Is there a relation between the concrete compressive strength for the columns and the slabs used in the same building)?

Hi,

This is a very interesting topic that most engineers are unaware of. So try to understand very carefully as many might disagree and some might even not understand. The slab will be subjected to only BEARING STRESS in the column-slab junction. There is no chance of slab to buckle at that point as it will be considered an endless section in width. On top of the concrete strength that junction will be having heavy reinforcements crossing through. Therefore, 50% of column fcu is enough as the column would be ok with similar fcu if it didn't had to be designed for buckling or bending. Some may ask you to use similar fcu as column at slabs junction which is ridiculous and un-engineered. Hope this helps.

yes of course  as a building it is the  column  main frame structure that hold the  slab  all times...as one whole structure

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concrete grade increases the capacity of columns and slabs

Yes. The higher slab weight loaded on a certain column the higher concrete compressive strenght is required for a fixed column cross section 

Yes its totally connected with each other.

For example if i have high rise building and the required Fcu for the columns is 70MPa ,shall i use for slabs Fcu 35Mpa or less ,I think there is a relation ,and it is better also to have a reference for answers, if any .