AISC V.13BEAM DESIGN (LRFD)

A. DESIGN DATA

A.1 MATERIAL PROPERTIES

Yield strength of structural steel W Shapes, ASTM A572 Fy 50ksi:= Fy 345 MPa⋅=

Modulus of Elasticity of Steel Es 29000 ksi:= Es 199948 MPa⋅=

Shear Modulus Gv 11200 ksi:= Gv 77221 MPa⋅=

B. BEAM DESIGN

W10X33B.1 SECTION PROPERTIES

Properties of : W10X33A = 9.71 in^2 Cross-sectional area of memberd = 9.73 in Depth of member, parallel to Y-axis

tw = 0.29 in Thickness of web of memberbf = 7.96 in Width of flange of member, parallel to X-axistf = 0.435 in Thickness of flange of member

k(des) = 0.935 in Distance from outer face of flange to web toe of filletk(det) = 1.125 in Distance from outer face of flange to web toe of fillet

k1 = 0.75 in Distance from web centerline to flange toe of filletT = 7.5 in Distance between fillets for wide-flange or channel shape = d(nom)-2*k(det)

wt./ft. = 33 plf. Beam weightbf/(2*tf) 9.15 Slenderness parameter for compact flange

h/tw = 27.1 Slenderness parameter for compact webIx = 171 in^4 Moment of inertia of member taken about X-axisSx = 35 in^3 Elastic section modulus of member taken about X-axisrx = 4.19 in Radius of gyration of member taken about X-axis = SQRT(Ix/A)Zx = 38.8 in^3 Plastic section modulus of member taken about X-axisIy = 36.6 in^4 Moment of inertia of member taken about Y-axisSy = 9.2 in^3 Elastic section modulus of member taken about Y-axisry = 1.94 in Radius of gyration of member taken about Y-axis = SQRT(Iy/A)Zy = 14 in^3 Plastic section modulus of member taken about Y-axisrts = 2.2 in SQRT(SQRT(Iy*Cw)/Sx)ho = 9.3 in Distance between centroid of flanges, d-tf

J = 0.583 in^4 Torsional moment of inertia of memberCw = 791 in^6 Warping constant

Wno = 18.5 in^2 Normalized warping function at a point at the flange edgeSw = 16 in^4 Warping statical moment at a point on the cross sectionQf = 7.75 in^3 Statical moment for a point in the flange directly above the vertical edge of the web

Qw = 18.9 in^3 Statical moment at the mid-depth of the section

B.2 BEAM DESIGN FORCES

Service Loads: from Analysis

Maximum Moment: Mmax 50 ft kip:= Mmax 67.791 kN m⋅=

Maximum Shear: Vmax 50kip:= Vmax 222.411 kN⋅=

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AISC V.13BEAM DESIGN (LRFD)

Factored Loads: (Use Load Factor, U 1.5:= for simplicity)

Maximum Moment: Mr Mmax U⋅:= Mr 101.686 kN m⋅=

Maximum Shear: Vr Vmax U⋅:= Vr 333.617 kN⋅=

Beam Length: Lbeam 30ft:= Lbeam 9.144 m⋅=

B.3 CHECK SHEARRequired Shear Strength Vr 75 kips⋅= Vr 333.617 kN⋅=

Web Slenderness ratio λwhtw

=d 2kdes−

tw= λw 27.1=

Resistance Fac & Web Shear Coef

Web Shear Coefficient ϕv 1=

Resistance Factor for Shear Cv 1=

Web area Aw d tw⋅:= Aw 1820.448 mm2⋅=

Nominal Shear Strength Vn 0.6 Fy⋅ Aw⋅ Cv⋅:= Vn 376.546 kN⋅= [AISC Eqn G2-1]

Available shear strength ϕVn ϕv Vn:= ϕVn 376.546 kN⋅=

Utilization Ratio URvVr

ϕVn:= URv 0.886=

Check_Shear if URv 1.0≤ "O.K., SAFE!", "N.G., REDESIGN", ( ):=

Check_Shear "O.K., SAFE!"=

B.4 DETERMINE SHAPE COMPACTNESS

UNSTIFFENED ELEMENTS

Flanges of W-Shape λfbf2tf

= λf 9.15=

Compact limit λpf 0.38EsFy

:= λpf 9.152= [AISC Table B4.1]

Noncompact limit λrf 1.0EsFy

:= λrf 24.083= [AISC Table B4.1]

Flange "is compact" λf λpf≤if

"is noncompact" λpf λf< λrf≤if

"is slender-element" λf λrf>if

:= Flange "is compact"=

STIFFENED ELEMENTS

Web of W-Shape λwhtw

=d 2kdes−

tw= λw 27.1=

Compact limit λpw 3.76EsFy

:= λpw 90.553= [AISC Table B4.1]

Noncompact limit λrw 5.70EsFy

:= λrw 137.274= [AISC Table B4.1]

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AISC V.13BEAM DESIGN (LRFD)

Web "is compact" λw λpw≤if

"is noncompact" λpw λw< λrw≤if

"is slender-element" λw λrw>if

:= Web "is compact"=

B.5 CHECK AVAILABLE FLEXURAL STRENGTHLength between points that are either braced against lateral displacementof compression flange or braced against twist of the cross section

Brace Points n 1:=

LbLbeamn 1+

:= Lb 15 ft⋅=Lateral-Torsional Buckling Modification Factor,conservatively, take

Cb 1.0:=

Shape Factor for doubly symmetric I-shape c 1.0:= [AISC Eqn F2-8a]

Limiting laterally unbraced length for the limitstate of yielding Lp 1.76 ry⋅

EsFy

⋅:= Lp 6.85 ft⋅= [AISC Eqn F2-5]

Limiting laterally unbraced length for the limitstate of inelastic lateral-torsional buckling

Lr 1.95rtsEs

0.7Fy

⎛⎜⎝

⎞⎟⎠

J cSx ho⋅

1 1 6.760.7Fy

Es

Sx ho⋅

J c⋅

⎛⎜⎝

⎞⎟⎠

2++:= Lr 21.78 ft⋅= [AISC Eqn F2-6]

Plastic Bending Moment Mp Fy Zx⋅:= Mp 219.191 kN m⋅= [AISC Eqn F2-1]

Resistance Factor for Flexure ϕb 0.90:=

YIELD LIMIT STATE, AISC SEC F2.1

MY Mp:= MY 219.191 kN m⋅⋅= [AISC Eqn F2-1]

LATERAL-TORSIONAL BUCKLING LIMIT STATE, AISC SEC F2.2 & F3.1

MLTB UbL( ) Mp UbL Lp≤if

Cb Mp Mp 0.7Fy Sx⋅−( ) UbL Lp−

Lr Lp−⎛⎜⎝

⎞⎟⎠

⋅−⎡⎢⎣

⎤⎥⎦

⋅ Lp UbL< Lr≤if

FcrCb π

2⋅ Es⋅

UbLrts

⎛⎜⎝

⎞⎟⎠

21 0.078

J cSx ho⋅

UbLrts

⎛⎜⎝

⎞⎟⎠

2⋅+⋅←

Fcr Sx⋅

UbL Lr>if

:= [AISC Eqn F2-1]

[AISC Eqn F2-2]

[AISC Eqn F2-4]

MLTB Lb( ) 175.085 kN m⋅⋅=

COMPRESSION FLANGE LOCAL BUCKLING LIMIT STATE, AISC SEC F3.2

MFLB Mp λf λpf≤if

Mp Mp 0.7Fy Sx⋅−( ) λf λpf−

λrf λpf−⎛⎜⎝

⎞⎟⎠

⋅−⎡⎢⎣

⎤⎥⎦

λpf λf< λrf≤if

kc max 0.35 min4

λw0.76, ⎛

⎜⎝

⎞⎟⎠

, ⎛⎜⎝

⎞⎟⎠

←

0.9Es kc⋅ Sx⋅

λf2

λf λrf>if

:= [AISC Eqn F2-3]

[AISC Eqn F2-1]

[AISC Eqn F3-1]

MFLB 219.191 kN m⋅⋅=

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AISC V.13BEAM DESIGN (LRFD)

NOMINAL FLEXURAL STRENGTH: Mn min MY MLTB Lb( ), MFLB, ( ):= Mn 175.085 kN m⋅= [AISC Eqn F3-2]

Available Flexural Strength: ϕMn ϕb Mn:= ϕMn 157.577 kN m⋅=

Utilization Ratio: URfMr

ϕMn:= URf 0.645=

Check_Flexure if URf 1.0≤ "O.K., SAFE!", "N.G., REDESIGN", ( ):= Check_Flexure "O.K., SAFE!"=

Beam Capacity

0 2 4 6 8 1050

100

150

200

250

Nominal Moment StrengthMoment at Unbraced Length

Beam Capacity as Function of Unbraced L

Unbraced Length, m

Mom

ent

Capa

city

, kN

-m

B.6 CHECK DEFLECTION

Maximum Deflection, from Analysis δmax 12mm:=

Allowable Deflection δallowLbeam240

:= δallow 38.1 mm⋅=

Utilization Ratio: URdδmaxδallow

:= URd 0.315=

Check_Deflection if δmax δallow≤ "O.K., SAFE!", "N.G., REDESIGN", ( ):= Check_Deflection "O.K., SAFE!"=

C. SUMMARY Beam_Shape "W10X33"=

BEAM CHECKS

SHEAR Utilization Ratio URv 0.886= Check_Shear "O.K., SAFE!"=

FLEXURE Utilization Ratio URf 0.645= Check_Flexure "O.K., SAFE!"=

DEFLECTION Utilization Ratio URd 0.315= Check_Deflection "O.K., SAFE!"=

End of Calculation

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