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V. AISC N690 1994 W Shaped

Verify the design of a wide-flange section used for a cantilever beam using the AISC N690 1994 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

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

h = clear distance flanges of the girder = D-2tf = 14.91 inch

Thus, a/h = 8.05, Therefore, k = 5.34 + [4.00/ (a/h)2] = 5.36

t = tw = 0.3 inch

Cv =1.475

Fv = (Fy/2.89)Cv ≥ 0.4×Fy = 14.4 ksi Hence allowable=14.4ksi

Actual Shear Stress

STAAD.Pro calculates the shear are based on the general shear stress equation, τ = V×Q/(I×t) from Timoshenko. Thus the shear area, Ay = I×t/Q = 4.401 in2

fv = Fy/Ay = 12.5 kip / 4.401 = 2.84 ksi

Stress ratio = fv/Fv = 0.18

Results

Table 1. Comparison of results
Parameter Hand Calculation STAAD.Pro Difference Comments
Slenderness ratio 76.68 76.68 none  
Allowable bending stress (ksi) 23.76 23.76 none  
Actual bending stress (ksi) 23.17 23.17 none
Critical stress ratio 0.975 0.975 none
Allowable shear stress (ksi) 14.4 14.4 none
Actual shear stress (ksi) 2.84 2.84 none

STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\US\AISC\N690\1994\AISC N690 1994 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 AISC N690 1994
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 - (  ANSI N690-1994)   v1.0
                       ********************************************
  |--------------------------------------------------------------------------|
  |                                                    Y        PROPERTIES   |
  |*************                                       |        IN INCH UNIT |
  |            *  |=============================|   ===|===     ------------ |
  |MEMBER   1  *  |  AISC SECTIONS              |      |        AX =  11.80  |
  |            *  | ST  W16X40                  |      |   --Z  AY =   4.39  |
  |DESIGN CODE *  |                             |      |        AZ =   4.73  |
  |ANSI N690-94*  ===============================   ===|===     SY =   8.26  |
  |            *                                                SZ =  64.75  |
  |            *  |&lt;---LENGTH (FT)=   10.00 --->|               RY =   1.56  |
  |*************                                                RZ =   6.63  |
  |                                                                          |
  |                125.0 (KIP-FEET)                                          |
  |PARAMETER        |L1                                         STRESSES     |
  |IN KIP  INCH     |   L1  L1                                  IN KIP  INCH |
  |---------------  +           L1                              -------------|
  | KL/R-Y=  76.68  |               L1                          FA  =  15.57 |
  | KL/R-Z=  18.11  +                                           fa  =   0.00 |
  | UNL   =  72.00  |                       L1                  FCZ =  23.76 |
  | CB    =   1.00  +                                           FTZ =  23.76 |
  | CMY   =   0.85  |                           L1  L1          FCY =  27.00 |
  | CMZ   =   0.85  +                                   L1      FTY =  27.00 |
  | FYLD  =  36.00  |                                       L0  fbz =  23.17 |
  | NSF   =   1.00  +---+---+---+---+---+---+---+---+---+---|   fby =   0.00 |
  | DFF   =   0.00  -6.9                                        Fey =  25.40 |
  | dff=      0.00               ABSOLUTE MZ ENVELOPE           Fez = 455.24 |
  | (KL/R)max =  76.68              (WITH LOAD NO.)             FV  =  14.40 |
  |                                                             fv  =   2.84 |
  |                                                                          |
  |                      MAX FORCE/ MOMENT SUMMARY  (KIP-FEET)               |
  |                      -------------------------                           |
  |                                                                          |
  |                AXIAL      SHEAR-Y    SHEAR-Z    MOMENT-Y    MOMENT-Z     |
  |                                                                          |
  |      VALUE       0.0        12.5        0.0         0.0       125.0      |
  |   LOCATION       0.0         0.0        0.0         0.0         0.0      |
  |    LOADING         0           1          0           0           1      |
  |                                                                          |
  |**************************************************************************|
  |*                                                                        *|
  |*                         DESIGN SUMMARY  (KIP-FEET)                     *|
  |*                         --------------                                 *|
  |*                                                                        *|
  |*       RESULT/     CRITICAL COND/     RATIO/         LOADING/           *|
  |         FX              MY             MZ           LOCATION             |
  |        ======================================================            |
  |          PASS        ANSI Q1.6-2      0.975              1               |
  |          0.00 T          0.00      -125.00             0.00              |
  |*                                                                        *|
  |**************************************************************************|