Member Check to AISC 360-10 and AISC Design Guide 9

Question

Hi, I have some questions regarding member check to AISC 360-10. 
 So I was doing some check on a simple member (attached output file), and then I checked it using hand calculation to verify the numbers (I need to know how the program do simpler problem before doing harder analysis not solvable by hand) and found some problem. 
 1. I came into the conclusion that the check for minor axis shear (Z-axis) uses shear area Aw of 4/3 bf*tf (width and thickness of flange) while the code suggests bf*tf (section G7). Is this intentional? And if it is, please sugggest the reasoning behind the 4/3 factor. 
 2. While doing the check for torsion, I also came to the conclusion that the formula that is used to calculate pure flexure shear stress at flange-web junction to be a bit weird, as I think the shear stress should be obtained by dividing the contribution by strong axis shear by the thickness of the web, and weak axis shear by the thickness of the flange, not otherwise (see below picture). Again please suggest the reasoning behind this, or if I used the wrong formula. 
 
 Thank you.

Fullscreen 
 S2.txt 
 Download 
 
 PAGE NO. 1



 **************************************************** 
 * * 
 * STAAD.Pro V8i SELECTseries5 * 
 * Version 20.07.10.65 * 
 * Proprietary Program of * 
 * Bentley Systems, Inc. * 
 * Date= APR 15, 2015 * 
 * Time= 9:51:36 * 
 * * 
 * USER ID: EMAS * 
 **************************************************** 



 1. STAAD SPACE
INPUT FILE: S2.STD
 2. START JOB INFORMATION
 3. ENGINEER DATE 10-APR-15
 4. END JOB INFORMATION
 5. INPUT WIDTH 79
 6. UNIT METER KN
 7. JOINT COORDINATES
 8. 1 0 0 0; 2 0 14.9998 0
 9. MEMBER INCIDENCES
 10. 1 1 2
 11. DEFINE MATERIAL START
 12. ISOTROPIC STEEL
 13. E 2.05E+008
 14. POISSON 0.3
 15. DENSITY 76.8195
 16. ALPHA 1.2E-005
 17. DAMP 0.03
 18. TYPE STEEL
 19. STRENGTH FY 253200 FU 407800 RY 1.5 RT 1.2
 20. END DEFINE MATERIAL
 21. MEMBER PROPERTY AMERICAN
 22. 1 TABLE ST W24X192
 23. CONSTANTS
 24. MATERIAL STEEL ALL
 25. SUPPORTS
 26. 1 2 FIXED
 27. LOAD 1 LOADTYPE NONE TITLE LOAD CASE 1

 **WARNING** - ALL DEGREES OF FREEDOM FIXED.
 STAAD WILL INFINITESIMALLY RELEASE MOMENT-X AT FIRST JOINT ENTERED.

 28. MEMBER LOAD
 29. 1 CON GY 300 5 0
 30. 1 CON GX -75 5 0
 31. 1 CON GZ 25 5 0
 32. 1 CMOM GY 35 5 0
 33. PERFORM ANALYSIS PRINT ALL
 STAAD SPACE -- PAGE NO. 2
 



 P R O B L E M S T A T I S T I C S
 -----------------------------------

 NUMBER OF JOINTS 2 NUMBER OF MEMBERS 1
 NUMBER OF PLATES 0 NUMBER OF SOLIDS 0
 NUMBER OF SURFACES 0 NUMBER OF SUPPORTS 2

 
 SOLVER USED IS THE OUT-OF-CORE BASIC SOLVER
 
 ORIGINAL/FINAL BAND-WIDTH= 1/ 1/ 1 DOF
 TOTAL PRIMARY LOAD CASES = 1, TOTAL DEGREES OF FREEDOM = 1
 TOTAL LOAD COMBINATION CASES = 0 SO FAR.
 SIZE OF STIFFNESS MATRIX = 0 DOUBLE KILO-WORDS
 REQRD/AVAIL. DISK SPACE = 12.0/ 675.0 MB


 STAAD SPACE -- PAGE NO. 3
 


 LOADING 1 LOADTYPE NONE TITLE LOAD CASE 1 
 -----------


 MEMBER LOAD - UNIT KN METE

 MEMBER UDL L1 L2 CON L LIN1 LIN2

 1 300.0000 GY 5.00
 1 -75.0000 GX 5.00
 1 25.0000 GZ 5.00
 1 35.000 GY 5.00 CONCENTRATED MOMENT


FOR LOADING - 1
APPLIED JOINT EQUIVALENT LOADS
 JOINT FORCE-X FORCE-Y FORCE-Z MOM-X MOM-Y MOM-Z
 1-5.55551E+01 1.99999E+02 1.85184E+01 5.55548E+01 2.33332E+01 1.66664E+02
 2-1.94449E+01 1.00001E+02 6.48163E+00-2.77780E+01 1.16668E+01-8.33339E+01

 STATIC LOAD/REACTION/EQUILIBRIUM SUMMARY FOR CASE NO. 1
 LOADTYPE NONE TITLE LOAD CASE 1 


 CENTER OF FORCE BASED ON X FORCES ONLY (METE).
 (FORCES IN NON-GLOBAL DIRECTIONS WILL INVALIDATE RESULTS)

 X = 0.000000000E+00
 Y = 0.500000001E+01
 Z = -0.466666709E+00

 CENTER OF FORCE BASED ON Y FORCES ONLY (METE).
 (FORCES IN NON-GLOBAL DIRECTIONS WILL INVALIDATE RESULTS)

 X = 0.277768515E+00
 Y = 0.500000025E+01
 Z = -0.925895147E-01

 CENTER OF FORCE BASED ON Z FORCES ONLY (METE).
 (FORCES IN NON-GLOBAL DIRECTIONS WILL INVALIDATE RESULTS)

 X = -0.140000015E+01
 Y = 0.500000040E+01
 Z = 0.000000000E+00
TOTAL APPLIED LOAD 1

 ***TOTAL APPLIED LOAD ( KN METE ) SUMMARY (LOADING 1 )
 SUMMATION FORCE-X = -75.00
 SUMMATION FORCE-Y = 300.00
 SUMMATION FORCE-Z = 25.00

 SUMMATION OF MOMENTS AROUND THE ORIGIN-
 MX= 125.00 MY= 35.00 MZ= 375.00

 STAAD SPACE -- PAGE NO. 4
 
TOTAL REACTION LOAD 1

 ***TOTAL REACTION LOAD( KN METE ) SUMMARY (LOADING 1 )
 SUMMATION FORCE-X = 75.00
 SUMMATION FORCE-Y = -300.00
 SUMMATION FORCE-Z = -25.00

 SUMMATION OF MOMENTS AROUND THE ORIGIN-
 MX= -125.00 MY= -35.00 MZ= -375.00


 MAXIMUM DISPLACEMENTS ( CM /RADIANS) (LOADING 1)
 MAXIMUMS AT NODE
 X = 0.00000E+00 0
 Y = 0.00000E+00 0
 Z = 0.00000E+00 0
 RX= 4.91696E-08 1
 RY= 0.00000E+00 0
 RZ= 0.00000E+00 0



 EXTERNAL AND INTERNAL JOINT LOAD SUMMARY ( KN METE )-

 JT EXT FX/ EXT FY/ EXT FZ/ EXT MX/ EXT MY/ EXT MZ/
 INT FX INT FY INT FZ INT MX INT MY INT MZ

 SUPPORT=1
 1 -55.56 200.00 18.52 55.55 23.33 166.66
 0.00 0.00 0.00 0.00 0.00 0.00 111111

 2 -19.44 100.00 6.48 -27.78 11.67 -83.33
 0.00 0.00 0.00 0.00 0.00 0.00 111111



 ************ END OF DATA FROM INTERNAL STORAGE ************


 34. PARAMETER 1
 35. CODE AISC UNIFIED 2010
 36. METHOD ASD
 37. BEAM 1 ALL
 38. CB 1 ALL
 39. FLX 1 ALL
 40. FU 410000 ALL
 41. FYLD 245000 ALL
 42. STP 1 ALL
 43. TORSION 1 ALL
 44. TRACK 2 ALL
 45. CHECK CODE ALL
STEEL DESIGN 
 
 STAAD SPACE -- PAGE NO. 5
 

 STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD) v1.3a
 ********************************************



 ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted)


 -------------------- START OF DESIGN OUTPUT OF MEMBER 1 --------------------

 *MEMBER NO: 1 CRITICAL RATIO: 1.207(FAIL) LOAD: 1
 LOCATION (ft): 0.00 CONDITION: Eq. H3-7 
 SECTION: ST W24X192 (AISC SECTIONS)

 UNIT: KIP FEET

 STRENGTH CHECKS:
 CRITICAL RATIO: 1.207(FAIL) LOAD CASE: 1 LOCATION (ft): 0.00 CONDITION: Eq. H3-7 
 DESIGN FORCES: Fx: 44.96(T) Fy: -12.49 Fz: -4.16
 Mx: -1.72E+01 My: 4.10E+01 Mz: -1.23E+02

 SECTION PROPERTIES: AZZ: 25.209 AYY: 20.631 CW: 76383.609
 SZZ: 491.559 SYY: 81.853
 IZZ: 6260.000 IYY: 530.000

 MATERIAL PROPERTIES: FYLD: 35.534 FU: 59.465

 ACTUAL MEMBER LENGTH(ft): 49.210
 PARAMETERS: KZ: 1.000 KY: 1.000 NSF: 1.000 SLF: 1.000 CSP: 1.000

 SLENDERNESS: ACTUAL SLENDERNESS RATIO: 192.472 LOAD: 1 LOC.(ft): 0.000
 ALLOWABLE SLENDERNESS RATIO: 300.000

 SECTION CLASS: FLANGE:/ l: lp: lr:
 WEB:
 COMPRESSION: Non-Slender 4.435 N/A 16.199
 Non-Slender 27.840 N/A 43.100
 FLEXURE: Compact 4.435 10.992 28.926
 Compact 27.840 108.763 164.880

 TENSION: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(ft):
 YIELDING: 44.961 1197.951 0.038 Eq. D2-1 1 0.000
 RUPTURE: 44.961 1673.953 0.027 Eq. D2-2 1 0.000
 STAAD SPACE -- PAGE NO. 6
 

 STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD) v1.3a
 ********************************************



 ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted)


 COMPRESSION: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(ft):
 MAJOR: 22.481 1021.885 0.022 Eq. E3-1 1 49.210
 MINOR: 22.481 234.202 0.096 Eq. E3-1 1 49.210
 INTERMEDIATE: Ag: KL/r: Fcr: Fe: Pn:
 MAJOR: 56.300 56.004 30.312 93.561 1706.548
 MINOR: 56.300 192.472 6.947 7.921 391.117

 FLEX TOR BUCK: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(ft):
 22.481 941.262 0.024 Eq. E4-1 1 49.210
 INTERMEDIATE: Ag: Fcr: Pn:
 56.300 27.920 1571.908

 SHEAR: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(ft):
 MAJOR(VZ): 4.163 321.834 0.013 Eq. G2-1 1 0.000
 MINOR(VY): -12.489 293.239 0.043 Eq. G2-1 1 0.000
 INTERMEDIATE: Aw: Cv: Kv: h/tw: Vn:
 MAJOR(VZ): 25.209 1.000 1.200 4.435 537.463
 MINOR(VY): 20.631 1.000 0.000 27.840 439.858

 UNIT: KIP FEET

 YIELDING: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(ft):
 MAJOR: 1.23E+02 9.91E+02 0.124 Eq. F2-1 1 0.000
 MINOR: 4.10E+01 2.23E+02 0.183 Eq. F6-1 1 0.000
 INTERMEDIATE: Mnr: My: Cb:
 MAJOR: 1.66E+03 0.00E+00 1.000
 MINOR: 3.73E+02 0.00E+00 1.000

 UNIT: KIP FEET

 LAT TOR BUCK: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(ft):
 MAJOR: 1.23E+02 6.57E+02 0.187 Eq. F2-2 1 0.000
 INTERMEDIATE: Mn: Me: Cb: Lp: Lr: Lb:
 MAJOR: 1.10E+03 0.00E+00 1.000 13.016 54.296 49.210

 UNIT: KIP FEET

 INTERACTION: RATIO: CRITERIA: LOAD CASE: LOCATION(ft):
 FLEXURE COMP: 0.370 Eq. H1-1b 1 0.000
 FLEXURE TENS: 0.389 Eq. H1-1b 1 0.000
 INTERMEDIATE: Mcx: Mcy: Mrx: Mry: Pc: Pr:
 FLEXURE COMP: 6.57E+02 2.23E+02 1.23E+02 4.10E+01 234.202 0.000
 FLEXURE TENS: 6.57E+02 2.23E+02 1.23E+02 4.10E+01 1197.951 44.961
 STAAD SPACE -- PAGE NO. 7
 

 STAAD.PRO CODE CHECKING - ( AISC-360-10-ASD) v1.3a
 ********************************************



 ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE Noted)


 UNIT: KIP FEET

 INTERACTION: RATIO: CRITERIA: LOAD CASE: LOCATION(ft):
 IN PLANE FLEX: 0.044 Eq. H1-1b 1 41.008
 OUT PLANE FLEX: 0.072 Eq. H1-2 1 41.008
 INTERMEDIATE: Pc: Pr: Mc: Mr:
 IN PLANE FLEX: 1.02E+03 1.12E+01 657.052 25.609
 OUT PLANE FLEX: 2.34E+02 1.12E+01 657.052 25.609

 -------------------- END OF DESIGN OUTPUT OF MEMBER 1 --------------------


 ****** AISC DESIGN GUIDE 9 ******

 MEMBER: 1 SECTION: W24X192 AISC 
 END CONDITION: FIX-FIX 
 SHEAR CAPACITY: 12.77 SHEAR CRITERIA: Eq. H3-8 
 NORMAL CAPACITY: 21.28 NORMAL CRITERIA: Eq. H3-7 

 STRESS LOC SHEAR RATIO LOAD CASE/ | STRESS LOC NORMAL RATIO LOAD CASE/
 SECTION | SECTION
 MID FLANGE 0.78 0.06 1 | FLANGE EDGE 25.67 1.21 1
 0.00 | 0.00
 FL-WB JUNC 6.38 0.50 1 |
 0.17 |
 MID WEB 3.72 0.29 1 |
 0.17 |

 PURE TORSION SHEAR STRESS CRITERIA: DG9 Eq. 4.1 
 FLANGE EDGE: 5.43 WEB EDGE: 3.01

 WARPING SHEAR STRESS CRITERIA: DG9 Eq. 4.2a
 MID FLANGE: 0.73

 WARPING NORMAL STRESS CRITERIA: DG9 Eq. 4.3a
 FLANGE EDGE: 15.87

 PURE FLEXURE SHEAR STRESS CRITERIA: DG9 Eq. 4.6 
 MID FLANGE: 0.05 FLANGE-WEB JUNC: 0.61 MID WEB: 0.71

 DIRECT AXIAL BENDING STRESS CRITERIA: DG9 Eq. 4.5 
 FLANGE EDGE: 9.81
 
 46. FINISH
 STAAD SPACE -- PAGE NO. 8
 


 *********** END OF THE STAAD.Pro RUN *********** 

 **** DATE= APR 15,2015 TIME= 9:51:41 ****

 ************************************************************
 * For technical assistance on STAAD.Pro, please visit *
 * http://selectservices.bentley.com/en-US/ *
 * *
 * Details about additional assistance from *
 * Bentley and Partners can be found at program menu *
 * Help->Technical Support *
 * *
 * Copyright (c) 1997-2014 Bentley Systems, Inc. 
 * http://www.bentley.com *
 ************************************************************

Biswatosh · Accepted Answer

Regarding your query 1, your point is correct. The software is calculating the shear area in minor axis as 2/3 x Total area of the flanges. But according to the section G7 ( Chapter G) of AISC, it should use the full areas of the flanges, Aw=(bf*tf). Our development team is already aware of this fact and they are working on to rectify this in the forthcoming Staad release.

Biswatosh · Answer

Regarding your second query, AISC 360-10 does not follow the first formula that you have cited in your illustration. It follows the second one one shown in your illustration.