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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

Table 1. Verification comparison for AISC_N690_1984_Tee
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\N690\1984\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:   9.61  AZZ:   6.32  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       -         -   |
 |-----------------------------------------------------------------------------|