# Calculating the Plastic Modulus



## ldu571

Probably not necessary for the test but how do you calculate the (Z) plastic modulus for steel? It appears that the ratio between Z/S is on average 1.14 if you pull it directly out of the charts and I can put my brain on autopilot and go with that when using the new steel book. (I still tend to want to use the green ASD columns.)

But I would like to know how to calculate it. My mechanics book defines it as: The plastic modulus is the arithmetic sum of th absolute values of the first moments, WRT the neutral axis of the areas on each side of the neutral axis. I tried to solve for Z for a W8 using this defination and came up with something completely different than the tables.


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## kevo_55

The plastic section modulus is a property of the cross section and not the material.

Take a look at pages 17-36 to 17-38 pf the AISC 13th edition and look for the section property "Z" for these standard shapes. Actually, all steel codes have this "section properties" section in the back.

Specifically for an I section with a flange width of B, a flange thickness of T, a total depth of d+2T, and a web thickness of t, the plastic section modulus is: 0.5*T*(B^2)+0.25*d*(t^2).

I hope this helps!


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