Calculating Plastic Section Modulus Again

[matt0627]

When this topic came up before the procedure was what I remembered but I have 2 channels welded together to form a box shape. I want to calculate the plastic section modulus for the combined section, both diections.I wanted to check what I remembered so I looked up a C3x4.1 channel and tried to calculate the plastic section modulus in the y-y axis for 2 channels that were placed back to back with zero space between them as shown in table 1-16 of AISC 13th Edition; Z = 1.43 in3 I know the area of a single channel = 1.20 in2, I know the NA or centroid x bar = 0.437 in from heel of channel & I know that the NA & PNA will be at the jointing webs of the two channels that are back to back. I calculate the Z by taking the area of one channel x it's distance from the heel of the channel out to 0.437" (CG of area of channel) & x 2 areas = 1.048 in3. The AISC manual gives a Z = 1.43 in3 in the Y-Y axis.
Before I go and try and calculate the channel section that's a box shape can some one steer me in the right direction as to what I'm missing? I know in the x-x axis the Plastic section modulus will be 2 x the single channel plastic section modulus, hopefully I'm right there as well.

 

[ToadJones]

Plastic section modulus for any shape is the Area/2 x the ILA (internal lever arm).
or ... [A(y1 + y2)]/2 where y1 and y2 are the distances to the centroid of the upper and lower sections respectively, taken from the neutral axis.
Or in other words, the first moment of area of the cross section above the n.a. plus the first moment of area of the cross section below the n.a.

 

[rb1957]

should you worry about the weld carrying the flexural shear ?

 

[a2mfk]

rb1957- yep, design it for shear flow

 

[chrislaope]

ToadJones:

seems there is a discripancy between AISC-13th manual listed value of Z=1.43 in3 and the value from your formula which will be the same as matt0627's calculattion i.e. Z=1.048 in3, where in your formula, y1=y2=0.437", A= 2.41 in*in.

 

[ToadJones]

I get 2.335 in^3

 

[ToadJones]

oops....that was for toe-to-toe

 

[ToadJones]

like this?

 

[rb1957]

sounds like it from "I have 2 channels welded together to form a box shape"

 

[chrislaope]

Checked the Zy value for 2C3x4.1 back to back shape by using IES-ShapeBuilder software, the Zy values listed in AISC-13th, Table 1-16 are wrong. The calculated values using ToadJones formula are right.

 

[ToadJones]

Yea, what the hell...i been trying other values from the table out and i cant get their answers.

 

[PMR06]

That table must have been calculated by a non-SE!

 

[matt0627]

Thanks to all:

I've checked other size channel and came up with lower numbers than the table in AISC so I figured I must be doing something wrong. I get the same results for two channels toe-to-toe for the Plastic Section Modulus as toadjones.

Once again thanks to all:

 

[WillisV]

See attached errata published in Oct 2019 (Errata No. 4). Updated value is 1.05.

 

[frv]

Check the errata for the 13th Ed. The entire pages have been replaced for tables 1-16 and 1-17.

 

[WillisV]

Errata No. 1 to my post - 2010 not 2019.

 

[ToadJones]

OH MY, Is there any SE's out there worth their salt?!?!?