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V. ASME NF 3000 1998 Tee

Verify the design of a pipe section used for a beam member per the ASME NF 3000 1998 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

Results

Table 1. Comparison of 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\ASME\NF 3000-1998\ASME NF 3000 1998 Tee.std is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 03-Aug-18
END JOB INFORMATION
SET SHEAR
INPUT WIDTH 79
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 NF3000 1998
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
TRACK 2 ALL
CHECK CODE ALL
FINISH

STAAD Output

                       STAAD.PRO CODE CHECKING - (  ASME NF3000-98)   v2.0
                       ********************************************
 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      NF-98-EQN-22      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: 2.16E+04  FTZ: 2.16E+04  FTY: 2.16E+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  KS:1.000  KV:1.000  KBK:1.000                 |
 |-----------------------------------------------------------------------------|
 | CRITICAL LOADS FOR EACH CLAUSE CHECK (UNITS POUN-INCH)                      |
 | CLAUSE       RATIO  LOAD       FX        VY        VZ        MZ        MY   |
 | TENSION      0.000    0    0.00E+00       -         -         -         -   |
 | COMPRESSION  0.000    0    0.00E+00       -         -         -         -   |
 | COMP&BEND    1.620    1    0.00E+00       -         -    1.92E+06 0.00E+00  |
 | TEN&BEND     0.000    0    0.00E+00       -         -    0.00E+00 0.00E+00  |
 | SHEAR-Y      0.403    1        -     6.20E+04       -         -         -   |
 | SHEAR-Z      0.000    0        -          -    0.00E+00       -         -   |
 |-----------------------------------------------------------------------------|