Soft story is related to the stiffness of the lateral resisting system of each story while weak story is relating to the strength of the the lateral resisting system.
So, if you have a 3 story building where the top 2 stories are shear walls (stiff) and the bottom story is a moment frame (flexible), you may have a soft story (depending on the relative stiffness between each system).
Now, take the same 3 story building, but instead of a moment frame at the bottom, you still have shear walls (stiff). However, these shear walls have lots of large openings, so your overall strength in the first story is much less than the upper stories. This, would give you a weak story condition.
Table 12.3-2 in ASCE 7 provides the actual numbers and discussions for categorizing these vertical irregularities.
So, if you have a soft story situation (failure), one would expect to see large deflections of the lower story before (and after) failure (due to it being less stiff and allowing large deflections). If you have a weak story failure, large deflections may not be present at failure, rather the story would simply break apart due to its lack of strength.
Thank you, Dauwerda for the explanation.
For a 3 story building, what is a vertical irregularity? Is it higher mass on level 2 (adjacent story) or on the roof compared to L1 (ground)?
Soft story and weak story are both types of vertical irregularities. Per ASCE 7, there are 5 types of vertical irregularities, see below:
As can be seen in the above table, a weight (mass) vertical irregularity compares the masses of adjacent stories. So for a 3 story building you would compare L1 to L2, or L2 to L3. You would not compare L1 to L3.
