Beam Fixed at Both Ends and subjected to nonuniform bending

[UMath1]

If a beam is fixed at both end and subjected to nonuniform bending would the upper section of the beam still be in compression. My intuition and free body diagrams suggest it would but geometrically in this case, wouldn't all sections of the beam, even the upper section, have to elongate/curve in order to maintain compatibility with the fixed joints?

 

[Dr.D]

You need to look at the moment diagram for this beam; that will tell you what parts are in tension and what parts are in tension. This is a statically indeterminate problem. Think about the deformed shape and that will tell you that parts of the upper edge are in tension and part in compression.