Welded Plate Girder Section Classification

Classifying a steel section, like a welded plate girder, is a crucial step in structural design as it determines the section's capacity and behavior under load. The classification helps engineers understand whether a section can reach its plastic moment capacity, only its yield capacity, or might buckle prematurely. Sections are typically classified as Plastic, Compact, Semi-compact, or Slender based on their slenderness ratios, which are related to the width-to-thickness ratio of their elements.

Understanding Section Classification Parameters

The classification of a welded plate girder section depends on the slenderness of its individual elements, primarily the outstanding element of the compression flange and the web. These slenderness ratios are compared against limits specified in design codes like IS 800:2007 (Indian Standard Code for General Construction in Steel).

• Flange Slenderness (b/t_f): This ratio considers the width (b) of the outstanding portion of the compression flange to its thickness (t_f).
• Web Slenderness (d/t_w): This ratio considers the clear depth (d) of the web between the flanges to its thickness (t_w).

The limiting values for these ratios are often expressed in terms of a factor \(\varepsilon\), which accounts for the yield strength of the steel.

\[ \varepsilon = \sqrt{\frac{250}{f_y}} \]

where \(f_y\) is the yield strength of the steel in MPa.

Given Data and Calculation of \(\varepsilon\)

From the question, we are provided with the following data for the welded plate girder:

• Flange slenderness ratio (\(b/t_f\)) = 6.7
• Web slenderness ratio (\(d/t_w\)) = 9.1
• Yield strength of steel (\(f_y\)) = 250 MPa

First, let's calculate the value of \(\varepsilon\):

\[ \varepsilon = \sqrt{\frac{250}{250}} = \sqrt{1} = 1 \]

Since \(f_y = 250 \text{ MPa}\), the value of \(\varepsilon\) is 1. This simplifies the comparison with the limiting values.

Classification Limits for Welded Plate Girders (IS 800:2007, Table 2)

The following table outlines the slenderness limits for different sections, which help in classifying them as Plastic, Compact, Semi-compact, or Slender.

Now, let's substitute \(\varepsilon = 1\) into these limits:

Classifying the Welded Plate Girder Section

We will now compare the given slenderness ratios with the calculated limits:

Flange Classification

• Given \(b/t_f = 6.7\)
• Plastic limit for flange = 9.4
• Since \(6.7 \le 9.4\), the outstanding element of the compression flange is classified as Plastic.

Web Classification

• Given \(d/t_w = 9.1\)
• Plastic limit for web = 84
• Since \(9.1 \le 84\), the web is classified as Plastic.

Overall Section Classification

For a steel section to be classified into a particular category (Plastic, Compact, Semi-compact, or Slender), all its component elements (flanges and web) must satisfy the criteria for that category. If any element falls into a less favorable category, the entire section is classified according to that least favorable category.

In this case, both the flange (based on \(b/t_f\)) and the web (based on \(d/t_w\)) are classified as Plastic. Therefore, the entire welded plate girder section is classified as Plastic.

A plastic section can develop a plastic hinge and has the capacity to form a mechanism, which is beneficial for plastic analysis and design, allowing for more economical designs.