In a recent model that I developed I found an issues with the program's reported unity ratios when using CB values and AISC 2010 design function. When you have an assigned CB>1.0 or the program computed values CB=0, the unity ratio reported from equation H1-2 is very low. For example, take the W18X40 beam below (see output below) with a Pcy=74.9kips, Pc=26.7kips, and Mr=122.9k-ft, Mcx=211.3k-ft. The Mcx of 211.3k-ft is based on a program computed Cb=2.272. The program is reported that the unity ratio with these loads is 0.538 which I understand comes from equation H1-2 as follows:
Pr/Pcy*(1.5-0.5*Pr/Pcy) + (Mrx/(CB*Mcx))^2
26.7/74.9*(1.5-0.5*26.7/74.9) + (122.9/(2.272*211.3)^2 = 0.538
However, based on how read the definitions under H1-2 in AISC 360-10 I believe this is an error! Mcx should be the available lateral torsional buckling strength for strong axis flexure determined in accordance with Chapter F USING CB = 1.0.
Therefore the correct form of this interaction equation should have the Mcx term = 93k-ft not 211.3k-ft
26.7/74.9*(1.5-0.5*26.7/74.9) + (122.9/(2.272*93)^2 = 0.81
Please let me know if anyone else has seen or experienced this or if i am misunderstanding the implementation of equation H1-2?
-------------------- START OF DESIGN OUTPUT OF MEMBER 234 --------------------
MEMBER NO: 234 CRITICAL RATIO: 0.633(PASS) LOAD: 55
LOCATION (ft):20.00 CONDITION: Eq. H1-1b
SECTION: W18X40 (AISC SECTIONS)
UNIT: KIP FEET
STRENGTH CHECKS:
CRITICAL RATIO: 0.633(PASS) LOAD CASE: 55 LOCATION (ft):20.00 CONDITION: Eq. H1-1b
DESIGN FORCES: Fx: 22.90(T) Fy: -14.40 Fz: 0.00
Mx: 8.33E-04 My: -6.76E-03 Mz: 1.29E+02
SECTION PROPERTIES: AXX: 11.800 AYY: 6.316 AZZ: 5.638
SZZ: 68.380 SYY: 6.351 CW: 1441.528
IZZ: 612.000 IYY: 19.100 IXX: 0.810
MATERIAL PROPERTIES: FYLD: 50.000 FU: 60.000
ACTUAL MEMBER LENGTH(ft): 19.999
PARAMETERS: KX: 1.000 KY: 1.000
SLENDERNESS: ACTUAL SLENDERNESS RATIO: 188.641 LOAD: 40 LOC.(ft): 8.333
ALLOWABLE SLENDERNESS RATIO: 200.000
SECTION CLASS: FLANGE:/ l: lp: lr:
WEB:
COMPRESSION: Non-Slender 5.729 13.487 N/A
Slender 53.492 35.884 N/A
FLEXURE: Compact 5.729 9.152 24.083
Compact 53.492 90.553 137.274
TENSION: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(ft):
23.003 531.000 0.043 Eq. D2-1 59 0.000
COMPRESSION: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(ft):
MAJOR: 26.647 439.903 0.061 Sec. E1 56 0.000
MINOR: 26.647 74.912 0.356 Sec. E1 56 0.000
INTERMEDIATE: Ae: KL/r: Fcr: Fe: Pn:
MAJOR: 10.509 33.325 41.422 257.718 488.781
MINOR: 11.800 188.641 7.054 8.043 83.235
STAAD SPACE -- PAGE NO. 47
STAAD.PRO CODE CHECKING - (AISC-360-10-LRFD) v1.2
********************************************
ALL UNITS ARE - KIP INCH (UNLESS OTHERWISE NOTED)
FLEX TOR BUCK: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(ft):
26.647 234.951 0.113 Sec. E4 56 0.000
INTERMEDIATE: Ae: Fcr: Pn:
11.800 22.123 261.056
SHEAR: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(ft):
MAJOR: 0.005 170.525 0.000 Eq. G2-1 55 0.000
MINOR: -14.403 169.155 0.085 Eq. G2-1 55 19.999
INTERMEDIATE: Aw: Cv: Kv: h/tw: Vn:
MAJOR: 6.316 1.000 1.200 5.729 189.472
MINOR: 5.638 1.000 0.000 53.492 169.155
UNIT: KIP FEET
YIELDING: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(ft):
MAJOR: -1.29E+02 2.94E+02 0.439 Sec. F1 55 19.999
MINOR: -8.94E-03 3.75E+01 0.000 Sec. F1 64 19.999
INTERMEDIATE: Mnr: My: Cb: Lp: Lr: Lb:
MAJOR: 3.27E+02 0.00E+00 2.098 4.494 13.086 19.999
MINOR: 4.17E+01 0.00E+00 2.098 4.494 13.086 19.999
UNIT: KIP FEET
LAT TOR BUCK: FORCE: CAPACITY: RATIO: CRITERIA: LOAD CASE: LOCATION(ft):
MAJOR: -1.29E+02 2.11E+02 0.611 Sec. F1 55 19.999
INTERMEDIATE: Mn: Me: Cb: Lp: Lr: Lb:
MAJOR: 2.35E+02 0.00E+00 2.272 4.494 13.086 19.999
UNIT: KIP FEET
INTERACTION: RATIO: CRITERIA: LOAD CASE: LOCATION(ft):
FLEXURE COMP: 0.611 Eq. H1-1b 55 19.999
FLEXURE TENS: 0.633 Eq. H1-1b 55 19.999
INTERMEDIATE: Mcx: Mcy: Mrx: Mry: Pc: Pr:
FLEXURE COMP: 2.11E+02 3.75E+01 -1.29E+02 -6.76E-03 74.912 0.000
FLEXURE TENS: 2.11E+02 3.75E+01 -1.29E+02 -6.76E-03 531.000 22.897
UNIT: KIP FEET
INTERACTION: RATIO: CRITERIA: LOAD CASE: LOCATION(ft):
IN PLANE FLEX: 0.617 Eq. H1-1b 56 0.000
OUT PLANE FLEX: 0.538 Eq. H1-2 56 0.000
INTERMEDIATE: Mc: Mr: Pc: Pr:
IN PLANE FLEX: 4.40E+02 2.66E+01 209.587 -122.878
OUT PLANE FLEX: 7.49E+01 2.66E+01 209.587 -122.878
-------------------- END OF DESIGN OUTPUT OF MEMBER 234 --------------------