Seismic Story Height Calculation

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    Michael Ermann

    Perhaps you're looking for how to calculate story drift factor? If so, let's do an example proglem:

    A ten-story building is built with a story drift factor of 0.01 and a story height of 12’. The door on the bottom floor has a maximum displacement of 1/4 inch before it gets jammed. How high can that door be? Scroll down for the answer. . . 

     

     

     

     

     

     

     

     

     

    Those who live in earthquake-prone regions know to scurry under a table when the earth starts to shake; but those who manage a restaurant, retail store, or funeral home know to prop the egress door open with a chair when they feel the tremors.

    Story drift is the side-sway displacement of one floor's facade, relative to the one below it, as a percentage of floor-to-floor height, in the event of an earthquake. Under seismic activity, the lateral forces pushing to the right will translate to a leaning (displacement) of the whole right-side building facade to the right. In our case, for every foot of height, the building's facade will lean over 0.01 feet. For every story of height, the facade might displace 12 feet * 0.01 = 0.12 feet (or more than an inch from the bottom of the floor to the top of the ceiling). A ten-story building times 12 feet per story gives us a 120-foot tall building. At a story drift factor of 0.01 times 120 feet tall, the top of our building could lean 0.01 * 120 = 1.2 feet! If it's a tall building, and the buildings are packed tightly on the street, the top of our tall building could collide with the tall building next to it in an earthquake! This means that, depending on how earthquake-prone the building's location, the facade will need to be stiff enough--and/or the building will need to be sufficiently far away from its neighbor--so that it doesn't touch its neighbor. See this table that relates the maximum allowable drift to facade construction type and "seismic use group." (This rates the building's life-saftey importance in an earthquake so an agricultural shed is Seismic Use Group I, a retail store is Group II, an elementary school is Group III, and a hospital is Group IV).

    A steel frame with only moment connections will have a higher story drift factor than one with cross-bracing. A story drift factor of 0.02 is serious; a story drift factor of 0.06 will bring about building damage, and a story drift factor of 0.10 will likely topple the building.

    Dealing with story drift factor might necessitate shoring interior non-load-bearing partitions so they don't topple, or expanding the gap of seismic joints in building facades to the point where filling the joints against weather infiltration becomes difficult. Below is an example of one of those large seismic joints that must be filled (they can reach a total width of two feet!). Architects on the west coast sarcastically refer to these as "beauty caps" and do their best to visually integrate them into a building's facade.

    Besides colliding with a neighbor's building, we also fear that a building's exterior facade will shift enough to misalign the doors and jamb them shut just when occupants need to flee a collapsing building in an earthquake. Egress doors, doors to exit stairs, and revolving doors are of particular concern and that is the topic at hand in this example. Here, we know that the door can displace no more than 1/4-inch and still swing, so how high can the door extend and still displace small enough laterally so that it still swings open in an earthquake?

    First, convert 1/4 inch to feet

    1/4  * 1/12 = 0.0208 feet for our allowable maximum lateral offset to ensure that we can escape when the facade drifts.

    0.01 * h = 0.0208

    h = 0.0208 / 0.01 = a maximum height of about 2 feet tall

    What does that mean? It means we have a problem because if our door is more than two feet tall, it may stick shut in an earthquake. We better find another door with greater tolerances, another way of detailing our door to allow for greater tolerances, or we better make our facade much more robust so it doesn't sway (drift) as much. . .  because we have no use for a 2-foot-tall egress door leading out of our building.

    Note that neither the total height of the building nor the floor-to-floor height was relevant to solve this problem.

    Watch this Amber Book : 40 Minutes of Competence for more.

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    Diane Colucci

    Wow. Thank you. This is beyond helpful. 

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    Elizabeth Hagberg

    Michael, great explanation, thank you!  I would like to add that I was perplexed that there are only 3 categories of Seismic Use Groups in the Table accessed through the link.  I did some further poking around in the code and the 4 Seismic Use Groups you list are actually called "Structural Occupancy Categories" in that table.  Occupancy Categories 1 and 2 are grouped together into Seismic Use Group I, Occupancy Category 3 is Seismic Use Group II and Occupany Category 4 is Seismic Use Group III.

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