Calculation for W10x30 A36 Beam with Concentrated Load at Center (ASD Method)

Engineering Analysisby Kevin Wilson

Conforms to Standards of AISC Steel Construction Manual 13th Edition

Modulus of Elasticity of Steel: E 29000000psi:=

Yield Strength of A36: Fy 36ksi:=

Concentrated Load on Beam: P 5kip:=

Beam Span: l 120in:=

Properties of the W10x30 Beam Section:

Depth of Section: d 10.5in:=

Flange Width: bf 5.81in:=

Thickness of Web: tw 0.300in:=

Flange Thickness: tf 0.510in:=

Moment of Inertia: I 170in4:=

Elastic Section Modulus: Z 36.6in3:=

Beam Loading Calculations: Section Modulus (X-Axis): Sx 32.4in3:=

Support Reactions: RP2

2.5 kip⋅=:= Radius of Gyration (Y-Axis): ry 1.37in:=

Maximum Shear: VMax R 2.5 kip⋅=:= Area of Section: Area 8.84in2:=__________________________________________________________________________________________________

Shear Stress Check AISC Steel Manual 13th Ed., Chapter G:

Shear Safety Factor: Ωv 1.67:= (Ref. AISC 13th Ed., Sect. 16, B1 )

Height of Web: h d tf− tf− 9.48 in=:=

Area of Web: Aw d tw⋅ 3.15 in2=:=

Web Height/Thickness Ratio: htw

31.6= < 260 Therefore:

Web Plate Buckling Coefficient for unstifened web: kv 5:= (Ref. AISC 13th Ed. Sect. 16, G2.1(b-i))

G1.10 1.10kv E⋅( )Fy

⋅ 69.811=:= > htw

31.6= Therefore:

Web Shear Coefficient: Cv 1.0:= (Ref. AISC 13th Ed., Sect. 16, G2-3, )

Nominal Shear Strength: Vn 0.6 Fy⋅ Aw⋅ Cv⋅ 68.04 kip⋅=:= (Ref. AISC 13th Ed., Sect. 16, G2-1, )

Required Shear Strength: VaVnΩv

40.743 kip⋅=:= (Ref. AISC 13th Ed., Sect. 16, B3-2, )

Va 40.743 kip⋅= > VMax 2.5 kip⋅= OK

Calculation for W10x30 A36 Beam with Concentrated Load at Center (ASD Method)

Engineering Analysisby Kevin Wilson

Conforms to Standards of AISC Steel Construction Manual 13th Edition

Flexure Check per AISC Steel Manual 8th Ed., Chapter F:

Bending Safety Factor: Ωb 1.67:= (Ref. AISC 13th Ed., Sect. 16, F1 )

Maximum Bending Moment: MmaxP l⋅4

150 kip in⋅⋅=:=

Moment A: MAP l 0.25⋅( )⋅[ ]

275 kip in⋅⋅=:= Moment B: MB Mmax 150 kip in⋅⋅=:=

Moment C: MC MA 75 kip in⋅⋅=:=

Cross-section monosymmetry parameter: Rm 1.0:=

Width Thickness Ratio Flange: λflange 5.70:= λweb 29.5:=

Compact Limiting Ratio: λp_flange 0.38EFy

⎛⎜⎝

⎞⎟⎠

⋅ 10.785=:= λp_web 3.76EFy

⎛⎜⎝

⎞⎟⎠

⋅ 106.717=:=

Non-Compact Limiting Ratio: λr_flange 1.0EFy

⎛⎜⎝

⎞⎟⎠

⋅ 28.382=:= λr_web 5.70EFy

⎛⎜⎝

⎞⎟⎠

⋅ 161.779=:=

λ < λp in all cases. Therefore, the Section is Compact.

Lateral Torsional Buckling Mod: Cb12.5 Mmax⋅( )

2.5 Mmax⋅( ) 3 MA⋅( )+ 4 MB⋅( )+ 3 MC⋅( )+

⎡⎢⎣

⎤⎥⎦Rm⋅ 1.316=:=

(Ref. AISC 13th Ed., Sect. 16, F1-1, )

Lp 4.84ft:= < Lb l 10 ft⋅=:= < Lr 16.1ft:=

Nominal Flexural Strength at Yielding: Mn_y Fy Z⋅ 1317.6 kip in⋅⋅=:= (Ref. AISC 13th Ed., Sect. 16, F2-1, )

Mp Fy Z⋅ 1317.6 kip in⋅⋅=:=Plastic Moment:

Mn_ltb Cb Mp Mp 0.7 Fy⋅ Sx⋅( )−⎡⎣ ⎤⎦Lb Lp−( )Lr Lp−( )

⎡⎢⎣

⎤⎥⎦

⋅−⎡⎢⎣

⎤⎥⎦

⋅ 1431.522 kip in⋅⋅=:=

Nominal Flexural Strength: Mn min Mn_y Mn_ltb, ( ) 1317.6 kip in⋅⋅=:=

Allowable Flexural Strength: MaMnΩb

788.982 kip in⋅⋅=:= IR =MmaxMa

0.19= < 1.0 OK

__________________________________________________________________________________________________

Deflection Check:

Allowable Deflection: Δallowl360

0.333 in=:=

Max. Deflection: ΔmaxP l3⋅

48 E⋅ I⋅

⎛⎜⎝

⎞⎟⎠

0.037 in=:= < Δallow 0.333 in= OK