D1.D.1.2 Allowable Stresses
The member design and code checking in STAAD.Pro is 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. It is beyond the scope of this manual to describe every aspect of structural steel design per AASHTO specifications because of practical reasons. This section will discuss the salient features of the allowable stresses specified by the AASHTO code. Table 10.32.1A of the AASHTO code specifies the allowable stresses.
Axial Stress
Allowable tension stress, as calculated in AASHTO is based on the net section. This tends to produce a slightly conservative result. Allowable tension stress on the net section is given by,
Ft = 0.55⋅Fy
Allowable compressive stress on the gross section of axially loaded compression members is calculated based on the following formula:
Fa = Fy/FS⋅[1-(Kl/r)2Fy]/(4π2E)
when (Kl/r) ≤ Cc
Fa = π2E/[FS⋅(Kl/r)2]
when (Kl/r) > Cc
Where:
Cc = (2π2E/Fy)1/2
It should be noted that AASHTO does not have a provision for increase in allowable stresses for a secondary member and when 1/r exceeds a certain value.
Bending Stress
Allowable stress in bending compression for rolled shape girders and built-up sections whose compression flanges are supported laterally through their full length by embedment in concrete is given by:
Fb = 0.55⋅Fy
For similar members with unsupported or partially supported flange lengths, the allowable bending compressive stress is given by
Fb = 0.55⋅Fy[1 - (1/r)2Fy/(4π2E)]
Where:
r2 = b2/12
Due to inadequate information in the AASHTO Code, the allowable tensile stresses due to bending for both axes are set to be the same as the corresponding allowable bending compressive stresses.
Shear Stress
Allowable shear stress on the gross section is given by:
Fv = 0.33 Fy
For shear on the web, the gross section is defined as the product of the total depth and the web thickness. The AASHTO code does not specify any allowable stress for shear on flanges. The program assumes the same allowable for shear stress (0.33Fy) for both shear on the web and shear on the flanges. For shear on the flanges, the gross section is taken as 2/3 times the total flange area.
Bending-Axial Stress Interaction
Members subjected to both axial and bending stresses are proportioned according to section 10.36 of the AASHTO steel code. All members subject to bending and axial compression are required to satisfy the following formula:
fa/Fa + Cmx⋅fbx/[(1 - fa/Fex)⋅Fbx] + Cmy⋅fby/[(1 - fa/Fey)⋅Fby] < 1.0
at intermediate points, and
fa/(0.472⋅Fy) + fbx/Fbx + fby/Fby < 1.0
at the ends of the member.
The start and end nodes of a member are treated as support points.
For members subject to axial tension and bending, the following equations are checked:
fa/Fa + fbx/Fbx + fby/Fby < 1.0
at intermediate points, and
fa/(0.472⋅Fy) + fbx/Fbx + fby/Fby < 1.0
at the ends of the member.