# Beam selection where moment capacity is exceeded

1. Dec 28, 2009

### Simon.T

Hi,

I'm having difficulty with an assignment.

Briefly, the question relates to a simply supported I beam containing a UDL and a point load. I've calculated the maximum bending moment resulting from these loads (neglecting beam mass) to be 5625kNm. I must select a universal beam from grade 43 steel (yield = 275 MN/m2) that can support this loading scenario.

Long story short, using this material the required elastic section modulus (20454.55cm3) is just too high for any standard beams. I've been told I cannot change the material, loading or fixing scenerio and that I have to 'find a way around' the problem.

Approach 1
I was considering using the UTS for grade 43 steel (430 MN/m^2) which would solve the problem, but that surely doesn't lend itself well to sound engineering practice.

Approach 2
The other thing I found is that on http://www.corusconstruction.com/en..._beams_structural_steel/use_of_bs5950_part_1/ moment capacity for a simply supported beam is the lesser of

Mc = py.Sx

and

Mc = 1.2 py.Zx

Where Py is material yield strength, Sx is plastic section modulus and Zx is elastic section modulus. I have read BS 5950 and it seems to back this up.

Approach 3
Could I stack two I beams on top of each other? How would this affect the second moment of area (would it be double, or .. just over double of one beam)?

I am confident I could produce answers which make sense (to me) but I obviously need to produce answers that have resulted from sound engineering process. Which approach should I use? Or maybe none of the above!?

Any help would be appreciated.

2. Dec 28, 2009

### PhanthomJay

I don't use SI, so I take your word for it that the section modulus required is beyond that of a 'universal' beam. The required modulus is largely a matter of codes, using a safety factor or overload factor of some sort. You can put two together, or use a cover plated beam, or a built up section, etc. If you put two beams together, you must be sure to size the welds (or space the bolts) between the 2 to carry the longitudinal shear, so that the composite beam can work together with a large second moment of area of the overall shape (I = sum of (I +Ad^2) of each beam).

3. Dec 29, 2009

### Simon.T

A quick question.

What is the difference between elastic modulus and plastic modulus (in this context)?

I realise that elastic deformation is non-permanent (elastic band) and plastic deformation is permanent (snapping/bending a ruler), but why is there a difference in the quoted values for elastic and plastic modulus?

For example

In beam x (picked at random),

Elastic Modulus (x-x axis) = 1571cm3
Plastic Modulus (x-x axis) = 1811cm3

Surely once you exceed the elastic modulus you create plastic deformation? Why is there a grey area in between? Is this the safety factor you refer too?

I believe the correct approach for this question is to recalculate the values using the plastic modulus as a limiting factor (ie, the bending moment absolutely cannot exceed this capacity), but I would like to be able to justify my approach.

Any help would be appreciated.

4. Dec 29, 2009

### PhanthomJay

Oh yes, I remember vaguely learning about the Plastic Section Modulus when I was in college years and years ago. But in 40 years of Structural Engineering practice, I have never used it. The elastic section modulus assumes linear stress distribution from the elastic neutral axis , with maximum bending stress occuring at the outer fibers of the cross-section, and no bending stress at the neutral axis. The Plastic Section Modulus, as I recall, allows all fibers from the plastic neutral axis to the outer fibers, to be at yield stress, creating a plastic hinge and collapse mechanism. If using the plastic modulus, you need a different safety factor. I'd stay clear of it, and stick with the elastic modulus. In absence of Code requirements, the simplest way to design the beam is to take the applied loading, and apply an overload factor (say 2.0) to the load. Then you calculate the maximum bending moment based on that factored load, and the elastic section modulus, S, required, is just $$S_{required} = M/\sigma_y$$, where $$M$$ is the factored maximum bending moment, and $$\sigma_y$$ is the yield stress of the steel. Now maybe someday you'll want to use the plastic modulus approach, but as for me, I don't need it, and never will.

NOTE: What I have called S, the elastic modulus, you have called Z. I'm from the States, you know...

Last edited: Dec 29, 2009
5. Dec 30, 2009

### Simon.T

PhanthomJay you are a gent. Thank you very much for your assistance!

6. Jan 9, 2010

### pongo38

Well, I am always using plastic modulus in structural engineering practice to determine the collapse load of a beam like this, and the second moment of area to determine deflections. The elastic modulus can be used, as Phantom says, with a safety factor. The formulas are looking similar but conceptually different. f=M/Z for elastic stress and fy=Mp/Sx for plastic analysis. The answer given by Phantom illustrates how culturally different is engineering in UK and USA. In UK we always use SI units now, and wonder why the USA doesn't do it too. The 'grey area' in between the use of Z and S represents a zone of stress redistribution which gives rise to higher load capacity. Finally, you could use more than one beam shoulder to shoulder.

7. Jan 9, 2010

### PhanthomJay

"They" tried to convert us to SI 40 years ago. In spite of laws and pseudo laws, it was not meant to be, and I suspect it will be at least another 40 before the USA ever converts, at least in the field of Structural Engineering. All structural engineers and construction folks are very familiar with psi for stress, cubic yards for concrete volume, inch-pounds or foot pounds for moments, pounds for force and weight, feet and miles for distance, etc., the list goes on. If I ever told a contractor to tighten up a wire to so many newtons or kN or MN, insted of so many pounds, he'd tell me to go jump in a lake and speak "English". Conversion would be disastrous, because then familiarity of the units would be lost. It would also be extremely costly. The Codes often address SI units, but we don't pay attention to them. I rip them to avoid turning to the wrong page. Like it or hate it (I'll admit its not a friendly system), pounds and feet and miles and inches and fractions of inches are here to stay in the USA for a long, long, time.