V. ASME NF 3000 1989 WShaped

Verify the design of a wide-flange section used for a cantilever beam using the ASME NF 3000 1989 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 about Major Axis (Z Axis)

Allowable Bending Stress

b_f/2t_f = 6.862 < 65/(Fy)^0.5 [Ref. NF3322.1(d)(2)]

Thus, allowable bending tensile stress = F_btz = Fy×[0.79-0.002×(b_f/2t_f)×√Fy] = 25.47 ksi

Actual Bending Stress

Bending Tensile Stress = Bending Compressive Stress = f_btz = f_bcz = M_zD/2I_z = 23.17 ksi

Stress ratio = 23.16 ksi / 25.47 ksi = 0.909

Shear

Allowable Shear Stress

a = clear distance between transverse stiffeners (here taken as length) = 120 in

h = clear distance flanges of the girder = D-2t_f = 14.91 in

Thus, a/h = 8.05, Therefore, k = 5.34 + [4.00/ (a/h)²] = 5.36 [Ref. NF3322.6(e)(2) ]

t = t_w = 0.3 inch

Cv =1.475

Allowable shear stress = Fv = (Fy/2.89)Cv = > 0.4Fy = 14.4 ksi Hence allowable=14.4ksi

Actual Shear Stress

Fy = 12.5 kip, Vy = Dt_w = 4.8 inch²

fv = Fy/Vy = 2.6 ksi

Stress ratio = fv/Fv = 0.18

Results

Table 1. Comparison of results
Parameter	Hand Calculation	STAAD.Pro	Difference
Slenderness ratio	76.68	76.68	none
Allowable bending stress (ksi)	25.47	25.4	0.3%
Actual bending stress (ksi)	23.2	23.2	none
Critical stress ratio	0.909	0.910	negligible
Allowable shear stress (ksi)	14.4	14.4	none
Actual shear stress (ksi)	2.6	2.56	1.5%
Shear stress ratio	0.18	0.178	1.1%

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\ASME\ASME NF 3000 1989 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 NF3000 1989
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 - (  ASME NF3000-89)   v2.0
                       ********************************************
 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      NF-89-Eqn-22      0.910         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: 2.54E+01  FCY: 2.70E+01  FTZ: 2.54E+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:   4.71  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  KS:1.000  KV:1.000  KBK:1.000                 |
 |-----------------------------------------------------------------------------|
 | CRITICAL LOADS FOR EACH CLAUSE CHECK (UNITS KIP -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    0.910    1    0.00E+00       -         -    1.50E+03 0.00E+00  |
 | TEN&BEND     0.000    0    0.00E+00       -         -    0.00E+00 0.00E+00  |
 | SHEAR-Y      0.178    1        -     1.25E+01       -         -         -   |
 | SHEAR-Z      0.000    0        -          -    0.00E+00       -         -   |
 |-----------------------------------------------------------------------------|