# Determination of Story Drifts

For any column or wall in the earthquake direction, storey drifts expressing the displacement difference between two floors, ∆_{i }^{(X)}, is automatically obtained by **Section 12.8.6**.

The condition given in **12.8.2** and also the minimum equivalent lateral force condition defined in **Section 12.9.1.4.2 **are taken into account automatically.

**Symbols**

* C_{d }= *Deflection amplification factor in Table 12.2-1

*Deflection at the location required by this section determined by an elastic analysis*

**δ**_{xe}=*Importance Factor*

**I**_{e}=

**Δ**= Story drift

_{i }**δ**= Total displacement

_{i }Eq. (12.8-15) is used to estimate inelastic deflections (δ_{x}), which are then used to calculate design story drifts, Δ. These story drifts must be less than the allowable story drifts, Δ_{a}, of Table 12.12-1. For structures without torsional irregularity, computations are performed using deflections of the centers of mass of the floors bounding the story. If the eccentricity between the centers of mass of two adjacent floors, or a floor and a roof, is more than 5% of the width of the diaphragm extents, it is permitted to compute the deflection for the bottom of the story at the point on the floor that is vertically aligned with the location of the center of mass of the top floor or roof. This situation can arise where a building has story offsets and the diaphragm extents of the top of the story are smaller than the extents of the bottom of the story. For structures assigned to Seismic Design Category C, D, E, or F that are torsionally irregular, the standard requires that deflections be computed along the edges of the diaphragm extents using two vertically aligned points.

If the structure remained elastic during an earthquake, the force developed would be V_{E}, and the corresponding displacement would be δ_{E}. V_{E} does not include R, which accounts primarily for ductility and system overstrength. According to the equal displacement approximation rule of seismic response, the maximum displacement of an inelastic system is approximately equal to that of an elastic system with the same initial stiffness. This condition has been observed for structures idealized with bilinear inelastic response and a fundamental period, T, greater than T_{s} (see Section 11.4.6). For shorter period structures, peak displacement of an inelastic system tends to exceed that of the corresponding elastic system. Because the forces are reduced by R, the resulting displacements are representative of an elastic system and need to be amplified to account for inelastic response.

First of all, the displacements of all columns and walls in each floor are obtained for each mode. The horizontal displacement differences between two consecutive floors are then calculated using the displacements obtained for each mode and combined with an earthquake code compliant method(CQC or SRSS).

The deflection amplification factor, C_{d}, in Eq. (12.8-15) amplifies the displacements computed from an elastic analysis using prescribed forces to represent the expected inelastic displacement for the design-level earthquake and is typically less than R (Section C12.1.1).

The R and I_{e} values used in the account are available in the ASCE 7-16 Options table in the Analysis Settings report.

**Determination of Story Drift Limit Value**

The displacements induced in a structure include inelastic effects, structural damage as the result of a design-level earthquake is the values of Δ_{a} stated in Table 12.12-1.

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