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.

 

[dik]

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

JAE:
thanks for the clarification...

 

[BAretired]

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

 

[JAE]

...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.

 

[ajk1]

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.

 

[rscassar]

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