Zx vs Sx - Elastic and Plastic Modulus for use on 2014 PE test 4

[HeavyCivil]

The PE exam is coming up on Friday and I keep stumbling on a certain problem in my practice tests.

The problem is very simple and should be easy points on the actual exam if it appears: "Given an allowable stress and a bending moment select the lightest wide flange". Cake, right? Mn=Mp=FyZx

The black book (aisc 13, which will be used for the test this spring) says plastic modulus Zx is used (both ASD and LRFD). But these practice tests want you to use the elastic section modulus Sx. Am I missing something or are these expensive practice test books incorrect? Frustrating to pay top dollar for the latest addition and have reference outdated steel code.

 

[steellion]

13th Edition ASD is allowable STRENGTH design. 9th Edition ASD is allowable STRESS design. When it is a question concerning allowable stress, the elastic section modulus Sx would be used. I'm not sure they would ask a question in that manner on the P.E. exam since the exam is based on 13th Ed. Just make sure you are aware of the subtle difference.

 

[HeavyCivil]

Black book covers both design methodologies...

The base bending equation in the spec F2-1 is applicable to both Stress and Strength design and modified accordingly (IE you either factor your loads and use strength reduction factor of 0.90 or you use service loads and reduce yield stress by 1.67). I am not sure I read the code the same way as you - I think the plastic modulus is used for both.

I have both books on my shelf (9 and 13) and work out of 9 almost exclusively (I am a contractor doing mostly temporary shoring/bracing/exc support design and don't design permanent structures that need to meet building code) and am not up on LRFD at all but that is the way I interpret the black book.

 

[Lion06]

For what it's worth, it comes out almost identical anyway. The new ASD divides the Mp by 1.67 and the old ASD multiplies the yield moment by 0.66.

1/1.67 = 0.6Mp
0.66My = about 0.6Mp (for Zx/Sx = 1.1).

Zx/Sx obviously varies for each section, but it's very close.

 

[Lion06]

9 and 13 are completely different. 9 is allowable STRESS design and 13 is allowable STRENGTH design. It's a subtle, but important, difference. The equations in the 13th edition are all LRFD equations, you're just using omega with service loads instead of phi with factored loads.

 

[BadgerPE]

As Stellion said, black book covers Allowable Strength Design. This should not be confused with Allowable Stress Design.
Allowable Strength Design is similar to Allowable Stress Design in that the same load combinations are being used. However, the main difference is that in Allowable Strength Design you are checking that the shear, moment, etc. capacity of a member are not exceeded. In Allowable Stress design, you are checking that the allowable stresses are not exceeded. So you are checking that Mu<Mn/omega as opposed to checking fb<Fb. Clear as mud?

See AISC 13th Pg. 2-7 for the full explanation.

 

[HeavyCivil]

Got it. Thanks for the explanation, I never picked up on that.

 

[TehMightyEngineer]

I'll third what Crackerjack and Lion said, 13th edition is completely different from 9th edition. Think of it this way, LRFD and ASD in the 13th book are both strength design. LRFD multiplies the loads by factors (1.2D + 1.6L for example) and then reduces the strength slightly (Phi of 0.9). Allowable strength design (ASD) in the 13th book uses service level loads and then divides the strength by a safety factor.

Assume our dead is 25% of our total load and live is 75% of total. Note that (1.2*0.25 + 1.6*0.75) / 0.9 = 1.67 = omega for flexure under ASD. All they did was change which side of the equals sign the factor was one.

9th edition says you can have an allowable stress of Fy/omega, don't exceed this. However, as you noted it doesn't take into account plastic section modulus (Zx), only yield (Sx). This is where the 13th edition will give you a little more credit.

As for your original question; yes a lot of these example books we pay good money for are poorly written. Many use older examples (even example books from NCEES) and often you will find a few errors in each book. Check on the publishers website for errata which may help a lot with errors. However, it does sound to me like the example you're looking at is based on an older code and they likely just didn't bother updating the example for the newest editions of the code. If it's a straight-forward beam, laterally braced, then yes it should just be Mn=Mp=FyZx. Divide Mn/Omega or multiply by Phi and compare to your ASD or LRFD load combinations (respectively).

P.S. I feel your pain, studying for the SE exam as well. Best of luck to us both.

Maine EIT, Civil/Structural.

 

[HeavyCivil]

Good luck to you. I'm taking the construction afternoon which is a bit of a wild card but certainly easier to pass that the SE.

 

[Lion06]

mightypirate-

The 9th edition does account for the plastic section modulus indirectly by increasing the allowable bending stress from 0.6Fy to 0.66Fy. This is a direct recognition of the additional capacity after yield and only applies to sections that can develop the plastic moment.

 

[BadgerPE]

Good Luck VT and Pirate! I will be joining in the fun Friday with the Structural Depth in the afternoon.

 

[TehMightyEngineer]

Lion: Good to know, I suspected there was something going on there as 1/0.66 = 1.515 vs the 1.67 used by 13th edition ASD but didn't know this was for plastic section. I learned using the 13th edition and rarely crack open the 9th edition.

Cracker: Are you taking lateral on Saturday as well?

Maine EIT, Civil/Structural.

 

[BadgerPE]

Pirate. No I am actually just taking the Civil PE-Structural Depth afternoon. Upon passing that, I will be taking the 16 hr SE exam. I will most likely take the gravity and the lateral at the same time.

What about you?

 

[TehMightyEngineer]

Cracker: Taking the 16 hour structural for PE licensure. I took the vertical half only last two times, past it on the second try. Taking lateral this Saturday, I'm cautiously optimistic about passing it first try.

Maine EIT, Civil/Structural.

 

[dik]

In Canada, Class 1 and Class 2 sections can use Z for flexural resistance. For 'Plastic Design' only Class 1 sections can use Z.

Dik