If you’ve read my previous post regarding balancing seismic and dynamic base shear that was seismic base shear balancing considering UBC97 where static equals dynamic or dynamic should not be less than a certain percentage of the static base shear depending on the structure regularity. And while the use of UBC97 is still prevalent, ASCE is already gaining popularity and not withstanding the fact that ASCE will eventually supersede the older UBC 97. Both codes still have a lot of similarities in their provisions but one provision that is worth noting is on how to balance static and dynamic base shears.

Here’s how we do the balancing, ASCE style.

cropped from ASCE 7-10

Let’s start by establishing the minimum dynamic base shear scale factor. Note that this scale factor is a calculation of the percentage of g, which is the gravitational acceleration constant and the percentage of which is given in 12.9.2 which is the ratio of Ie/R, Ie being the importance factor and R as the response modification coefficient. So initially, our scale factor for the dynamic base shear on one direction is g*I/R (that is if you have different R values on your principal axes).

Now that we’ve established the minimum, let’s now proceed with the comparison:

If Initial Vt < V

cropped from ASCE 7-10

The ratio of the initial dynamic base shear over the static base shear need not be unity. In fact, 12.9.4.1 states that Vt need not exceed 85% of V disregarding structural irregularities which are present in UBC 97.

Now what if the initial dynamic base shear is greater than the static, are we going to scale it down? Truth is, we won’t be able to find any clause prohibiting us from doing so. But that’s the reason why the minimum had been established. So no you cant scale down the already minimum dynamic base shear.

We’re clear are we? Now to summarize:

Initial Scale Factor = g*Ie/R

If initial Vt < V; Final scale factor = Initial Scale Factor * 0.85*V/Vt   If initial Vt > V

No further scaling is required .