# D9.B.2 Member Capacities

Member design and code checking per AIJ 2005 are based upon the allowable stress design method. It is a method for proportioning structural members using design loads and forces, allowable stresses, and design limitations for the appropriate material under service conditions. The basic measure of member capacities are the allowable stresses on the member under various conditions of applied loading such as allowable tensile stress, allowable compressive stress etc. These depend on several factors such as cross sectional properties, slenderness factors, unsupported width to thickness ratios and so on. Explained here is the procedure adopted in STAAD.Pro for calculating such capacities.

## D9.B.2.1 Design Capabilities

All types of available shapes like H-Shape, I-Shape, L-Shapes, 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.

1. Calculation of sectional properties

The program extracts section properties cross sectional area, A, moment of inertia about Y and Z axes, Iyy and Izz, and the St. Venant torsional constant, J, from the built-in steel tables. The program then calculates the elastic section moduli, Zz and Zy, torsional section modulus, Zx, and radii of gyration, iy and iz, using the appropriate formulas.

2. Calculation of actual and allowable stresses

Program calculates actual and allowable stresses by following methods:

1. Axial Stress:

Actual tensile stresses,

 FT = force / ( A × NSF )

where
 NSF = Net Section Factor for tension input as a design parameter

Actual compressive stress , FC = force / A

Allowable tensile stress, ft

• = FYLD / 1.5 (For Permanent Case)
• = FYLD ( For Temporary Case )
where
 FYLD = Yield stress input as a design parameter

Allowable compressive stress, fc

 = fc x 1.5 (for Temporary case)

where
 Λ = $π 2 E 0.6 F$ ν = $3 2 + 2 3 ( λ Λ ) 2$ λ = maximum slenderness, considering both principal axis E = Modulus of elasticity of steel (Young's Modulus)

Actual torsional stress, ft = torsion / Zx

where
 Zx = J / max(tf, tw) tf = flange thickness tw = web thickness
2. Bending Stress:

Actual bending stress for My for compression:

( Fbcy) = My / Zcy

Actual bending stress for Mz for compression

( Fbcz) = Mz / Zcz

Actual bending stress for My for tension

( Fbty ) = My / Zty

Actual bending stress for Mz for tension

 ( Fbtz ) = Mz / Ztz

where
 Zcy, Zcz = elastic section modulus for compression due to bending about the y and z axes, respectively Zty, Ztz = elastic section modulus for tension due to bending about the y and z axes, respectively

Allowable bending stress for My

(fbcy) = ft

Allowable bending stress for Mz

When λbpλb , fb = F/ν

When pλb < λbeλb ,

$f b = F ( 1 − 0.4 λ b − λ p b λ b e − λ p b ) ν$

When eλb < λb ,

$f b = 1 λ b 2 F 2.17$
where
 λb = $M y / M e$ eλb = $1 / 0.6$ ν = $3 2 + 2 3 ( λ b λ e b ) 2$ Me = $C π 4 E I y E I w I b 4 + π 2 E I y G J I b 2$ pλb = $0.6 + 0.3 ( M 2 M 1 )$ 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
Note: M2/M1 will be +ve for double curvature and -ve for single curvature.

For Temporary case, fbcz = 1.5 x (fbcz for Permanent case)

where
 ft = Allowable bending stress for My, fbty fbcz = Allowable bending stress for Mz, fbtz
Note: The parameter CB can be used to specify a value for C directly.
3. Shear Stress

Actual shear stresses are calculated by the following formula:

 Qy = Fy / Aww

where
 Aww = web shear area = depth times web thickness

 Qz = Fz / Aff

where
 Aff = flange shear area = 2/3 times total flange area

Allowable shear stress:

• Permanent Loads: fs = (Fy/√(3))/ 1.5
• Temporary Loads: fs = Fy / √(3)
where
 Fy = yield strength of steel, specified by the FYLD parameter.
3. 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:

1. Axial tensile stress ratio = FT / ft
2. Axial compressive stress ratio = FC / fc
3. Combined compression & bending compressive ratio = FC / fc+Fbcz/fbcz+Fbcy/fbcy
4. Combined compression & bending tensile ratio = (Fbtz+Fbty-FC) / ft
5. Combined tension & bending tensile ratio = (FT+Fbtz+Fbty) / ft
6. Combined tension & bending compressive ratio = Fbcz/fbcz+Fbcy/fbcy- FT/ft

7. Shear stress ratio in Y = qy / fs
8. Shear stress ratio in Z = qz / fs
9. von Mises stress ratio (if the von Mises stresses were set to be checked) = fm/(k⋅ft)
Note: All other member capacities (axial tension, axial compression, and shear) are calculated as for AIJ 2002. Refer to D9.C.5 Member Capacities