V. ASME NF 3000 1977 Channel

Verify the design of channel section used for a beam member using the ASME NF 3000 1977 code.

Details

The beam is a propped cantilever 80 inches long. The beam is loaded with a 2 kip concentrated load at midspan and a uniformly distributed load of 1 kip/in over the entire length.

The member is C15x50 channel section with Grade A36 steel.

Validation

Maximum shear force (at fixed end): V = 51.375 kips (taken from STAAD.Pro analysis)

Maximum moment (at fixed end): M = 830.0 in-kip (taken from STAAD.Pro analysis)

Slenderness Ratio

About z-axis: (KL/r)_z = 0.85(80 in)/(5.25 in) = 12.95

About y-axis: (KL/r)_y = 0.85(80 in)/(0.865 in) = 78.61

Max. slenderness ratio < 300, OK.

Bending About Major Axis (Z Axis)

\frac{b_{f}}{t_{f}} = 4.62 < \frac{65}{\sqrt{F_{y}}} = 10.83

The laterally unsupported length of the compression flange, $L_{b} = 80 < \frac{76 b_{f}}{\sqrt{F_{y}}} = 120$

and $< \frac{20, 000}{(d / A_{f}) F_{y}} = 89.56$

As b_f/t_f is not in the range of 65/√(Fy) and 95/√(Fy) , the value of allowable bending compressive and tensile stress = F_bty = F_bcy = 0.6×F_y = 21.6 ksi

Actual bending stress:

Bending Tensile Stress = bending compressive stress = f_btz = f_bcz= MzD / (2I_z) = 15.4 ksi

830.0 (15.0) / (2 × 404) = 15.41 ksi

Critical ratio = 15.41 ksi / 21.6 ksi = 0.713

Shear

Actual shear:

F_y = 51.375 kips

V_y = D×t_w = 10.8 in²

fv,y = Fy/Vy = 4.76 ksi

Allowable shear:

a = clear distance between transverse stiffeners (here taken as length) = 80 in

h = clear distance flanges of the girder = D-2t_f = 14.35 in

Thus, a/h = 5.57, Therefore, k = 5.34 + [4.00/ (a/h)²] = 5.46

t = t_w = 0.72 inch

Cv =17.2

F_v = (F_y/2.89)C_v ≥ 0.4×F_y = 14.4 ksi

Hence allowable=14.4 ksi

Therefore, Ratio = f_v/F_v = 0.330

Results

Table 1. Comparison of results
Parameter	Hand Calculation	STAAD.Pro	Difference
Slenderness ratio	78.61	78.61	none
Allowable bending stress (ksi)	21.6	21.6	none
Actual bending stress (ksi)	15.4	15.4	none
Critical ratio	0.713	0.713	none
Allowable shear stress (ksi)	14.4	14.4	none
Actual shear stress (ksi)	4.76	4.78	0.4%

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\ASME\ASME NF 3000 1977 Channel.std is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 10-Aug-18
END JOB INFORMATION
SET SHEAR
INPUT WIDTH 79
UNIT INCHES POUND
JOINT COORDINATES
1 0 0 0; 2 80 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 ST C15X50
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
2 PINNED
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
MEMBER LOAD
1 CON GY -2000 40
1 UNI GY -1000 0 80
PERFORM ANALYSIS
PARAMETER 1
CODE NF3000 1977
CMY 1 ALL
CMZ 1 ALL
FU 58000 ALL
FYLD 36000 ALL
KY 0.85 ALL
KZ 0.85 ALL
UNT 80 ALL
UNB 80 ALL
MAIN 200 ALL
NSF 0.9 ALL
RATIO 1 ALL
TMAIN 300 ALL
TRACK 2 ALL
CHECK CODE ALL
PRINT ANALYSIS RESULTS
FINISH

STAAD Output

                       STAAD.PRO CODE CHECKING - (  ASME NF3000-77)   v2.0
                       ********************************************
 ALL UNITS ARE - POUN INCH (UNLESS OTHERWISE Noted)
 MEMBER     TABLE       RESULT/   CRITICAL COND/     RATIO/     LOADING/
                          FX            MY             MZ       LOCATION
 =======================================================================
      1  ST   C15X50                   (AISC SECTIONS)
                           PASS      NF-77-EQN-21      0.713         1
                        0.00 T          0.00      829999.94        0.00
 |-----------------------------------------------------------------------------|
 | SLENDERNESS CHECK:    ACTUAL RATIO:  78.61 ALLOWABLE RATIO: 300.00          |
 | ALLOWABLE STRESSES:   (UNIT - POUN INCH)                                    |
 | AXIAL: 1.55E+04  FCZ: 2.16E+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: 1.54E+04  FBY: 0.00E+00 SHEAR: 4.78E+03               |
 |-----------------------------------------------------------------------------|
 | SECTION PROPERTIES: (UNIT - INCH)                                           |
 | AXX:  14.70  AYY:  10.74  AZZ:   3.22  RZZ:  5.24  RYY:  0.87               |
 | SZZ:      53.87  SYY:       3.77                                            |
 |-----------------------------------------------------------------------------|
 | PARAMETER: (UNIT - POUN INCH)                                               |
 | KL/R-Z: 12.97   KL/R-Y: 78.61   UNL:   80.0   CMZ:  1.00   CMY:  1.00       |
 | CB: 1.00   FYLD: 36000.00   FU: 58000.00   NET SECTION FACTOR: 0.90         |
 | 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    0.713    1    0.00E+00       -         -    8.30E+05 0.00E+00  |
 | TEN&BEND     0.000    0    0.00E+00       -         -    0.00E+00 0.00E+00  |
 | SHEAR-Y      0.332    1        -     5.14E+04       -         -         -   |
 | SHEAR-Z      0.000    0        -          -    0.00E+00       -         -   |
 |-----------------------------------------------------------------------------|