D9.C.5.1 Design Capabilities

All types of available shapes such as 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. The steel tables available within STAAD.Pro or user provided table (UPTABLE) can be used for member properties.

D9.C.5.2 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, the moment of inertia about Y and Z axes, I_yy and I_zz, and the St. Venant torsional constant, J, from the built-in 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.

   For I shapes, H shapes, and channel sections, the program calculates the radius of gyration needed for bending using following formula:  

   $i=\sqrt{I_i/A_i}$

2. Calculation of actual and allowable stresses

   Allowable stresses for structural steel under permanent loading shall be determined on the basis of the values of F given in the following table.

   Table 1. Table: Values of F (N/mm²)

   	Steel for Construction Structures		Steel for General Structures			Steel for Welded Structures
   Thickness	SN400 SNR400 STKN400	SN490 SNR490 STKN490	SS400 STK400 STKR400 SSC400 SWH400	SS490	SS540	SM400 SMA400	SM490 SM490 Y SMA490 STKR490 STK490	SM520	SM570
   t≤ 40	235	325	235	275	375	235	325	355	400
   40< t ≤ 100	215	295	215	255	-	215	295*	335	400

   * F = 325 N/mm² when t > 75mm

   Note: In checking members for temporary loading be the combination of stresses described in Chap.3, allowable stresses specified in this chapter may be increases by 50%

   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 , F_C = force / A

      Allowable tensile stress, f_t

      • = FYLD / 1.5 (For Permanent Case)
      • = FYLD ( For Temporary Case )
      where

      FYLD

      =

      Yield stress input as a design parameter

      Allowable compressive stress, f_c

      $f_c=\{\begin{array}{c}\frac{[1-0.4{\left(\frac{\lambda }{\Lambda }\right)}^2]F}{\nu }\text{when}\lambda \le \Lambda \\ \frac{\begin{array}{c}0.277F\end{array}}{{\left(\frac{\lambda }{\Lambda }\right)}^2}\text{when}\lambda >\Lambda \end{array}$

      = fc × 1.5 (for Temporary case)

      where

      Λ	=	$\sqrt{\frac{{\pi }^{2}E}{0.6F}}$
      ν	=	$\frac{3}{2}+\frac{2}{3}{\left(\frac{\lambda }{\Lambda }\right)}^2$

      Actual torsional stress, f_t = torsion / Z_x

      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

      Note: The web is ignored in the calculation of Z_z for H-shape, I-shape, and channel sections when the MBG parameter = 1.

      Allowable bending stress for M_y

      (f_bcy) = f_t

      Allowable bending stress for M_z

      (fbcz) = { 1 - .4 x (lb / i)2 / (C λ2)} ft max

      = 89,000/ (lb × h / Af )

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

      where

      C

      =

      1.75 - 1.05 (M2 / M1) + 0.3 (M2 / M1)2

      • Allowable bending stress for M_y, f_bty = f_t
      • Allowable bending stress for M_z, f_btz = f_bcz
      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 = Qy / Aww

      where

      Aww

      =

      web shear area = product of depth and web thickness

      qz = Qz / Aff

      where

      Aff	=	flange shear area = 2/3 times total flange area
      fs	=	Allowable shear stress, Fs / 1.5, Fs = F / √(3)

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, the program gives the message that the section fails.

   Conditions:

   1. Axial tensile stress ratio = F_T / f_t
   2. Axial compressive stress ratio = F_C / f_c
   3. Combined compression & bending compressive ratio = F_C / f_c+F_bcz/f_bcz+F_bcy/f_bcy
   4. Combined compression & bending tensile ratio = (F_btz+F_bty-F_C) / f_t
   5. Combined tension & bending tensile ratio = (F_T+F_btz+F_bty) / f_t
   6. Combined tension & bending compressive ratio = F_bcz/f_bcz+F_bcy/f_bcy- F_T/f_t
   7. Shear stress ratio in Y = q_y / f_s
   8. Shear stress ratio in Z = q_z / f_s
   9. von Mises stress ratio (if the von Mises stresses were set to be checked) = f_m/(k⋅f_t)

D9.C.5.4 Allowable stress for Axial Tension

Allowable axial stress in tension is calculated per section 5.1 (1) of the AIJ code. In members with axial tension, the tensile load must not exceed the tension capacity of the member. The tension capacity of the member is calculated on the basis of the member area. STAAD calculates the tension capacity of a given member based on a user supplied net section factor (NSF-a default value of 1.0 is present but may be altered by changing the input value, see Table 8B.1) and proceeds with member selection or code checking.

D9.C.5.5 Allowable stress for Axial Compression

The allowable stress for members in compression is determined according to the procedure of section 5.1 (3). Compressive resistance is a function of the slenderness of the cross-section (Kl/r ratio) and the user may control the slenderness value by modifying parameters such as KY, LY, KZ and LZ. In the absence of user provided values for effective length, the actual member length will be used. The slenderness ratios are checked against the permissible values specified in Chapter 11 of the AIJ code.

D9.C.5.6 Allowable stress for Bending

The permissible bending compressive and tensile stresses are dependent on such factors as length of outstanding legs, thickness of flanges, unsupported length of the compression flange (UNL, defaults to member length) etc.  The allowable stresses in bending (compressive and tensile) are calculated as per the criteria of Clause 5.1 (4) of the code.

D9.C.5.7 Allowable stress for Shear

Shear capacities are a function of web depth, web thickness etc. The allowable stresses in shear are computed according to Clause 5.1 (2) of the code.