Sum of Ratios for Mixed Occupancy A2 & R1

  The new hotel building  is a 4-story type VA that sits on a type I podium used for parking and entry lobby. There is also 1-1/2 levels of basement parking. The second floor has a restaurant and guest units on the same level.  Because of the sprinklers, we are able to raise it 1-story and an additional 12,000 sf.  Will the sprinkler help per floor to increase the allowable area (table 503) which is 12,000 to a much higher figure for the sum of ratios calculation?  Based on 506.4, the sum of ratios for Group A & R and some others cannot exceed 2 in multi-story buildings. The numbers add up to more than that (3.25 to be exact) especially adding one more floor due to sprinklers.  Can you subtract areas that are non-occupiable such as restrooms, corridors,  and stair/ elevator shafts?  It's hard to get a sum of two.  Is it a catch 22?

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Originally Posted by HTBLS:

Thanks rlga_AZ for a thorough breakdown.  It's crystal clear to me now to use fire walls.  This forum is awesome.

Glad to be of some assistance.

Thanks rlga_AZ for a thorough breakdown.  It's crystal clear to me now to use fire walls.  This forum is awesome.

Table 503 gives the allowable area per story, which means that each story can have a maximum area of 12,000 sf.  However, that does not mean you get a total of 48,000 sf for the four stories--that is where the sum of ratios enters the process.  With a ratio of 0.75, I assume each story has an area of 9,000 sf.


What is the area of the Group A-2 on the second story?  For purposes of illustration, I'll assume the Group A-2 has an area of 3,000 sf and is separated from the Group R-1 with a 1-hour fire barrier per Table 508.4.  Also for illustration, I'll refer to the podium and the basement levels as "Building A" and the Type VA portion as "Building B."


Since Building A is required to be of Type IA construction, it is permitted unlimited area per Table 503, so it does not factor into the floor area calculations.


Tabular Areas per Table 503 for Type VA construction:

Group A-2:  11:500 sf

Group R-1:  12,000 sf


The first story of Building B (second story overall) has the following ratios:

Group A-2:  3,000 sf/11,500 sf = 0.26

Group R-1:  9,000 sf/12,000 sf = 0.75


The second, third, and fourth stories of Building B (third, fourth, and fifth stories overall, respectively) will each have the following ratio:

Group R-1:  9,000 sf/12,000 sf = 0.75


Sum of ratios for Building B:

0.75 + 0.26 + 0.75 + 0.75 + 0.75 = 3.26 > 2, therefore, not okay


To resolve the problem, you have several options available:

1.  Reduce area per story.

2.  Eliminate one story.

3.  Use fire walls to divide Building B into two buildings.

4.  Increase allowable areas by adding the frontage increase (if any).


If the building is surrounded on all sides by open spaces having a width of 30 feet or greater, then you can get the maximum frontage increase factor of 0.75.  Assuming you do, the ratio calculations can be redone as follows:


Allowable Areas:

Group A-2:  11,500 sf + (11,500 x 0.75) = 20,125 sf

Group R-1:  12,000 sf + (12,000 x 0.75) = 21,000 sf


First Story:

Group A-2:  3,000 sf/20,125 sf = 0.15

Group R-1:  9,000 sf/21,000 sf = 0.43


Second, Third, and Fourth Stories:

Group R-1:  9,000 sf/21,000 sf = 0.43 (each)


Sum of ratios:  0.15 + 0.43 + 0.43 + 0.43 + 0.43 = 1.87 < 2, therefore okay


If the Group A-2 is not separated from the Group R-2, then the entire first story of Building B will be based on the Group A-2 area (I don't see why you would want to, since the Group R-1 requires 1-hour fire partitions around the sleeping units, any way, all you need to do is make the fire partitions between the Group R-1 and Group A-2 fire barriers, which is minimal).  If this is the case, then the ratio for the Building B first story is as follows:


Group A-2:  12,000 sf/20,125 sf = 0.60


The sum of ratios would be as follows: 0.60 + 0.43 + 0.43 + 0.43 = 1.89 < 2, therefore okay


If you cannot get a frontage increase factor of 0.75, you could probably still make it with a factor of 0.64 (this assumes the Group A-2 isn't much larger than what I have shown in the example calculations above).


If you can't get the frontage increase to the point that it would work, then I suggest using a fire wall dividing Building B.


The project is in Los Angeles. The sprinkler is used to increase the height from 3 stories to 4 for the type VA and gain 12,000 s.f. tabular area for the 4th floor based on table 503 which comes to type VA total building area of 48,000.  If what is stated is correct, it is not helping out the sum of ratios calculation because it way exceeds 2.  R1 use ratio (.75) is multiplied by 4 stories.  The mixed occupancy on the 2nd floor is another confusing aspect to this project. The restaurant (A2) has greater than 50 occupant load and on a type VA has a height limit of 2 stories. Based on what you've stated, if the second floor is non-separated then do wen not have to count that floor to the sum of ratios considering it is based on allowable area and height for the more restrictive occupancy which is A2? Then we can just add 3 stories of R1 instead of counting the floor with mixed occupancies, is this right?  Anyway that we can get a sum of 2 with it including the core shafts and corridors.  Any suggestions?

Since you mention that the ratio cannot exceed 2, I assume you're in California.  If that is true, then the sprinkler cannot be used to increase both height (in feet and in stories) and area.  If the sprinkler is used to increase height, then only the tabular area per CBC Table 503 plus any allowable increase for frontage is permitted.  If the sprinkler is used for an area increase, then only the tabular height per CBC Table 503 is permitted.


The sum of ratios is based on actual areas to allowable areas for each occupancy group for each story if the occupancies are separated per CBC Section 508.4.  If the nonseparated occupancies method is used, then the use of ratios is unnecessary--it is based on the allowalble area and height for the most restrictive occupancy, which would be the Group A-2.


To answer your specific question, you cannot subtract the areas you indicated--they must be included in one of the two occupancy Groups.

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