Plastic Section Modulas of a Channel about the weak axis 2

[fabengr]

How to you calculate the Plastic Section Modulus of a member made from three plates in the shape of a channel. This is bending about the weak axis.

 

[BridgeSmith]

The plastic section modulus of any shape is equal to half the cross-sectional area multiplied by the distance between centroids of the areas of the two respective halves. The basic formula is: Z = Ac • dc + At •dt, where Ac = At and dc and dt are the respective distances from the plastic neutral axis to the centroids of Ac and At.

 

[KootK]

And your plastic neutral axis will be located such that have of your cross section lies above it an half lies below it.

 

[Agent666]

You also need to assess the 'compactness' of your section in accordance with the code you are working to. This might necessitate some of the section being ignored due to local plate slenderness limits being exceeded for each element of the channel.

 

[helfreco]

As Agent666 said, you need to check compactness. That check could determine if you should use the plastic (Z) or elastic (S) section modulus. The elastic section modulus is just the moment of inertia divided by the distance from the neutral axis to the most extreme fiber of the section.

If you are using AISC, you will need S anyway to check F6.1, and depending on the compactness section F6.2 may also apply