column bending stress under vertical earthquake load

In Fema national US&R response system - Structrual collapse technicican training manual

It says:

"There are also vertical loads generated in a structure by earthquake shaking, but as mentioned previously, these forces rarely overload the vertical load resisting system. Earthquake induced vertical forces have caused damage to heavy concrete structures with high dead load compared to design live load. These vertical forces also increase the chance of collapse in concrete frame buildings due to either increased or decreased compression forces in the columns. (Increased compression that overloads columns or decreased compression that reduces column bending strength.)"

I didn't understand the second part of last sentence in paranthesis, where it says "....or decreases compression that reduces column bending strength".... what does this mean and why?

For a symmetrical column with maximum bending stress $$B$$ and compressive stress $$C$$, the combined stresses range from $$C+B$$ on one side of the column to $$C-B$$ on the other side.

If $$C$$ is reduced, then $$C-B$$ reaches the design limit (in tension) for a smaller value of $$B$$.

• So the sentence in original paragraph assumes there is already a lateral force acting on the structure at that moment and not just vertical earthquake stress? which means there is already a moment trying to bend the column which would put the column in tension on one side , which would be so strong that it overcomes the compression from gravity, plus if earthquake vertical stress act upwards ? the sentence is only for that instant? Mar 10 '20 at 3:53
• Yes, Many columns have moment redistributed to them from a beam or a joint, before the seismic moments come into play. After the start of building vibrations to things are going to change due to S and P waves, the axial stress on the section and the moment causing compression and tensile stress. Compression is up to a certain level beneficial because like a prestress force it cancels the tensile stress. But there my be uplifting due to the overturning moment of the building and additional moment due to earthquake lateral force. Mar 10 '20 at 4:24
• Thanks a lot i understand Mar 10 '20 at 9:56

In a concrete column with bending moment and compression, the tensile stress is reduced and the compression stress is increased by the shift of the neutral axis location. However, this condition is OK because for ductility concrete members are designed to fail on the tensile stress because of the large stretch the steel re-bars take before the yield point.

But when during the earthquake the compression decreases the tensile stress goes back up and because of the lateral forces of the quake there is likely even more moment applied to the column and more tensile stress which could be in excess of design stress, refer to the diagram.

• So the sentence in original paragraph assumes there is already a lateral force acting on the structure at that moment and not just vertical earthquake stress? which means there is already a moment trying to bend the column which would put the column in tension on one side , which would be so strong that it overcomes the compression from gravity, plus if earthquake vertical stress act upwards ? so the tension on your graph = Tension from lateral - Gravity + Tension from UPWARDS acting earthquake force? your graph is only for that moment right? Mar 10 '20 at 3:51

So the answer is for this instant: When there is already a lateral earthquake force which may crate tension on a column, MINUS gravity compression, PLUS the UPWARDS acting earthquake vertical force. (Or sometimes there can be moments on top of columns even before earthquake due to load distributions on beams which would put one side of column in tension already and when an UPWARDS earthquake vertical force act on it, it will put further tension demand on column)