# V. AISC N690 1984 W Shaped

Verify the design of a wide-flange section used for a cantilever beam using the AISC N690 1984 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

Allowable Bending Stress About Major Axis (Z Axis)

bf/2tf = 6.862 < 65/√(Fy)

Thus, allowable bending tensile stress = Fbtz = 0.66×Fy = 23.76 ksi

Actual bending stress About Major Axis

fbtz = MzD / 2×Iz = 23.2 ksi

Stress ratio = 23.2 ksi / 23.76 kis = 0.975

Shear

Allowable Shear Stress

Fv = 0.4×Fy = 14.4 ksi

Actual Shear Stress

Vy = D×tw = 4.8 in2

fv = Fy/Vy = 2.6 ksi

Stress ratio = fv/Fv = 0.18

## Results

Table 1. Comparison of results
Slenderness ratio 76.68 76.68 none
Allowable bending stress (ksi) 23.8 23.8 none
Actual bending stress (ksi) 23.2 23.2 none
Critical stress ratio 0.975 0.975 none
Allowable shear stress (ksi) 14.4 14.4 none
Actual shear stress (ksi) 2.60 2.56 1.5%
Shear stress ratio 0.180 0.178 1.1%

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\N690\1984\AISC N690 1984 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
2 FY 12.5
PERFORM ANALYSIS
UNIT INCHES KIP
PARAMETER 1
CODE AISC N690 1984
MAIN 2 ALL
FYLD 36 ALL
UNB 72 ALL
UNT 72 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
``````

```                       STAAD.PRO CODE CHECKING - (  AISC N690 1984)   v1.0
********************************************
ALL UNITS ARE - KIP  INCH (UNLESS OTHERWISE Noted)
FX            MY             MZ       LOCATION
=======================================================================
1  ST   W16X40                   (AISC SECTIONS)
PASS      Q1.6-Eqn 2        0.975         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: 2.38E+01  FCY: 2.70E+01  FTZ: 2.38E+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                                                |
|-----------------------------------------------------------------------------|
| CRITICAL LOADS FOR EACH CLAUSE CHECK (UNITS KIP -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    0.975    1    0.00E+00       -         -    1.50E+03 0.00E+00  |
| TEN&BEND     0.000    1    0.00E+00       -         -    1.50E+03 0.00E+00  |
| SHEAR-Y      0.178    1        -     1.25E+01       -         -         -   |
| SHEAR-Z      0.000    1        -          -    0.00E+00       -         -   |
|-----------------------------------------------------------------------------|
```