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

[engr567]

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.

 

[rb1957]

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

 

[slickdeals]

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.

 

[engr567]

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

 

[slickdeals]

Yes.

 

[slickdeals]

Check out Section F11.

 

[nutte]

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

 

[kieran1]

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

Kieran

 

[BAretired]

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

 

[engr567]

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.

 

[JAE]

It depends on which AISC specification you are using.

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

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

 

[BAretired]

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

 

[connectegr]

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

 

[dik]

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

 

[BAretired]

So would I, Dik.

Using LSD:

Pf = 200*1.5 = 300#
Mf = 300*3.5 = 1050'# = 12,600"#
Z req'd. = Mf/[&phi;]Fy = 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

 

[wannabeSE]

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

 

[JAE]

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.

 

[engr567]

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.

 

[racookpe1978]

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.

 

[slickdeals]

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