

Calc. No.




CALCULATION SHEET


Project No.




Project Title:



Calc. By

Date

Rev.



Subject:





















Steel beam capacity
calculation in accordance with the "Manual of Steel Construction"
Load and Resistance Factor Design" (LRFD)


Beam Design for
Flexure and LateralTortional Buckling.















Section properties






Braced length





Section







L_{b}
=

150

in




A =


in^{2}

beam crosssectional area

L_{b}  distance between points braced against lateral



I_{y} =


in^{4}

moment of inertia about Y axis

displacementof the compression flange or between


S_{x} =


in^{3}

elastic section modulus  major axis

points braced to prevent twist of the cross section.


r_{y} =


in

radius of gyration about minor axis

(This parameter can not be mdoified in the Demo
Version)


J =


in^{4}

tortional constant







C_{w} =


in^{6}

warping constant







Z_{x} =


in^{3}
























Steel properties












E =


ksi

modulus of elasticity of steel


per Manual of Steel Construcion (LRFD)


G =


ksi

shear modulus of elasticity of steel


Chapter F Section 2.a


Fy =


ksi

minimum yield stress of the type of steel being used






Fyf =


ksi

yield stress of flange






Fyw =


ksi

yield stress of web






Fr =


ksi

compressive residual stress in flange for rolled
shapes F_{r} = 10
ksi, for welded shapes F_{r} = 16.5 ksi


Cb =



bending coefficient dependent upon moment gradient
C_{b} is permitted
to be conservatively taken as 1.0


fb =



resistance factor for flexure



















Yielding flexural
design strength







per Manual of Steel Construcion (LRFD)


M_{p} =

F_{y}
* Z_{x} =


kipft

plastic section moment < 1.5 M_{y}

Chapter F Section 1.




1.5*M_{y} = F_{y} * S_{x} =


kipft








M_{n} = M_{p} =


kipft











f_{b} * M_{n} =


kipft

Yielding flexural design bending moment













Lateral  torsional
Buckling





per Manual of Steel Construcion (LRFD)


L_{r}  limiting laterally unbraced length

Chapter F


L_{p} =

1.76*r_{y}*sqrt(E/F_{yf}) =


in




Eq. F14

for I shaped members and channels


F_{L} =

smaller of (F_{yf}  F_{r}) or F_{yw}










F_{L} =


ksi











M_{r} =

F_{L}
* S_{x} =


kipft





Eq. F17





X_{1} =

(p/S_{x})*sqrt(EGJA/2) =


ksi




Eq. F18





X_{2} =

4*(C_{w}/I_{y})*(S_{x}/GJ)^{2} =


ksi^{2}




Eq. F19





L_{r} =

(r_{y}*X_{1}/F_{L})*sqrt(1+sqrt(1+X_{2}*F_{L}^{2})) =


in



Eq. F16





for L_{b} < L_{r}





Chapter F Section 2.a applies


M_{n} =

C_{b}*[M_{p}(M_{p}M_{r})*(L_{b}L_{p})/(L_{r}L_{p})] =



Eq. F12





f_{b} * M_{n} =























for L_{b} > L_{r}





Chapter F Section 2.b applies


M_{n} =

M_{cr}












M_{cr} =

C_{b}*S_{x}*X_{1}*sqrt(2)/(L_{b}/r_{y})*sqrt(1+X_{1}^{2}*X_{2}/(2*(L_{b}/r_{y})^{2})








M_{cr} =








f_{b} * M_{n} =














References:



Manual of Steel
Construction  American Institute of Steel Construction Inc., 2005
















