# D4.E.6.1 Members Subject to Axial Forces

## Axial Tension

The criteria governing the capacity of tension members are based on two
limit states: resistance due to yielding and resistance due to rupture. The resistance
due to rupture depends on effective net section area. You may specify the net section
area through the `NSF` design parameter. Additionally, the shear lag
factor, U, may be entered using the `SLF` parameter. STAAD.Pro calculates the tension capacity of a member based
on these two limits states per Cl.13.2 of CAN/CSA-S16-09. Design parameters
`FYLD`, `FU`, `NSF`, and
`SLF` (Refer to
D4.E.7
Design Parameters) are applicable for these
calculations

## Axial Compression

The compressive resistance of columns is determined based
on Clause 13.3 of the code. The equations presented in this section of the code
assume that the compressive resistance is a function of the compressive
strength of the gross section (Gross section Area times the Yield Strength) as
well as the slenderness factor (KL/r ratios). The effective length for the
calculation of compression resistance may be provided through the use of the
parameters
`KT`,
`KY`,
`KZ`,
`LT`,
`LY`, and
`LZ` (Refer to
D4.E.7
Design Parameters). Some of the
aspects of the axial compression capacity calculations are :

- For doubly symmetric sections
meeting the requirement of Table 1, resistance is:
Resistance due to Major axis buckling per Cl. 13.3.1.

Resistance due to Minor axis buckling per Cl. 13.3.1

${C}_{r}=\varphi A{F}_{y}{(1+{\lambda}^{2n})}^{-1/n}$where- n
= - 1.34 for hot-rolled, fabricated structural sections and hollow structural sections manufactured in accordance with CSA G40.20, Class C (cold-formed non-stress-relieved)
2.24 for doubly symmetric welded three-plate members with flange edges oxy-flame-cut and hollow structural sections manufactured in accordance with CSA G40.20, Class H (hot-formed or cold-formed stress-relieved)

Design parameters

`NCR`and`STP`are used to evaluate the value of n for a member.- λ
= - $\sqrt{{F}_{y}/{F}_{e}}$
- F
_{e}= - $\frac{{\pi}^{2}E}{{\left(\frac{kL}{r}\right)}^{2}}$
- For any
other section not covered under Cl. 13.3.1, the factored compressive
resistance,
C
_{r}, is computed using the expression given in Cl. 13.3.1 with a value of n = 1.34 and the value of F_{e}taken as follows:- For
doubly symmetric sections and axisymmetric sections, the least of
F
_{ex}, F_{ey}, and F_{ez}. - For
singly symmetric sections with the Y axis taken as the axis of symmetry, the
lesser of
F
_{ex}and F_{eyz}where- F
_{eyz}= - $\frac{{F}_{ey}+{F}_{ez}}{2\Omega}[1-\sqrt{1-\frac{4{F}_{ey}{F}_{ez}\Omega}{{({F}_{ey}+{F}_{ez})}^{2}}}]$
- F
_{ex}= - $\frac{{\pi}^{2}E}{{\left(\frac{{k}_{x}{L}_{x}}{{r}_{x}}\right)}^{2}}$
- F
_{ey}= - $\frac{{\pi}^{2}E}{{\left(\frac{{k}_{y}{L}_{y}}{{r}_{y}}\right)}^{2}}$
- F
_{ez}= - $[\frac{{\pi}^{2}E{C}_{w}}{{\left({K}_{z}{L}_{z}\right)}^{2}}+GJ]\frac{1}{A{\overline{r}}_{0}^{2}}$
- x
_{0},y_{0}= - the principal coordinates of the shear center with respect to the centroid of the cross section
- ${{\stackrel{\u23af}{r}}_{0}}^{2}$
= - ${x}_{0}^{2}+{y}_{0}^{2}+{r}_{x}^{2}+{r}_{y}^{2}$
- Ω
= - $\frac{{r}_{\mathrm{x}}^{2}+{r}_{\mathrm{y}}^{2}}{{{\stackrel{\u23af}{r}}_{0}}^{2}}$
- F
- For asymmetric sections the smallest
root of: $({F}_{e}-{F}_{ex})({F}_{e}-{F}_{ey})({F}_{e}-{F}_{ez})-{F}_{e}^{2}({F}_{e}-{F}_{ey}){\left(\frac{{x}_{0}}{{\stackrel{\u23af}{r}}_{0}}\right)}^{2}-{F}_{e}^{2}({F}_{e}-{F}_{ex}){\left(\frac{{y}_{0}}{{\stackrel{\u23af}{r}}_{0}}\right)}^{2}=0$

- For
doubly symmetric sections and axisymmetric sections, the least of
F
- For Class 4
member subjected to axial compression, the factored compressive resistance is:
${C}_{r}=\varphi {A}_{e}{F}_{y}{(1-{\lambda}^{2n})}^{-1/n}$
A

_{e}is calculated using reduced element widths meeting the maximum width to thickness ratio specified in Table 1.