# Plate Center Stresses vs. Plate Corner Stresses

I have a concrete circular tank I am designing with plate elements. I am looking at the Mx and My to design the steel reinforcement. I have values for the center of the plate and the corners of the plate. One of my corner values is much higher than the other three as well as the center value. Which value do I use in design? The center value or do I design for the highest corner value? What is the difference between the center of the plate values and the corner values?

Thank you

• I trust you are speaking about the  bottom slab of the circular tank because circular wall will either have tension or compression depending on the loading condition. In the above case the depth of the bottom slab has to be determined with respect to the highest  moment i.e. corner value.  The reinforcemet on the respective face has to be determined with respect to the corresponding moment and further checked as per the requirement of the cracked section.

• Thank you for your response. There is moment (Mx) in the tank walls because of the fixity of the wall to the base slab which then requires the design of vertical reinforcing. I also didn't mention that there are rectangular  walls in this particular tank to divide it into 3 chambers. I will design my section for this higher corner stress. Thanks.

• Megan,

In this case, the base of wall moment will be the corner stress at the bottom of the plate.  The center stress (at least in my limited understanding) is more of an average of the 4 corner stresses.  For instance, if you have 1 foot square plates, your center stress would give you the results 6" from the base of wall.  Like you said, the corner stress is probably most appropriate for your base of wall steel.

Another alternative reason for high corner stresses is a hot spot in the analysis.  Sometimes, if you reduce your plate size, you can localize the high moment region to just a small, localized area and then assume that the moments will re-distribute themselves after some deflection.  The hard part in STAAD is making your plate size smaller without totally reconstructing your model.  A localized hot spot probably isn't the case in your base of wall connection, just something to think about in the future.

• In plate theory, stresses are correctly calculated at locations called Gauss points. Anywhere else on the element, including the center and corners, the stresses are either an average of the Gauss point stresses, or an extrapolation of those stresses.

Another aspect of plate theory is that at nodes of elements, the continuity of stresses across that node from one element to the next is not guaranteed. This means, the stress that is calculated there from one element may not match the stresses for that same node calculated from each of the other elements. Typically, this limitation is addressed by using the average stress at that node from all the elements connected to that node. One inaccuracy in this approach is that if elements that are meeting at that node have different directions for their local X and Y axes, averaging must be done after performing a transformation of axis so that each element's stresses are measured to a common axis of reference. For example, when you consider the edge that is common to a slab and a wall for example. The local X for the slab element will be in a horizontal plane, while that for the wall element will be in the vertical plane. So, averaging the MX from the wall element and slab element makes no sense.

If you find that the stress at a corner node is high, check the average stress, provided averaging can be done without running into the aforementioned issues. If the average too is significantly higher than the center stresses of the surrounding elements, using a finer mesh at that location may help. If you have a point load, try replacing it with a pressure load over a localised region.

• Thanks Lose,

Your last posting on the topic proved to be extraordinarily educative for me. I can not say about others.

Thanks again,

sureshprsharma