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)
RE: Elastic section modulus (S) vs. plastic section modulus (Z)
RE: Elastic section modulus (S) vs. plastic section modulus (Z)
RE: Elastic section modulus (S) vs. plastic section modulus (Z)
RE: Elastic section modulus (S) vs. plastic section modulus (Z)
RE: Elastic section modulus (S) vs. plastic section modulus (Z)
RE: Elastic section modulus (S) vs. plastic section modulus (Z)
Kieran
RE: Elastic section modulus (S) vs. plastic section modulus (Z)
BA
RE: Elastic section modulus (S) vs. plastic section modulus (Z)
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)
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)
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)
http://www.FerrellEngineering.com
RE: Elastic section modulus (S) vs. plastic section modulus (Z)
I would typically use limit states (LRFD) and fy and Z, myself.
Dik
RE: Elastic section modulus (S) vs. plastic section modulus (Z)
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)
RE: Elastic section modulus (S) vs. plastic section modulus (Z)
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)
FYI, this project is in US, and codes are IBC 2006 and AISC 13ed.
RE: Elastic section modulus (S) vs. plastic section modulus (Z)
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)
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)
JAE:
thanks for the clarification...
RE: Elastic section modulus (S) vs. plastic section modulus (Z)
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)
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)
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)