The bending moment capacity is generally the first place you start in the design of a steel element, it will tell you the maximum moment your selected element can handle.
Always remember, this maximum moment may not be your worst case failure method. To all my existing students, when unsure head over to the ‘How Steel Fails’ lecture in the Principles of Steel Design course to run through these failure methods again.
Before we are able to solve for the moment capacity, there are a few key pieces of information that we need first. Let’s take a quick look at each.

 

When looking at the grade of steel you will generally be picking between S275 or S355 steel. These are in MPa or N/mm².
Steel of grade 275MPa is most commonly used in beams where deflection is the critical case because the higher yield stress of 355MPa is not needed. It is also more ductile which can be of use in seismic design.
In everyday structures it will usually come down to price, S275 steel can be cheaper than S355. This fluctuates a lot. Currently in the UK the price differences are negligible and I haven’t personally specified S275 beams in a long time.
 
Class of Beam
The class of the beam is calculated based on the slenderness of the flange and web sections which will dictate if the beam can attain and maintain it’s plastic resistance or only it’s elastic resistance.
For class 1 and 2 sections the Plastic Section Modulus can be used, and in a class 3 section the Elastic Section Modulus must be used. All but one universal beam (I) section is class 3 so you will almost always be using the Plastic Section Modulus.
 
   

or

 
The elastic and plastic section modulus is found from reference tables like that found here: https://www.steelforlifebluebook.co.uk/ub/
You could calculate it for every section, but I would not recommend this! Do it a few times as an engineering student so that you understand exactly what’s happening, but then use the reference tables.
The section modulus will always be in the form of a distance cubed, eg 500cm³.
 

Gamma is a Eurocode specific partial material factor, the value of which will be different in each country and noted in the relevant National Annex. In the UK, the National Annex specifies a value of 1 (great for keeping the calculations nice and clean!)
That closes out all of the pieces needed to complete the calculation, so how do they all fit together.
 
 
Here we have the final calculation. You multiply the relevant section modulus by the yield stress of steel and apply/divide the partial material factor. Pretty simple once you know what all of the symbols mean.
 
Taking a quick look at the units, you have a distance cubed multiplied by a stress divided by a static value. A bit hard to picture so let’s write that out.

From this we can see that the distance squared from the stress will cancel out two of the distances from the section modulus which will leave us with a force multiplied by a distance ie a moment!
 
Thanks for reading and I will see you in the next article!
 
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