V. AISC N690 1994 Channel
Verify the design of channel section used for a beam member using the AISC N690 1994 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)
The laterally unsupported length of the compression flange,
and
As bf/tf is not in the range of 65/√(Fy) and 95/√(Fy) , the value of allowable bending compressive and tensile stress = Fbty = Fbcy = 0.6×Fy = 21.6 ksi
Actual bending stress:
Bending Tensile Stress = bending compressive stress = fbtz = fbcz= MzD / (2Iz) = 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:
Fy = 51.375 kips
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 = 8.47 in2
fv = 51.375 / 8.47 = 6.07 ksi
Allowable shear:
a = clear distance between transverse stiffeners (here taken as length) = 80 in
h = clear distance flanges of the girder = D-2tf = 14.35 in
Thus, a/h = 5.57, Therefore, k = 5.34 + [4.00/ (a/h)2] = 5.46
t = tw = 0.72 in
If
Cv =17.2
Hence allowable=14.4 ksi
Therefore, Ratio = fv/Fv = 6.07 / 14.4 = 0.422
Results
Parameter | Hand Calculation | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Slenderness ratio | 78.61 | 78.61 | none | |
Allowable bending stress (ksi) | 21.6 | 21.6 | none | |
Actual bending stress (ksi) | 15.41 | 15.41 | none | |
Critical ratio | 0.713 | 0.713 | none | |
Allowable shear stress (ksi) | 14.4 | 14.4 | none | |
Actual shear stress (ksi) | 6.07 | 6.06 | negligible |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\US\AISC\AISC N690 1994 Channel.std is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 10-Aug-18
END JOB INFORMATION
INPUT WIDTH 79
SET SHEAR
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+07
POISSON 0.3
DENSITY 0.283
ALPHA 1.2e-05
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 AISC N690 1994
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
STYPE 1 ALL
TRACK 2 ALL
CHECK CODE ALL
PRINT ANALYSIS RESULTS
FINISH
STAAD Output
STAAD.PRO CODE CHECKING - ( ANSI N690-1994) v1.0 ******************************************** |--------------------------------------------------------------------------| | Y PROPERTIES | |************* | IN INCH UNIT | | * |=============================| |=== ------------ | |MEMBER 1 * | AISC SECTIONS | | AX = 14.70 | | * | ST C15X50 | | --Z AY = 8.47 | |DESIGN CODE * | | | AZ = 2.67 | |ANSI N690-94* =============================== |=== SY = 3.83 | | * SZ = 53.87 | | * |<---LENGTH (FT)= 6.67 --->| RY = 0.87 | |************* RZ = 5.24 | | | | 69.2 (KIP-FEET) | |PARAMETER |L1 STRESSES | |IN KIP INCH | IN KIP INCH | |--------------- + -------------| | KL/R-Y= 78.61 | L1 FA = 9.71 | | KL/R-Z= 12.97 + L1 L1 fa = 0.00 | | UNL = 80.00 | L1 L1 FCZ = 21.60 | | CB = 1.00 + L1 L1 FTZ = 21.60 | | CMY = 1.00 | L1 FCY = 21.60 | | CMZ = 1.00 + FTY = 21.60 | | FYLD = 36.00 | L1 L0 fbz = 15.41 | | NSF = 0.90 +---+---+---+---+---+---+---+---+---+---| fby = 0.00 | | DFF = 0.00 -3.8 Fey = 21.54 | | dff= 0.00 ABSOLUTE MZ ENVELOPE Fez = 791.24 | | (KL/R)max = 78.61 (WITH LOAD NO.) FV = 14.40 | | fv = 6.06 | | | | MAX FORCE/ MOMENT SUMMARY (KIP-FEET) | | ------------------------- | | | | AXIAL SHEAR-Y SHEAR-Z MOMENT-Y MOMENT-Z | | | | VALUE 0.0 51.4 0.0 0.0 69.2 | | 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 0.713 1 | | 0.00 T 0.00 69.17 0.00 | |* *| | |