# Determination of Story Drift According to ASCE 7-16 Under Seismic Loads

### Technical Article

001543

11/07/2018

The story drift of a building provides valuable information about its structural behavior under seismic loads.

Section 12.8.6 [1] gives the following equation to calculate the entire story drift:

${\mathrm\delta}_\mathrm x\;=\;\frac{{\mathrm C}_\mathrm d\;\cdot\;{\mathrm\delta}_\mathrm{xe}}{{\mathrm I}_\mathrm e}$
with
δx = total displacement of a story [in (mm)]
Cd = deflection amplification factor according to Table 12.2-1
δxe = deflection at the location required by this section determined
by an elastic analysis [in (mm)]
Ie = importance factor determined in accordance with Section

11.5.1

The mutual story drift Δ is the difference of the total displacement at the top and bottom of the story. It has to be determined in the corresponding centers of gravity. If the building is classified as Class C or worse or if horizontal irregularities are present, the largest difference of two vertical oriented points at the top and bottom of the considered story along a corner has to be determined. The following example shows the determination of the story drift in RFEM.

#### Entering the Response Spectrum in RF-DYNAM Pro

To get an insight into this topic, the three-story building, shown in Figure 01, is used with a L-shaped ground plan. Three load cases will be defined: self-weight, live loads and snow loads. The front view of the building is continuous.

An eigenvalue analysis has to be performed first to be able to generate the response spectrum. Only the masses in both horizontal directions are considered in this example. The masses are combined according to ASCE 7-16 Section 12.7.2 [1].

There is the possibility to create the response spectrum according to an implemented standard or to import a user-defined response spectrum. To consider all necessary parameters, a user-defined spectrum is imported in this case with the parameters as shown in Figure 02. By using this spectrum, the parameters Cd and Ie are considered in the calculation of the deformations.

The method with structural equivalent loads will be used for the calculation which is based on the multi-modal response spectrum analysis. It is important here to consider at least 90 % of the effective mass. Mode shapes which activate no or only little mass can be excluded from the calculation in the "Dynamic Load Cases - Mode Shapes" tab. The generated response spectrum with all mode shapes is shown in Figure 03. After the calculation, the load cases and the resulting result combinations are generated, separately for each direction and combined with the 100/30 % rule.

#### Determination of Story Drift in RFEM

At first, it is necessary to create the combination required for the design. This is performed according to ASCE 7-16 Section 2.3.6 [1], Formula (6). With this combination, it is then possible to determine the story drifts. Since it is not possible to perform story definitions in RFEM, it is recommended to generate views which contain all objects of a story. By using the "Center of Gravity and Info" shortcut menu, it is possible to determine the center of gravity and to generate a node in this point. The position of the center of gravity is shown in Figure 04. Since the story drift has to be determined always at the top and bottom of the story, the node of the center of gravity should be moved to the ceiling plane. In the following, the procedure will be explained with the top floor.

After having determined the centers of gravity in the ceiling plane, the structure has to be recalculated. The global deformations have to be examined for the results evaluation. They show the total displacements of the single stories. The story drift Δ results from the differences of coincident points which has to be determined manually. The best way is to only display the results of the nodes in the corners and in the center of gravity to find the maximum difference in the total displacement (see Figure 05). It is necessary to compare the maximum and minimum displacements.

In this example, the maximum story drift is at the outer edge of the building and not in the center of gravity. Moreover, the maximum displacement difference in this story is not the maximum total displacement.

Δmax = 7.652 in - 6.526 in = 1.126 in

This procedure has to be carried out for each story and in this way, the maximum story drift for the entire building can be determined.