design of steel w in biaxial flexure.pdf

Client:Project:Location:

Job #:Description:Revision #:

Done by:_______Checked by:_______

Date:_______

Company NameDesign of Structural Steel W Shapes

Subject to Biaxial Flexure Rev #

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Revision Description Revised By Date

Notes

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Date:_______

Design of Structural Steel W ShapesSubject to Biaxial Flexure

Description:This worksheet will choose a hot rolled steel wide flange shape in biaxial flexure based on input loadsand parameters.The capacity is calculated using AISC 360-05, Sections F2, F3, F6, G2, G7, and H 1.The user can input loading as uniformly distributed and point loads with an inclination angle, separateuniformly distributed and point loads for each axis, or separate ultimate shear and moment in thebeam when an outside analysis program has been used. This worksheet allows to user to choosebetween flange loading and loading through the shear center of the member. This worksheet checksshear and moment capacities of each axis as well as combined loading effects.

Notes:

According to AISC 360-05Only valid for Steel Wide Flange Shapes with a yield strength of 50 ksi

Annotation Guide (Open to View)

Worksheet Instructions (Open to View)

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Date:_______

Inputs Beam Properties

Cb 1:= Lateral Torsional Buckling Modification Factor (A value of 1 can be used for a conservat ive design)

L 20 ft:= Length of Beam

Lbx 5 ft:= Strong Axis Laterally U nbraced Length

Lby 10 ft:= Weak Axis Laterally Unbraced Length

Depthmax 40 in:= Maximum Allowable Beam Depth

Loading Factor 5 %:= Minimum Desired Factor Between Mu and b Mn

Choose How to Input Beam Loading

Loading Case Diagrams (Open to View)

Choose the Loading Case (View Above Diagrams for Clarification)

Case 1: Both components of load applied through shear center of member.Case 2: Only vertical component of load is applied through shear center of member.

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Date:_______

Inputs (continued)Loading (continued)

Input Loads With Inclination Angle (Open to View)

Loads on Beam

Factored Uniformly Distributed Loads

Factored Point Loads Distance to Point Loads From Beam End

wui

3.621

klf:= Pi

3.520

kip:= Ci

3170

ft:=

20 := Angle Between Loading Plane and Web Plane (Open Load Case Diagrams to View)

Input Loads With Inclination Angle (Open to View)

Input Separate Loads for Each Axis (Open to View)

Internal Moment and Shear (Open to View)

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Date:_______

Calculations Loading Calculations

Vux 65 kip= Max Shear Force in Strong Axis

Vuy 24 kip= Max Shear Force in Weak Axis

Mux 318 kip ft= Max Moment in Strong Axis

Muy 116 kip ft= Max Moment in Weak Axis

Beam Property Calculations

Beam "W36X160"=

Notes ""=

A 47 in2= Area of Beam Ix 9760 in4

= Strong Axis Mom ent of Inertia

d 36 in= Depth of Beam Zx 624 in3

= Strong Axis Plastic Sect ion Modulus

bf 12 in= Width of FlangeSx 542 in

3= Strong Axis Elastic Sect ion Modulus

tw 0.65 in= Thickness of Web

rx 14.4 in= Strong Axis Radius of Gyrationtf 1.02 in= Thickness of Flange

Cw 90200 in6

= Warping Constant Iy 295 in4

= Weak Axis Moment of Inertia

J 12.4 in4= Torsional Moment of Inert ia Zy 77.3 in3

= Weak Axis Plastic Section Modulus

ratiobf2tf 5.88= Ratio bf

2 tf Sy 49.1 in3

= Weak Axis Elastic Section Modulus

ratiohtw 49.9= Ratio htw

ry 2.5 in= Weak Axis Radius of Gyration

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Date:_______

Calculations (continued) Compactness Check (AISC Section B4)

Check for flange compactness, Table B4.1 Case 1

flan ratiobf2tf 5.88=:= Width Thickness Ratio

pflan 0.38EFy

9.152=:= Limiting Width Thickness Ratio for Compact

rflan 1.0EFy

24.083=:= Limiting Width Thickness Ratio for Noncompact

Check for web compactness, Table B4.1 Case 9

web ratiohtw 49.9=:= Width Thickness Ratio

pweb 3.76EFy

90.553=:= Limiting Width Thickness Ratio for Compact

rweb 5.70EFy

137.274=:= Limiting Width Thickness Ratio for Noncompact

Check1 "Flange is compact"= Check for Flange Compactness

Check2 "Web is compact"= Check for Web Compactness

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Calculations (continued) Limiting Lengths (AISC Section F2)

c 1:= AISC 360-05 Eq F2-8a

ho d tf 34.98 in=:= Distance Between the Flange Centroids

rtsIy Cw

Sx3.085 in=:= Effective Radius of Gyration (AISC 360-05 Eq F2-7)

Lp 1.76 ryEFy

8.831 ft=:= Limiting Laterally Unbraced Length for Yielding(AISC 360-05 Eq F2-5)

Limiting Laterally UnbracedLength for Inelastic LateralTorsional Buckling (AISC 360-05 Eq F2-6)

Lr 1.95 rtsE

0.7 Fy

J cSx ho

1 1 6.760.7 Fy

E

Sx ho

J c

2

++ 25.805 ft=:=

Lp 8.8 ft= Limiting Laterally Unbraced Length for Yielding

Lr 25.8 ft= Limiting Laterally Unbraced Length for Inelastic Lateral Torsional Buckling

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Date:_______

Strong Axis Calculations

Compact Flange Moment Capacity (AISC Section F2)F2.1 Yielding

Mpx Fy Zx:= Flexural Yielding Moment Capacity (AISC 360-05 Eq F2-1)

Mn2.1 Mpx 2600 kip ft=:=

F2.2b Inelastic LTB

Inelastic Lateral Torsional BucklingMoment Capacity (AISC 360-05 Eq F2-2)

Mn2.2b min Cb Mpx Mpx 0.7 Fy Sx( ) Lbx LpLr Lp

Mpx,

:=

Mn2.2b 2600 kip ft=

F2.2c Elastic LTB

FcrCb pi

2 E

Lbxrts

21 0.078

J cSx ho

Lbxrts

2

+ 764 ksi=:= Critical Stress (AISC 360-05 Eq F2-4)

Mn2.2c min Fcr Sx Mpx, ( ):= Elastic Lateral Torsional Buckling Moment Capacity (AISC 360-05 Eq F2-3)Mn2.2c 2600 kip ft=

Resulting Compact Flange Moment Capacity

Mncom Mn2.1 Lbx Lpif

Mn2.2b Lbx Lp> Lbx Lrif

Mn2.2c Lbx Lr>if

0 Check1 "Flange is compact" Check2 "Web is compact"if

:=

Determination of Compact Moment Capacity,0 if Flange or Web is Not Compact

Mncom 2600 kip ft=

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Date:_______

Strong Axis Calculations (continued) Noncompact and Slender Flange Moment Capacity (AISC Section F3)

F3.1 LTB

Note: Section F2.2 Appl ies for Lateral Torsional Buckling

- F2.2b Inelastic LTB

Inelastic Lateral Torsional BucklingMoment Capacity (AISC 360-05 Eq F2-2)

Mn2.2b min Cb Mpx Mpx 0.7 Fy Sx( ) Lbx LpLr Lp

Mpx,

:=

Mn2.2b 2600 kip ft=

- F2.2c Elastic LTB

FcrCb pi

2 E

Lbxrts

21 0.078

J cSx ho

Lbxrts

2

+ 764 ksi=:= Critical Stress (AISC 360-05 Eq F2-4)

Mn2.2c min Fcr Sx Mpx, ( ):= Elastic Lateral Torsional Buckling Moment Capacity (AISC 360-05 Eq F2-3)Mn2.2c 2600 kip ft=

Mn3.1 Mn2.2b Lbx Lp> Lbx Lrif

Mn2.2c Lbx Lr>if

0 otherwise

:=

Determination of LTB failure, 0 if LTB Doesn't Apply

Mn3.1 0 kip ft=

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Date:_______

Strong Axis Calculations (continued) Noncompact and Slender Flange Moment Capacity (AISC Section F3)

F3.2a Compression Flange Local Buckling with Noncompact Flanges

Mn3.2a Mpx Mpx 0.7 Fy Sx( ) flan pflanrflan pflan

:= AISC 360-05 Eq F3-1

Mn3.2a 2823 kip ft=

F3.2b Compression Flange Local Buckling with Slender Flanges

x4

ratiohtw:=

kc 0.35 x 0.35if

:=Coefficient for Slender Unstiffened Elements

kc 0.566=

Mn3.2b0.9 E kc Sx

flan2

:= AISC 360-05 Eq F3-2

Mn3.2b 19307 kip ft=

Mn3.2 Mn3.2a Check1 "Flange is non-compact"=if

Mn3.2b Check1 "Flange is slender"=if

0 otherwise

:=

Determination of FLB, 0 if FLB doesn't apply

Mn3.2 0 kip ft=

Resulting Noncompact and Slender Flange Moment CapacityDetermination ofNoncompact and SlenderMoment Capacity, 0 ifFlange is Compact or Webis Not Compact

Mnncs min Mn3.1 Mn3.2, ( ) Mn3.1 0 Mn3.2 0if0 Check1 "Flange is compact"= Check2 "Web is compact"if

max Mn3.1 Mn3.2, ( ) otherwise

:=

Mnncs 0 kip ft=

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Date:_______

Strong Axis Calculations (continued)Strong Axis Moment Capacity

Mnx 2600 kip ft= Nominal Strong Axis Moment Capacity

b Mnx 2340 kip ft= Design Strong Axis Moment Capac ity for Selected Beam

Mux 318 kip ft= Maximum Applied Strong Axis Moment

Check if Beam is Adequate in Strong Axis FlexureMust Not Exceed 100%Checkbx

Muxb Mnx

13.6 %=:=

Shear Capacity Calculations (AISC Section G2)G2.1 Nominal Shear Strength

v 1.0 ratiohtw 2.24EFy

if

0.9 otherwise

:= AISC 360-05 Section G2.1a

v 1.0=

Cv 1:= AISC 360-05 Eq G2-2

Aw d tw 23.4 in2

=:= Web Area

Vnx 0.6 Fy Aw Cv:= Nominal Strong Axis Shear Capacity (AISC 360-05 Eq G2-1)

Vnx 702 kip=

Strong Axis Shear CapacityVnx 702 kip= Nominal Strong Axis Shear Capacity

v Vnx 702 kip= Design Strong Axis Shear Capacity for Selected Beam

Vux 65 kip= Maximum Applied Strong Axis Shear

Check if Beam is Adequate in Strong Axis ShearMust Not Exceed 100%Checkvx

Vuxv Vnx

9.3 %=:=

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Date:_______

Weak Axis CalculationsCompact, Noncompact, and Slender Flange Moment Capacity (AISC Section F6)

F6.1 Yielding

Mpy min Fy Zy 1.6 Fy Sy, ( ):= Weak Axis Flexural Yielding Moment Capacity (AISC 360-05 Eq F6-1)Mn6.1 Mpy 322 kip ft=:=

F6.2 Flange Local Buckling

F6.2a Compact FlangesFor Compact Flange Shapes, the Limit State of Yielding Applies.

F6.2b Noncompact FlangesNoncompact Flange FLB MomentCapacity (AISC 360-05 Eq F6-2)Mn6.2b Mpy Mpy 0.7 Fy Sy( ) flan pflan

rflan pflan

:=

Mn6.2b 361 kip ft=

F6.2c Slender Flanges

Fcr0.69 E

bf2 tf

2578 ksi=:= Critical Stress (AISC 360-05 Eq F6-4)

Mn6.2c Fcr Sy:= Slender Flange FLB Moment Capacity (AISC 360-05 Eq F6-3)

Mn6.2c 2 103

kip ft=

Resulting Weak Axis Moment Capacity

Mny Mn6.1 Check1 "Flange is compact"=if

min Mn6.1 Mn6.2b, ( ) Check1 "Flange is non-compact"=ifmin Mn6.1 Mn6.2c, ( ) Check1 "Flange is slender"=if

:= Determination of Weak AxisMoment Capacity Based onFlange Slenderness

Mny 322 kip ft=

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Date:_______

Weak Axis Calculations (continued)Weak Axis Moment Capacity

Mny 322 kip ft= Nominal Weak Axis Moment Capacity

b Mny 290 kip ft= Design Weak Axis Moment Capacity for Selected Beam

Muy 116 kip ft= Maximum Applied Weak Axis Mom ent

Check if Beam is Adequate in Weak Axis FlexureMust Not Exceed 100%Checkby

Muyb Mny

39.9 %=:=

Shear Capacity Calculations (AISC Section G7)kv 1.2:= AISc 360-05 Section G7

Cv 1.0bftf

1.10kv E

Fyif

1.10kv E

Fy

bftf

bftf

1.10kv E

Fy>

bftf

1.37kv E

Fyif

1.51 E kv

bftf

2

Fy

bftf

1.37kv E

Fy>if

:=

Web Shear Coefficient (AISC Eqs G2-3, G2-4, and G2-5)

Cv 1.00=

Aw 2 bf tf:= Shear Area (AISC 360-05 Section G7)

Aw 24.48 in2

=

Vny 0.6 Fy Aw Cv:= Nominal Weak Axis Shear Capacity (AISC 360-05 Eq G2-1)

Vny 734 kip=

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Date:_______

Weak Axis Calculations (continued)Weak Axis Shear Capacity

Vny 734 kip= Nominal Weak Axis Shear Capacity

v Vny 734 kip= Design Weak Axis Shear Capacity for Selected Beam

Vuy 24 kip= Maximum Applied Weak Axis Shear

Check if Beam is Adequate in Weak Axis ShearMust Not Exceed 100%Checkvy

Vuyv Vny

3.2 %=:=

Interaction Calculations Force Interaction Check (AISC Section H1)b Mnx 2340 kip ft= Design Moment Capacity About Strong Axis

b Mny 290 kip ft= Design Moment Capacity About Weak Axis

Mux 318 kip ft= Ultimate Moment About Strong Axis

Muy 116 kip ft= Ultimate Moment About Weak Axis

CheckMux

b Mnx

Muyb Mny

+

Case 1=if

Muxb Mnx

Muy0.5 b Mny( )+

Case 2=if

:=Check of Force Interactions Based onLoading Conditions (AISC 360-05 Eq H1-1)

Check 0.93=

Check if Beam is Adequate for Com bined ForcesMust Not Exceed 100%Checki

Check1.00

93.4 %=:=

Final Results

Beam "W36X160"=

Results "Selected Beam is Adequate for Given Parameters"=

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design of steel w in biaxial flexure.pdf

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