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AC11: Use of Resistance Tables

Use of Factored Axial Compressive Resistance tables

See also the CISC Handbook: bottom of page 4-15 and examples on page 4-16.

The tables are computed using the length ($KL$) with respect to weak-axis bending. For most structural shapes, by convention, we call this the $y-$axis, and the properties and dimensions tables in Part 6 use this convention.

Sometimes it is necessary to also investigate buckling strength with respect to strong axis bending, particularly when the unbraced lengths are different (often due to additional bracing in one direction).

The tables can still be used by realizing that the compressive resistances, $C_r$, are computed using the slenderness ratio, $L/r$ (specifically $L_y/r_y$). All we have to do, then is to compute a length that gives us the same slenderness ratio as the strong or $x-$axis.

After all, if

$$ \frac{L_y}{r_y} = \frac{L_x}{r_x} $$

then $C_r$ will be the same for each direction. As the $L_y$ values are tabulated in the tables, we use

$$ L_y = \frac{L_x}{r_x} r_y$$

or

$$ L_y = \frac{L_x}{r_x/r_y} $$

$r_x/r_y$ values are tabulated for each shape.

Example

For example, evaluate a W310x67 of A992 steel for strong axis buckling where $KL = 4400~\text{mm}$. See pages 4-24, 4-25.

$r_x/r_y = 2.65$ (page 4-24)

$4400/2.65 = 1660~\text{mm}$. Therefore use 1660 mm as the length to determine $C_r$.

At $L = 1500$, $C_r = 2470$. At $L = 2000$, $C_r = 2310$. Interpolating:

$$ C_r = 2470 - \frac{1660-1500}{2000-1500}(2470-2310) = 2417~\text{kN}$$

If it is necessary to investigate another cross-section, the length calculation must be redone as the $r_x/r_y$ ratios vary. For example, for a W250x67:

$r_x/r_y = 2.16$ (page 4-25).

$4400/2.16 = 2037~\text{mm}$. Therefore use $L = 2037$ for the W250x67 column.

At $L = 2000$, $C_r = 2360$. At $L = 2500$, $C_r = 2170$. Interpolating:

$$C_r = 2360 - \frac{2037-2000}{2500-2000}(2360-2170) = 2346~\text{kN}$$