# How to calculate effective section modulus of a slender section?

Hi how to calculate the effective section modulus of a class 4 section using Eurocode 1993? Can someone show me an example? I tried searching online but cannot find anything useful. My main problem is to determine the stress at both ends of the web plate. Is the stress ratio always -1 since the code mention pure bending? But if so, then the web is always fully effective.

Class 4 sections are designed to EC3-1-5 (more properly known as EN1993-1-5).

Clause 4.3(4) states:

The effective section modulus Weff should be determined assuming the cross section is subject only to bending stresses

Clause 4.4(3) states:

For web elements the stress ratio used in Table 4.1 should be obtained using a stress distribution based on the effective area of the compression flange

NB My interpretation is that the "effective area" of the compression flange is Aeff from Clause 3.3(1), which allows for both shear lag and plate buckling.

Table 4.1 shows the stress ratio to be the stress at one end of the internal compression element relative to the other. Hence for a section with equal flanges the stress ratio would be -1 for the web, but only if the compression flange isn't reduced by plate buckling or shear lag.

A stress ratio of -1 doesn't guarantee that a web is always fully effective. Table 4.1 states that a stress ratio of -1 gives you a buckling factor of 23.9 (or 23,9 in European notation, as used in the code). This plugs into the equations in clause 4.4(2) for determining plate buckling. If your web is slender enough, it can still be reduced for plate buckling, whatever your buckling factor is.

If neither your flange nor your web is reduced for either plate buckling or shear lag, then you don't have a Class 4 section.

Hence the entire process is:

• Plate buckling for compression flange to Clause 4.4(2)
• Shear lag of compression flange to Clause 3.3(1)
• Shear lag of tension flange to Clause 3.2.1
• Using the flanges from above, calculate stress ratio in web. Plate buckling for web to Clause 4.4(2)
• Using all the reduced elements above, calculate section modulus.

You may wish to refer to "Commentary and Worked Examples to EN 1993-1-5". I have found it of some use, but not as clear as I would like it in some areas.

• But if stress ratio is always -1 for a doubly symmetric section, does that mean that the neutral axis of the effective section remains at the centre? – Brandon Nov 8 '16 at 10:34
• @Brandon - The stress ratio in the web is only -1 if the compression flange isn't reduced. The neutral axis will only stay at the centre if neither the flange or the web is reduced. And if neither is reduced, you don't have a class 4 section! – AndyT Nov 8 '16 at 10:36
• Hmm, so how do you calculate the effective section modulus for a class 4 I-section? I can't find any relevant example from the link above. – Brandon Nov 8 '16 at 10:43
• @Brandon - My apologies, my answer only covered the web and had left out the main thrust of your question (or had only implied it). I've added in a summary of the entire process, as I understand it. – AndyT Nov 8 '16 at 11:15