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Width Thickness Ratio

Module by: Michael Terk. E-mail the author

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In order to use section E2 (page 16.1-27) of the Manual, the width-thickness ratios must be less than λ r λ r This means the member is slender.

Width Thickness Ratio

For compact members: bt≤ λ p b t λ p . For non-compact members: λ p ≤bt≤ λ r λ p b t λ r .

In this case, bt b t is the Width Thickness Ratio. The specifications for the widths of different shaped members, bb 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 find the Limiting Width-Thickness Ratios for Compression Elements tables. These tables will give the an equation for λ p λ p (compact) and for λ r λ 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 to the 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 one end. Also, a C-shaped member has two unstiffened elements and one stiffened element. The web is stiffened because it is supported on both sides as opposed to the flanges which are unstiffened .

Exercise 1

How many unstiffened and stiffened elements would an I-shaped member have?

Solution

Four unstiffened elements (the flanges) and one stiffened element (the web). In this case, each half of one of the flanges consists of two elements joined at the web.

B5: Local Buckling

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

Values for Width Thickness Ratio

An easy way of finding values for bt b t can be found on page 16.1-150. Here, Table 6: Slenderness Ratios of Elements as a Function of F y 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 in cutting back on calculating errors.

For example, the flanges of I-shaped sections in pure compression with F y =50ksi F y 50 ksi , Table 6 gives the value of 15.9 for:

λ r =0.56E F y =15.9 λ r 0.56 E F y 15.9 (1)

NOTE:

Values for the ratios b f 2 t f b f 2 t f and h t w h t w are tabulated in the dimensions and properties tables in Part 1 of the Manual

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