# Beam selection where moment capacity is exceeded

by Simon.T
Tags: beam, engineering, modulus, moment, section
 Sci Advisor HW Helper PF Gold P: 6,035 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).
 P: 15 Hey, thanks for the reply. 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.
HW Helper
PF Gold
P: 6,035
Beam selection where moment capacity is exceeded

 Quote by Simon.T Hey, thanks for the reply. 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.
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...
 P: 15 PhanthomJay you are a gent. Thank you very much for your assistance!
 P: 696 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.
 Sci Advisor HW Helper PF Gold P: 6,035 "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.

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