1.3 Width thickness ratio

In order to use section E2 (page 16.1-27) of the Manual , the width-thickness ratios must be less than ${\lambda }_r$ This means the member is slender.

Width thickness ratio

For compact members: $\frac{b}{t}\le {\lambda }_p$ . For non-compact members: ${\lambda }_p\le \frac{b}{t}\le {\lambda }_r$ .

In this case, $\frac{b}{t}$ is the Width Thickness Ratio. The specifications for the widths of different shaped members, $b$ can be found on page 16.1-12 of the Manual . The t refers to the thickness of the member. Also, on pages 16.1-14 and 16.1-15, you will findthe Limiting Width-Thickness Ratios for Compression Elements tables. These tables will give the an equation for ${\lambda }_p$ (compact) and for ${\lambda }_r$ (non-compact) depending on a description of the element.

Stiffness

"Two types of elements must be considered: unstiffened elements, which are unsupported along one edge parallel tothe direction of the load, and stiffened elements, which are supported along both edges." LRFD Steel Design Second Edition: William T. Segui, 1999

For example, an L-shaped member has two unstiffened elements because each member is only supported (or connected) at oneend. Also, a C-shaped member has two unstiffened elements and one stiffened element. The web is stiffened because itis supported on both sides as opposed to the flanges which are unstiffened .

B5: local buckling

One example of using the section B5: LOCAL BUCKLING 1. Classification of Steel Sections on page 16.1-12 in theAISC Steel Manual is with an I-shaped member. Since the flanges are unstiffed, and it is I-shaped, use a width, $b$ , from part (a). Therefore, $b$ can be taken as half the full-flange width, $b_f()$ . This means the Width Thickness Ratio is: $\frac{b_f}{t}$ . Then, since the web is a stiffened element, use part (a) of the stiffened elements section and use thedistance $h$ for the "width." This gives the Width Thickness Ratio as: $\frac{h}{t}$ .

Values for width thickness ratio

An easy way of finding values for $\frac{b}{t}$ can be found on page 16.1-150. Here, Table 6: Slenderness Ratios of Elements as a Function of $F_y$ From Table B5.1, gives values for the ratios that are given in formula form in Table B5.1 (16.1-14). This is useful incutting back on calculating errors.

For example, the flanges of I-shaped sections in pure compression with $F_y=50\mathrm{ksi}$ , Table 6 gives the value of 15.9 for: