plastic section modulus
plastic section modulus
(OP)
Does anyone know the equation for the plastic section modulus of a built up wide flange with a plate welded to the bottom?
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RE: plastic section modulus
A quick synopsis is as follows.
Find the PNA by locating the axis about which there is an equal area of steel above and below. Basically, divide the total As by 2 and determine what axis will satisfy that condition - That is your PNA.
Next find the centroid of the area above the PNA and the centroid of the area below the PNA.
Now multiply the area of steel above (or below - the will be equal) the PNA by teh distance between the centroids of teh areas above and below.
This will give you the plastic sections modulus in in^3.
It should be noted this is only valid for a homeogenous material such as all steel with the same yield stress. If you have a different yield stress (which it sounds like you probably do with the plate below - you can spec a 50 ksi plate ) or follow the same procedure as above with a slight modfication.
Instead of locating the PNA where there is an equal area of steel above and below, locate it such that you satisfy statics above and below (i.e. find the axis about which when the entire section yields you have an equal C and T). This shouldn't be that hard to do and I don't feel like writing out an equation. I would find Mp first in this case and back calc into Z.
Sum moments of each portion of the cross-section about the PNA (making sure to use the correct Fy for the plate if it happens to be 36 ksi) and that will give you Mp. I'm not sure if you can get a true Z since Fy is not constant.
RE: plastic section modulus
RE: plastic section modulus
RE: plastic section modulus
RE: plastic section modulus
if you can't get the plate to work, an option I have used in the past to reinforce exisiting steels beams is to use a WT for reinforcement instead of a plate. It works quite well.
RE: plastic section modulus
StructuralEIT, why do you say 50 ksi plate is uncommon? Many of the fabricators we work with use it all the time, often replacing A36 plate for Grade 50 in the shop.
RE: plastic section modulus
The original beam will maintain the stress from dead loads and the reinforcement + original will act as one to take the loads that were not present during installation.