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Elastic section modulus (S) vs. plastic section modulus (Z)

Elastic section modulus (S) vs. plastic section modulus (Z)

Elastic section modulus (S) vs. plastic section modulus (Z)

(OP)
I am designing a freestanding steel handrail post (3'-6") spaced at 4'-0" on center maximumu. Per IBC, I am desiging this post for a point load of 200 lbs at the tip of free end. Per ASD design, can I use plastic section modulus (Z) in lieu of elastic section modulus (S)? The steel is 1" square solid ASTM A500 Grade B (Fy = 46 ksi). Thank you in advance for your input.

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

FWIW, i'd use the plastic section for this "abuse" loading

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

If it is a welded base, I think the base connection will a problem with the 1" square. If it will be placed in grouted pocket, I agree with rb1957.

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

(OP)
It is installed with grouted pocket. However, the question is - per AISC ASD design method - am I allowed to use plastic section modulus (Z)?

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

Yes.

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

Check out Section F11.

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

What edition of AISC ASD are you using?  If you're using the 2005 specification, then yes.

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

Minor point of confusion, In europe Z is elastic modulus and S the plastic modulus.

Kieran
 

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

I don't think I agree with most of the above.  You should use plastic section modulus for factored loads and elastic section modulus for unfactored loads, i.e. 200#.

BA

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

(OP)
Yes it is AISC 13th ed. So, this is what I will do. Please correct if I am missing something here.

Mact = 200 * 3.5 = 700 lbs-ft. [at the base of the cantilever post)
Reqd. section modulus (S) = (700*12)/(1.67*46000) = x in3, where 1.67 = omega factor
Plastic section modulus (Z) = y in3
Since y is more than x, so the design is OK.
 

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

It depends on which AISC specification you are using.

ASD 9th Edition (Green manual)
  Per section F2:
  fb < Fb = 0.75 x Fy  with stresses calculated per the elastic section modulus, S.

ASD 13th Edition (Black combined LRFD-ASD manual)
  Per Section F11:
  M(service) < [Mn = Mp = FyZ]/1.67
  This uses the Plastic Section Modulus Z


 

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

engr567,

No, that is not right.  The factor 1.67 should be in the numerator because allowable stress = 46,000/1.67 = 27,500 psi.

P = 200#
M = 200*3.5 = 700'#
S = 700*12/27,500 = 0.305 in^3

BA

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

AISC allows the use of the plastic section modulus.  And IBC allows 1/3 stress increase.  The results are similar.  I would not use both.   

http://www.FerrellEngineering.com

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

Under the old ASD (in Canada) they permitted a greater fs to be used to accommodate the (0.75fy, I think) shape factor difference.  For a solid square post, the shape factor Z/S is 1.5. We were the first class to use limit states, and I haven't used anything else since 1969...

I would typically use limit states (LRFD) and fy and Z, myself.

Dik

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

So would I, Dik.

Using LSD:

Pf = 200*1.5 = 300#
Mf = 300*3.5 = 1050'# = 12,600"#
Z req'd. = Mf/φFy = 12,600/(0.9*46000) = 0.304 in^3

This is almost the same result as I found for S earlier which suggests that elastic design is more conservative.  

BA

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

Also, ASTM A500 is a tube steel specification. Square bars are not covered by this specification.

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

engr567,

Just be aware when reviewing BAretired's and dik's responses as they are referring to Canadian codes/specs - their responses are most likely correct as far as the Canada codes go but you did refer to the IBC which refers to AISC specifications which differ somewhat.

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

(OP)
BAretired, you are correct. 1.67 should be in the numerator. Thanks.
FYI, this project is in US, and codes are IBC 2006 and AISC 13ed.

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

1x1 inch posts are a little smaller than what is usually installed.  1-1/2 x 1-1/2 look better, and are the usual posts, with 1x1 tube steel as the top and bottom of the rail.  

Or a 1 inch channel, punched at 4 inch interval for the 1/2 square vertical rods.    Punched channel is adequate and only sags "a little" after several years service, but it is  not very artistic or pretty.    

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

@BA:
Is the 1.5 multiplier an overload factor?
If it is considered a live load, the multiplier is 1.6. Right?

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

The 1.5 is a load factor for live loads (in Canada)...

JAE:
thanks for the clarification...

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

As Dik says, the live load factor is 1.5 in Canada but we also have a resistance factor, φ which modifies the yield strength of the material.  In the case of flexural strength of steel, φ = 0.9, so in effect our overall factor is 1.5/0.9 = 1.67, not significantly different than the AISC formulation.

It is true that different codes will have different fudge factors, but some things are universally true.  

One is that, provided a beam cross section is within the elastic region, the flexural stress at any point is M*y/I and the maximum stress at the outer fiber is M/S where S is the elastic section modulus.

Another is that the failure moment of a steel beam is Z*Fy where Z is the plastic section modulus and Fy is the yield stress.

Since the ratio Z/S varies depending on the shape of cross section, Limit States Design (LSD in Canada, LRFD in USA) is a better method for determining strength.  For determining deflection or stress, elastic design is used throughout the world.

BA

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

...but again, in the current 13th edition of AISC, they primarily use Z when using ASD (see my post above) and check it against 1.6My = 1.6FyS as a maximum limit.

They do NOT use S for the ASD approach in the F11 section dealing with solid bars.

 

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

I agree with what BARetired said, but be careful that the section meets the requirements for LSD including symmetry. Some balustrade posts are extruded open hollow sections that although square are not symmetrical and therefore cannot use plastic section modulus when using LSD.

Is this a high rise building? If so, wind load effects may exceed minimum specified rail loads.

Having spent so much of my career in dealing with corrosion, I am concerned about embedment in grout. If the post is steel, even galvanized steel, it will eventually corrode at the base. If that is the type of anchorage you are using, then it really should be stainless steel, unless you can solve the corrosion problem some other way.  

RE: Elastic section modulus (S) vs. plastic section modulus (Z)

b*d^2/4...I would be more concerned about keeping the movement at the top of the post to less than 3" for this load

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