D1.D.2.2 Capacities per AASHTO (LRFD) Code

Axial Strength

The criteria governing the capacity of tension members is based on two limit states. The limit state of yielding in the gross section is intended to prevent excessive elongation of the member. The second limit state involves fracture at the section with the minimum effective net area. The net section area may be specified through the use of the parameter NSF. STAAD calculates the tension capacity of a given member based on these two limit states and proceeds with member selection or code check accordingly

P_r = φ_yP_ny = φ_yF_yA_g

P_r = φ_uP_nu = φ_uF_uA_nU

where

P_ny	=	Nominal tensile resistance for yielding in gross section (kip)
F_y	=	Yield strength (ksi)
A_g	=	Gross cross-sectional area of the member (in²)
P_nu	=	Nominal tensile resistance foe the fracture in the net section (kip)
F_u	=	Tensile strength (ksi)
A_n	=	Net area of the member
U	=	reduction factor to account for shear lag
φ_y	=	resistance factor for yielding of tension member
φ_u	=	resistance factor for fracture of tension members

Allowable compressive stress on the gross section of axially loaded compression members is calculated based on the following formula:

λ = {(\frac{K l}{r_{z} π})}^{2} \frac{F_{y}}{E}

if λ ≤ 2.25

Nominal compressive resistance,

P_n = 0.66^λF_yA_s

if λ > 2.25

Nominal compressive resistance

P_n = 0.88F_yA_s/λ

where

A_s

=

Gross sectional area

The Factored resistance

P_r = φ_c Pn

Bending Strength

The flow to calculate the allowable bending strength for rolled shape girders and built-up sections is given by the flowing flow chart.

Flow used to calculate the allowable bending strength for rolled shape girders and built-up sections

Shear Strength

The nominal shear resistance of un-stiffened webs of homogeneous girders shall be calculated as.

If D/t_w ≤ 2.46√(E/F_y), then

V_n = V_p =0.58F_ywDt_w

If 2.46√(E/F_y) < D/t_w ≤ 3.07√(E/F_y), then

V_n = 1.48·t_w ²√(E·F_y)

If D/t_w > 3.07√(E/F_y), then

V_n = 4.55·t_w ³·E/D

Bending-Axial Interaction

Members subjected to both axial forces and bending moments are proportioned according to section 6.9.2.2 of the AASHTO steel code. All members subject to bending and axial compression or axial tension are required to satisfy the following formula:

If P_u/P_r < 0.2, then

\frac{P_{u}}{2.0 P_{r}} + (\frac{M_{u x}}{M_{r x}} + \frac{M_{u y}}{M_{r y}}) \leq 1.0

If P_u/P_r ≥ 0.2, then

\frac{P_{u}}{P_{r}} + \frac{8}{9} (\frac{M_{u x}}{M_{r x}} + \frac{M_{u y}}{M_{r y}}) \leq 1.0