rectangular duct

file:///tt/file_convert/55cf9a7e550346d033a201c5/document.xlsx1 of 77

Larson Engineering, Inc. SUBJECT: Straight Duct SHEET NO.

PROJECT NO.

JMH

Rectangular Duct Design

The duct lateral force system of the ducts will consist of moment frames with pinned connections at the top and moment connections at the interface of the columns and floor beams. Intermediate stiffener rings will be placed between the moments frames to stiffen the shell plate and the flanges will not be considered strutural. Design will be based on the AISC 13th Edition Steel Construction Manual.

132.00 in 12.00 in 60.00 intyp

96.0

0 in

504.00 in

Duct Loads Duct Geometry

Insulation = 11.00 psf = 8.00 ft = 96.00 in

Roof Live = 20.00 psf = 11.00 ft = 132.00 in

Floor Live = 90.00 psf = 42.00 ft = 504.00 in

Snow = 10.00 psf = 8.05 ft = 96.63 in

Operating (+) = 0 in H2O = 11.05 ft = 132.63 in

Operating (-) = 10 in H2O = 7 stiffeners

Design (+) = 35 in H2O = 5.00 ft = 60.00 in

Design (-) = 35 in H2O = 1.00 ft = 12.00 in

= 0.067 g = 62.33 ft = 748.00 in

25.60 psf

Member Shell PlateMaterial A36 = 0.38 inRoof Stiffener WT6X13 w/ 0 flange braces = 0.06 inSidewall Stiffener WT6X7 w/ 0 flange braces Material = A36 Column WT9X25 w/ 0 flange bracesFloor Stiffener WT6X13 w/ 0 flange bracesFloor Frame Beam WT9X25 w/ 0 flange braces

ResultsSpan Max Span Unity Ratio

5.00 ft 5.68 ft

1.00 ft 1.64 ft

62.33 ft 130.29 ft 0.41

Roof Stiffener 11.05 ft 9.95 ft 0.78

Side Wall Stiffener 8.05 ft 10.43 ft 0.72

Column 8.05 ft 15.47 ft 0.95

Floor Stiffener 11.05 ft 7.66 ft 0.78

Floor Frame 11.05 ft 43.87 ft 0.55

5950 Live Oak Parkway, Suite 300Norcross, GA 30093-1744770.279.6010 Fax: 770.279.6015www.larsonengr.com

BY

hgas path

wgas path

ℓduct

hduct

wduct

nstiffeners

ℓ1

ℓ2

Sesimic Cs ℓsupport

(qz)(Kz)

tplate

tcorrosion

Shell Plate Span Between Stiffener Rings (ℓ1)

Shell Plate Span @ Flange (ℓ2)

Duct Span Between Supports (ℓsupport)



PROJECT NO.

JMH


BY

DEAD LOADAssume the dead load is transferred through the shell plate, to the columns, then to the duct support

= 15.30 psf

= 11.00 psf

= 26.30 psf

LIVE LOADAssume the live load is applied to the floor & roof of the duct

20.00 psf

90.00 psf

SNOW LOADAssume the snow load is applied to the roof of the duct

= 10.00 psf

OPERATING LOADSide wall load

= 0.00 = 0.00 psf

= 10.00 = 52.00 psf

DESIGN LOADSide wall load

= 35.00 = 182.00 psf

= 35.00 = 182.00 psf

SEISMIC LOAD

= 0.067

= 1.76 psf

WIND LOAD - Refer to ASCE 7-05, Section 6.5.15, Figure 6-6 & Figure 6-21

= = (25.60 psf)(0.85)(1.4) = 30.46 psf

= = 0.8(25.60 psf)(0.85) = 17.41 psf

= = 0.5(25.60 psf)(0.85) = 10.88 psf

= = 0.7(25.60 psf)(0.85) = 15.23 psf

= = (0.8)(1.3)(25.60 psf)(0.85) = 22.63 psf

Roof Load Combinations For Shell Plate Design and Stiffener Design - Refer to ASCE7-05, Section 2.4.1Load #1.1 - Dead Weight - Postive Design Pressure (D + F)

= 26.30 psf - 182.00 psf = 155.70 psf

Load #1.2 - Dead Weight + Negative Design Pressure

= 26.30 psf + 182.00 psf = 208.30 psf

= 26.30 psf + 20.00 psf + 52.00 psf = 98.30 psf

= 26.30 psf + 20.00 psf - 0.00 psf = 46.30 psf

Load #2.3 - Dead Weght + Snow Pressure + Negative Operating Pressure (D + F + S)

= 26.30 psf + 52.00 psf + 10.00 psf = 88.30 psf

Load #3 - Dead Weight - Positive Operating Pressure + Uplift Wind Pressure (D + F + W)

= 0.00 psf - 26.30 psf + 22.63 psf = 3.67 psf

Sidewall Load Combinations For Shell Plate and Stiffener DesignLoad #1 - Maximum Design Pressure (F)

Wshell

Winsul

Wdead

Wlive-r

Wlive-f

Wsnow

W+operating in H2O

W-operating in H2O

W+design in H2OW-design in H2O

Vseismic

Wshell

Wglobal (qz)(Kz)(G)(Cf)Wwindward 0.8(qz)(Kz)(G)(Cf)Wleeward 0.5(qz)(Kz)(G)(Cf)Wsidewall 0.7(qz)(Kz)(G)(Cf)Wuplift (0.8)(1.3)(qz)(Kz)(G)(Cf)

Wdead - W+design

Wdead - W+design

Load #2.1 - Dead Weght + Live Pressure + Negative Operating Pressure (D + F + Lr)

Wdead + Wlive + W+operating

Load #2.2 - Dead Weight - Positive Operating Pressure (D + F + Lr)

Wdead - W+operating + Wlive

Wdead + Wsnow

W+operating - Wdead + Wuplift



PROJECT NO.

JMH


BY

= 182.00 psf

Load #2.1 - Positive Operating Pressure + Sidewall Wind Pressure (F + W)

= 15.23 psf + 0.00 psf = 15.23 psf

Load #2.2 - Negative Operating Pressure + Windward Wind Pressure (F + W)

= 52.00 psf + 17.41 psf = 69.41 psf

Load #2.3 - Positive Operating Pressure + Seismic Pressure (F + 0.7E)

= 52.00 psf + 0.7(1.76 psf) = 53.23 psf

Floor Load Combinations For Shell Plate Design and Stiffener DesignLoad #1.1 - Dead Weight + Positive Design Pressure (D + F)

= 26.30 psf + 182.00 psf = 208.30 psf

Load #1.2 - Dead Weight + Positive Design Pressure (D +F)

= 26.30 psf + 182.00 psf = 208.30 psf

Load #1.3 - Dead Weight + Positive Operating Pressure (D + F)

= 26.30 psf + 0.00 psf = 26.30 psf

Load #2 - Dead Weght + Live Pressure (D + L)

= 26.30 psf + 90.00 psf = 116.30 psf

Load #3 - Dead Weight + Positive Operating Pressure + Live (D + F +L)

= 26.30 psf + 0.00 psf + 90.00 psf = 116.30 psf

Load #4 - Dead Weight + Positive Operating Pressure + Sidewall Wind Pressure (D + F + 0.75W + .75L)

= 0.00 psf + 26.30 psf + 0.75(15.23 psf) + 0.75(90.00 psf) = 105.22 psf

Check Stresses & Deflections on Shell Plate SpansRefer to Equation H1-1b on page 16.1-60 & assume the flanges are non-structural, thus the shell at the flange acts as a cantileverFor a 1 ft. wide strip

= = 1.6(0.20 in³) (36.00 ksi) = 6725.75 lb-in1.67 1.67

= =(12)(6725.75 lb-in)

= 68.19 in(208.30 psf)(1ft²/144 in²)(12 in)

= =(2)(6725.75 lb-in)

= 27.84 in(208.30 psf)(1ft²/144 in²)(12 in)

= = 60.00 in = 0.600 in100 100

= =12.00 in

= 0.120 in100 100

= =384(29,000 ksi)(0.05 in ) (0.60 in)

= 77.638 in(116.30 psf)(1000 lb/kip)(1ft²/144in²)(12 in)

= =8(29,000 ksi)(0.05 in ) (0.12 in)

= 19.725 in(116.30 psf)(1000 lb/kip)(1ft²/144in²)(12 in)

Check Duct Flexural Strength to span between supports

=

= (2(11.05 ft) + 2(8.05 ft)) (26.30 psf) = 1005 plf

W+/-design

Wsidewall - W+operating

W-operating + Wwindward

W+/-operating + Wseismic

Wdead + W+design

Wdead + W+design

Wdead + W+operating

Wdead + Wlive

Wdead + W+operating + Wlive-f

W+operating + Wdead + Wsidewall + Wlive-f

Mn

1.6(Sx-plate) (Fy)

ℓ1-max

(12)(Mmax) ½

Wmax

ℓ2-max (2)(Mmax) ½

Wmax

d1-allowableℓ1

d2-allowableℓ2

ℓ1-max (384)(E)(Iplate)(δ1-allowable) ¼ ¼

(Wnon-event)(12 in)

ℓ2-max (8)(E)(Iplate)(δ2-allowable) ¼ ¼

(Wnon-event)(12 in)

Wduct (2(wduct) + 2(hduct))(Wdead)

Wduct



PROJECT NO.

JMH


BY

= = (1005 plf) (62.33 ft)² = 488.05 kip-ft8 8(1000 lb/kip)

= = (90.00 psf + 20.00 psf) (11.00 ft) ( 62.33 ft)² = 587.67 kip-ft8 (8)(1000 lb/kip)

= 1075.72 kip-ft

Duct Cross-Section Properties

= = (132.63 in) ( 96.63 in)³ - (132.63 in - 0.63 in) (96.63 in - 0.63 in)³12 12

= 238306.06 in

= =(132.63 in) ( 96.63 in)³ - (132.63 in - 0.63 in) (96.63 in - 0.63 in)³

6( 96.63 in)

= 4932.60 in³

= - = (132.63 in) (96.63 in)² - (132.63 in - 0.63 in) (96.63 in - 0.63 in)²4 4 4 4

= 5431.70 in³

Criteria For Flange Compactness

b/t > 1.12E

= 424.40 > 31.79

b/t > 1.40E

= 424.40 > 39.74 Therefore flange is slender, local buckling must be a design consideration

Criteria For Web Compactness

h/t > 2.42E

= 309.20 > 68.69

h/t > 5.70E

= 309.20 > 161.78 Therefore web is slender, local buckling must be a design consideration

Flexural Moment Capacity

= = ( 5431.70 in³) ( 36.00 ksi) = 195541.26 kip-in

= 3.57b/t - 4.0E

= 195541.26 kip-in - ( 195541.26 kip-in - ( 36.00 ksi) ( 4932.60 in³)) 3.57( 424.40 ) 36.00 ksi - 4.029,000 ksi

= N.A.

= 1.92tE

1 -0.38 E

= 1.92( 0.31 in)29,000 ksi

1 -0.38 29,000 ksi

b/t 36.00 ksi 424.40 36.00 ksi

= 16.60 in < 132.63 in

Mduct(Wduct)(ℓsupport)²

Mlive(Wlive-r + Wlive-f)(wgas path)(ℓsupport)²

Mu

Ix(wduct)(hduct)³ - (wduct-2t)(hduct-2t)³

Ix

Sx

(wduct)(hduct)³ - (wduct-2t)(hduct-2t)³

6hduct

Sx

Zx(wduct)(hduct)² (wduct-2t)(hduct-2t)²

Zx

Refer to Table B4.1, on p16.1-17 for λp & λr.½

Fy

½

Fy

Refer to Table B4.1, on p16.1-17 for λp & λr.½

Fy

½

Fy

Refer to Equation F7-1 on p.16.1-55 for Mp.

Mp (Zx) (Fy)

Refer to Equation F7-2 on p.16.1-55 for Mn.

Mn Mp - (Mp - (Fy) (Sx)) Fy½

Mn

½

Mn

Refer to Equation F7-4 on p.16.1-56 for Mn.

be

½ ½ ½ ½

Fy Fy

be



PROJECT NO.

JMH


BY

= = (16.60 in) ( 96.63 in)³ - (16.60 in - 0.63 in) (96.63 in - 0.63 in)³6h 6( 96.63 in)

= 1451.70 in³

= = ( 1451.70 in³) ( 36.00 ksi) = 52261.05 kip-in

= 0.305h/t - 0.738E

= 195541.26 kip-in - ( 195541.26 kip-in - ( 36.00 ksi) ( 4932.60 in³)) 0.305( 309.20 ) 36.00 ksi - 0.73829,000 ksi

= 149099.84 kip-in

=31294.04 kip-in

= 2607.84 kip-ft12 in/ft

Deflection Check

= = 748.00 in = 2.078 in360 360

= =384(29,000 ksi)(238306.06 in ) (2.078 in)

5(1005 plf) + (20.00 psf + 90.00 psf) (11.00 ft)(1kip/1000 lb)(1 ft/12 in)

= 1563.440 in

Design Roof Stiffener

Roof stiffeners will be designed to carry the maximum pressure on the maximum tributary area, assuming simple span. As aforementioned, the shell plate will act as a shear wall and resist all axial (compressive and tensile) forces. Therefore, the roof stiffeners must be designed to resist only bending moments that result from pressure loads.

= = (208.30 psf) (5.00 ft + 1.00 ft) (11.05 ft)² = 19.08 kip-ft8 (8)(1000 lb/kip)

Deflection Check

= = 132.63 in = 1.326 in100 100

= =384(29,000 ksi)(40.52 in ) (1.326 in)

= 119.351 in5(98.30 psf) (72.00 in)(1 kip/1000 lb)(1ft²/144in²)

Design Sidewall Stiffener

Sidewall stiffeners will be designed to carry the maximum pressure on the maximum tributary area, assuming simple span. The sidewallstiffener will not resist lateral loads because they are not attached to a support.


= 12.23 kip-ft > = 8.85 kip-ft

Deflection Check

= = 96.63 in = 0.403 in240 240

= =384(29,000 ksi)(25.00 in ) (0.403 in)


Seff(be) (h)³ - (be - 2t) (h - 2t)³

Seff


Mn (Seff) (Fy)


Mn Mp - (Mp - (Fy) (Sx)) Fy½

Mn

½

Mn

Mn

Ωb

dallowableℓsupport

ℓsupport-max (384)(E)(Ix)(δallowable)

¼ ¼

5(Wduct + (Wlive-r + Wlive-f)(wgas path))

ℓsupport-max

Mu(Wmax)(ℓ1 + ℓ2)(wduct)2

dallowable

wduct

ℓstiffener-max (384)(E)(Istiffener)(δallowable) ¼ ¼

5(Wnon-event)(ℓ1 + ℓ2)

Mu(Wmax)(ℓ1 + ℓ2)(hduct)2

MnMu

Ωb

dallowable

hduct





PROJECT NO.

JMH


BY

Design Duct ColumnThe columns will be designed to resist moments from lateral loads, where they act is cantilevers that are free to rotate and translate at the top. The columns must also resist bending loads from pressure loading as well as, where they act as a simple-span member. Load #1 - Dead Load + Maximum Design Pressure (D + F)Conservatively check the columns for maximum design pressure in the pinned-pinned condition only

= 31.69 kip

= =(182.00 psf) (5.00 ft + 1.00 ft) (8.05 ft)²

= 8.85 kip-ft8 (8)(1000 lb/kip)

Load #2.1 - Dead Weight + Maximum Operating Pressure + Seismic Load - perpendicular to flow (D + F + 0.7E)Check the columns for seismic pressure, where the nearside wall will receive seismic pressure acting on its face to determine the moment being placed on the cantilevered columns, where it will act concurrently with operating pressure, along with compression developed by dead load.

= =(26.30 psf) (62.33 ft) (11.05 ft) + (13.00 plf) (11.05 ft) (7)

= 9.56 kip2 (2)(1000 lb/kip)

= = (0.067 g) (9.56 kip) (8.05 ft) = 5.16 kip-ft

= + +2

=(26.30 psf) (62.33 ft) (11.05 ft) +

(13.00 plf) (11.05 ft)+ (26.30 psf) (62.33 ft) + 1.00 ft) (8.05 ft) + (11.04 plf) (8.05 ft)

21000 lb/kip

= 31.69 kip

Deflection of Seismic column under wind loading to conservatively account for P-delta effects

= =0.7(0.067 g) (26.30 psf)(1ft²/144in²) (748.00 in) (96.63 in )

= 0.0199 in8(29,000 ksi)(120.96 in )(1 kip/1000 lb)

= = (31.69 kip) (0.0199 in)(1 ft/12 in) = 0.05 kip-ft

= = (0.067 g) (26.30 psf) (62.33 ft) (8.05 ft)² = 3.56 kip-ft2 (2)(1000 lb/kip)


= 11.30 kip-ft

Load #2.2 - Dead Weight + Operating Pressure + Leeward Wind Pressure (D + F + W)The leeward column wall will be checked, where positive operating pressure will act concurrently with leeward wind pressures, as well as developed by the dead load acting on the tributary area. The windward column will also be checked, where windward pressure willact concurrently with negative operating pressure.

= 31.69 kip

Deflection of leeward column under wind loading to conservatively account for P-delta effects

= =(10.88 psf)(1ft²/144in²) (748.00 in) (96.63 in)

= 0.1755 in8(29,000 ksi)(120.96 in )(1 kip/1000 lb)

= = (31.69 kip) (0.1755 in) (1 ft/12 in) = 0.46 kip-in

Pu

Mu

(Wdesign)(ℓ1 + ℓ2)(hduct)2

Proof

(Wdead)(ℓsupport)(wduct) + (Wroof stiff)(wduct)(nstiffeners)

Mroof (Cs)(Proof)(hduct)

Pu = Pdead (Wshell)(ℓsupport)(wduct)(Wroof stiff)(wduct) (Wshell)(ℓsupport) + (Wside stiff)(hduct)

Pu

Pu

δmax

0.7(Cs)(Wshell)(ℓsupport)(hduct)4

(8)(E)(Istiffener)

MP-Δ (Pu)(δmax)

Mseismic

(Cs)(Wshell)(ℓsupport)(hduct)2

Moperating

(Woperating)(ℓ1 + ℓ2)(hduct)2

Mu

Pu

δmax

(Wleeward)(ℓsupport)(hduct)4

(8)(E)(Istiffener)

MP-Δ (Pu)(δmax)



PROJECT NO.

JMH


BY

= = (10.88 psf) (62.33 ft) (8.05 ft)² = 21.99 kip-ft2 (2)(1000 lb/kip)


= 22.45 kip-ft

Load #2.3 - Dead Load + Positive Operating Pressure + Sidewall Pressure (D + F + W)Conservatively check the columns for maximum design pressure in the pinned-pinned condition only

= 31.69 kip



= 7.69 kip-ft

Load #2.4 - Dead Weight + Negative Operating Pressure + Windward Wind Pressure (D + F + W)The windward column will be checked, where operating pressure will act concurrently with windward wind pressures, as well as compression developed by dead load.

= 31.69 kipDeflection of leeward column under wind loading to conservatively account for P-delta effects

= =(17.41 psf)(1ft²/144in²) (748.00 in) (96.63 in)

= 0.2809 in8(29,000 ksi)(120.96 in )(1 kip/1000 lb)

= = (31.69 kip) (0.2809 in) (1 ft/12 in) = 0.74 kip-in



= 38.45 kip-ft

Deflection Check

= = 96.63 in = 0.403 in240 240

= =384(29,000 ksi)(120.96 in ) (0.403 in)


Design Floor StiffenerFloor stiffeners will be designed to carry the maximum pressure on the maximum tributary area, assuming simple span.


Deflection Check

= = 132.63 in = 0.553 in240 240

= =384(29,000 ksi)(40.52 in ) (0.553 in)


Mwind


Moperating


Mu

Pu

Mwind

(Wsidewall)(ℓsupport)(hduct)2

Moperating


Mu

Pu

δmax

(Wwindward)(ℓsupport)(hduct)4

(8)(E)(Istiffener)

MP-Δ (Pu)(δmax)

Mwind


Moperating


Mu

dallowable

hduct



Mu(Wmax)(ℓ1 + ℓ2)(wduct)2

dallowable

wduct





PROJECT NO.

JMH


BY

Design Floor Frame BeamEach floor beam must be able to carry the pressure loads acting on the floor of the duct, along with the moment from the duct columns. Load #1 - Dead Load + Positive Design Pressure (D + F)

= = (26.30 psf + 182.00 psf) (5.00 ft + 1.00 ft) (11.05 ft)² = 12.72 kip-ft12 (12)(1000 lb/kip)


= 18.22 kip-ft

Load #2 - Dead Load + Negative Design Pressure + Live (D + F + L)

= = (26.30 psf - 182.00 psf) (5.00 ft + 1.00 ft) (11.05 ft)² = 9.51 kip-ft12 (12)(1000 lb/kip)


= 15.01 kip-ft

Load #3.1 - Dead Weight + Operating Pressure + Y-Seismic Load - perpendicular to flow + 0.75Live (D + F + 0.7E + 0.75L)Check floor beam under farside wall. Refer to pressure loading on floor stiffeners and moments from the duct column design.



= = 0.75(90.00 psf) (5.00 ft + 1.00 ft) (11.05 ft)² = 4.12 kip-ft12 (12)(1000 lb/kip)

= 3.56 kip-ft

= 12.47 kip-ft

Load #3.2 - Dead Weight + Negative Operating Pressure + Leeward & Windward Wind Pressure + 0.75Live (D + F + 0.75W + 0.75L)Check floor beam under leeward wall and conservatively neglect outward wind pressure. Refer to moments from the duct column design.




= 0.75(21.99 kip-ft) = 16.49 kip-ft

= 25.39 kip-ft

Load #3.3 - Dead Weight + Live Load + Wind Load + Operating (D + 0.75W + 0.75L)




Mdesign(Wshell + Wdesign)(ℓ1 + ℓ2)(wduct)2

Mlive(Wlive-f)(ℓ1 + ℓ2)(wduct)2

Mu

Mdesign(Wshell - Wdesign)(ℓ1 + ℓ2)(wduct)2

Mlive(Wlive-f)(ℓ1 + ℓ2)(wduct)2

Mu

Mdead(Wshell)(ℓ1 + ℓ2)(wduct)2

Moperating

(Woperating)(ℓ1 + ℓ2)(wduct)2

Mlive0.75(Wlive-f)(ℓ1 + ℓ2)(wduct)2

Mseismic

Mu


Moperating



0.75Mleeward

Mu



Mwind(Wsidewall)(ℓ1 + ℓ2)(wduct)2



PROJECT NO.

JMH


BY


= 6.66 kip-ft

Deflection Check

= = 132.63 in = 0.553 in240 240

= =384(29,000 ksi)(120.96 in ) (0.553 in)

= 526.442 in(116.30 psf)(1000 lb/kip)(1ft²/144in²)

Moperating


Mu

dallowable

wduct


(Wnon-event)(ℓ1 + ℓ2)

Larson Engineering, Inc. SUBJECT: SHEET NO. OF

PROJECT NO.

DATE

Combined Section Properties for a T Stiffener

6.49 inConstants & Beam Information

6.4

2 in

E 29,000 ksi (modulus of elasticity for steel)

0.3

8 in 1.14 (lateral-torsional buckling modification factor)

132.63 in (flexural unbraced length of beam)

36.00 ksi (beam yield strength)

0.23 in

0.3

1 in

5.23 in

T Information Combined Information

Section: WT6X13 5.45 in² (cross sectional area)d 6.11 in (height of T section) y 3.67 in (vertical centroidal axis)

6.49 in (width of flange) x 0.00 in (horizontal centroidal axis)

0.23 in (web thickness) 4.99 in (vertical plastic neutral axis)

0.38 in (flange thicness) 40.52 in (moment of inertia about strong axis)

A 3.82 in² (cross sectional area) 12.39 in (moment of inertia about strong axis)

11.70 in (moment of inertia about x axis) 2.73 in (radius of gyration about strong axis)

8.66 in (moment of inertia about y axis) 1.51 in (radius of gyration about weak axis)

y 5.17 in (distance from top of flange to elastic neutral axis) 14.72 in³ (strong-axis elastic section modulus at top)

W 13.00 plf (weight per linear foot) 11.04 in³ (strong-axis elastic section modulus at bottom)

2.47 in (area of flange) 3.82 in³ (strong-axis elastic section modulus at top)

1.41 in (area of web) 4.74 in³ (weak-axis elastic section modulus at bottom)

13.61 in³ (strong-axis plastic section modulus)

Shell plate information 6.21 in³ (weak-axis plastic section modulus)

t 0.38 in (thickness of shell) 1.48 in² (web area for vertical shear)

corrosion 0.06 in (corrosion allowance) 4.10 in² (flange area for horizontal shear)

0.31 in (modified thickness of shell) J 0.20 in (torsional constant)

5.23 in (effective width=stem width + (2)(8)(plate thickness)A 1.63 in² (cross sectional area of shell)

0.01 in (moment of inertia of weak axis of plate)

3.73 in (moment of inertia of strong axis of plate)y 0.16 in (centroid of shell plate)

56.45 in

192.68 in

Web Classification For Local Buckling Compact

Flange Classification For Local Buckling Compact

Required Resistance Factored Nominal Resistance19.08 kip-ft 24.45 kip-ft

Unity Ratio = 0.78 Based on Strong-Axis Flexure


BY

Cb

Lb

Fy

Ax

bf

twyz

tfIx

Iy

Ixrx

Iyry

Sx-top

Sx-bottom

AflangeSy-top

AwebSy-bottom

Zx

Zy

Aw

Af

tmod

ws

Ix

Iy

Limiting Unbraced Length For Inelastic Lateral Torsional Buckling (Lp)

Limiting Unbraced Length For Elastic Lateral Torsional Buckling (Lr)

Strong-Axis Flexure (Mrx) Strong-Axis Flexure (Mcx)

Criteria For Flange Compactnessb

= =6.49 in

= 8.54t 0.76 in

= 0.38E

= 0.3829,000 ksi

= 10.7936.00 ksi

=

4

=

4

= 0.784h 5.99 in Use 0.7600.23 in

= 1.00E

= 1.0029,000 ksi

= 28.3836.00 ksi

b< = 8.54 < 10.79 - therefore section has compact flanges

t

b< = 8.54 < 28.38

t


= = 2(6.11 in) + 0.31 in - 0.38 in - 3.67 in) = 4.75 in

= = 2(6.11 in) + 0.31 in - 0.38 in - 4.99 in) = 2.11 in

E 4.75 in 29,000 ksi

= = 2.11 in 36.00 ksi

= 192.44

0.54 - 0.09²

0.5413.61 in³

- 0.09²

11.04 in³

= 5.70E

= 5.7029,000 ksi

= 161.7836.00 ksi

h< = 23.26 < 192.44 - therefore section has a compact web

h< = 23.26 < 161.78

Beam Strong-Axis Moment Capacity1. Strong-Axis Moment Capacity Based on Yielding With Compact Webs and Flanges

= = ( 13.61 in³) ( 36.00 ksi) = 489.88 kip-in

= = 5.42 in - 0.07 in = 5.35 in

Refer to Section F3, part 2 for λ.

λ =b

= 8.54t

2. Strong-Axis Moment Capacity Based on Compression Flange Yielding For Members With Noncompact Webs h

= =5.35 in

= 23.260.23 in

= 4.75 in

< = 20.64 < 192.44 - therefore Equation F-4-9a Applies

= = =13.61 in³

= 1.2311.04 in³


λ = = 23.26

bf

2tf

Refer to Table B4.1, on p16.1-16 for λpf = λp & λrf = λr.

λpf

½ ½

Fy

Refer to [a] on p16.1-18 for kc. However kc shall not be less than 0.35, nor greater than 0.76

kc½ ½

tw

λrf

½ ½

Fy

λpf

λrf


hc 2(dtee +tplate -tf - ycomb)

hp 2(dtee +tplate -tf - yz)

hc ½ ½

λpw

hp Fy

Zx

Sx

λrw

½ ½

Fy

λpwtw

λrwtw


Mp (Zx) (Fy)

Refer to Section F2, part 2. Lateral Torsional Buckling (ii) on p16.1-48 for ho.

ho d - tf - tmod

ho

tw tw

Refer to Section F4 in commentary, on p16.1-274 for hc.

hc

hcλpf

tw

Refer to Equation F4-9a on p16.1-51 for Rpc. Note: Fy cancels out of the equation, leaving only the section moduli.

Rpc

Mp (Zx) (Fy)

Myc (Sx) (Fy)

hc

tw

= - - 1 =13.61 in³

-13.61 in³

- 123.26 - 192.44

= -0.0511.04 in³ 11.04 in³ 161.78 - 192.44

= = (1.23) (36.00 ksi) (11.04 in³) = 489.88 kip-in

3. Strong-Axis Moment Capacity Based on Lateral Torsional Buckling For Members With Compact or Noncompact Webs

= =(4.75 in) (0.23 in)

= 0.44(6.49 in) (0.38 in)

= =6.49 in

= 1.81 in12 1 +

112 1 +

1( 0.44 in)

6 6

=E

= 1.1(1.81 in)29,000 ksi

= 56.45 in36.00 ksi

= = (0.70) ( 36.00 ksi) = 25.20 ksi

=E

1 + 1 + 6.762

E J

= 1.95(1.81 in)29,000 ksi 0.20 in

1 + 1 + 6.760.7(25.20 ksi) (11.04 in³) ( 5.35in) 2

= 492.70 in0.7(25.20 ksi) (11.04 in³) (5.35 in) 29,000 ksi 0.20 in

Refer to Section F4, part 2. Lateral Torsional Buckling (a) on p16.1-50.

> = 132.63 in > 56.45 in - Therefore lateral-torsional buckling applies

Refer to Section F4, part 2. Lateral Torsional Buckling (b) on p16.1-50.

< < = 56.45 in < 132.63 in < 492.70 in

=

= 1.14 489.88 kip-in - ( 489.88 kip-in - 0.7(25.20 ksi) ( 11.04 in³))132.63 in - 56.45 in

= 499.72 kip-in492.70 in - 56.45 in

Refer to Section F4, part 2. Lateral Torsional Buckling (c) on p16.1-50.

< = 132.63 in < 492.70 in

= 1 + 0.078

²

=

1.14 (π²) (29,000 ksi) 1 + 0.078

0.20 in 132.63 in ²

= 94.79 ksi² 132.63 in ² (11.04 in³) (5.35 in) 1.81 in

1.81 in

= = ( 94.79 ksi) ( 11.04 in³) = 1046.66 kip-in

4. Strong-Axis Moment Capacity Based on Compression Flange Local Buckling For Members With Compact or Noncompact Webs

=

= 489.88 kip-in - ( 489.88 kip-in - 0.7(25.20 ksi) ( 11.04 in³))8.54 in - 10.79 in

= 527.55 kip-in28.38 in - 10.79 in

= = (0.9) ( 29,000 ksi) ( 0.760 ) ( 11.04 in³) = 3003.44 kip-inλ² ( 8.54 )²

5. Strong-Axis Moment Capacity Based on Tension Flange Yielding For Members With Compact or Noncompact Webs

= = =13.61 in³

= 1.2311.04 in³

Refer to Equation F4-9b on p16.1-51 for Rpc. Note: Fy cancels out of the equation, leaving only the section moduli.

Rpc

Mp Mp λ - λpw

Myc Myc λrw - λpw

Refer to Equation F4-1 on p16.1-50 for Mn.

Mn (Rpc) (Fy) (Sx)

Refer to Equation F4-11 on p16.1-51 for aw.

aw(hc)(tw)

(bf)(tf)

Refer to to User Note on p16.1-52 for rt.

rt

bf

aw

½ ½

Refer to Equation F4-7 on p16.1-50 for Lp.

Lp 1.1 rt

½ ½

Fy

Refer to Equation F4-6a on p16.1-50 for Lp. Note: the section is doubly symmetric, therefore the Sxt/Sxc > 1

FL (0.70) (Fy)

Refer to Equation F4-8 on p16.1-50 for Lr. Note: c = 1 for doubly symetric I-shaped members and is therefore neglected.

Lr 1.95 rt

(J) ½ 0.7FL(Sx) (ho) ½ ½

0.7 FL(Sx) (ho)

Lr

½ ½ ½

Lb Lp

Lp Lb Lr


Mn (Cb) (Rpc(Myc) - Rpc(Myc) - (FL) (Sx)) Lb - Lp

Lr - Lp

Mn

Lb Lr

Refer to Equation F4-5 on p16.1-50 for Fcr.

Fcr

Cb(π²) (E) J Lb½ ½

Lb(Sx) (ho) rt

rt


Mn (Fcr) (Sx)


Mn (Rpt(Mp) - Rpt(Mp) - 0.7(Fy) (Sx)) λ - λpf

λrf - λpf

Mn


Mn(0.9) (E) (kc) (Sx)

Refer to Equation F4-15a on p16.1-52 for Rpt. Note: Fy cancels out of the equation, leaving only the section moduli.

Rpt

Mp (Zx) (Fy)

Myt (Sx) (Fy)


= - - 1 =13.61 in³

-13.61 in³

- 123.26 - 192.44

= -0.0511.04 in³ 11.04 in³ 161.78 - 192.44

= = ( 1.23 ) ( 36.00 ksi) ( 11.04 in³) = 489.88 kip-in

6. Strong-Axis Moment Capacity Based on Compression Flange Yielding For Members With Slender Webs

= 1 - - 5.7E

= 1 -0.44 in³ 4.75 in

- 5.729,000 ksi

= 1.051200 + 300(0.44 in³) 0.23 in 36.00 ksi

= = ( 1.00 ) ( 36.00 ksi) ( 11.04 in³) = 397.49 kip-in

7. Strong-Axis Moment Capacity Based on Lateral Torsional Buckling For Members With Slender Webs

=E

= π(1.81 in)29,000 ksi

= 192.68 in0.7(36.00 ksi)




< < = 56.45 in < 132.63 in < 192.68 in

= = 1.14 36.00 ksi - 0.3(36.00 ksi)132.63 in - 56.45 in

= 34.16 ksi192.68 in - 56.45 in

= = ( 1.00 ) ( 36.00 ksi) ( 11.04 in³) = 397.49 kip-in

8. Strong-Axis Moment Capacity Based on Compression Flange Buckling For Members With Slender Webs

= =

0.9(29,000 ksi) ( 0.76 )= 34342.11 ksi

² 0.760 ²

= = 36.00 ksi - 0.3(36.00 ksi)8.54 in - 10.79 in

= 37.38 ksi28.38 in - 10.79 in

= = ( 1.00 ) ( 36.00 ksi) ( 11.04 in³) = 397.49 kip-in

9. Strong-Axis Moment Capacity Based on Tension Flange Yielding For Members With Slender Webs

= = ( 36.00 ksi) ( 11.04 in³) = 397.49 kip-in

Design Flexural Strength

= = (0.9) ( 489.88 kip-in) = 440.90 kip-in

Allowable flexural Strength

= =489.88 kip-in

= 293.34 kip-in1.67

Rpt

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)

Refer to Equation F5-6 on p16.1-54 for Rpg.

Rpgaw hc

½ ½

1200 + 300aw tw Fy


Mn (Rpg) (Fy) (Sx)

Refer to Equation F5-5 on p16.1-53 for Lr.

Lr π rt

½ ½

0.7 FL

Lb Lp

Lp Lb Lr


Fcr (Cb) Fy - 0.3(Fy)Lb - Lp

Lr - Lp


Mn (Rpg) (Fcr) (Sx)


Fcr

0.9(E)(kc)

bf

2tf


Fcr Fy - 0.3(Fy)λ - λpf

λrf - λpf


Mn (Rpg) (Fcr) (Sx)


Mn (Fy) (Sx)

Mu (Φb) (Mn)

MuMn

Ωb


PROJECT NO.

DATE



6.2

7 in


0.2




0.20 in

0.3

1 in

5.20 in





















31.91 in

108.93 in






BY

Cb

Lb

Fy

Ax

bf

twyz

tfIx

Iy

Ixrx

Iyry

Sx-top

Sx-bottom

AflangeSy-top

AwebSy-bottom

Zx

Zy

Aw

Af

tmod

ws

Ix

Iy





= =3.97 in

= 8.82t 0.45 in

= 0.38E

= 0.3829,000 ksi

= 10.7936.00 ksi

=

4

=

4

= 0.737h 5.89 in Use 0.7370.20 in

= 1.00E

= 1.0029,000 ksi

= 28.3836.00 ksi


t

b< = 8.82 < 28.38

t


= = 2(5.96 in) + 0.31 in - 0.23 in - 2.60 in) = 6.89 in

= = 2(5.96 in) + 0.31 in - 0.23 in - 1.35 in) = 9.39 in

E 6.89 in 29,000 ksi

= = 9.39 in 36.00 ksi

= 136.45

0.54 - 0.09²

0.548.55 in³

- 0.09²

9.61 in³

= 5.70E

= 5.7029,000 ksi

= 161.7836.00 ksi


h< = 27.55 < 161.78


= = ( 8.55 in³) ( 36.00 ksi) = 307.82 kip-in

= = 5.42 in - - 0.09 in = 5.51 in


λ =b

= 8.82t


= =5.51 in

= 27.550.20 in

= 6.89 in


= = =8.55 in³

= 1.266.81 in³


λ = = 27.55

bf

2tf


λpf

½ ½

Fy


kc½ ½

tw

λrf

½ ½

Fy

λpf

λrf




hc ½ ½

λpw

hp Fy

Zx

Sx

λrw

½ ½

Fy

λpwtw

λrwtw


Mp (Zx) (Fy)


ho d - tf - tmod

ho

tw tw


hc

hcλpf

tw


Rpc

Mp (Zx) (Fy)

Myc (Sx) (Fy)

hc

tw

= - - 1 =8.55 in³

-8.55 in³

- 127.55 - 136.45

= 2.356.81 in³ 6.81 in³ 161.78 - 136.45

= = (1.26) (36.00 ksi) (6.81 in³) = 307.82 kip-in


= =(6.89 in) (0.20 in)

= 1.54(3.97 in) (0.23 in)

= =3.97 in

= 1.02 in12 1 +

112 1 +

1( 1.54 in)

6 6

=E

= 1.1(1.02 in)29,000 ksi

= 31.91 in36.00 ksi

= = (0.70) ( 36.00 ksi) = 25.20 ksi

=E

1 + 1 + 6.762

E J

= 1.95(1.02 in)29,000 ksi 0.09 in

1 + 1 + 6.760.7(25.20 ksi) (6.81 in³) ( 5.51in) 2

= 235.58 in0.7(25.20 ksi) (6.81 in³) (5.51 in) 29,000 ksi 0.09 in




< < = 31.91 in < 132.63 in < 235.58 in

=


= 245.11 kip-in235.58 in - 31.91 in


< = 132.63 in < 235.58 in

= 1 + 0.078

²

=

1.14 (π²) (29,000 ksi) 1 + 0.078

0.09 in 132.63 in ²

= 39.13 ksi² 132.63 in ² (6.81 in³) (5.51 in) 1.02 in

1.02 in

= = ( 39.13 ksi) ( 6.81 in³) = 266.45 kip-in


=


= 328.76 kip-in28.38 in - 10.79 in

= = (0.9) ( 29,000 ksi) ( 0.737 ) ( 6.81 in³) = 1683.19 kip-inλ² ( 8.82 )²


= = =8.55 in³

= 1.266.81 in³


Rpc

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)


aw(hc)(tw)

(bf)(tf)


rt

bf

aw

½ ½


Lp 1.1 rt

½ ½

Fy


FL (0.70) (Fy)


Lr 1.95 rt

(J) ½ 0.7FL(Sx) (ho) ½ ½

0.7 FL(Sx) (ho)

Lr

½ ½ ½

Lb Lp

Lp Lb Lr



Lr - Lp

Mn

Lb Lr


Fcr

Cb(π²) (E) J Lb½ ½

Lb(Sx) (ho) rt

rt


Mn (Fcr) (Sx)



λrf - λpf

Mn


Mn(0.9) (E) (kc) (Sx)


Rpt

Mp (Zx) (Fy)

Myt (Sx) (Fy)


= - - 1 =8.55 in³

-8.55 in³

- 127.55 - 136.45

= 2.356.81 in³ 6.81 in³ 161.78 - 136.45

= = ( 1.26 ) ( 36.00 ksi) ( 6.81 in³) = 307.82 kip-in


= 1 - - 5.7E

= 1 -1.54 in³ 6.89 in

- 5.729,000 ksi

= 1.121200 + 300(1.54 in³) 0.20 in 36.00 ksi

= = ( 1.00 ) ( 36.00 ksi) ( 6.81 in³) = 245.14 kip-in


=E

= π(1.02 in)29,000 ksi

= 108.93 in0.7(36.00 ksi)




< > = 31.91 in < 132.63 in > 108.93 in

= = 1.14 36.00 ksi - 0.3(36.00 ksi)132.63 in - 31.91 in

= 24.94 ksi108.93 in - 31.91 in

= = ( 1.00 ) ( 24.94 ksi) ( 6.81 in³) = 169.83 kip-in


= =

0.9(29,000 ksi) ( 0.74 )= 95004.54 ksi

² 0.450 ²

= = 36.00 ksi - 0.3(36.00 ksi)8.82 in - 10.79 in

= 37.20 ksi28.38 in - 10.79 in

= = ( 1.00 ) ( 36.00 ksi) ( 6.81 in³) = 245.14 kip-in


= = ( 36.00 ksi) ( 6.81 in³) = 245.14 kip-in


= = (0.9) ( 245.11 kip-in) = 220.60 kip-in


= =245.11 kip-in

= 146.77 kip-in1.67

Rpt

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)


Rpgaw hc

½ ½

1200 + 300aw tw Fy


Mn (Rpg) (Fy) (Sx)


Lr π rt

½ ½

0.7 FL

Lb Lp

Lp Lb Lr



Lr - Lp


Mn (Rpg) (Fcr) (Sx)


Fcr

0.9(E)(kc)

bf

2tf



λrf - λpf


Mn (Rpg) (Fcr) (Sx)


Mn (Fy) (Sx)

Mu (Φb) (Mn)

MuMn

Ωb


PROJECT NO.

DATE



9.31

in


0.57

in

G 11,200 ksi (shear modulus of elasticity for steel)

1.00 (lateral-torsional buckling modification factor)


96.63 in (compression unbraced length of beam)

0.36 in 36.00 ksi (beam yield strength)

0.3

1 in K 1.00 (effective buckling length factor)

5.36 in














Shell plate i 10.52 in³ (weak-axis plastic section modulus)

t 0.38 in (thickness of shell) 209.91 in⁶ (warping constant)

corrosion 0.06 in (corrosion allowance) 3.31 in² (web area for vertical shear)

0.31 in (modified thickness of shell) 5.95 in² (flange area for horizontal shear)

5.36 in (effective shell width=stem width + (2)(8)(plate thickness) J 0.67 in (torsional constant)A 1.67 in² (cross sectional area of shell)



44.02 in

150.26 in



Required Resistance Factored Nominal Resistance31.69 kip 242.59 kip

22.45 kip-ft 45.94 kip-ft

0.00 kip 47.61 kip

Re. 13th Edition AISC Steel Construction Manual - Equation H1-1a on p. 16.1-70

+8

+ =31.69 kip

+8 22.45 kip-in

+0.00 kip-in

9 242.59 kip 9 45.94 kip-in 0.00 kip-in

Re. 13th Edition AISC Steel Construction Manual - Equation H1-1b on p. 16.1-70

+ + =31.69 kip

+22.45 kip-in

+0.00 kip-in

= 0.55242.589476166 45.94 kip-in 0.00 kip-in

Re. 13th Edition AISC Steel Construction Manual - Equation H3-6 on p. 16.1-72

+²

=31.69 kip

+22.45 kip-in ²

= 0.37242.59 kip 45.94 kip-in

Unity Ratio = 0.37 - Design Based on Equation H3-6


BY

Cb

Lb

Lc

Fy

Ax

bf

twyz

tfIx

Iy

Ixrx

Iyry

Sx-top

Sx-bottom

AflangeSy-top

AwebSy-bottom

Zx

Zy

Cw

Aw

tmodAf

ws

Ix

Iy



Compressive (Pr) Compressive (Pc)


Strong-Axis Shear (Vrx) Strong-Axis Shear (Vcx)

Pr Mrx Mry

Pc Mcx Mcy

Pr Mrx Mry

2Pc Mcx Mcy

Pr Mr

Pco Mc


Beam Compresive Load CapacityRefer to Section E3 on p16.1-33 for limit state based on flexural buckling & Table C-C2.2 on p16.1-240 for effective length factor, K.

KL = = ( 1.00 ) ( 96.63 in) = 59.18r r 1.63 in

=(π²) (E)

=(π²) (29,000 ksi)

= 81.72 ksiKL ² ( 59.18 )²r

= + (G)(J)1

=(π²) (29,000 ksi) 209.91 in⁶

+ 11,200 ksi 0.67 in1

= 96.42 ksi((1.00) (96.63 in))² 120.96 in + 24.00 in

4.71E

= 4.7129,000 ksi

= 133.6836.00 ksi

4.71E

>KL

= 133.68 > 59.18 - Therefore Equation E3-2 appliesr

Refer to Equation E3-2 on p.16.1-33

ξ = =36.00 ksi

= 0.44181.72 ksi

0.441

= = 0.658 ( 36.00 ksi) = 29.94 ksi


= = (0.877)( 81.72 ksi) = 71.66 ksi

Ultimate Compressive Strength

= = (0.9) ( 29.94 ksi) 9.00 in² = 242.59 kip

Allowable Compressive Strength

= =( 29.94 ksi) 9.00 in²

= 161.40 kip1.67


= =7.50 in

= 6.58t 1.14 in

= 0.38E

= 0.3829,000 ksi

= 10.7936.00 ksi

=

4

=

4

= 0.802h 8.82 in Use 0.7600.36 in

= 1.00(E)

= 1.00(29,000 ksi)

= 28.3836.00 ksi


t

b< = 6.58 < 28.38

t


= = 2(9.00 in) + 0.31 in - 0.57 in - 5.88 in) = 5.72 in

= = 2(9.00 in) + 0.31 in - 0.57 in - 8.19 in) = 1.10 in

E 5.72 in 29,000 ksi

= = 1.10 in 36.00 ksi

= 350.67

0.54 - 0.09²

0.5428.09 in³

- 0.09²

20.56 in³

= 5.70E

= 5.7029,000 ksi

= 161.78

(K)(Lc)

Refer to Equation E3-4 on p16.1-33 for Fey.

Fe


Fe(π²)(E)(Cw)

((K)(Lc))2 Ix + Iy

½ ½

Fy

½

Fy

Fy

Fe

ξ

Fcr 0.658 (Fy)

Fcr (0.877) (Fe)

Pn (Φb) (Fcr) (Ax)

Pn(Fcr)(Ax)

Ωb

bf

2tf


λpf

½ ½

Fy


kc½ ½

tw

λrf

½ ½

Fy

λpf

λrf




hc ½ ½

λpw

hp Fy

Zx

Sx

λrw

½ ½

= 5.70 = 5.7036.00 ksi

= 161.78


h< = 22.14 < 161.78


= = ( 28.09 in³) ( 36.00 ksi) = 1011.36 kip-in

= = 8.12 in - 0.26 in = 7.86 in


λ =b

= 6.58t


= =7.86 in

= 22.140.36 in

= 5.72 in


= = =28.09 in³

= 1.3720.56 in³


λ = = 22.14

= - - 1 =28.09 in³

-28.09 in³

- 122.14 - 350.67

= 0.7320.56 in³ 20.56 in³ 161.78 - 350.67

= = (1.37) (36.00 ksi) (20.56 in³) = 1011.36 kip-in


= =(5.72 in) (0.36 in)

= 1.21(5.36 in) (0.31 in)

= =5.36 in

= 1.41 in12 1 +

112 1 +

1( 1.21 in)

6 6

=E

= 1.1(1.41 in)29,000 ksi

= 44.02 in36.00 ksi

= = (0.70) ( 36.00 ksi) = 25.20 ksi

=E

1 + 1 + 6.762

E J

= 1.95(1.41 in)29,000 ksi 0.67 in

1 + 1 + 6.760.7(25.20 ksi) (20.56 in³) ( 7.86in) 2

= 419.81 in0.7(25.20 ksi) (20.56 in³) (7.86 in) 29,000 ksi 0.67 in



λrwFy

λpwtw

λrwtw


Mp (Zx) (Fy)


ho d - tf - tmod

ho

tw tw


hc

hcλpf

tw


Rpc

Mp (Zx) (Fy)

Myc (Sx) (Fy)

hc

tw


Rpc

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)


aw(hc) (tw)

(bf) (tf)


rt

bf

aw

½ ½


Lp 1.1 rt

½ ½

Fy


FL (0.70) (Fy)


Lr 1.95 rt

(J) ½ 0.7 FL(Sx) (ho) ½ ½

0.7 FL(Sx) (ho)

Lr

½ ½ ½

Lb Lp

< < = 44.02 in < 96.63 in < 419.81 in

=


= 920.54 kip-in419.81 in - 44.02 in

< = 96.63 in < 419.81 in

= 1 + 0.078

²

=

1.00 (π²) (29,000 ksi) 1 + 0.078

0.67 in 96.63 in ²

= 96.88 ksi² 96.63 in ² (20.56 in³) (7.86 in) 1.41 in

1.41 in

= = ( 96.88 ksi) ( 20.56 in³) = 1991.39 kip-in


=


= 1166.43 kip-in28.38 in - 10.79 in

= = (0.9) ( 29,000 ksi) ( 0.760 ) ( 20.56 in³) = 9420.53 kip-inλ² ( 6.58 )²


= = =28.09 in³

= 1.3720.56 in³

= - - 1 =28.09 in³

-28.09 in³

- 122.14 - 350.67

= 0.7320.56 in³ 20.56 in³ 161.78 - 350.67

= = ( 1.37 ) ( 36.00 ksi) ( 20.56 in³) = 1011.36 kip-in


= 1 - - 5.7E

= 1 -1.21 in³ 5.72 in

- 5.729,000 ksi

= 1.111200 + 300(1.21 in³) 0.36 in 36.00 ksi

= = ( 1.00 ) ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in


=E

= π(1.41 in)29,000 ksi

= 150.26 in0.7(36.00 ksi)



< < = 44.02 in < 96.63 in < 150.26 in

= = 1.00 36.00 ksi - 0.3(36.00 ksi)96.63 in - 44.02 in

= 30.65 ksi150.26 in - 44.02 in

= = ( 1.00 ) ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in


Refer to Section F4, part 2. Lateral Torsional Buckling (b) on p16.1-50, Cb is conservatively assumed to be 1.00.

Lp Lb Lr



Lr - Lp

Mn

Refer to Section F4, part 2. Lateral Torsional Buckling (c) on p16.1-50, Cb is conservatively assumed to be 1.00.

Lb Lr


Fcr

Cb(π²) (E) J Lb½ ½

Lb(Sx) (ho) rt

rt


Mn (Fcr) (Sx)



λrf - λpf

Mn


Mn(0.9) (E) (kc) (Sx)


Rpt

Mp (Zx) (Fy)

Myt (Sx) (Fy)


Rpt

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)


Rpgaw hc

½ ½

1200 + 300aw tw Fy


Mn (Rpg) (Fy) (Sx)


Lr π rt

½ ½

0.7 FL

Lb Lp


Lp Lb Lr



Lr - Lp


Mn (Rpg) (Fcr) (Sx)


= =

0.9(29,000 ksi) ( 0.76 )= 15263.16 ksi

² 1.140 ²

= = 36.00 ksi - 0.3(36.00 ksi)6.58 in - 10.79 in

= 38.58 ksi28.38 in - 10.79 in

= = ( 1.00 ) ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in9. Strong-Axis Moment Capacity Based on Tension Flange Yielding For Members With Slender Webs

= = ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in


= = (0.9) ( 920.54 kip-in) = 828.49 kip-in


= =920.54 kip-in

= 551.22 kip-in1.67

Strong -Axis Shear StrengthRefer to Section G2 on page 16.1-65

h= =

7.65 in= 21.558

0.36 in

= 5

1.10 1.105 ( 29,000 ksi)

= 69.81136.00 ksi

h≤ 1.10 = 21.558 ≤ 69.811 Therefore Equation G2-3 Applies

Refer to Equation G2-3 on page 16.1-65

= 1.00

1.37 1.375 ( 29,000 ksi)

= 86.94736.00 ksi

1.10 ≥h

≤ 1.37 = 69.811 ≥ 21.558 ≤ 86.947


=

1.10

= = 3.23869.811h 21.558

h≤ 1.37 = 21.558 ≤ 86.947


==

(1.51) (29,000 ksi) ( 5.00 )= 13.087

h ( 21.56 )² ( 36.00 ksi)

Design Shear StrengthRefer to Equation G2-1 on page 16.1-65

= = 1.00(0.6) ( 36.00 ksi) ( 3.31 in² ) ( 1.000 ) = 71.41 kip

Allowable Shear StrengthRefer to Equation G2-1 on page 16.1-65

= = (0.6) ( 36.00 ksi) ( 3.31 in² ) ( 1.000 ) = 47.61 kip1.50

Fcr

0.9(E)(kc)

bf

2tf



λrf - λpf


Mn (Rpg) (Fcr) (Sx)


Mn (Fy) (Sx)

Mu (Φb) (Mn)

MuMn

Ωb

d - 2tf - k

tw tw

kv

(kv) (E) ½ ½

Fy

(kv) (E) ½

tw Fy

Cv

(kv) (E) ½ ½

Fy

(kv) (E) ½ (kv) (E) ½

Fy tw Fy

Cv

(kv) (E) ½

Fy

tw

(kv) (E) ½

tw Fy

Cv

1.51(E) (kv) 2 (Fy)

tw

Vu Φv(0.6) (Fy) (Aw) (Cv)

Vu(0.6) (Fy) (Aw) (Cv)

Ωv


PROJECT NO.

DATE



9.31

in


0.57

in






0.3


5.36 in





















44.02 in

150.26 in





0.00 kip 47.61 kip


+8

+ =31.69 kip

+8 8.85 kip-in

+0.00 kip-in

= 0.429 129.36 kip 9 45.94 kip-in 0.00 kip-in


+ + =31.69 kip

+8.85 kip-in

+0.00 kip-in

129.358317017 45.94 kip-in 0.00 kip-in


+²

=31.69 kip

+8.85 kip-in ²

= 0.28129.36 kip 45.94 kip-in



BY

Cb

Lb

Lc

Fy

Ax

bf

twyz

tfIx

Iy

Ixrx

Iyry

Sx-top

Sx-bottom

AflangeSy-top

AwebSy-bottom

Zx

Zy

Cw

Aw

tmodAf

ws

Ix

Iy






Pr Mrx Mry

Pc Mcx Mcy

Pr Mrx Mry

2Pc Mcx Mcy

Pr Mr

Pco Mc



KL = = ( 2.10 ) ( 96.63 in) = 124.28r r 1.63 in

=(π²) (E)

=(π²) (29,000 ksi)

= 18.53 ksiKL ² ( 124.28 )²r

= + (G)(J)1

=(π²) (29,000 ksi) 209.91 in⁶

+ 11,200 ksi 0.67 in1

= 62.10 ksi((2.10) (96.63 in))² 120.96 in + 24.00 in

4.71E

= 4.7129,000 ksi

= 133.6836.00 ksi

4.71E

>KL



ξ = =36.00 ksi

= 1.94318.53 ksi

1.943

= = 0.658 ( 36.00 ksi) = 15.96 ksi


= = (0.877)( 18.53 ksi) = 16.25 ksi


= = (0.9) ( 15.96 ksi) 9.00 in² = 129.36 kip


= =( 15.96 ksi) 9.00 in²

= 86.07 kip1.67


= =7.50 in

= 6.58t 1.14 in

= 0.38E

= 0.3829,000 ksi

= 10.7936.00 ksi

=

4

=

4

= 0.802h 8.82 in Use 0.7600.36 in

= 1.00(E)

= 1.00(29,000 ksi)

= 28.3836.00 ksi


t

b< = 6.58 < 28.38

t


= = 2(9.00 in) + 0.31 in - 0.57 in - 5.88 in) = 5.72 in

= = 2(9.00 in) + 0.31 in - 0.57 in - 8.19 in) = 1.10 in

E 5.72 in 29,000 ksi

= = 1.10 in 36.00 ksi

= 350.67

0.54 - 0.09²

0.5428.09 in³

- 0.09²

20.56 in³

= 5.70E

= 5.7029,000 ksi

= 161.78

(K)(Lc)


Fe


Fe(π²)(E)(Cw)

((K)(Lc))2 Ix + Iy

½ ½

Fy

½

Fy

Fy

Fe

ξ

Fcr 0.658 (Fy)

Fcr (0.877) (Fe)

Pn (Φb) (Fcr) (Ax)

Pn(Fcr)(Ax)

Ωb

bf

2tf


λpf

½ ½

Fy


kc½ ½

tw

λrf

½ ½

Fy

λpf

λrf




hc ½ ½

λpw

hp Fy

Zx

Sx

λrw

½ ½

= 5.70 = 5.7036.00 ksi

= 161.78


h< = 22.14 < 161.78


= = ( 28.09 in³) ( 36.00 ksi) = 1011.36 kip-in

= = 8.12 in - 0.26 in = 7.86 in


λ =b

= 6.58t


= =7.86 in

= 22.140.36 in

= 5.72 in


= = =28.09 in³

= 1.3720.56 in³


λ = = 22.14

= - - 1 =28.09 in³

-28.09 in³

- 122.14 - 350.67

= 0.7320.56 in³ 20.56 in³ 161.78 - 350.67

= = (1.37) (36.00 ksi) (20.56 in³) = 1011.36 kip-in


= =(5.72 in) (0.36 in)

= 1.21(5.36 in) (0.31 in)

= =5.36 in

= 1.41 in12 1 +

112 1 +

1( 1.21 in)

6 6

=E

= 1.1(1.41 in)29,000 ksi

= 44.02 in36.00 ksi

= = (0.70) ( 36.00 ksi) = 25.20 ksi

=E

1 + 1 + 6.762

E J

= 1.95(1.41 in)29,000 ksi 0.67 in

1 + 1 + 6.760.7(25.20 ksi) (20.56 in³) ( 7.86in) 2

= 419.81 in0.7(25.20 ksi) (20.56 in³) (7.86 in) 29,000 ksi 0.67 in



λrwFy

λpwtw

λrwtw


Mp (Zx) (Fy)


ho d - tf - tmod

ho

tw tw


hc

hcλpf

tw


Rpc

Mp (Zx) (Fy)

Myc (Sx) (Fy)

hc

tw


Rpc

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)


aw(hc) (tw)

(bf) (tf)


rt

bf

aw

½ ½


Lp 1.1 rt

½ ½

Fy


FL (0.70) (Fy)


Lr 1.95 rt

(J) ½ 0.7 FL(Sx) (ho) ½ ½

0.7 FL(Sx) (ho)

Lr

½ ½ ½

Lb Lp

< < = 44.02 in < 96.63 in < 419.81 in

=


= 920.54 kip-in419.81 in - 44.02 in

< = 96.63 in < 419.81 in

= 1 + 0.078

²

=

1.00 (π²) (29,000 ksi) 1 + 0.078

0.67 in 96.63 in ²

= 96.88 ksi² 96.63 in ² (20.56 in³) (7.86 in) 1.41 in

1.41 in

= = ( 96.88 ksi) ( 20.56 in³) = 1991.39 kip-in


=


= 1166.43 kip-in28.38 in - 10.79 in

= = (0.9) ( 29,000 ksi) ( 0.760 ) ( 20.56 in³) = 9420.53 kip-inλ² ( 6.58 )²


= = =28.09 in³

= 1.3720.56 in³

= - - 1 =28.09 in³

-28.09 in³

- 122.14 - 350.67

= 0.7320.56 in³ 20.56 in³ 161.78 - 350.67

= = ( 1.37 ) ( 36.00 ksi) ( 20.56 in³) = 1011.36 kip-in


= 1 - - 5.7E

= 1 -1.21 in³ 5.72 in

- 5.729,000 ksi

= 1.111200 + 300(1.21 in³) 0.36 in 36.00 ksi

= = ( 1.00 ) ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in


=E

= π(1.41 in)29,000 ksi

= 150.26 in0.7(36.00 ksi)



< < = 44.02 in < 96.63 in < 150.26 in

= = 1.00 36.00 ksi - 0.3(36.00 ksi)96.63 in - 44.02 in

= 30.65 ksi150.26 in - 44.02 in

= = ( 1.00 ) ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in



Lp Lb Lr



Lr - Lp

Mn


Lb Lr


Fcr

Cb(π²) (E) J Lb½ ½

Lb(Sx) (ho) rt

rt


Mn (Fcr) (Sx)



λrf - λpf

Mn


Mn(0.9) (E) (kc) (Sx)


Rpt

Mp (Zx) (Fy)

Myt (Sx) (Fy)


Rpt

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)


Rpgaw hc

½ ½

1200 + 300aw tw Fy


Mn (Rpg) (Fy) (Sx)


Lr π rt

½ ½

0.7 FL

Lb Lp


Lp Lb Lr



Lr - Lp


Mn (Rpg) (Fcr) (Sx)


= =

0.9(29,000 ksi) ( 0.76 )= 15263.16 ksi

² 1.140 ²

= = 36.00 ksi - 0.3(36.00 ksi)6.58 in - 10.79 in

= 38.58 ksi28.38 in - 10.79 in


= = ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in


= = (0.9) ( 920.54 kip-in) = 828.49 kip-in


= =920.54 kip-in

= 551.22 kip-in1.67


h= =

7.65 in= 21.558

0.36 in

= 5

1.10 1.105 ( 29,000 ksi)

= 69.81136.00 ksi



= 1.00

1.37 1.375 ( 29,000 ksi)

= 86.94736.00 ksi

1.10 ≥h

≤ 1.37 = 69.811 ≥ 21.558 ≤ 86.947


=

1.10

= = 3.23869.811h 21.558

h≤ 1.37 = 21.558 ≤ 86.947


==

(1.51) (29,000 ksi) ( 5.00 )= 13.087

h ( 21.56 )² ( 36.00 ksi)


= = 1.00(0.6) ( 36.00 ksi) ( 3.31 in² ) ( 1.000 ) = 71.41 kip


= = (0.6) ( 36.00 ksi) ( 3.31 in² ) ( 1.000 ) = 47.61 kip1.50

Fcr

0.9(E)(kc)

bf

2tf



λrf - λpf


Mn (Rpg) (Fcr) (Sx)


Mn (Fy) (Sx)

Mu (Φb) (Mn)

MuMn

Ωb

d - 2tf - k

tw tw

kv

(kv) (E) ½ ½

Fy

(kv) (E) ½

tw Fy

Cv

(kv) (E) ½ ½

Fy

(kv) (E) ½ (kv) (E) ½

Fy tw Fy

Cv

(kv) (E) ½

Fy

tw

(kv) (E) ½

tw Fy

Cv

1.51(E) (kv) 2 (Fy)

tw


Vu(0.6) (Fy) (Aw) (Cv)

Ωv


PROJECT NO.

DATE



9.31

in


0.57

in






0.3


5.36 in





















44.02 in

150.26 in





0.00 kip 47.61 kip


+8

+ =31.69 kip

+8 11.30 kip-in

+0.00 kip-in

= 0.469 129.36 kip 9 45.94 kip-in 0.00 kip-in


+ + =31.69 kip

+11.30 kip-in

+0.00 kip-in

129.358317017 45.94 kip-in 0.00 kip-in


+²

=31.69 kip

+11.30 kip-in ²

= 0.31129.36 kip 45.94 kip-in



BY

Cb

Lb

Lc

Fy

Ax

bf

twyz

tfIx

Iy

Ixrx

Iyry

Sx-top

Sx-bottom

AflangeSy-top

AwebSy-bottom

Zx

Zy

Cw

Aw

tmodAf

ws

Ix

Iy






Pr Mrx Mry

Pc Mcx Mcy

Pr Mrx Mry

2Pc Mcx Mcy

Pr Mr

Pco Mc



KL = = ( 2.10 ) ( 96.63 in) = 124.28r r 1.63 in

=(π²) (E)

=(π²) (29,000 ksi)

= 18.53 ksiKL ² ( 124.28 )²r

= + (G)(J)1

=(π²) (29,000 ksi) 209.91 in⁶

+ 11,200 ksi 0.67 in1

= 62.10 ksi((2.10) (96.63 in))² 120.96 in + 24.00 in

4.71E

= 4.7129,000 ksi

= 133.6836.00 ksi

4.71E

>KL



ξ = =36.00 ksi

= 1.94318.53 ksi

1.943

= = 0.658 ( 36.00 ksi) = 15.96 ksi


= = (0.877)( 18.53 ksi) = 16.25 ksi


= = (0.9) ( 15.96 ksi) 9.00 in² = 129.36 kip


= =( 15.96 ksi) 9.00 in²

= 86.07 kip1.67


= =7.50 in

= 6.58t 1.14 in

= 0.38E

= 0.3829,000 ksi

= 10.7936.00 ksi

=

4

=

4

= 0.802h 8.82 in Use 0.7600.36 in

= 1.00(E)

= 1.00(29,000 ksi)

= 28.3836.00 ksi


t

b< = 6.58 < 28.38

t


= = 2(9.00 in) + 0.31 in - 0.57 in - 5.88 in) = 5.72 in

= = 2(9.00 in) + 0.31 in - 0.57 in - 8.19 in) = 1.10 in

E 5.72 in 29,000 ksi

= = 1.10 in 36.00 ksi

= 350.67

0.54 - 0.09²

0.5428.09 in³

- 0.09²

20.56 in³

= 5.70E

= 5.7029,000 ksi

= 161.78

(K)(Lc)


Fe


Fe(π²)(E)(Cw)

((K)(Lc))2 Ix + Iy

½ ½

Fy

½

Fy

Fy

Fe

ξ

Fcr 0.658 (Fy)

Fcr (0.877) (Fe)

Pn (Φb) (Fcr) (Ax)

Pn(Fcr)(Ax)

Ωb

bf

2tf


λpf

½ ½

Fy


kc½ ½

tw

λrf

½ ½

Fy

λpf

λrf




hc ½ ½

λpw

hp Fy

Zx

Sx

λrw

½ ½

= 5.70 = 5.7036.00 ksi

= 161.78


h< = 22.14 < 161.78


= = ( 28.09 in³) ( 36.00 ksi) = 1011.36 kip-in

= = 8.12 in - 0.26 in = 7.86 in


λ =b

= 6.58t


= =7.86 in

= 22.140.36 in

= 5.72 in


= = =28.09 in³

= 1.3720.56 in³


λ = = 22.14

= - - 1 =28.09 in³

-28.09 in³

- 122.14 - 350.67

= 0.7320.56 in³ 20.56 in³ 161.78 - 350.67

= = (1.37) (36.00 ksi) (20.56 in³) = 1011.36 kip-in


= =(5.72 in) (0.36 in)

= 1.21(5.36 in) (0.31 in)

= =5.36 in

= 1.41 in12 1 +

112 1 +

1( 1.21 in)

6 6

=E

= 1.1(1.41 in)29,000 ksi

= 44.02 in36.00 ksi

= = (0.70) ( 36.00 ksi) = 25.20 ksi

=E

1 + 1 + 6.762

E J

= 1.95(1.41 in)29,000 ksi 0.67 in

1 + 1 + 6.760.7(25.20 ksi) (20.56 in³) ( 7.86in) 2

= 419.81 in0.7(25.20 ksi) (20.56 in³) (7.86 in) 29,000 ksi 0.67 in



λrwFy

λpwtw

λrwtw


Mp (Zx) (Fy)


ho d - tf - tmod

ho

tw tw


hc

hcλpf

tw


Rpc

Mp (Zx) (Fy)

Myc (Sx) (Fy)

hc

tw


Rpc

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)


aw(hc) (tw)

(bf) (tf)


rt

bf

aw

½ ½


Lp 1.1 rt

½ ½

Fy


FL (0.70) (Fy)


Lr 1.95 rt

(J) ½ 0.7 FL(Sx) (ho) ½ ½

0.7 FL(Sx) (ho)

Lr

½ ½ ½

Lb Lp

< < = 44.02 in < 96.63 in < 419.81 in

=


= 920.54 kip-in419.81 in - 44.02 in

< = 96.63 in < 419.81 in

= 1 + 0.078

²

=

1.00 (π²) (29,000 ksi) 1 + 0.078

0.67 in 96.63 in ²

= 96.88 ksi² 96.63 in ² (20.56 in³) (7.86 in) 1.41 in

1.41 in

= = ( 96.88 ksi) ( 20.56 in³) = 1991.39 kip-in


=


= 1166.43 kip-in28.38 in - 10.79 in

= = (0.9) ( 29,000 ksi) ( 0.760 ) ( 20.56 in³) = 9420.53 kip-inλ² ( 6.58 )²


= = =28.09 in³

= 1.3720.56 in³

= - - 1 =28.09 in³

-28.09 in³

- 122.14 - 350.67

= 0.7320.56 in³ 20.56 in³ 161.78 - 350.67

= = ( 1.37 ) ( 36.00 ksi) ( 20.56 in³) = 1011.36 kip-in


= 1 - - 5.7E

= 1 -1.21 in³ 5.72 in

- 5.729,000 ksi

= 1.111200 + 300(1.21 in³) 0.36 in 36.00 ksi

= = ( 1.00 ) ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in


=E

= π(1.41 in)29,000 ksi

= 150.26 in0.7(36.00 ksi)



< < = 44.02 in < 96.63 in < 150.26 in

= = 1.00 36.00 ksi - 0.3(36.00 ksi)96.63 in - 44.02 in

= 30.65 ksi150.26 in - 44.02 in

= = ( 1.00 ) ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in



Lp Lb Lr



Lr - Lp

Mn


Lb Lr


Fcr

Cb(π²) (E) J Lb½ ½

Lb(Sx) (ho) rt

rt


Mn (Fcr) (Sx)



λrf - λpf

Mn


Mn(0.9) (E) (kc) (Sx)


Rpt

Mp (Zx) (Fy)

Myt (Sx) (Fy)


Rpt

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)


Rpgaw hc

½ ½

1200 + 300aw tw Fy


Mn (Rpg) (Fy) (Sx)


Lr π rt

½ ½

0.7 FL

Lb Lp


Lp Lb Lr



Lr - Lp


Mn (Rpg) (Fcr) (Sx)


= =

0.9(29,000 ksi) ( 0.76 )= 15263.16 ksi

² 1.140 ²

= = 36.00 ksi - 0.3(36.00 ksi)6.58 in - 10.79 in

= 38.58 ksi28.38 in - 10.79 in


= = ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in


= = (0.9) ( 920.54 kip-in) = 828.49 kip-in


= =920.54 kip-in

= 551.22 kip-in1.67


h= =

7.65 in= 21.558

0.36 in

= 5

1.10 1.105 ( 29,000 ksi)

= 69.81136.00 ksi



= 1.00

1.37 1.375 ( 29,000 ksi)

= 86.94736.00 ksi

1.10 ≥h

≤ 1.37 = 69.811 ≥ 21.558 ≤ 86.947


=

1.10

= = 3.23869.811h 21.558

h≤ 1.37 = 21.558 ≤ 86.947


==

(1.51) (29,000 ksi) ( 5.00 )= 13.087

h ( 21.56 )² ( 36.00 ksi)


= = 1.00(0.6) ( 36.00 ksi) ( 3.31 in² ) ( 1.000 ) = 71.41 kip


= = (0.6) ( 36.00 ksi) ( 3.31 in² ) ( 1.000 ) = 47.61 kip1.50

Fcr

0.9(E)(kc)

bf

2tf



λrf - λpf


Mn (Rpg) (Fcr) (Sx)


Mn (Fy) (Sx)

Mu (Φb) (Mn)

MuMn

Ωb

d - 2tf - k

tw tw

kv

(kv) (E) ½ ½

Fy

(kv) (E) ½

tw Fy

Cv

(kv) (E) ½ ½

Fy

(kv) (E) ½ (kv) (E) ½

Fy tw Fy

Cv

(kv) (E) ½

Fy

tw

(kv) (E) ½

tw Fy

Cv

1.51(E) (kv) 2 (Fy)

tw


Vu(0.6) (Fy) (Aw) (Cv)

Ωv


PROJECT NO.

DATE



9.31

in


0.57

in






0.3


5.36 in





















44.02 in

150.26 in





0.00 kip 47.61 kip


+8

+ =31.69 kip

+8 7.69 kip-in

+0.00 kip-in

= 0.399 129.36 kip 9 45.94 kip-in 0.00 kip-in


+ + =31.69 kip

+7.69 kip-in

+0.00 kip-in

129.358317017 45.94 kip-in 0.00 kip-in


+²

=31.69 kip

+7.69 kip-in ²

= 0.27129.36 kip 45.94 kip-in



BY

Cb

Lb

Lc

Fy

Ax

bf

twyz

tfIx

Iy

Ixrx

Iyry

Sx-top

Sx-bottom

AflangeSy-top

AwebSy-bottom

Zx

Zy

Cw

Aw

tmodAf

ws

Ix

Iy






Pr Mrx Mry

Pc Mcx Mcy

Pr Mrx Mry

2Pc Mcx Mcy

Pr Mr

Pco Mc



KL = = ( 2.10 ) ( 96.63 in) = 124.28r r 1.63 in

=(π²) (E)

=(π²) (29,000 ksi)

= 18.53 ksiKL ² ( 124.28 )²r

= + (G)(J)1

=(π²) (29,000 ksi) 209.91 in⁶

+ 11,200 ksi 0.67 in1

= 62.10 ksi((2.10) (96.63 in))² 120.96 in + 24.00 in

4.71E

= 4.7129,000 ksi

= 133.6836.00 ksi

4.71E

>KL



ξ = =36.00 ksi

= 1.94318.53 ksi

1.943

= = 0.658 ( 36.00 ksi) = 15.96 ksi


= = (0.877)( 18.53 ksi) = 16.25 ksi


= = (0.9) ( 15.96 ksi) 9.00 in² = 129.36 kip


= =( 15.96 ksi) 9.00 in²

= 86.07 kip1.67


= =7.50 in

= 6.58t 1.14 in

= 0.38E

= 0.3829,000 ksi

= 10.7936.00 ksi

=

4

=

4

= 0.802h 8.82 in Use 0.7600.36 in

= 1.00(E)

= 1.00(29,000 ksi)

= 28.3836.00 ksi


t

b< = 6.58 < 28.38

t


= = 2(9.00 in) + 0.31 in - 0.57 in - 5.88 in) = 5.72 in

= = 2(9.00 in) + 0.31 in - 0.57 in - 8.19 in) = 1.10 in

E 5.72 in 29,000 ksi

= = 1.10 in 36.00 ksi

= 350.67

0.54 - 0.09²

0.5428.09 in³

- 0.09²

20.56 in³

= 5.70E

= 5.7029,000 ksi

= 161.78

(K)(Lc)


Fe


Fe(π²)(E)(Cw)

((K)(Lc))2 Ix + Iy

½ ½

Fy

½

Fy

Fy

Fe

ξ

Fcr 0.658 (Fy)

Fcr (0.877) (Fe)

Pn (Φb) (Fcr) (Ax)

Pn(Fcr)(Ax)

Ωb

bf

2tf


λpf

½ ½

Fy


kc½ ½

tw

λrf

½ ½

Fy

λpf

λrf




hc ½ ½

λpw

hp Fy

Zx

Sx

λrw

½ ½

= 5.70 = 5.7036.00 ksi

= 161.78


h< = 22.14 < 161.78


= = ( 28.09 in³) ( 36.00 ksi) = 1011.36 kip-in

= = 8.12 in - 0.26 in = 7.86 in


λ =b

= 6.58t


= =7.86 in

= 22.140.36 in

= 5.72 in


= = =28.09 in³

= 1.3720.56 in³


λ = = 22.14

= - - 1 =28.09 in³

-28.09 in³

- 122.14 - 350.67

= 0.7320.56 in³ 20.56 in³ 161.78 - 350.67

= = (1.37) (36.00 ksi) (20.56 in³) = 1011.36 kip-in


= =(5.72 in) (0.36 in)

= 1.21(5.36 in) (0.31 in)

= =5.36 in

= 1.41 in12 1 +

112 1 +

1( 1.21 in)

6 6

=E

= 1.1(1.41 in)29,000 ksi

= 44.02 in36.00 ksi

= = (0.70) ( 36.00 ksi) = 25.20 ksi

=E

1 + 1 + 6.762

E J

= 1.95(1.41 in)29,000 ksi 0.67 in

1 + 1 + 6.760.7(25.20 ksi) (20.56 in³) ( 7.86in) 2

= 419.81 in0.7(25.20 ksi) (20.56 in³) (7.86 in) 29,000 ksi 0.67 in



λrwFy

λpwtw

λrwtw


Mp (Zx) (Fy)


ho d - tf - tmod

ho

tw tw


hc

hcλpf

tw


Rpc

Mp (Zx) (Fy)

Myc (Sx) (Fy)

hc

tw


Rpc

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)


aw(hc) (tw)

(bf) (tf)


rt

bf

aw

½ ½


Lp 1.1 rt

½ ½

Fy


FL (0.70) (Fy)


Lr 1.95 rt

(J) ½ 0.7 FL(Sx) (ho) ½ ½

0.7 FL(Sx) (ho)

Lr

½ ½ ½

Lb Lp

< < = 44.02 in < 96.63 in < 419.81 in

=


= 920.54 kip-in419.81 in - 44.02 in

< = 96.63 in < 419.81 in

= 1 + 0.078

²

=

1.00 (π²) (29,000 ksi) 1 + 0.078

0.67 in 96.63 in ²

= 96.88 ksi² 96.63 in ² (20.56 in³) (7.86 in) 1.41 in

1.41 in

= = ( 96.88 ksi) ( 20.56 in³) = 1991.39 kip-in


=


= 1166.43 kip-in28.38 in - 10.79 in

= = (0.9) ( 29,000 ksi) ( 0.760 ) ( 20.56 in³) = 9420.53 kip-inλ² ( 6.58 )²


= = =28.09 in³

= 1.3720.56 in³

= - - 1 =28.09 in³

-28.09 in³

- 122.14 - 350.67

= 0.7320.56 in³ 20.56 in³ 161.78 - 350.67

= = ( 1.37 ) ( 36.00 ksi) ( 20.56 in³) = 1011.36 kip-in


= 1 - - 5.7E

= 1 -1.21 in³ 5.72 in

- 5.729,000 ksi

= 1.111200 + 300(1.21 in³) 0.36 in 36.00 ksi

= = ( 1.00 ) ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in


=E

= π(1.41 in)29,000 ksi

= 150.26 in0.7(36.00 ksi)



< < = 44.02 in < 96.63 in < 150.26 in

= = 1.00 36.00 ksi - 0.3(36.00 ksi)96.63 in - 44.02 in

= 30.65 ksi150.26 in - 44.02 in

= = ( 1.00 ) ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in



Lp Lb Lr



Lr - Lp

Mn


Lb Lr


Fcr

Cb(π²) (E) J Lb½ ½

Lb(Sx) (ho) rt

rt


Mn (Fcr) (Sx)



λrf - λpf

Mn


Mn(0.9) (E) (kc) (Sx)


Rpt

Mp (Zx) (Fy)

Myt (Sx) (Fy)


Rpt

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)


Rpgaw hc

½ ½

1200 + 300aw tw Fy


Mn (Rpg) (Fy) (Sx)


Lr π rt

½ ½

0.7 FL

Lb Lp


Lp Lb Lr



Lr - Lp


Mn (Rpg) (Fcr) (Sx)


= =

0.9(29,000 ksi) ( 0.76 )= 15263.16 ksi

² 1.140 ²

= = 36.00 ksi - 0.3(36.00 ksi)6.58 in - 10.79 in

= 38.58 ksi28.38 in - 10.79 in


= = ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in


= = (0.9) ( 920.54 kip-in) = 828.49 kip-in


= =920.54 kip-in

= 551.22 kip-in1.67


h= =

7.65 in= 21.558

0.36 in

= 5

1.10 1.105 ( 29,000 ksi)

= 69.81136.00 ksi



= 1.00

1.37 1.375 ( 29,000 ksi)

= 86.94736.00 ksi

1.10 ≥h

≤ 1.37 = 69.811 ≥ 21.558 ≤ 86.947


=

1.10

= = 3.23869.811h 21.558

h≤ 1.37 = 21.558 ≤ 86.947


==

(1.51) (29,000 ksi) ( 5.00 )= 13.087

h ( 21.56 )² ( 36.00 ksi)


= = 1.00(0.6) ( 36.00 ksi) ( 3.31 in² ) ( 1.000 ) = 71.41 kip


= = (0.6) ( 36.00 ksi) ( 3.31 in² ) ( 1.000 ) = 47.61 kip1.50

Fcr

0.9(E)(kc)

bf

2tf



λrf - λpf


Mn (Rpg) (Fcr) (Sx)


Mn (Fy) (Sx)

Mu (Φb) (Mn)

MuMn

Ωb

d - 2tf - k

tw tw

kv

(kv) (E) ½ ½

Fy

(kv) (E) ½

tw Fy

Cv

(kv) (E) ½ ½

Fy

(kv) (E) ½ (kv) (E) ½

Fy tw Fy

Cv

(kv) (E) ½

Fy

tw

(kv) (E) ½

tw Fy

Cv

1.51(E) (kv) 2 (Fy)

tw


Vu(0.6) (Fy) (Aw) (Cv)

Ωv


PROJECT NO.

DATE



9.31

in


0.57

in






0.3


5.36 in





















44.02 in

150.26 in





0.00 kip 47.61 kip


+8

+ =31.69 kip

+8 38.45 kip-in

+0.00 kip-in

= 0.999 129.36 kip 9 45.94 kip-in 0.00 kip-in


+ + =31.69 kip

+38.45 kip-in

+0.00 kip-in

129.358317017 45.94 kip-in 0.00 kip-in


+²

=31.69 kip

+38.45 kip-in ²

= 0.95129.36 kip 45.94 kip-in



BY

Cb

Lb

Lc

Fy

Ax

bf

twyz

tfIx

Iy

Ixrx

Iyry

Sx-top

Sx-bottom

AflangeSy-top

AwebSy-bottom

Zx

Zy

Cw

Aw

tmodAf

ws

Ix

Iy






Pr Mrx Mry

Pc Mcx Mcy

Pr Mrx Mry

2Pc Mcx Mcy

Pr Mr

Pco Mc



KL = = ( 2.10 ) ( 96.63 in) = 124.28r r 1.63 in

=(π²) (E)

=(π²) (29,000 ksi)

= 18.53 ksiKL ² ( 124.28 )²r

= + (G)(J)1

=(π²) (29,000 ksi) 209.91 in⁶

+ 11,200 ksi 0.67 in1

= 62.10 ksi((2.10) (96.63 in))² 120.96 in + 24.00 in

4.71E

= 4.7129,000 ksi

= 133.6836.00 ksi

4.71E

>KL



ξ = =36.00 ksi

= 1.94318.53 ksi

1.943

= = 0.658 ( 36.00 ksi) = 15.96 ksi


= = (0.877)( 18.53 ksi) = 16.25 ksi


= = (0.9) ( 15.96 ksi) 9.00 in² = 129.36 kip


= =( 15.96 ksi) 9.00 in²

= 86.07 kip1.67


= =7.50 in

= 6.58t 1.14 in

= 0.38E

= 0.3829,000 ksi

= 10.7936.00 ksi

=

4

=

4

= 0.802h 8.82 in Use 0.7600.36 in

= 1.00(E)

= 1.00(29,000 ksi)

= 28.3836.00 ksi


t

b< = 6.58 < 28.38

t


= = 2(9.00 in) + 0.31 in - 0.57 in - 5.88 in) = 5.72 in

= = 2(9.00 in) + 0.31 in - 0.57 in - 8.19 in) = 1.10 in

E 5.72 in 29,000 ksi

= = 1.10 in 36.00 ksi

= 350.67

0.54 - 0.09²

0.5428.09 in³

- 0.09²

20.56 in³

= 5.70E

= 5.7029,000 ksi

= 161.78

(K)(Lc)


Fe


Fe(π²)(E)(Cw)

((K)(Lc))2 Ix + Iy

½ ½

Fy

½

Fy

Fy

Fe

ξ

Fcr 0.658 (Fy)

Fcr (0.877) (Fe)

Pn (Φb) (Fcr) (Ax)

Pn(Fcr)(Ax)

Ωb

bf

2tf


λpf

½ ½

Fy


kc½ ½

tw

λrf

½ ½

Fy

λpf

λrf




hc ½ ½

λpw

hp Fy

Zx

Sx

λrw

½ ½

= 5.70 = 5.7036.00 ksi

= 161.78


h< = 22.14 < 161.78


= = ( 28.09 in³) ( 36.00 ksi) = 1011.36 kip-in

= = 8.12 in - 0.26 in = 7.86 in


λ =b

= 6.58t


= =7.86 in

= 22.140.36 in

= 5.72 in


= = =28.09 in³

= 1.3720.56 in³


λ = = 22.14

= - - 1 =28.09 in³

-28.09 in³

- 122.14 - 350.67

= 0.7320.56 in³ 20.56 in³ 161.78 - 350.67

= = (1.37) (36.00 ksi) (20.56 in³) = 1011.36 kip-in


= =(5.72 in) (0.36 in)

= 1.21(5.36 in) (0.31 in)

= =5.36 in

= 1.41 in12 1 +

112 1 +

1( 1.21 in)

6 6

=E

= 1.1(1.41 in)29,000 ksi

= 44.02 in36.00 ksi

= = (0.70) ( 36.00 ksi) = 25.20 ksi

=E

1 + 1 + 6.762

E J

= 1.95(1.41 in)29,000 ksi 0.67 in

1 + 1 + 6.760.7(25.20 ksi) (20.56 in³) ( 7.86in) 2

= 419.81 in0.7(25.20 ksi) (20.56 in³) (7.86 in) 29,000 ksi 0.67 in



λrwFy

λpwtw

λrwtw


Mp (Zx) (Fy)


ho d - tf - tmod

ho

tw tw


hc

hcλpf

tw


Rpc

Mp (Zx) (Fy)

Myc (Sx) (Fy)

hc

tw


Rpc

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)


aw(hc) (tw)

(bf) (tf)


rt

bf

aw

½ ½


Lp 1.1 rt

½ ½

Fy


FL (0.70) (Fy)


Lr 1.95 rt

(J) ½ 0.7 FL(Sx) (ho) ½ ½

0.7 FL(Sx) (ho)

Lr

½ ½ ½

Lb Lp

< < = 44.02 in < 96.63 in < 419.81 in

=


= 920.54 kip-in419.81 in - 44.02 in

< = 96.63 in < 419.81 in

= 1 + 0.078

²

=

1.00 (π²) (29,000 ksi) 1 + 0.078

0.67 in 96.63 in ²

= 96.88 ksi² 96.63 in ² (20.56 in³) (7.86 in) 1.41 in

1.41 in

= = ( 96.88 ksi) ( 20.56 in³) = 1991.39 kip-in


=


= 1166.43 kip-in28.38 in - 10.79 in

= = (0.9) ( 29,000 ksi) ( 0.760 ) ( 20.56 in³) = 9420.53 kip-inλ² ( 6.58 )²


= = =28.09 in³

= 1.3720.56 in³

= - - 1 =28.09 in³

-28.09 in³

- 122.14 - 350.67

= 0.7320.56 in³ 20.56 in³ 161.78 - 350.67

= = ( 1.37 ) ( 36.00 ksi) ( 20.56 in³) = 1011.36 kip-in


= 1 - - 5.7E

= 1 -1.21 in³ 5.72 in

- 5.729,000 ksi

= 1.111200 + 300(1.21 in³) 0.36 in 36.00 ksi

= = ( 1.00 ) ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in


=E

= π(1.41 in)29,000 ksi

= 150.26 in0.7(36.00 ksi)



< < = 44.02 in < 96.63 in < 150.26 in

= = 1.00 36.00 ksi - 0.3(36.00 ksi)96.63 in - 44.02 in

= 30.65 ksi150.26 in - 44.02 in

= = ( 1.00 ) ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in



Lp Lb Lr



Lr - Lp

Mn


Lb Lr


Fcr

Cb(π²) (E) J Lb½ ½

Lb(Sx) (ho) rt

rt


Mn (Fcr) (Sx)



λrf - λpf

Mn


Mn(0.9) (E) (kc) (Sx)


Rpt

Mp (Zx) (Fy)

Myt (Sx) (Fy)


Rpt

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)


Rpgaw hc

½ ½

1200 + 300aw tw Fy


Mn (Rpg) (Fy) (Sx)


Lr π rt

½ ½

0.7 FL

Lb Lp


Lp Lb Lr



Lr - Lp


Mn (Rpg) (Fcr) (Sx)


= =

0.9(29,000 ksi) ( 0.76 )= 15263.16 ksi

² 1.140 ²

= = 36.00 ksi - 0.3(36.00 ksi)6.58 in - 10.79 in

= 38.58 ksi28.38 in - 10.79 in


= = ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in


= = (0.9) ( 920.54 kip-in) = 828.49 kip-in


= =920.54 kip-in

= 551.22 kip-in1.67


h= =

7.65 in= 21.558

0.36 in

= 5

1.10 1.105 ( 29,000 ksi)

= 69.81136.00 ksi



= 1.00

1.37 1.375 ( 29,000 ksi)

= 86.94736.00 ksi

1.10 ≥h

≤ 1.37 = 69.811 ≥ 21.558 ≤ 86.947


=

1.10

= = 3.23869.811h 21.558

h≤ 1.37 = 21.558 ≤ 86.947


==

(1.51) (29,000 ksi) ( 5.00 )= 13.087

h ( 21.56 )² ( 36.00 ksi)


= = 1.00(0.6) ( 36.00 ksi) ( 3.31 in² ) ( 1.000 ) = 71.41 kip


= = (0.6) ( 36.00 ksi) ( 3.31 in² ) ( 1.000 ) = 47.61 kip1.50

Fcr

0.9(E)(kc)

bf

2tf



λrf - λpf


Mn (Rpg) (Fcr) (Sx)


Mn (Fy) (Sx)

Mu (Φb) (Mn)

MuMn

Ωb

d - 2tf - k

tw tw

kv

(kv) (E) ½ ½

Fy

(kv) (E) ½

tw Fy

Cv

(kv) (E) ½ ½

Fy

(kv) (E) ½ (kv) (E) ½

Fy tw Fy

Cv

(kv) (E) ½

Fy

tw

(kv) (E) ½

tw Fy

Cv

1.51(E) (kv) 2 (Fy)

tw


Vu(0.6) (Fy) (Aw) (Cv)

Ωv


PROJECT NO.

DATE



6.4

2 in


0.3




0.23 in

0.3

1 in

5.23 in





















56.45 in

192.68 in






BY

Cb

Lb

Fy

Ax

bf

twyz

tfIx

Iy

Ixrx

Iyry

Sx-top

Sx-bottom

AflangeSy-top

AwebSy-bottom

Zx

Zy

Aw

Af

tmod

ws

Ix

Iy





= =6.49 in

= 8.54t 0.76 in

= 0.38E

= 0.3829,000 ksi

= 10.7936.00 ksi

=

4

=

4

= 0.784h 5.99 in Use 0.7600.23 in

= 1.00E

= 1.0029,000 ksi

= 28.3836.00 ksi


t

b< = 8.54 < 28.38

t


= = 2(6.11 in) + 0.31 in - 0.38 in - 3.67 in) = 4.75 in

= = 2(6.11 in) + 0.31 in - 0.38 in - 4.99 in) = 2.11 in

E 4.75 in 29,000 ksi

= = 2.11 in 36.00 ksi

= 192.44

0.54 - 0.09²

0.5413.61 in³

- 0.09²

11.04 in³

= 5.70E

= 5.7029,000 ksi

= 161.7836.00 ksi


h< = 23.26 < 161.78


= = ( 13.61 in³) ( 36.00 ksi) = 489.88 kip-in

= = 5.42 in - 0.07 in = 5.35 in


λ =b

= 8.54t


= =5.35 in

= 23.260.23 in

= 4.75 in


= = =13.61 in³

= 1.2311.04 in³


λ = = 23.26

bf

2tf


λpf

½ ½

Fy


kc½ ½

tw

λrf

½ ½

Fy

λpf

λrf




hc ½ ½

λpw

hp Fy

Zx

Sx

λrw

½ ½

Fy

λpwtw

λrwtw


Mp (Zx) (Fy)


ho d - tf - tmod

ho

tw tw


hc

hcλpf

tw


Rpc

Mp (Zx) (Fy)

Myc (Sx) (Fy)

hc

tw

= - - 1 =13.61 in³

-13.61 in³

- 123.26 - 192.44

= -0.0511.04 in³ 11.04 in³ 161.78 - 192.44

= = (1.23) (36.00 ksi) (11.04 in³) = 489.88 kip-in


= =(4.75 in) (0.23 in)

= 0.44(6.49 in) (0.38 in)

= =6.49 in

= 1.81 in12 1 +

112 1 +

1( 0.44 in)

6 6

=E

= 1.1(1.81 in)29,000 ksi

= 56.45 in36.00 ksi

= = (0.70) ( 36.00 ksi) = 25.20 ksi

=E

1 + 1 + 6.762

E J

= 1.95(1.81 in)29,000 ksi 0.20 in

1 + 1 + 6.760.7(25.20 ksi) (11.04 in³) ( 5.35in) 2

= 492.70 in0.7(25.20 ksi) (11.04 in³) (5.35 in) 29,000 ksi 0.20 in




< < = 56.45 in < 132.63 in < 492.70 in

=


= 499.72 kip-in492.70 in - 56.45 in


< = 132.63 in < 492.70 in

= 1 + 0.078

²

=

1.14 (π²) (29,000 ksi) 1 + 0.078

0.20 in 132.63 in ²

= 94.79 ksi² 132.63 in ² (11.04 in³) (5.35 in) 1.81 in

1.81 in

= = ( 94.79 ksi) ( 11.04 in³) = 1046.66 kip-in


=


= 527.55 kip-in28.38 in - 10.79 in

= = (0.9) ( 29,000 ksi) ( 0.760 ) ( 11.04 in³) = 3003.44 kip-inλ² ( 8.54 )²


= = =13.61 in³

= 1.2311.04 in³


Rpc

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)


aw(hc)(tw)

(bf)(tf)


rt

bf

aw

½ ½


Lp 1.1 rt

½ ½

Fy


FL (0.70) (Fy)


Lr 1.95 rt

(J) ½ 0.7FL(Sx) (ho) ½ ½

0.7 FL(Sx) (ho)

Lr

½ ½ ½

Lb Lp

Lp Lb Lr



Lr - Lp

Mn

Lb Lr


Fcr

Cb(π²) (E) J Lb½ ½

Lb(Sx) (ho) rt

rt


Mn (Fcr) (Sx)



λrf - λpf

Mn


Mn(0.9) (E) (kc) (Sx)


Rpt

Mp (Zx) (Fy)

Myt (Sx) (Fy)


= - - 1 =13.61 in³

-13.61 in³

- 123.26 - 192.44

= -0.0511.04 in³ 11.04 in³ 161.78 - 192.44

= = ( 1.23 ) ( 36.00 ksi) ( 11.04 in³) = 489.88 kip-in


= 1 - - 5.7E

= 1 -0.44 in³ 4.75 in

- 5.729,000 ksi

= 1.051200 + 300(0.44 in³) 0.23 in 36.00 ksi

= = ( 1.00 ) ( 36.00 ksi) ( 11.04 in³) = 397.49 kip-in


=E

= π(1.81 in)29,000 ksi

= 192.68 in0.7(36.00 ksi)




< < = 56.45 in < 132.63 in < 192.68 in

= = 1.14 36.00 ksi - 0.3(36.00 ksi)132.63 in - 56.45 in

= 34.16 ksi192.68 in - 56.45 in

= = ( 1.00 ) ( 36.00 ksi) ( 11.04 in³) = 397.49 kip-in


= =

0.9(29,000 ksi) ( 0.76 )= 34342.11 ksi

² 0.760 ²

= = 36.00 ksi - 0.3(36.00 ksi)8.54 in - 10.79 in

= 37.38 ksi28.38 in - 10.79 in

= = ( 1.00 ) ( 36.00 ksi) ( 11.04 in³) = 397.49 kip-in


= = ( 36.00 ksi) ( 11.04 in³) = 397.49 kip-in


= = (0.9) ( 489.88 kip-in) = 440.90 kip-in


= =489.88 kip-in

= 293.34 kip-in1.67

Rpt

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)


Rpgaw hc

½ ½

1200 + 300aw tw Fy


Mn (Rpg) (Fy) (Sx)


Lr π rt

½ ½

0.7 FL

Lb Lp

Lp Lb Lr



Lr - Lp


Mn (Rpg) (Fcr) (Sx)


Fcr

0.9(E)(kc)

bf

2tf



λrf - λpf


Mn (Rpg) (Fcr) (Sx)


Mn (Fy) (Sx)

Mu (Φb) (Mn)

MuMn

Ωb


PROJECT NO.

DATE



9.3

1 in


0.5




0.36 in

0.3

1 in

5.36 in





















65.07 in

222.12 in






BY

Cb

Lb

Fy

Ax

bf

twyz

tfIx

Iy

Ixrx

Iyry

Sx-top

Sx-bottom

AflangeSy-top

AwebSy-bottom

Zx

Zy

Aw

Af

tmod

ws

Ix

Iy





= =7.50 in

= 6.58t 1.14 in

= 0.38E

= 0.3829,000 ksi

= 10.7936.00 ksi

=

4

=

4

= 0.802h 8.82 in Use 0.7600.36 in

= 1.00E

= 1.0029,000 ksi

= 28.3836.00 ksi


t

b< = 6.58 < 28.38

t


= = 2(9.00 in) + 0.31 in - 0.57 in - 5.88 in) = 5.72 in

= = 2(9.00 in) + 0.31 in - 0.57 in - 8.19 in) = 1.10 in

E 5.72 in 29,000 ksi

= = 1.10 in 36.00 ksi

= 350.67

0.54 - 0.09²

0.5428.09 in³

- 0.09²

20.56 in³

= 5.70E

= 5.7029,000 ksi

= 161.7836.00 ksi


h< = 22.14 < 161.78


= = ( 28.09 in³) ( 36.00 ksi) = 1011.36 kip-in

= = 8.12 in - 0.26 in = 7.86 in


λ =b

= 6.58t


= =7.86 in

= 22.140.36 in

= 5.72 in


= = =28.09 in³

= 1.3720.56 in³


λ = = 22.14

bf

2tf


λpf

½ ½

Fy


kc½ ½

tw

λrf

½ ½

Fy

λpf

λrf




hc ½ ½

λpw

hp Fy

Zx

Sx

λrw

½ ½

Fy

λpwtw

λrwtw


Mp (Zx) (Fy)


ho d - tf - tmod

ho

tw tw


hc

hcλpf

tw


Rpc

Mp (Zx) (Fy)

Myc (Sx) (Fy)

hc

tw

= - - 1 =28.09 in³

-28.09 in³

- 122.14 - 350.67

= 0.7320.56 in³ 20.56 in³ 161.78 - 350.67

= = (1.37) (36.00 ksi) (20.56 in³) = 1011.36 kip-in


= =(5.72 in) (0.36 in)

= 0.47(7.50 in) (0.57 in)

= =7.50 in

= 2.08 in12 1 +

112 1 +

1( 0.47 in)

6 6

=E

= 1.1(2.08 in)29,000 ksi

= 65.07 in36.00 ksi

= = (0.70) ( 36.00 ksi) = 25.20 ksi

=E

1 + 1 + 6.762

E J

= 1.95(2.08 in)29,000 ksi 0.67 in

1 + 1 + 6.760.7(25.20 ksi) (20.56 in³) ( 7.86in) 2

= 620.57 in0.7(25.20 ksi) (20.56 in³) (7.86 in) 29,000 ksi 0.67 in




< < = 65.07 in < 132.63 in < 620.57 in

=


= 932.46 kip-in620.57 in - 65.07 in


< = 132.63 in < 620.57 in

= 1 + 0.078

²

=

1.00 (π²) (29,000 ksi) 1 + 0.078

0.67 in 132.63 in ²

= 107.58 ksi² 132.63 in ² (20.56 in³) (7.86 in) 2.08 in

2.08 in

= = ( 107.58 ksi) ( 20.56 in³) = 2211.45 kip-in


=


= 1166.43 kip-in28.38 in - 10.79 in

= = (0.9) ( 29,000 ksi) ( 0.760 ) ( 20.56 in³) = 9420.53 kip-inλ² ( 6.58 )²


= = =28.09 in³

= 1.3720.56 in³


Rpc

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)


aw(hc)(tw)

(bf)(tf)


rt

bf

aw

½ ½


Lp 1.1 rt

½ ½

Fy


FL (0.70) (Fy)


Lr 1.95 rt

(J) ½ 0.7FL(Sx) (ho) ½ ½

0.7 FL(Sx) (ho)

Lr

½ ½ ½

Lb Lp

Lp Lb Lr



Lr - Lp

Mn

Lb Lr


Fcr

Cb(π²) (E) J Lb½ ½

Lb(Sx) (ho) rt

rt


Mn (Fcr) (Sx)



λrf - λpf

Mn


Mn(0.9) (E) (kc) (Sx)


Rpt

Mp (Zx) (Fy)

Myt (Sx) (Fy)


= - - 1 =28.09 in³

-28.09 in³

- 122.14 - 350.67

= 0.7320.56 in³ 20.56 in³ 161.78 - 350.67

= = ( 1.37 ) ( 36.00 ksi) ( 20.56 in³) = 1011.36 kip-in


= 1 - - 5.7E

= 1 -0.47 in³ 5.72 in

- 5.729,000 ksi

= 1.051200 + 300(0.47 in³) 0.36 in 36.00 ksi

= = ( 1.00 ) ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in


=E

= π(2.08 in)29,000 ksi

= 222.12 in0.7(36.00 ksi)




< < = 65.07 in < 132.63 in < 222.12 in

= = 1.00 36.00 ksi - 0.3(36.00 ksi)132.63 in - 65.07 in

= 31.35 ksi222.12 in - 65.07 in

= = ( 1.00 ) ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in


= =

0.9(29,000 ksi) ( 0.76 )= 15263.16 ksi

² 1.140 ²

= = 36.00 ksi - 0.3(36.00 ksi)6.58 in - 10.79 in

= 38.58 ksi28.38 in - 10.79 in

= = ( 1.00 ) ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in


= = ( 36.00 ksi) ( 20.56 in³) = 740.01 kip-in


= = (0.9) ( 932.46 kip-in) = 839.22 kip-in


= =932.46 kip-in

= 558.36 kip-in1.67

Rpt

Mp Mp λ - λpw

Myc Myc λrw - λpw


Mn (Rpc) (Fy) (Sx)


Rpgaw hc

½ ½

1200 + 300aw tw Fy


Mn (Rpg) (Fy) (Sx)


Lr π rt

½ ½

0.7 FL

Lb Lp

Lp Lb Lr



Lr - Lp


Mn (Rpg) (Fcr) (Sx)


Fcr

0.9(E)(kc)

bf

2tf



λrf - λpf


Mn (Rpg) (Fcr) (Sx)


Mn (Fy) (Sx)

Mu (Φb) (Mn)

MuMn

Ωb

1 2 3 4 5 6 7 8AISC_MANUAL_LABEL W A D BF TW TF KDES

WT22X167.5 168 49.2 22.0 15.9 1.03 1.77 2.56WT22X145 145 42.7 21.8 15.8 0.865 1.58 2.37WT22X131 131 38.4 21.7 15.8 0.785 1.42 2.21WT22X115 115 33.8 21.5 15.8 0.710 1.22 2.01

WT20X296.5 296 87.2 21.5 16.7 1.79 3.23 4.41WT20X251.5 252 73.9 21.0 16.4 1.54 2.76 3.94WT20X215.5 215 63.4 20.6 16.2 1.34 2.36 3.54WT20X198.5 198 58.4 20.5 16.1 1.22 2.20 3.38WT20X186 186 54.6 20.3 16.1 1.16 2.05 3.23WT20X181 181 53.3 20.3 16.0 1.12 2.01 3.19WT20X162 162 47.7 20.1 15.9 1.00 1.81 2.99

WT20X148.5 148 43.7 19.9 15.8 0.930 1.65 2.83WT20X138.5 138 40.7 19.8 15.8 0.830 1.58 2.76WT20X124.5 125 36.7 19.7 15.8 0.750 1.42 2.60WT20X107.5 108 31.7 19.5 15.8 0.650 1.22 2.40WT20X99.5 100 29.2 19.3 15.8 0.650 1.07 2.25WT20X196 196 57.6 20.8 12.4 1.42 2.52 3.70

WT20X165.5 166 48.7 20.4 12.2 1.22 2.13 3.31WT20X163.5 164 48.0 20.4 12.1 1.18 2.13 3.31WT20X147 147 43.1 20.2 12.0 1.06 1.93 3.11WT20X139 139 41.0 20.1 12.0 1.03 1.81 2.99WT20X132 132 38.8 20.0 11.9 0.960 1.73 2.91

WT20X117.5 118 34.5 19.8 11.9 0.830 1.58 2.76WT20X105.5 106 31.0 19.7 11.8 0.750 1.42 2.60WT20X91.5 91.5 26.7 19.5 11.8 0.650 1.20 2.40WT20X83.5 83.5 24.6 19.3 11.8 0.650 1.03 2.21WT20X74.5 74.5 21.9 19.1 11.8 0.630 0.830 2.01WT18X400 400 118 21.0 18.0 2.38 4.29 5.24WT18X326 325 96.1 20.2 17.6 1.97 3.54 4.49

WT18X264.5 264 77.8 19.6 17.2 1.61 2.91 3.86WT18X243.5 244 71.7 19.7 17.1 1.50 2.68 3.63WT18X220.5 220 64.9 19.1 17.0 1.36 2.44 3.39WT18X197.5 198 58.2 18.9 16.8 1.22 2.20 3.15WT18X180.5 180 53.0 18.7 16.7 1.12 2.01 2.96WT18X165 165 48.5 18.5 16.6 1.02 1.85 2.80WT18X151 151 44.4 18.4 16.7 0.945 1.68 2.63WT18X141 141 41.5 18.3 16.6 0.885 1.57 2.52WT18X131 131 38.5 18.1 16.6 0.840 1.44 2.39

WT18X123.5 124 36.3 18.0 16.5 0.800 1.35 2.30WT18X116 116 34.5 18.6 12.1 0.870 1.57 2.32WT18X128 128 37.7 18.7 12.2 0.960 1.73 2.48

WT18X115.5 116 34.1 18.6 12.1 0.870 1.57 2.32WT18X105 105 30.9 18.3 12.2 0.830 1.36 2.11WT18X97 97.0 28.5 18.2 12.1 0.765 1.26 2.01WT18X91 91.0 26.8 18.2 12.1 0.725 1.18 1.93WT18X85 85.0 25.0 18.1 12.0 0.680 1.10 1.85WT18X80 80.0 23.5 18.0 12.0 0.650 1.02 1.77WT18X75 75.0 22.1 17.9 12.0 0.625 0.940 1.69

WT18X67.5 67.5 19.9 17.8 12.0 0.600 0.790 1.54WT16.5X193.5 194 57.0 18.0 16.2 1.26 2.28 3.07WT16.5X177 177 52.1 17.8 16.1 1.16 2.09 2.88WT16.5X159 159 46.8 17.6 16.0 1.04 1.89 2.68

WT16.5X145.5 146 42.8 17.4 15.9 0.960 1.73 2.52WT16.5X131.5 132 38.7 17.3 15.8 0.870 1.57 2.36WT16.5X120.5 120 35.5 17.1 15.9 0.830 1.40 2.19

WT16.5X110.5 110 32.6 17.0 15.8 0.775 1.28 2.06WT16.5X100.5 100 29.6 16.8 15.7 0.715 1.15 1.94WT16.5X84.5 84.5 24.8 16.9 11.5 0.670 1.22 1.92WT16.5X76 76.0 22.4 16.7 11.6 0.635 1.06 1.76

WT16.5X70.5 70.5 20.8 16.7 11.5 0.605 0.960 1.66WT16.5X65 65.0 19.2 16.5 11.5 0.580 0.855 1.56WT16.5X59 59.0 17.3 16.4 11.5 0.550 0.740 1.44

WT15X195.5 196 57.6 16.6 15.6 1.36 2.44 3.23WT15X178.5 178 52.5 16.4 15.5 1.24 2.24 3.03WT15X163 163 47.9 16.2 15.4 1.14 2.05 2.84WT15X146 146 42.9 16.0 15.3 1.02 1.85 2.64

WT15X130.5 130 38.4 15.8 15.2 0.930 1.65 2.44WT15X117.5 118 34.6 15.7 15.1 0.830 1.50 2.29WT15X105.5 106 31.1 15.5 15.1 0.775 1.32 2.10WT15X95.5 95.5 28.1 15.3 15.0 0.710 1.19 1.97WT15X86.5 86.5 25.5 15.2 15.0 0.655 1.07 1.85WT15X74 74.0 21.7 15.3 10.5 0.650 1.18 1.83WT15X66 66.0 19.4 15.2 10.5 0.615 1.00 1.65WT15X62 62.0 18.2 15.1 10.5 0.585 0.930 1.58WT15X58 58.0 17.1 15.0 10.5 0.565 0.850 1.50WT15X54 54.0 15.9 14.9 10.5 0.545 0.760 1.41

WT15X49.5 49.5 14.5 14.8 10.5 0.520 0.670 1.32WT15X45 45.0 13.2 14.8 10.4 0.470 0.610 1.26

WT13.5X269.5 270 79.3 16.3 15.3 1.97 3.54 4.33WT13.5X184 184 54.2 15.2 14.7 1.38 2.48 3.27WT13.5X168 168 49.5 15.0 14.6 1.26 2.28 3.07

WT13.5X153.5 154 45.2 14.8 14.4 1.16 2.09 2.88WT13.5X140.5 140 41.4 14.6 14.4 1.06 1.93 2.72WT13.5X129 129 38.0 14.5 14.3 0.980 1.77 2.56

WT13.5X117.5 118 34.7 14.3 14.2 0.910 1.61 2.40WT13.5X108.5 108 32.0 14.2 14.1 0.830 1.50 2.29

WT13.5X97 97.0 28.6 14.1 14.0 0.750 1.34 2.13WT13.5X89 89.0 26.2 13.9 14.1 0.725 1.19 1.98

WT13.5X80.5 80.5 23.8 13.8 14.0 0.660 1.08 1.87WT13.5X73 73.0 21.6 13.7 14.0 0.605 0.975 1.76

WT13.5X64.5 64.5 18.9 13.8 10.0 0.610 1.10 1.70WT13.5X57 57.0 16.8 13.6 10.1 0.570 0.930 1.53WT13.5X51 51.0 15.0 13.5 10.0 0.515 0.830 1.43WT13.5X47 47.0 13.8 13.5 10.0 0.490 0.745 1.34WT13.5X42 42.0 12.4 13.4 10.0 0.460 0.640 1.24WT12X185 185 54.4 14.0 13.7 1.52 2.72 3.22

WT12X167.5 168 49.2 13.8 13.5 1.38 2.48 2.98WT12X153 153 44.9 13.6 13.4 1.26 2.28 2.78

WT12X139.5 140 41.0 13.4 13.3 1.16 2.09 2.59WT12X125 125 36.8 13.2 13.2 1.04 1.89 2.39

WT12X114.5 114 33.6 13.0 13.1 0.960 1.73 2.23WT12X103.5 103 30.4 12.9 13.0 0.870 1.57 2.07

WT12X96 96.0 28.1 12.7 13.0 0.810 1.46 1.96WT12X88 88.0 25.8 12.6 12.9 0.750 1.34 1.84WT12X81 81.0 23.9 12.5 13.0 0.705 1.22 1.72WT12X73 73.0 21.5 12.4 12.9 0.650 1.09 1.59

WT12X65.5 65.5 19.3 12.2 12.9 0.605 0.960 1.46WT12X58.5 58.5 17.2 12.1 12.8 0.550 0.850 1.35WT12X52 52.0 15.3 12.0 12.8 0.500 0.750 1.25

WT12X51.5 51.5 15.1 12.3 9.00 0.550 0.980 1.48WT12X47 47.0 13.8 12.2 9.07 0.515 0.875 1.38WT12X42 42.0 12.4 12.1 9.02 0.470 0.770 1.27

WT12X38 38.0 11.2 12.0 8.99 0.440 0.680 1.18WT12X34 34.0 10.0 11.9 8.97 0.415 0.585 1.09WT12X31 31.0 9.11 11.9 7.04 0.430 0.590 1.19

WT12X27.5 27.5 8.10 11.8 7.01 0.395 0.505 1.01WT10.5X100.5 100 29.6 11.5 12.6 0.910 1.63 2.13

WT10.5X91 91.0 26.8 11.4 12.5 0.830 1.48 1.98WT10.5X83 83.0 24.4 11.2 12.4 0.750 1.36 1.86

WT10.5X73.5 73.5 21.6 11.0 12.5 0.720 1.15 1.65WT10.5X66 66.0 19.4 10.9 12.4 0.650 1.04 1.54WT10.5X61 61.0 17.9 10.8 12.4 0.600 0.960 1.46

WT10.5X55.5 55.5 16.3 10.8 12.3 0.550 0.875 1.38WT10.5X50.5 50.5 14.9 10.7 12.3 0.500 0.800 1.30WT10.5X46.5 46.5 13.7 10.8 8.42 0.580 0.930 1.43WT10.5X41.5 41.5 12.2 10.7 8.36 0.515 0.835 1.34WT10.5X36.5 36.5 10.7 10.6 8.30 0.455 0.740 1.24WT10.5X34 34.0 10.0 10.6 8.27 0.430 0.685 1.19WT10.5X31 31.0 9.13 10.5 8.24 0.400 0.615 1.12

WT10.5X27.5 27.5 8.10 10.4 8.22 0.375 0.522 1.02WT10.5X24 24.0 7.07 10.3 8.14 0.350 0.430 0.930

WT10.5X28.5 28.5 8.37 10.5 6.56 0.405 0.650 1.15WT10.5X25 25.0 7.36 10.4 6.53 0.380 0.535 1.04WT10.5X22 22.0 6.49 10.3 6.50 0.350 0.450 0.950WT9X155.5 156 45.8 11.2 12.0 1.52 2.74 3.24WT9X141.5 142 41.6 10.9 11.9 1.40 2.50 3.00WT9X129 129 37.9 10.7 11.8 1.28 2.30 2.70WT9X117 117 34.4 10.5 11.7 1.16 2.11 2.51

WT9X105.5 106 31.1 10.3 11.6 1.06 1.91 2.31WT9X96 97.0 28.2 10.2 11.5 0.960 1.75 2.15

WT9X87.5 87.5 25.7 10.0 11.4 0.890 1.59 1.99WT9X79 79.0 23.2 9.86 11.3 0.810 1.44 1.84

WT9X71.5 71.5 21.0 9.75 11.2 0.730 1.32 1.72WT9X65 65.0 19.1 9.63 11.2 0.670 1.20 1.60

WT9X59.5 59.5 17.5 9.49 11.3 0.655 1.06 1.46WT9X53 53.0 15.6 9.37 11.2 0.590 0.940 1.34

WT9X48.5 48.5 14.3 9.30 11.1 0.535 0.870 1.27WT9X43 43.0 12.7 9.20 11.1 0.480 0.770 1.17WT9X38 38.0 11.2 9.11 11.0 0.425 0.680 1.08

WT9X35.5 35.5 10.4 9.24 7.64 0.495 0.810 1.21WT9X32.5 32.5 9.55 9.18 7.59 0.450 0.750 1.15WT9X30 30.0 8.82 9.12 7.56 0.415 0.695 1.10

WT9X27.5 27.5 8.10 9.06 7.53 0.390 0.630 1.03WT9X25 25.0 7.33 9.00 7.50 0.355 0.570 0.972WT9X23 23.0 6.77 9.03 6.06 0.360 0.605 1.01WT9X20 20.0 5.88 8.95 6.02 0.315 0.525 0.927

WT9X17.5 17.5 5.15 8.85 6.00 0.300 0.425 0.827WT8X50 50.0 14.7 8.49 10.4 0.585 0.985 1.39

WT8X44.5 44.5 13.1 8.38 10.4 0.525 0.875 1.58WT8X38.5 38.5 11.3 8.26 10.3 0.455 0.760 1.47WT8X33.5 33.5 9.84 8.17 10.2 0.395 0.665 1.37WT8X28.5 28.5 8.39 8.22 7.12 0.430 0.715 1.12WT8X25 25.0 7.37 8.13 7.07 0.380 0.630 1.03

WT8X22.5 22.5 6.63 8.07 7.04 0.345 0.565 0.967WT8X20 20.0 5.89 8.01 7.00 0.305 0.505 0.907WT8X18 18.0 5.29 7.93 6.99 0.295 0.430 0.832

WT8X15.5 15.5 4.56 7.94 5.53 0.275 0.440 0.842WT8X13 13.0 3.84 7.85 5.50 0.250 0.345 0.747

WT7X365 365 107 11.2 17.9 3.07 4.91 5.51

WT7X332.5 332 97.8 10.8 17.7 2.83 4.52 5.12WT7X302.5 302 88.9 10.5 17.4 2.60 4.16 4.76WT7X275 275 80.9 10.1 17.2 2.38 3.82 4.42WT7X250 250 73.5 9.80 17.0 2.19 3.50 4.10

WT7X227.5 228 66.9 9.51 16.8 2.02 3.21 3.81WT7X213 213 62.6 9.34 16.7 1.88 3.04 3.63WT7X199 199 58.5 9.15 16.6 1.77 2.85 3.44WT7X185 185 54.4 8.96 16.5 1.66 2.66 3.26WT7X171 171 50.3 8.77 16.4 1.54 2.47 3.07

WT7X155.5 156 45.7 8.56 16.2 1.41 2.26 2.86WT7X141.5 142 41.6 8.37 16.1 1.29 2.07 2.67WT7X128.5 128 37.8 8.19 16.0 1.18 1.89 2.49WT7X116.5 116 34.2 8.02 15.9 1.07 1.72 2.32WT7X105.5 106 31.0 7.86 15.8 0.980 1.56 2.16WT7X96.5 96.5 28.4 7.74 15.7 0.890 1.44 2.04WT7X88 88.0 25.9 7.61 15.7 0.830 1.31 1.91

WT7X79.5 79.5 23.4 7.49 15.6 0.745 1.19 1.79WT7X72.5 72.5 21.3 7.39 15.5 0.680 1.09 1.69WT7X66 66.0 19.4 7.33 14.7 0.645 1.03 1.63WT7X60 60.0 17.7 7.24 14.7 0.590 0.940 1.54

WT7X54.5 54.5 16.0 7.16 14.6 0.525 0.860 1.46WT7X49.5 49.5 14.6 7.08 14.6 0.485 0.780 1.38WT7X45 45.0 13.2 7.01 14.5 0.440 0.710 1.31WT7X41 41.0 12.0 7.16 10.1 0.510 0.855 1.45WT7X37 37.0 10.9 7.09 10.1 0.450 0.785 1.38WT7X34 34.0 10.0 7.02 10.0 0.415 0.720 1.31

WT7X30.5 30.5 8.96 6.95 10.0 0.375 0.645 1.24WT7X26.5 26.5 7.80 6.96 8.06 0.370 0.660 1.25WT7X24 24.0 7.07 6.90 8.03 0.340 0.595 1.19

WT7X21.5 21.5 6.31 6.83 8.00 0.305 0.530 1.12WT7X19 19.0 5.58 7.05 6.77 0.310 0.515 0.915WT7X17 17.0 5.00 6.99 6.75 0.285 0.455 0.855WT7X15 15.0 4.42 6.92 6.73 0.270 0.385 0.785WT7X13 13.0 3.85 6.96 5.03 0.255 0.420 0.820WT7X11 11.0 3.25 6.87 5.00 0.230 0.335 0.735

WT6X168 168 49.4 8.41 13.4 1.78 2.96 3.55WT6X152.5 152 44.8 8.16 13.2 1.63 2.71 3.30WT6X139.5 140 41.0 7.93 13.1 1.53 2.47 3.07WT6X126 126 37.0 7.71 13.0 1.40 2.25 2.85WT6X115 115 33.9 7.53 12.9 1.29 2.07 2.67WT6X105 105 30.9 7.36 12.8 1.18 1.90 2.50WT6X95 95.0 27.9 7.19 12.7 1.06 1.74 2.33WT6X85 85.0 25.0 7.02 12.6 0.960 1.56 2.16WT6X76 76.0 22.4 6.86 12.5 0.870 1.40 2.00WT6X68 68.0 20.0 6.71 12.4 0.790 1.25 1.85WT6X60 60.0 17.6 6.56 12.3 0.710 1.11 1.70WT6X53 53.0 15.6 6.45 12.2 0.610 0.990 1.59WT6X48 48.0 14.1 6.36 12.2 0.550 0.900 1.50

WT6X43.5 43.5 12.8 6.27 12.1 0.515 0.810 1.41WT6X39.5 39.5 11.6 6.19 12.1 0.470 0.735 1.33WT6X36 36.0 10.6 6.13 12.0 0.430 0.670 1.27

WT6X32.5 32.5 9.54 6.06 12.0 0.390 0.605 1.20WT6X29 29.0 8.52 6.10 10.0 0.360 0.640 1.24

WT6X26.5 26.5 7.78 6.03 10.0 0.345 0.575 1.17WT6X25 25.0 7.30 6.10 8.08 0.370 0.640 1.14

WT6X22.5 22.5 6.56 6.03 8.05 0.335 0.575 1.08WT6X20 20.0 5.84 5.97 8.01 0.295 0.515 1.02

WT6X17.5 17.5 5.17 6.25 6.56 0.300 0.520 0.820WT6X15 15.0 4.40 6.17 6.52 0.260 0.440 0.740WT6X13 13.0 3.82 6.11 6.49 0.230 0.380 0.680WT6X11 11.0 3.24 6.16 4.03 0.260 0.425 0.725WT6X9.5 9.50 2.79 6.08 4.01 0.235 0.350 0.650WT6X8 8.00 2.36 6.00 3.99 0.220 0.265 0.565WT6X7 7.00 2.08 5.96 3.97 0.200 0.225 0.525

WT5X56 56.0 16.5 5.68 10.4 0.755 1.25 1.75WT5X50 50.0 14.7 5.55 10.3 0.680 1.12 1.62WT5X44 44.0 12.9 5.42 10.3 0.605 0.990 1.49

WT5X38.5 38.5 11.3 5.30 10.2 0.530 0.870 1.37WT5X34 34.0 10.0 5.20 10.1 0.470 0.770 1.27WT5X30 30.0 8.82 5.11 10.1 0.420 0.680 1.18WT5X27 27.0 7.91 5.05 10.0 0.370 0.615 1.12

WT5X24.5 24.5 7.21 4.99 10.0 0.340 0.560 1.06WT5X22.5 22.5 6.63 5.05 8.02 0.350 0.620 1.12WT5X19.5 19.5 5.73 4.96 7.99 0.315 0.530 1.03WT5X16.5 16.5 4.85 4.87 7.96 0.290 0.435 0.935WT5X15 15.0 4.42 5.24 5.81 0.300 0.510 0.810WT5X13 13.0 3.81 5.17 5.77 0.260 0.440 0.740WT5X11 11.0 3.24 5.09 5.75 0.240 0.360 0.660WT5X9.5 9.50 2.81 5.12 4.02 0.250 0.395 0.695WT5X8.5 8.50 2.50 5.06 4.01 0.240 0.330 0.630WT5X7.5 7.50 2.21 5.00 4.00 0.230 0.270 0.570WT5X6 6.00 1.77 4.94 3.96 0.190 0.210 0.510

WT4X33.5 33.5 9.84 4.50 8.28 0.570 0.935 1.33WT4X29 29.0 8.54 4.38 8.22 0.510 0.810 1.20WT4X24 24.0 7.05 4.25 8.11 0.400 0.685 1.08WT4X20 20.0 5.87 4.13 8.07 0.360 0.560 0.954

WT4X17.5 17.5 5.14 4.06 8.02 0.310 0.495 0.889WT4X15.5 15.5 4.56 4.00 8.00 0.285 0.435 0.829WT4X14 14.0 4.12 4.03 6.54 0.285 0.465 0.859WT4X12 12.0 3.54 3.97 6.50 0.245 0.400 0.794

WT4X10.5 10.5 3.08 4.14 5.27 0.250 0.400 0.700WT4X9 9.00 2.63 4.07 5.25 0.230 0.330 0.630

WT4X7.5 7.50 2.22 4.06 4.02 0.245 0.315 0.615WT4X6.5 6.50 1.92 4.00 4.00 0.230 0.255 0.555WT4X5 5.00 1.48 3.95 3.94 0.170 0.205 0.505

WT3X12.5 12.5 3.67 3.19 6.08 0.320 0.455 0.705WT3X10 10.0 2.94 3.10 6.02 0.260 0.365 0.664WT3X7.5 7.50 2.21 3.00 5.99 0.230 0.260 0.559WT3X8 8.00 2.37 3.14 4.03 0.260 0.405 0.655WT3X6 6.00 1.78 3.02 4.00 0.230 0.280 0.530

WT3X4.5 4.50 1.34 2.95 3.94 0.170 0.215 0.465WT3X4.25 4.25 1.26 2.92 3.94 0.170 0.195 0.444WT2.5X9.5 9.50 2.78 2.58 5.03 0.270 0.430 0.730WT2.5X8 8.00 2.35 2.51 5.00 0.240 0.360 0.660WT2X6.5 6.50 1.91 2.08 4.06 0.280 0.345 0.595

MT6.25X6.2 6.20 1.80 6.27 3.75 0.155 0.228 0.563MT6.25X5.9 5.90 1.69 6.25 3.50 0.155 0.211 0.563

MT6X5.9 5.90 1.72 6.00 3.07 0.177 0.225 0.563MT6X5.4 5.40 1.58 5.99 3.07 0.160 0.210 0.563MT6X5 5.00 1.46 5.99 3.25 0.149 0.180 0.500

MT5X4.5 4.50 1.32 5.00 2.69 0.157 0.206 0.563MT5X4 4.00 1.17 4.98 2.69 0.141 0.182 0.563

MT5X3.75 3.75 1.10 5.00 2.69 0.130 0.173 0.438MT4X3.25 3.25 0.953 4.00 2.28 0.135 0.189 0.563

MT4X3.1 3.10 0.904 4.00 2.28 0.129 0.177 0.438MT3X2.2 2.20 0.643 3.00 1.84 0.114 0.171 0.375

MT3X1.85 1.85 0.540 2.96 2.00 0.0980 0.129 0.313MT2.5X9.45 9.45 2.76 2.50 5.00 0.316 0.416 0.813

MT2X3 3.00 0.855 1.90 3.80 0.130 0.160 0.500ST12X60.5 60.5 17.8 12.3 8.05 0.800 1.09 2.00ST12X53 53.0 15.6 12.3 7.87 0.620 1.09 2.00ST12X50 50.0 14.7 12.0 7.25 0.745 0.870 1.75ST12X45 45.0 13.2 12.0 7.13 0.625 0.870 1.75ST12X40 40.0 11.7 12.0 7.00 0.500 0.870 1.75ST10X48 48.0 14.1 10.2 7.20 0.800 0.920 1.75ST10X43 43.0 12.7 10.2 7.06 0.660 0.920 1.75

ST10X37.5 37.5 11.0 10.0 6.39 0.635 0.795 1.63ST10X33 33.0 9.69 10.0 6.26 0.505 0.795 1.63ST9X35 35.0 10.3 9.00 6.25 0.711 0.691 1.50

ST9X27.35 27.4 8.02 9.00 6.00 0.461 0.691 1.50ST7.5X25 25.0 7.34 7.50 5.64 0.550 0.622 1.38

ST7.5X21.45 21.5 6.30 7.50 5.50 0.411 0.622 1.38ST6X25 25.0 7.32 6.00 5.48 0.687 0.659 1.44

ST6X20.4 20.4 5.96 6.00 5.25 0.462 0.659 1.44ST6X17.5 17.5 5.12 6.00 5.08 0.428 0.544 1.19ST6X15.9 15.9 4.65 6.00 5.00 0.350 0.544 1.19ST5X17.5 17.5 5.14 5.00 4.94 0.594 0.491 1.13ST5X12.7 12.7 3.73 5.00 4.66 0.311 0.491 1.13ST4X11.5 11.5 3.38 4.00 4.17 0.441 0.425 1.00ST4X9.2 9.20 2.70 4.00 4.00 0.271 0.425 1.00ST3X8.6 8.60 2.53 3.00 3.57 0.465 0.359 0.813

ST3X6.25 6.25 1.83 3.00 3.33 0.232 0.359 0.813ST2.5X5 5.00 1.47 2.50 3.00 0.214 0.326 0.750

ST2X4.75 4.75 1.39 2.00 2.80 0.326 0.293 0.750ST2X3.85 3.85 1.13 2.00 2.66 0.193 0.293 0.750

ST1.5X3.75 3.75 1.10 1.50 2.51 0.349 0.260 0.625ST1.5X2.85 2.85 0.830 1.50 2.33 0.170 0.260 0.625

9 10 11 12 13 14 15 16 17 18KDET Y YP BF_2TF H_TW D_T IX ZX SX RX2.625 5.53 1.54 4.50 19.1 21.5 2170 234 131 6.63

2.4375 5.26 1.35 5.02 22.3 25.2 1830 196 111 6.542.25 5.19 1.22 5.57 24.6 27.6 1640 176 99.4 6.53

2.0625 5.17 1.07 6.45 27.4 30.2 1440 157 88.6 6.534.5 5.66 2.61 2.58 9.54 12.0 3310 379 209 6.164 5.38 2.25 2.98 11.1 13.7 2730 314 174 6.07

3.625 5.18 1.95 3.44 12.8 15.4 2290 266 148 6.013.5 5.03 1.81 3.66 14.0 16.8 2070 240 134 5.96

3.3125 4.98 1.70 3.93 14.7 17.5 1930 225 126 5.953.25 4.91 1.66 3.99 15.3 18.1 1870 217 122 5.92

3.0625 4.77 1.50 4.40 17.1 20.1 1650 192 108 5.882.9375 4.71 1.38 4.80 18.4 21.4 1500 176 98.9 5.872.875 4.50 1.29 5.03 20.6 23.9 1360 157 88.6 5.78

2.6875 4.41 1.16 5.55 22.8 26.3 1210 140 79.4 5.752.5 4.28 1.01 6.45 26.3 30.0 1030 120 68.0 5.71

2.3125 4.47 0.929 7.39 26.3 29.7 988 117 66.5 5.813.8125 5.94 2.33 2.45 12.0 14.7 2270 275 153 6.273.375 5.74 2.00 2.86 14.0 16.7 1880 231 128 6.213.375 5.66 1.98 2.85 14.5 17.3 1840 224 125 6.19

3.1875 5.51 1.80 3.11 16.1 19.1 1630 199 111 6.143.0625 5.51 1.71 3.31 16.8 19.6 1550 191 106 6.14

3 5.41 1.63 3.45 17.8 20.8 1450 178 99.2 6.112.875 5.17 1.45 3.77 20.6 23.9 1260 153 85.7 6.04

2.6875 5.08 1.31 4.17 22.8 26.2 1120 137 76.7 6.012.5 4.97 1.13 4.92 26.3 30.0 955 117 65.7 5.98

2.3125 5.19 1.10 5.76 26.3 29.7 899 115 63.7 6.052.125 5.45 1.72 7.11 27.1 30.3 815 108 59.7 6.10

5.5625 5.80 3.28 2.10 6.62 8.94 4090 491 264 5.894.8125 5.35 2.73 2.48 7.99 10.4 3160 383 208 5.744.1875 4.96 2.26 2.96 9.78 12.4 2440 298 164 5.60

4 4.84 2.10 3.19 10.7 13.1 2220 272 150 5.573.6875 4.69 1.91 3.48 11.6 14.3 1980 242 134 5.523.4375 4.53 1.73 3.83 12.9 15.7 1740 213 119 5.47

3.25 4.42 1.59 4.16 14.1 17.0 1570 192 107 5.433.125 4.30 1.46 4.49 15.4 18.5 1410 173 97.0 5.39

2.9375 4.22 1.33 4.96 16.7 19.8 1280 158 88.8 5.372.8125 4.16 1.25 5.29 17.8 21.0 1190 146 82.6 5.362.6875 4.14 1.16 5.75 18.7 21.9 1110 137 77.5 5.362.625 4.12 1.10 6.11 19.7 22.9 1040 129 73.3 5.36

2.4375 4.10 1.03 6.54 20.7 24.0 978 122 69.1 5.362.625 4.92 1.54 3.53 16.9 19.5 1210 156 87.4 5.66

2.4375 4.82 1.40 3.86 18.7 21.3 1080 140 78.5 5.632.3125 4.87 1.27 4.48 19.6 22.1 985 131 73.1 5.652.1875 4.80 1.18 4.81 21.2 23.8 901 120 67.0 5.622.125 4.77 1.11 5.12 22.4 25.1 845 113 63.1 5.62

2 4.73 1.04 5.47 23.9 26.6 786 105 58.9 5.611.9375 4.74 0.980 5.88 25.0 27.7 740 100 55.8 5.611.875 4.78 0.923 6.37 26.0 28.7 698 95.5 53.1 5.62

1.6875 4.96 1.23 7.56 27.1 29.6 637 90.1 49.7 5.663.1875 4.27 1.76 3.55 11.8 14.3 1460 193 107 5.072.9375 4.15 1.62 3.85 12.8 15.3 1320 174 96.8 5.03

2.75 4.02 1.46 4.23 14.3 16.9 1160 154 85.8 4.992.625 3.93 1.35 4.60 15.5 18.1 1060 140 78.3 4.96

2.4375 3.83 1.23 5.03 17.1 19.8 943 125 70.2 4.932.25 3.84 1.12 5.66 18.0 20.6 872 116 65.8 4.96

2.125 3.81 1.03 6.20 19.2 21.9 799 107 60.8 4.952 3.77 0.940 6.85 20.8 23.6 725 97.8 55.5 4.95

2.125 4.21 1.08 4.71 22.4 25.2 649 90.8 51.1 5.121.9375 4.26 0.967 5.48 23.6 26.4 592 84.5 47.4 5.141.8125 4.29 0.901 6.01 24.8 27.5 552 79.8 44.7 5.15

1.75 4.36 0.832 6.73 25.8 28.5 513 75.6 42.1 5.181.625 4.47 0.862 7.76 27.3 29.9 469 70.8 39.2 5.203.375 4.00 1.85 3.19 9.83 12.2 1220 177 96.9 4.613.125 3.87 1.70 3.45 10.8 13.2 1090 159 87.2 4.56

2.9375 3.76 1.56 3.75 11.7 14.2 981 143 78.8 4.522.75 3.62 1.41 4.12 13.1 15.7 861 125 69.6 4.48

2.5625 3.54 1.27 4.59 14.4 17.0 765 112 62.4 4.462.375 3.41 1.15 5.02 16.1 18.9 674 98.2 55.1 4.412.25 3.39 1.03 5.74 17.2 20.0 610 89.5 50.5 4.43

2.0625 3.34 0.935 6.35 18.8 21.6 549 80.8 45.7 4.422 3.31 0.851 7.40 20.4 23.2 497 73.5 41.7 4.42

2.0625 3.84 1.04 4.44 20.8 23.6 466 72.2 40.6 4.631.875 3.90 0.921 5.27 22.0 24.6 421 66.8 37.4 4.66

1.8125 3.90 0.867 5.65 23.1 25.8 396 63.1 35.3 4.661.75 3.94 0.815 6.17 23.9 26.6 373 60.4 33.7 4.67

1.6875 4.01 0.757 6.89 24.8 27.4 349 57.7 32.0 4.691.5625 4.09 0.912 7.80 26.0 28.5 322 54.4 30.0 4.71

1.5 4.04 0.835 8.52 28.7 31.4 290 49.0 27.1 4.694.4375 4.34 2.60 2.15 6.06 8.25 1530 242 128 4.393.375 3.71 1.85 2.96 8.64 11.0 939 151 81.7 4.16

3.1875 3.58 1.70 3.19 9.47 11.9 839 135 73.4 4.123 3.47 1.56 3.46 10.3 12.8 753 121 66.4 4.08

2.8125 3.35 1.44 3.72 11.3 13.8 677 109 59.9 4.042.6875 3.27 1.33 4.03 12.2 14.8 613 98.9 54.7 4.02

2.5 3.20 1.22 4.41 13.1 15.7 556 89.9 50.0 4.002.375 3.10 1.13 4.71 14.4 17.1 502 81.1 45.2 3.962.25 3.02 1.02 5.24 15.9 18.7 444 71.8 40.3 3.94

2.0625 3.04 0.932 5.92 16.5 19.2 414 67.7 38.2 3.972 2.98 0.849 6.49 18.1 20.9 372 60.8 34.4 3.95

1.875 2.94 0.772 7.16 19.7 22.6 336 55.0 31.2 3.952 3.39 0.945 4.55 19.9 22.6 323 55.1 31.0 4.13

1.8125 3.42 0.832 5.41 21.3 23.9 289 50.4 28.3 4.151.75 3.37 0.750 6.03 23.5 26.3 258 45.0 25.3 4.14

1.625 3.41 0.692 6.70 24.7 27.5 239 42.4 23.8 4.161.5625 3.48 0.621 7.78 26.3 29.0 216 39.2 21.9 4.183.625 3.57 1.99 2.51 7.09 9.21 779 140 74.7 3.783.375 3.42 1.82 2.73 7.81 10.0 686 123 66.3 3.73

3.1875 3.29 1.67 2.94 8.56 10.8 611 110 59.4 3.693 3.18 1.54 3.18 9.29 11.5 546 98.8 53.6 3.65

2.8125 3.05 1.39 3.49 10.4 12.7 478 86.5 47.2 3.612.625 2.96 1.28 3.79 11.2 13.6 431 78.1 42.9 3.58

2.5 2.87 1.17 4.14 12.4 14.8 382 69.3 38.3 3.552.375 2.80 1.09 4.43 13.3 15.7 350 63.5 35.2 3.532.25 2.74 1.00 4.81 14.4 16.8 319 57.8 32.2 3.51

2.125 2.70 0.921 5.31 15.3 17.7 293 53.3 29.9 3.502 2.66 0.833 5.92 16.6 19.0 264 48.2 27.2 3.50

1.875 2.65 0.750 6.70 17.8 20.2 238 43.9 24.8 3.521.75 2.62 0.672 7.53 19.6 22.1 212 39.2 22.3 3.51

1.625 2.59 0.600 8.50 21.6 24.1 189 35.1 20.0 3.511.875 3.01 0.841 4.59 19.6 22.3 204 39.2 22.0 3.671.75 2.99 0.764 5.18 20.9 23.6 186 36.1 20.3 3.67

1.6875 2.97 0.685 5.86 22.9 25.6 166 32.5 18.3 3.67

1.5625 3.00 0.622 6.61 24.5 27.2 151 30.1 16.9 3.681.5 3.06 0.560 7.66 26.0 28.6 137 27.9 15.6 3.701.5 3.46 1.28 5.97 24.8 27.6 131 28.4 15.6 3.79

1.4375 3.50 1.53 6.94 27.0 29.8 117 25.6 14.1 3.802.5 2.57 1.18 3.86 10.3 12.7 285 58.6 31.9 3.10

2.375 2.48 1.07 4.22 11.3 13.7 253 52.1 28.5 3.072.25 2.39 0.983 4.57 12.5 15.0 226 46.3 25.5 3.04

2 2.39 0.864 5.44 13.0 15.3 204 42.4 23.7 3.081.9375 2.33 0.780 6.01 14.4 16.8 181 37.6 21.1 3.061.8125 2.28 0.724 6.45 15.6 18.1 166 34.3 19.3 3.04

1.75 2.23 0.662 7.05 17.1 19.6 150 31.0 17.5 3.031.6875 2.18 0.605 7.68 18.8 21.4 135 27.9 15.8 3.011.625 2.74 0.812 4.53 16.2 18.6 144 31.8 17.9 3.25

1.5 2.66 0.728 5.00 18.2 20.8 127 28.0 15.7 3.221.4375 2.60 0.647 5.60 20.6 23.3 110 24.4 13.8 3.211.375 2.59 0.606 6.04 21.8 24.6 103 22.9 12.9 3.20

1.3125 2.58 0.554 6.70 23.4 26.2 93.8 21.1 11.9 3.211.1875 2.64 0.493 7.87 25.0 27.7 84.4 19.4 10.9 3.231.125 2.74 0.459 9.47 26.8 29.5 74.9 17.8 9.90 3.26

1.3125 2.85 0.638 5.04 23.2 26.0 90.4 21.2 11.8 3.291.25 2.93 0.771 6.10 24.7 27.4 80.3 19.4 10.7 3.30

1.125 2.98 1.06 7.22 26.8 29.5 71.1 17.6 9.68 3.313.4375 2.93 1.91 2.19 5.21 7.34 383 90.6 46.6 2.890.1875 2.80 1.75 2.38 5.66 7.80 337 80.2 41.5 2.85

3 2.68 1.61 2.56 6.27 8.38 298 71.0 37.0 2.802.75 2.55 1.48 2.76 6.91 9.08 261 62.4 32.7 2.75

0.5625 2.44 1.34 3.02 7.57 9.75 229 55.0 29.1 2.722.4375 2.34 1.23 3.27 8.36 10.6 202 48.5 25.8 2.682.4375 2.26 1.13 3.58 9.02 11.3 181 43.6 23.4 2.662.375 2.17 1.02 3.92 9.90 12.2 160 38.5 20.8 2.63

2.1875 2.09 0.937 4.25 11.0 13.3 142 34.0 18.5 2.602.0625 2.02 0.856 4.65 12.0 14.4 127 30.5 16.7 2.581.9375 2.03 0.778 5.31 12.2 14.5 119 28.7 15.9 2.601.8125 1.97 0.695 5.96 13.6 15.9 104 25.2 14.1 2.59

1.75 1.91 0.640 6.41 15.0 17.4 93.8 22.6 12.7 2.561.625 1.86 0.570 7.20 16.7 19.2 82.4 19.9 11.2 2.55

1.5625 1.80 0.505 8.11 18.9 21.4 71.8 17.3 9.83 2.541.5 2.26 0.683 4.71 16.2 18.7 78.2 20.0 11.2 2.74

1.4375 2.20 0.629 5.06 17.8 20.4 70.7 18.0 10.1 2.721.375 2.16 0.583 5.44 19.3 22.0 64.7 16.5 9.29 2.71

1.3125 2.16 0.538 5.98 20.6 23.2 59.5 15.3 8.63 2.711.25 2.12 0.489 6.57 22.6 25.3 53.5 13.8 7.79 2.701.25 2.33 0.558 5.01 22.3 25.1 52.1 13.9 7.77 2.77

1.1875 2.29 0.489 5.73 25.5 28.4 44.8 12.0 6.73 2.761.125 2.39 0.450 7.06 26.7 29.5 40.1 11.2 6.21 2.791.875 1.76 0.706 5.29 11.6 14.5 76.8 20.7 11.4 2.281.75 1.70 0.631 5.92 12.9 16.0 67.2 18.1 10.1 2.27

1.625 1.63 0.549 6.77 14.9 18.2 56.9 15.3 8.59 2.241.5625 1.56 0.481 7.70 17.2 20.7 48.6 13.0 7.36 2.221.375 1.94 0.589 4.98 16.5 19.1 48.7 13.8 7.77 2.41

1.3125 1.89 0.521 5.61 18.7 21.4 42.3 12.0 6.78 2.401.25 1.86 0.471 6.23 20.6 23.4 37.8 10.8 6.10 2.39

1.1875 1.81 0.421 6.93 23.3 26.2 33.1 9.43 5.35 2.371.125 1.88 0.378 8.12 24.1 26.9 30.6 8.93 5.05 2.411.125 2.02 0.413 6.28 25.8 28.9 27.5 8.27 4.64 2.45

1.0625 2.09 0.372 7.97 28.4 31.4 23.5 7.36 4.09 2.476.1875 3.47 3.00 1.82 1.86 3.65 739 211 95.4 2.62

5.8125 3.25 2.77 1.95 2.01 3.82 622 182 82.1 2.525.4375 3.05 2.55 2.09 2.20 4.03 524 157 70.6 2.435.125 2.85 2.35 2.25 2.40 4.25 442 136 60.9 2.34

4.8125 2.67 2.16 2.43 2.60 4.47 375 117 52.7 2.264.5 2.51 1.99 2.62 2.83 4.72 321 102 45.9 2.19

4.3125 2.40 1.88 2.75 3.04 4.98 287 91.7 41.4 2.144.125 2.30 1.76 2.92 3.22 5.17 257 82.9 37.6 2.10

3.9375 2.19 1.65 3.10 3.45 5.41 229 74.4 33.9 2.053.75 2.09 1.54 3.31 3.70 5.69 203 66.2 30.4 2.01

3.5625 1.97 1.41 3.59 4.04 6.07 176 57.7 26.7 1.963.375 1.86 1.29 3.89 4.42 6.49 153 50.4 23.5 1.92

3.1875 1.75 1.18 4.23 4.85 6.97 133 43.9 20.7 1.883 1.65 1.08 4.62 5.33 7.50 116 38.2 18.2 1.84

2.875 1.57 0.980 5.06 5.82 8.02 102 33.4 16.2 1.812.75 1.49 0.903 5.45 6.41 8.70 89.8 29.4 14.4 1.78

2.625 1.43 0.827 5.97 6.87 9.17 80.5 26.3 13.0 1.762.5 1.35 0.751 6.54 7.65 10.1 70.2 22.8 11.4 1.73

2.375 1.29 0.688 7.11 8.39 10.9 62.5 20.2 10.2 1.712.3125 1.29 0.658 7.15 8.84 11.4 57.8 18.6 9.57 1.73

2.25 1.24 0.602 7.80 9.66 12.3 51.7 16.5 8.61 1.712.1875 1.17 0.548 8.49 10.9 13.6 45.3 14.4 7.56 1.682.0625 1.14 0.500 9.34 11.8 14.6 40.9 12.9 6.88 1.67

2 1.09 0.456 10.2 13.0 15.9 36.5 11.5 6.16 1.661.6875 1.39 0.593 5.92 11.2 14.0 41.2 13.2 7.14 1.851.625 1.32 0.541 6.41 12.7 15.7 36.0 11.5 6.25 1.82

1.5625 1.29 0.498 6.97 13.8 16.9 32.6 10.4 5.69 1.811.5 1.25 0.448 7.75 15.2 18.5 28.9 9.15 5.07 1.801.5 1.38 0.484 6.11 15.4 18.8 27.6 8.87 4.94 1.88

1.4375 1.35 0.440 6.75 16.8 20.3 24.9 8.00 4.49 1.881.375 1.31 0.395 7.54 18.7 22.4 21.9 7.05 3.98 1.861.25 1.54 0.412 6.57 19.8 22.7 23.3 7.45 4.22 2.04

1.1875 1.53 0.371 7.41 21.5 24.5 20.9 6.74 3.83 2.041.125 1.58 0.329 8.74 22.7 25.6 19.0 6.25 3.55 2.071.125 1.72 0.383 5.98 24.1 27.3 17.3 5.89 3.31 2.12

1.0625 1.76 0.325 7.46 26.7 29.9 14.8 5.20 2.91 2.143.875 2.31 1.84 2.26 2.74 4.74 190 68.4 31.2 1.963.625 2.16 1.69 2.45 2.99 5.02 162 59.1 27.0 1.903.375 2.05 1.56 2.66 3.17 5.18 141 51.9 24.1 1.863.125 1.92 1.42 2.89 3.48 5.52 121 44.8 20.9 1.81

2.9375 1.82 1.31 3.11 3.78 5.86 106 39.4 18.5 1.772.8125 1.72 1.21 3.37 4.12 6.23 92.1 34.5 16.4 1.732.625 1.62 1.10 3.65 4.58 6.78 79.0 29.8 14.2 1.68

2.4375 1.52 0.994 4.03 5.06 7.31 67.8 25.6 12.3 1.652.3125 1.43 0.896 4.46 5.58 7.88 58.5 22.0 10.8 1.622.125 1.35 0.805 4.96 6.15 8.49 50.6 19.0 9.46 1.59

2 1.28 0.716 5.57 6.84 9.24 43.4 16.2 8.22 1.571.875 1.19 0.637 6.17 7.96 10.6 36.3 13.6 6.92 1.53

1.8125 1.13 0.580 6.76 8.83 11.6 32.0 11.9 6.12 1.511.6875 1.10 0.527 7.48 9.43 12.2 28.9 10.7 5.60 1.501.625 1.06 0.480 8.22 10.3 13.2 25.8 9.49 5.03 1.49

1.5625 1.02 0.439 8.99 11.3 14.2 23.2 8.48 4.54 1.481.5 0.985 0.398 9.92 12.5 15.5 20.6 7.50 4.06 1.471.5 1.03 0.426 7.82 13.5 16.9 19.1 6.97 3.76 1.50

1.375 1.02 0.389 8.69 14.1 17.5 17.7 6.46 3.54 1.511.5 1.17 0.452 6.31 13.4 16.5 18.7 6.88 3.79 1.60

1.375 1.13 0.408 7.00 14.8 18.0 16.6 6.10 3.39 1.591.375 1.09 0.365 7.77 16.8 20.2 14.4 5.28 2.95 1.57

1.1875 1.30 0.394 6.31 18.1 20.8 16.0 5.71 3.23 1.761.125 1.27 0.337 7.41 20.9 23.7 13.5 4.83 2.75 1.75

1.0625 1.25 0.295 8.54 23.6 26.6 11.7 4.20 2.40 1.750.9375 1.63 0.402 4.74 20.9 23.7 11.7 4.63 2.59 1.900.875 1.65 0.348 5.72 23.1 25.9 10.1 4.11 2.28 1.90

0.8125 1.74 0.639 7.53 24.7 27.3 8.70 3.72 2.04 1.920.75 1.76 0.760 8.82 27.2 29.8 7.67 3.32 1.83 1.92

1.9375 1.21 0.791 4.17 5.21 7.52 28.6 13.4 6.40 1.321.8125 1.13 0.711 4.62 5.78 8.16 24.5 11.4 5.56 1.291.6875 1.06 0.631 5.18 6.50 8.96 20.8 9.65 4.77 1.271.5625 0.990 0.555 5.86 7.42 10.0 17.4 8.06 4.05 1.241.4375 0.932 0.493 6.58 8.36 11.1 14.9 6.85 3.49 1.221.375 0.884 0.438 7.41 9.36 12.2 12.9 5.87 3.04 1.21

1.3125 0.836 0.395 8.15 10.6 13.6 11.1 5.05 2.64 1.191.25 0.807 0.361 8.93 11.6 14.7 10.0 4.52 2.39 1.18

1.3125 0.907 0.413 6.47 11.2 14.4 10.2 4.65 2.47 1.241.1875 0.876 0.359 7.53 12.5 15.7 8.84 3.99 2.16 1.241.125 0.869 0.305 9.15 13.6 16.8 7.71 3.48 1.93 1.261.125 1.10 0.380 5.70 14.8 17.5 9.28 4.01 2.24 1.45

1.0625 1.06 0.330 6.56 17.0 19.9 7.86 3.39 1.91 1.440.9375 1.07 0.282 7.99 18.4 21.2 6.88 3.02 1.72 1.460.9375 1.28 0.349 5.09 17.7 20.5 6.68 3.10 1.74 1.540.875 1.32 0.311 6.08 18.4 21.1 6.06 2.90 1.62 1.56

0.8125 1.37 0.305 7.41 19.2 21.7 5.45 2.71 1.50 1.570.75 1.36 0.322 9.43 23.3 26.0 4.35 2.20 1.22 1.57

1.625 0.936 0.594 4.43 5.56 7.89 10.9 6.29 3.05 1.051.5 0.874 0.520 5.07 6.22 8.58 9.12 5.25 2.61 1.03

1.375 0.777 0.435 5.92 7.93 10.6 6.85 3.94 1.97 0.9861.25 0.735 0.364 7.21 8.81 11.5 5.73 3.25 1.69 0.988

1.1875 0.688 0.321 8.10 10.2 13.1 4.82 2.71 1.43 0.9681.125 0.668 0.285 9.19 11.1 14.0 4.28 2.39 1.28 0.969

0.9375 0.734 0.315 7.03 11.1 14.1 4.23 2.38 1.28 1.010.875 0.695 0.272 8.12 12.9 16.2 3.53 1.98 1.08 0.9990.875 0.831 0.292 6.59 13.8 16.6 3.90 2.11 1.18 1.12

0.8125 0.834 0.251 7.95 15.0 17.7 3.41 1.86 1.05 1.140.8125 0.998 0.276 6.37 14.0 16.6 3.28 1.91 1.07 1.22

0.75 1.03 0.240 7.84 15.0 17.4 2.89 1.74 0.974 1.230.6875 0.953 0.188 9.61 20.2 23.2 2.15 1.27 0.717 1.200.9375 0.610 0.302 6.68 7.61 10.0 2.29 1.68 0.886 0.7890.875 0.560 0.244 8.25 9.37 11.9 1.76 1.29 0.693 0.7740.75 0.558 0.185 11.5 10.6 13.0 1.41 1.03 0.577 0.797

0.875 0.676 0.294 4.98 9.56 12.1 1.69 1.25 0.685 0.8440.75 0.677 0.222 7.14 10.8 13.1 1.32 1.01 0.564 0.862

0.6875 0.623 0.170 9.16 14.6 17.4 0.950 0.720 0.408 0.8420.6875 0.637 0.160 10.1 14.5 17.1 0.905 0.700 0.397 0.8480.8125 0.487 0.276 5.85 6.83 9.54 1.01 0.970 0.485 0.604

0.75 0.458 0.235 6.94 7.69 10.4 0.845 0.801 0.413 0.5990.75 0.440 0.236 5.88 5.30 7.43 0.526 0.616 0.321 0.524

0.5625 1.74 0.372 0.00 36.7 40.4 7.29 2.92 1.61 2.010.5625 1.84 0.808 0.00 36.8 40.3 6.94 2.86 1.57 2.030.5625 1.89 1.13 0.00 30.8 33.9 6.61 2.89 1.61 1.960.5625 1.86 1.05 0.00 34.3 37.4 6.03 2.63 1.46 1.95

0.5 1.86 1.08 0.00 36.9 40.2 5.62 2.45 1.36 1.960.5625 1.54 0.808 0.00 29.2 31.8 3.47 1.81 1.00 1.620.5625 1.52 0.809 0.00 32.6 35.3 3.08 1.61 0.894 1.620.4375 1.51 0.759 0.00 35.7 38.4 2.91 1.51 0.836 1.630.5625 1.18 0.472 0.00 27.3 29.6 1.57 1.01 0.558 1.29

0.4375 1.18 0.497 0.00 28.7 31.0 1.50 0.967 0.533 1.290.375 0.841 0.190 0.00 24.5 26.3 0.579 0.483 0.268 0.949

0.3125 0.827 0.174 0.00 28.2 30.2 0.483 0.409 0.226 0.9450.8125 0.512 0.276 0.00 2.91 7.91 1.05 1.03 0.528 0.617

0.5 0.341 0.112 0.00 10.8 14.6 0.208 0.241 0.133 0.4932 3.63 1.26 0.00 13.2 15.3 259 54.5 30.1 3.822 3.28 1.02 0.00 17.0 19.8 216 43.3 24.1 3.72

1.75 3.84 2.16 0.00 14.1 16.1 215 47.5 26.3 3.831.75 3.60 1.42 0.00 16.8 19.2 190 41.1 22.6 3.791.75 3.30 0.909 0.00 21.1 24.0 162 33.6 18.6 3.721.75 3.13 1.35 0.00 10.8 12.7 143 36.9 20.3 3.181.75 2.91 0.972 0.00 13.1 15.4 124 31.1 17.2 3.13

1.625 3.07 1.34 0.00 13.6 15.7 109 28.6 15.8 3.151.625 2.81 0.841 0.00 17.0 19.8 92.9 23.4 12.9 3.10

1.5 2.94 1.78 0.00 11.0 12.7 84.5 25.1 14.0 2.871.5 2.51 0.737 0.00 16.9 19.5 62.3 17.3 9.60 2.79

1.375 2.25 0.826 0.00 11.6 13.6 40.5 14.0 7.72 2.351.375 2.01 0.605 0.00 15.5 18.2 32.9 10.8 5.99 2.29

1.4375 1.84 0.758 0.00 7.05 8.73 25.1 11.0 6.04 1.851.4375 1.58 0.577 0.00 10.6 13.0 18.9 7.71 4.27 1.781.1875 1.65 0.543 0.00 11.9 14.0 17.2 7.12 3.95 1.831.1875 1.51 0.480 0.00 14.5 17.1 14.8 5.94 3.30 1.781.125 1.56 0.673 0.00 6.90 8.42 12.5 6.58 3.62 1.561.125 1.20 0.403 0.00 13.2 16.1 7.79 3.70 2.05 1.45

1 1.15 0.439 0.00 7.27 9.07 5.00 3.19 1.76 1.221 0.942 0.336 0.00 11.8 14.8 3.49 2.07 1.14 1.14

0.8125 0.915 0.394 0.00 5.01 6.45 2.12 1.85 1.02 0.9150.8125 0.692 0.271 0.00 10.0 12.9 1.26 1.01 0.547 0.831

0.75 0.570 0.239 0.00 8.71 11.7 0.671 0.650 0.348 0.6770.75 0.553 0.250 0.00 4.34 6.13 0.462 0.592 0.319 0.5750.75 0.448 0.204 0.00 7.34 10.4 0.307 0.381 0.198 0.522

0.625 0.432 0.219 0.00 2.84 4.30 0.200 0.351 0.187 0.4260.625 0.329 0.171 0.00 5.82 8.82 0.114 0.196 0.0970 0.370

19 20 21 22 23 24 25 26IY ZY SY RY J CW H QS

600 118 75.2 3.49 37.2 438 0.723 0.817521 102 65.9 3.49 25.4 275 0.733 0.636462 90.9 58.6 3.47 18.6 200 0.731 0.532398 78.3 50.5 3.43 12.4 139 0.723 0.438

1260 240 151 3.80 221 2340 0.762 1.001020 197 124 3.72 138 1400 0.760 1.00843 164 104 3.65 88.2 881 0.756 1.00771 150 95.7 3.63 70.6 677 0.760 1.00709 138 88.3 3.60 57.7 558 0.756 1.00691 135 86.3 3.60 54.2 511 0.759 0.993609 119 76.6 3.57 39.6 362 0.760 0.893546 107 69.0 3.54 30.5 279 0.756 0.825522 102 65.9 3.58 25.7 218 0.770 0.699463 90.8 58.8 3.55 19.0 158 0.770 0.580398 77.8 50.5 3.54 12.4 101 0.771 0.445347 68.2 44.1 3.45 9.12 83.5 0.746 0.452401 106 64.9 2.64 85.4 796 0.679 1.00322 85.7 52.9 2.57 52.5 484 0.674 1.00320 85.0 52.7 2.58 51.4 449 0.680 1.00281 75.0 46.7 2.55 38.2 322 0.681 1.00261 69.9 43.5 2.52 32.4 282 0.675 0.913246 66.0 41.3 2.52 27.9 233 0.679 0.855222 59.0 37.3 2.54 20.6 156 0.691 0.699195 52.1 33.0 2.51 15.2 113 0.690 0.581165 44.0 28.0 2.49 9.65 71.2 0.688 0.445141 37.8 23.9 2.40 6.99 62.9 0.659 0.454114 30.9 19.4 2.29 4.66 51.9 0.626 0.435

2100 371 234 4.22 525 5810 0.797 1.001610 290 184 4.10 295 3070 0.795 1.001240 227 145 4.00 163 1600 0.794 1.001120 206 131 3.96 128 1250 0.792 1.00997 184 117 3.92 96.6 914 0.792 1.00877 162 104 3.88 70.7 652 0.792 1.00786 146 94.0 3.85 54.1 491 0.792 1.00711 132 85.5 3.83 42.0 372 0.793 0.989648 120 77.8 3.82 32.1 285 0.792 0.925599 112 72.2 3.80 26.3 231 0.791 0.865545 102 65.8 3.76 20.8 185 0.785 0.817507 94.8 61.4 3.74 17.3 155 0.783 0.768470 88.0 57.0 3.71 14.3 129 0.780 0.714264 68.5 43.2 2.65 26.4 205 0.703 0.922234 60.9 38.6 2.62 19.7 151 0.703 0.829206 53.4 33.8 2.58 13.9 119 0.687 0.791187 48.8 30.9 2.56 11.1 92.7 0.688 0.702174 45.3 28.8 2.55 9.20 77.6 0.685 0.637160 41.8 26.6 2.53 7.51 63.2 0.684 0.566147 38.6 24.6 2.50 6.17 53.6 0.678 0.521135 35.4 22.5 2.47 5.04 46.0 0.670 0.486113 29.8 18.9 2.38 3.48 37.3 0.644 0.456810 156 100 3.77 73.9 615 0.803 1.00729 141 90.6 3.74 57.1 468 0.803 1.00645 125 80.7 3.71 42.1 335 0.804 1.00581 113 73.1 3.68 32.5 256 0.802 0.991517 101 65.5 3.65 24.3 188 0.802 0.905466 90.8 58.8 3.62 18.0 146 0.792 0.867

420 82.1 53.2 3.59 13.9 113 0.788 0.801375 73.3 47.6 3.56 10.4 84.9 0.784 0.717155 42.1 27.0 2.50 8.81 55.4 0.715 0.628136 36.9 23.6 2.47 6.16 43.0 0.700 0.575123 33.4 21.3 2.43 4.84 35.4 0.691 0.528109 29.7 18.9 2.38 3.67 29.3 0.677 0.49293.5 25.6 16.3 2.32 2.64 23.4 0.659 0.448774 155 99.2 3.67 86.3 636 0.817 1.00693 140 89.6 3.64 66.6 478 0.818 1.00622 126 81.0 3.60 51.2 361 0.817 1.00549 111 71.9 3.58 37.5 257 0.819 1.00480 97.9 63.3 3.53 26.9 184 0.815 1.00427 87.5 56.8 3.51 20.1 133 0.818 0.955378 77.2 50.1 3.49 14.1 96.4 0.809 0.899336 68.9 44.7 3.46 10.5 71.2 0.807 0.816299 61.4 39.9 3.42 7.78 53.0 0.802 0.733114 33.9 21.7 2.28 7.24 37.6 0.716 0.71598.0 29.2 18.6 2.25 4.85 28.5 0.698 0.66290.4 27.0 17.2 2.23 3.98 23.9 0.694 0.60282.1 24.6 15.6 2.19 3.21 20.5 0.683 0.56773.0 21.9 13.9 2.15 2.49 17.3 0.668 0.53463.9 19.3 12.2 2.10 1.88 14.3 0.653 0.49257.3 17.3 11.0 2.09 1.41 10.5 0.654 0.4051060 218 138 3.65 247 1740 0.831 1.00655 140 89.3 3.48 84.5 532 0.828 1.00587 126 80.8 3.45 65.4 401 0.829 1.00527 113 72.9 3.41 50.5 304 0.828 1.00477 103 66.4 3.39 39.6 232 0.830 1.00430 93.3 60.2 3.36 30.7 178 0.828 1.00384 83.8 54.2 3.33 23.4 135 0.825 1.00352 77.0 49.9 3.32 18.8 105 0.828 1.00309 67.8 44.1 3.29 13.5 74.3 0.827 0.961278 60.8 39.4 3.25 10.0 57.7 0.815 0.938248 54.5 35.4 3.23 7.53 42.7 0.814 0.851222 48.8 31.7 3.20 5.62 31.7 0.812 0.76492.2 28.8 18.4 2.21 5.55 24.0 0.732 0.76379.3 24.6 15.8 2.18 3.65 17.5 0.716 0.69869.6 21.7 13.9 2.15 2.63 12.6 0.713 0.57862.0 19.4 12.4 2.12 2.01 10.2 0.702 0.53052.8 16.6 10.6 2.07 1.40 7.79 0.685 0.475581 133 85.1 3.27 100 553 0.837 1.00513 119 75.9 3.23 75.6 405 0.837 1.00460 107 68.6 3.20 58.4 305 0.837 1.00412 96.3 61.9 3.17 45.1 230 0.837 1.00362 85.2 54.9 3.14 33.2 165 0.838 1.00326 77.0 49.7 3.11 25.5 125 0.836 1.00289 68.6 44.4 3.08 19.1 91.3 0.836 1.00265 63.1 40.9 3.07 15.3 72.5 0.836 1.00240 57.3 37.2 3.04 11.9 55.8 0.835 1.00221 52.6 34.2 3.05 9.22 43.8 0.832 1.00195 46.6 30.3 3.01 6.70 31.9 0.827 0.946170 40.7 26.5 2.97 4.74 23.1 0.818 0.885149 35.7 23.2 2.94 3.35 16.4 0.814 0.793130 31.2 20.3 2.91 2.35 11.6 0.809 0.69259.7 20.7 13.3 1.99 3.53 12.3 0.733 0.78154.5 18.7 12.0 1.98 2.62 9.57 0.727 0.71547.2 16.3 10.5 1.95 1.84 6.90 0.720 0.609

41.3 14.3 9.18 1.92 1.34 5.30 0.709 0.54135.2 12.3 7.85 1.87 0.932 4.08 0.691 0.48917.2 7.85 4.90 1.38 0.850 3.92 0.619 0.52514.5 6.65 4.15 1.34 0.588 2.93 0.606 0.449271 66.5 43.1 3.02 20.4 85.4 0.859 1.00241 59.5 38.6 3.00 15.3 63.0 0.859 1.00217 53.9 35.0 2.99 11.8 47.3 0.861 1.00188 46.3 30.0 2.95 7.69 32.5 0.846 1.00166 41.1 26.7 2.93 5.62 23.4 0.845 1.00152 37.8 24.6 2.91 4.47 18.4 0.846 0.995137 34.1 22.2 2.90 3.40 13.8 0.845 0.919124 30.8 20.2 2.89 2.60 10.4 0.846 0.82846.4 17.3 11.0 1.84 3.01 9.33 0.730 0.96640.7 15.2 9.74 1.83 2.16 6.50 0.732 0.85635.3 13.3 8.51 1.81 1.51 4.42 0.732 0.72832.4 12.2 7.83 1.80 1.22 3.62 0.728 0.66628.7 10.9 6.97 1.77 0.913 2.78 0.721 0.58124.2 9.18 5.89 1.73 0.617 2.08 0.703 0.52019.4 7.44 4.76 1.66 0.400 1.52 0.676 0.46115.3 7.40 4.67 1.35 0.884 2.50 0.665 0.59212.5 6.08 3.82 1.30 0.570 1.89 0.640 0.53210.3 5.07 3.18 1.26 0.383 1.40 0.623 0.459398 104 66.2 2.95 87.2 339 0.875 1.00352 92.5 59.2 2.91 66.5 251 0.873 1.00314 83.1 53.4 2.88 51.1 189 0.874 1.00279 74.4 47.9 2.85 39.1 140 0.875 1.00246 66.1 42.7 2.82 29.1 102 0.874 1.00220 59.4 38.4 2.79 22.3 75.7 0.875 1.00196 53.1 34.4 2.76 16.8 56.5 0.872 1.00174 47.4 30.7 2.74 12.5 41.2 0.872 1.00156 42.7 27.7 2.72 9.58 30.7 0.874 1.00139 38.3 24.9 2.70 7.23 22.8 0.873 1.00126 34.5 22.5 2.69 5.30 17.4 0.862 1.00110 30.2 19.7 2.66 3.73 12.1 0.860 1.00100 27.6 18.0 2.65 2.92 9.29 0.863 1.0087.6 24.2 15.8 2.63 2.04 6.42 0.861 0.93976.2 21.1 13.8 2.61 1.41 4.37 0.861 0.82530.1 12.3 7.89 1.70 1.74 3.96 0.752 0.96527.4 11.2 7.22 1.69 1.36 3.01 0.755 0.87725.0 10.3 6.63 1.68 1.08 2.35 0.756 0.79722.5 9.26 5.97 1.67 0.830 1.84 0.749 0.73420.0 8.28 5.35 1.65 0.619 1.36 0.748 0.62311.3 5.84 3.71 1.29 0.609 1.20 0.695 0.6369.55 4.97 3.17 1.27 0.404 0.788 0.693 0.4957.67 4.02 2.56 1.22 0.252 0.598 0.662 0.46093.1 27.4 17.9 2.51 3.85 10.4 0.878 1.0081.3 24.0 15.7 2.49 2.72 7.19 0.877 1.0069.2 20.5 13.4 2.47 1.78 4.61 0.877 0.99059.5 17.7 11.6 2.46 1.19 3.01 0.879 0.86321.6 9.42 6.06 1.60 1.10 1.99 0.770 0.94218.6 8.15 5.26 1.59 0.760 1.34 0.769 0.82616.4 7.22 4.67 1.57 0.555 0.974 0.767 0.72614.4 6.36 4.12 1.56 0.396 0.673 0.769 0.58112.2 5.42 3.50 1.52 0.272 0.516 0.745 0.5546.20 3.51 2.24 1.17 0.230 0.366 0.695 0.4804.79 2.73 1.74 1.12 0.130 0.243 0.667 0.4062360 408 264 4.69 714 5250 0.966 1.00

2080 365 236 4.62 555 3920 0.966 1.001840 326 211 4.55 430 2930 0.966 1.001630 292 189 4.49 331 2180 0.966 1.001440 261 169 4.43 254 1620 0.967 1.001280 234 152 4.38 196 1210 0.967 1.001180 217 141 4.34 164 991 0.968 1.001090 201 131 4.31 135 801 0.968 1.00994 185 121 4.27 110 640 0.968 1.00903 169 110 4.24 88.3 502 0.968 1.00807 152 99.4 4.20 67.5 375 0.969 1.00722 137 89.7 4.17 51.8 281 0.969 1.00645 123 80.7 4.13 39.3 209 0.969 1.00576 110 72.5 4.10 29.6 154 0.970 1.00513 98.9 65.0 4.07 22.2 113 0.970 1.00466 90.1 59.3 4.05 17.3 87.2 0.971 1.00419 81.3 53.5 4.02 13.2 65.2 0.970 1.00374 73.0 48.1 4.00 9.84 47.9 0.971 1.00338 66.2 43.7 3.98 7.56 36.3 0.971 1.00274 56.5 37.2 3.76 6.13 26.6 0.966 1.00247 51.2 33.7 3.74 4.67 20.0 0.966 1.00223 46.3 30.6 3.73 3.55 15.0 0.968 1.00201 41.8 27.6 3.71 2.68 11.1 0.967 1.00181 37.8 25.0 3.70 2.03 8.31 0.968 1.0074.1 22.4 14.6 2.48 2.53 5.63 0.912 1.0066.9 20.2 13.3 2.48 1.93 4.19 0.916 1.0060.7 18.4 12.1 2.46 1.50 3.21 0.916 1.0053.7 16.4 10.7 2.45 1.09 2.29 0.915 0.97228.8 11.0 7.15 1.92 0.967 1.46 0.868 0.95725.7 9.80 6.40 1.91 0.723 1.07 0.866 0.88322.6 8.64 5.65 1.89 0.522 0.751 0.865 0.77613.3 6.07 3.94 1.55 0.398 0.554 0.799 0.75811.6 5.32 3.45 1.53 0.284 0.400 0.792 0.6689.79 4.49 2.91 1.49 0.190 0.287 0.772 0.6094.45 2.76 1.77 1.08 0.179 0.207 0.712 0.5383.50 2.19 1.40 1.04 0.104 0.134 0.689 0.448593 137 88.6 3.47 120 481 0.958 1.00525 122 79.3 3.42 92.0 356 0.959 1.00469 110 71.3 3.38 70.9 267 0.958 1.00414 97.9 63.6 3.34 53.5 195 0.958 1.00371 88.4 57.5 3.31 41.6 148 0.958 1.00332 79.7 51.9 3.28 32.1 112 0.958 1.00295 71.2 46.5 3.25 24.3 82.1 0.960 1.00259 62.9 41.2 3.22 17.7 58.3 0.960 1.00227 55.6 36.4 3.19 12.8 41.3 0.960 1.00199 48.9 32.1 3.16 9.21 28.9 0.959 1.00172 42.7 28.0 3.13 6.42 19.7 0.959 1.00151 37.5 24.7 3.11 4.55 13.6 0.961 1.00135 33.7 22.2 3.09 3.42 10.1 0.962 1.00120 30.2 19.9 3.07 2.54 7.34 0.960 1.00108 27.1 17.9 3.05 1.91 5.43 0.960 1.0097.5 24.6 16.2 3.04 1.46 4.07 0.960 1.0087.2 22.0 14.5 3.02 1.09 2.97 0.960 1.0053.5 16.2 10.7 2.51 1.05 2.08 0.944 1.0047.9 14.5 9.58 2.48 0.788 1.53 0.939 1.0028.2 10.6 6.97 1.96 0.855 1.23 0.899 1.0025.0 9.47 6.21 1.95 0.627 0.885 0.898 0.99822.0 8.38 5.50 1.94 0.452 0.620 0.901 0.885

12.2 5.73 3.73 1.54 0.369 0.437 0.834 0.85510.2 4.78 3.12 1.52 0.228 0.267 0.830 0.7088.66 4.08 2.67 1.51 0.150 0.174 0.827 0.5672.33 1.83 1.15 0.847 0.146 0.137 0.683 0.7111.88 1.49 0.939 0.821 0.0899 0.0934 0.665 0.5981.41 1.13 0.706 0.773 0.0511 0.0678 0.624 0.5391.18 0.947 0.593 0.753 0.0350 0.0493 0.611 0.451118 34.6 22.6 2.67 7.50 16.9 0.963 1.00103 30.5 20.0 2.65 5.41 11.9 0.964 1.0089.3 26.5 17.4 2.63 3.75 8.02 0.964 1.0076.8 22.9 15.1 2.60 2.55 5.31 0.964 1.0066.7 20.0 13.2 2.58 1.78 3.62 0.965 1.0058.1 17.5 11.5 2.57 1.23 2.46 0.964 1.0051.7 15.6 10.3 2.56 0.909 1.78 0.966 1.0046.7 14.1 9.34 2.54 0.693 1.33 0.966 1.0026.7 10.1 6.65 2.01 0.753 0.981 0.940 1.0022.5 8.57 5.64 1.98 0.487 0.616 0.936 1.0018.3 7.00 4.60 1.94 0.291 0.356 0.927 1.008.35 4.41 2.87 1.37 0.310 0.273 0.849 1.007.05 3.75 2.44 1.36 0.201 0.173 0.848 0.9045.71 3.05 1.99 1.33 0.119 0.107 0.830 0.8372.15 1.67 1.07 0.874 0.116 0.0796 0.729 0.8731.78 1.40 0.887 0.844 0.0776 0.0610 0.703 0.8431.45 1.15 0.723 0.810 0.0518 0.0475 0.672 0.8101.09 0.869 0.551 0.785 0.0272 0.0255 0.661 0.59344.3 16.3 10.7 2.12 2.51 3.56 0.962 1.0037.5 13.9 9.13 2.10 1.66 2.28 0.961 1.0030.5 11.4 7.51 2.08 0.977 1.30 0.966 1.0024.5 9.24 6.08 2.04 0.558 0.715 0.961 1.0021.3 8.05 5.31 2.03 0.384 0.480 0.963 1.0018.5 7.03 4.64 2.02 0.267 0.327 0.961 1.0010.8 5.04 3.31 1.62 0.268 0.230 0.935 1.009.14 4.28 2.81 1.61 0.173 0.144 0.936 1.004.88 2.84 1.85 1.26 0.141 0.0916 0.877 1.003.98 2.33 1.52 1.23 0.0855 0.0562 0.863 1.001.70 1.33 0.849 0.876 0.0679 0.0382 0.760 1.001.36 1.07 0.682 0.843 0.0433 0.0269 0.733 1.001.05 0.826 0.531 0.840 0.0212 0.0114 0.749 0.7358.53 4.28 2.81 1.52 0.229 0.171 0.953 1.006.64 3.36 2.21 1.50 0.120 0.0858 0.953 1.004.66 2.37 1.56 1.45 0.0504 0.0342 0.937 1.002.21 1.69 1.10 0.966 0.111 0.0426 0.880 1.001.50 1.16 0.748 0.918 0.0449 0.0178 0.846 1.001.10 0.856 0.557 0.905 0.0202 0.00736 0.852 1.00

0.995 0.778 0.505 0.890 0.0166 0.00620 0.839 1.004.56 2.76 1.81 1.28 0.157 0.0775 0.964 1.003.75 2.28 1.50 1.26 0.0958 0.0453 0.962 1.001.93 1.46 0.950 1.00 0.0750 0.0233 0.947 1.001.00 0.839 0.536 0.746 0.0246 0.0284 0.634 0.340

0.756 0.684 0.432 0.669 0.0206 0.0268 0.602 0.3420.543 0.575 0.354 0.561 0.0249 0.0337 0.567 0.4830.506 0.532 0.330 0.566 0.0196 0.0250 0.574 0.3970.517 0.509 0.318 0.594 0.0145 0.0202 0.572 0.3440.336 0.403 0.250 0.505 0.0156 0.0138 0.585 0.5480.296 0.354 0.220 0.502 0.0112 0.00989 0.583 0.4460.281 0.334 0.209 0.505 0.00932 0.00792 0.588 0.3760.188 0.264 0.165 0.444 0.00917 0.00463 0.612 0.633

0.176 0.247 0.154 0.441 0.00778 0.00403 0.608 0.5780.0897 0.155 0.0973 0.374 0.00494 0.00124 0.646 0.7790.0863 0.136 0.0863 0.400 0.00265 0.000754 0.644 0.609

4.35 2.66 1.74 1.26 0.156 0.0732 0.955 1.000.732 0.588 0.385 0.926 0.00919 0.00193 0.942 1.0041.5 18.1 10.3 1.53 6.38 27.5 0.640 1.0038.4 16.7 9.76 1.57 5.05 15.0 0.686 1.0023.7 12.0 6.55 1.27 3.76 19.5 0.584 1.0022.3 11.2 6.27 1.30 3.01 12.1 0.615 1.0021.0 10.4 6.00 1.34 2.44 6.94 0.656 0.87825.0 12.5 6.93 1.33 4.16 15.0 0.625 1.0023.3 11.6 6.59 1.36 3.30 9.17 0.659 1.0014.8 8.36 4.62 1.16 2.28 7.21 0.613 1.0013.7 7.70 4.39 1.19 1.78 4.02 0.654 1.0012.0 7.17 3.84 1.08 2.02 7.03 0.582 1.0010.4 6.06 3.45 1.14 1.16 2.26 0.660 1.007.79 4.99 2.76 1.03 1.05 2.02 0.635 1.007.13 4.54 2.59 1.06 0.765 0.995 0.689 1.007.79 5.16 2.84 1.03 1.36 1.97 0.662 1.006.74 4.43 2.57 1.06 0.842 0.787 0.732 1.004.92 3.40 1.94 0.980 0.524 0.556 0.695 1.004.66 3.22 1.87 1.00 0.438 0.364 0.731 1.004.15 3.10 1.68 0.899 0.633 0.725 0.653 1.003.36 2.49 1.44 0.950 0.300 0.173 0.767 1.002.13 1.84 1.02 0.795 0.271 0.168 0.704 1.001.84 1.59 0.922 0.827 0.167 0.0642 0.788 1.001.14 1.17 0.642 0.673 0.181 0.0772 0.705 1.00

0.901 0.930 0.541 0.702 0.0830 0.0197 0.819 1.000.597 0.686 0.398 0.638 0.0568 0.0100 0.839 1.000.444 0.565 0.317 0.564 0.0590 0.00995 0.797 1.000.374 0.485 0.281 0.576 0.0364 0.00457 0.869 1.000.289 0.411 0.230 0.513 0.0432 0.00496 0.830 1.000.223 0.328 0.192 0.518 0.0216 0.00189 0.911 1.00

rectangular duct

Documents