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)
Thus, allowable bending tensile stress = Fbtz = 0.66×Fy = 23.76 ksi
Actual bending stress About Major Axis
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
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
Stress ratio = fv/Fv = 0.18
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 2024\Samples \Verification Models\09 Steel Design\US\AISC\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 |
| * |<---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 |
|* *|
| |