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
| 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\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 | |* *| | |