------------------------------------------------| | PARAMETER: (UNIT - POUN INCH) | | KL/R-Z: 21.22 KL/R-Y: 50.53 UNL: 60.0 CMZ: 1.00 CMY: 1.00 | | CB: 1.00 FYLD: 36000.00 FU: 58000.00 NET SECTION FACTOR: 0.90 | | CT: 0.85 STEEL TYPE: 0.0 | |-----------------------------------------------------------------------------| | CRITICAL LOADS FOR EACH CLAUSE CHECK (UNITS POUN-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 1.620 1 0.00E+00 - - 1.92E+06 0.00E+00 | | TEN&BEND 0.000 1 0.00E+00 - - 1.92E+06 0.00E+00 | | SHEAR-Y 0.403 1 - 6.20E+04 - - - | | SHEAR-Z 0.000 1 - - 0.00E+00 - - | |-----------------------------------------------------------------------------|