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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⋅=
AISCV13 (LRFD) Beam Design.xmcd Page 1 of 4 LNT4: Dec 2010
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]
AISCV13 (LRFD) Beam Design.xmcd Page 2 of 4 LNT4: Dec 2010
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⋅⋅=
AISCV13 (LRFD) Beam Design.xmcd Page 3 of 4 LNT4: Dec 2010
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
AISCV13 (LRFD) Beam Design.xmcd Page 4 of 4 LNT4: Dec 2010