D9.B.2 Member Capacities
D9.B.2.1 Design Capabilities
All types of available shapes like HShape, IShape, LShapes, CHANNEL, PIPE, TUBE, etc. can be used as member property and STAAD.Pro will automatically adopt the design procedure for that particular shape if Steel Design is requested. STEEL TABLE available within STAAD.Pro or UPTABLE facility can be used for member property.
D9.B.2.2 Methodology
For steel design, STAAD.Pro compares the actual stresses with the allowable stresses as required by AIJ specifications. The design procedure consist of following three steps.

Calculation of sectional properties
The program extracts section properties cross sectional area, A, moment of inertia about Y and Z axes, I_{yy} and I_{zz}, and the St. Venant torsional constant, J, from the builtin steel tables. The program then calculates the elastic section moduli, Z_{z} and Z_{y}, torsional section modulus, Z_{x}, and radii of gyration, i_{y} and i_{z}, using the appropriate formulas.

Calculation of actual and allowable stresses
Program calculates actual and allowable stresses by following methods:

Axial Stress:
Actual tensile stresses,
whereF_{T} = force / ( A × NSF )  NSF
=  Net Section Factor for tension input as a design parameter
Actual compressive stress , F_{C} = force / A
Allowable tensile stress, f_{t}
 = FYLD / 1.5 (For Permanent Case)
 = FYLD ( For Temporary Case )
 FYLD
=  Yield stress input as a design parameter
Allowable compressive stress, f_{c}
${f}_{c}=\{\begin{array}{c}\frac{[10.4{\left(\frac{\lambda}{\Lambda}\right)}^{2}]F}{\nu}\phantom{\rule{0ex}{0ex}}\text{when}\phantom{\rule{0ex}{0ex}}\lambda \le \Lambda \\ \frac{\begin{array}{c}0.277F\end{array}}{{\left(\frac{\lambda}{\Lambda}\right)}^{2}}\phantom{\rule{0ex}{0ex}}\text{when}\phantom{\rule{0ex}{0ex}}\lambda \Lambda \end{array}$
where= f_{c} x 1.5 (for Temporary case)  Λ
=  $\sqrt{\frac{{\pi}^{2}E}{0.6F}}$
 ν
=  $\frac{3}{2}+\frac{2}{3}{\left(\frac{\lambda}{\Lambda}\right)}^{2}$
 λ
=  maximum slenderness, considering both principal axis
 E
=  Modulus of elasticity of steel (Young's Modulus)
Actual torsional stress, f_{t} = torsion / Z_{x}
where Z_{x}
=  J / max(t_{f}, t_{w})
 t_{f}
=  flange thickness
 t_{w}
=  web thickness

Bending Stress:
Actual bending stress for My for compression:
( F_{bcy}) = M_{y} / Z_{cy}
Actual bending stress for Mz for compression
( F_{bcz}) = M_{z} / Z_{cz}
Actual bending stress for My for tension
( F_{bty} ) = M_{y} / Z_{ty}
Actual bending stress for Mz for tension
where( F_{btz} ) = M_{z} / Z_{tz}  Z_{cy}, Z_{cz}
=  elastic section modulus for compression due to bending about the y and z axes, respectively
 Z_{ty}, Z_{tz}
=  elastic section modulus for tension due to bending about the y and z axes, respectively
Allowable bending stress for M_{y}
(f_{bcy}) = f_{t}
Allowable bending stress for M_{z}
When λ_{b} ≤ _{p}λ_{b} , f_{b} = F/ν
When _{p}λ_{b} < λ_{b} ≤ _{e}λ_{b} ,
${f}_{b}=\frac{F(10.4\frac{{\lambda}_{b}{{}_{p}\lambda}_{b}}{{}_{e}{\lambda}_{b}{{}_{p}\lambda}_{b}})}{\nu}$When _{e}λ_{b} < λ_{b} ,
${f}_{b}=\frac{1}{{\lambda}_{b}^{2}}\frac{F}{2.17}$where λ_{b}
=  $\sqrt{{M}_{y}/{M}_{e}}$
 _{e}λ_{b}
=  $1/\sqrt{0.6}$
 ν
=  $\frac{3}{2}+\frac{2}{3}{\left(\frac{{\lambda}_{b}}{{{}_{e}\lambda}_{b}}\right)}^{2}$
 M_{e}
=  $C\sqrt{\frac{{\pi}^{4}E{I}_{y}E{I}_{w}}{{I}_{b}^{4}}+\frac{{\pi}^{2}E{I}_{y}GJ}{{I}_{b}^{2}}}$
 _{p}λ_{b}
=  $0.6+0.3\left(\frac{M2}{M1}\right)$
or taken as the value of PLB if not 0
 C
=  1.75 + 1.05 (M2 / M1) + 0.3 (M2 / M1)^{2} ≤ 2.3
 M1
=  the larger of end moments about the major axis
 M2
=  the smaller of end moments about the major axi
For Temporary case, f_{bcz} = 1.5 x (f_{bcz} for Permanent case)
where f_{t}
=  Allowable bending stress for M_{y}, f_{bty}
 f_{bcz}
=  Allowable bending stress for M_{z}, f_{btz}

Shear Stress
Actual shear stresses are calculated by the following formula:
whereQ_{y} = F_{y} / A_{ww}  A_{ww}
=  web shear area = depth times web thickness
whereQ_{z} = F_{z} / A_{ff}  A_{ff}
=  flange shear area = 2/3 times total flange area
Allowable shear stress:
 Permanent Loads: f_{s} = (F_{y}/√(3))/ 1.5
 Temporary Loads: f_{s} = F_{y} / √(3)
 F_{y}
=  yield strength of steel, specified by the FYLD parameter.


Checking design requirements:
User provided RATIO value (default 1.0) is used for checking design requirements:
The following conditions are checked to meet the AIJ specifications. For all the conditions calculated value should not be more than the value of RATIO. If for any condition value exceeds RATIO, program gives the message that the section fails.
Conditions:
 Axial tensile stress ratio = F_{T} / f_{t}
 Axial compressive stress ratio = F_{C} / f_{c}
 Combined compression & bending compressive ratio = F_{C} / f_{c}+F_{bcz}/f_{bcz}+F_{bcy}/f_{bcy}
 Combined compression & bending tensile ratio = (F_{btz}+F_{bty}F_{C}) / f_{t}
 Combined tension & bending tensile ratio = (F_{T}+F_{btz}+F_{bty}) / f_{t}

Combined tension & bending compressive ratio = F_{bcz}/f_{bcz}+F_{bcy}/f_{bcy} F_{T}/f_{t}
 Shear stress ratio in Y = q_{y} / f_{s}
 Shear stress ratio in Z = q_{z} / f_{s}
 von Mises stress ratio (if the von Mises stresses were set to be checked) = f_{m}/(k⋅f_{t})