Story drift and P-delta
Takes what an elastic analysis gives, level by level, and checks it: the design story drift against the allowable drift, the stability coefficient against its maximum, and the separation from an adjacent structure or a property line. The analysis stays yours. Use it for results from a frame program, or from the Seismic base shear type, whose drift line has no stability coefficient and no separation. Nothing links the types: you copy the values.
Inputs of the story drift #
- Cd, R, Ω0, Ie, risk category and Seismic Design Category: from Table 12.2-1, Table 1.5-2 and 11.6. R is used only for the Maximum Considered Earthquake Displacement, Ω0 only for the lower limit of β.
- Structure (Table 12.12-1): the row of the table, or your own coefficient. The first row needs interior walls, partitions and ceilings designed for the drift, and four stories or fewer: that first condition is your judgment.
- Single story, interior walls and partitions designed for the drift: note a of the table, no drift limit. Off by default. It applies only with one story, and you confirm the condition.
- The system is only moment frames, ρ: in SDC D to F the limit is divided by ρ (12.12.1.1). ρ is used for nothing else here.
- The table's column holds: elastic displacements of the levels, elastic story drifts, or either already amplified by Cd/Ie. Modal programs combine the drifts of each mode (12.9.1): enter those as drifts, not differences of combined displacements.
- Stories, from the top down: the name of the level, hsx (the height of the story below it), the displacement or drift, the story shear Vx of the same analysis, the gravity load added at that level (Px accumulates down), β (0 means 1.0, which the code permits as the conservative value), and δdi if you want diaphragm deformation in δDE and δMCE.
- Type 1 torsional irregularity: in SDC C to F, enter the largest difference at the edges with diaphragm rotation (12.8.6.5). The box adds a reminder; it cannot change the numbers you enter.
- The analysis already includes P-delta: θ is divided by (1 + θ) before the check of Eq. 12.8-19, and the drifts are not multiplied.
- Separation: an adjacent structure on the same property, with its δDE2 at the adjacent edge, or a property line. With a distance entered it is checked; at 0 the required distance is only reported.
The results you enter should come from forces with a load factor of 1.0 on Eh and expected gravity loads of at least 1.0D + 0.5L, with L reduced as 12.8.6.1 says. Eq. 12.8-6 need not be considered and the computed period may be used without the Cu Ta limit (12.8.6.2).
Checks performed #
| Check or result | Basis |
|---|---|
| Design Earthquake Displacement | Eq. 12.8-16: δDE = Cd δe / Ie + δdi |
| Maximum Considered Earthquake Displacement | Eq. 12.8-17: δMCE = 1.5 (R δe / Ie + δdi) |
| Design story drift against Δa | 12.8.6.5, 12.12.1, Table 12.12-1, 12.12.1.1. The governing story is the check; every story is listed |
| Stability coefficient against θmax | Eq. 12.8-18: θ = (Px / hsx) / (Vx / Δxe). Eq. 12.8-19: θmax = 0.5 / (β Cd), at most 0.25, need not be less than 0.10; β not less than 1.25/Ω0 |
| Factor above 0.10 | 12.8.7: drifts multiplied by 1/(1 − θ) before the drift check; an advisory says to multiply the member forces too, or use a rational analysis |
| Separation | Eq. 12.12-2: δSS = √(δDE1² + δDE2²); property line setback δDE; 12.12.2 |
The check is on the drift and on θ, so a passing calculation reads Adequate. There is nothing to size: the system is outside the calculation, so there is no auto-design.
Limitations #
- No analysis is run. Displacements, shears and loads are taken as entered.
- Torsion, accidental torsion and the torsional amplification Ax are in your entered values, not added here.
- δdi is taken as entered and left out of the story drift, as 12.8.6.5 permits.
- Separation uses the largest δDE of the structure, which is the usual top of the building. The exception of 12.12.2 (a smaller distance by rational analysis) is your call.
- 12.12.3 (members spanning between structures) and 12.12.4 (deformation compatibility) are not checked.
- Nonbuilding structures and Chapter 16 to 18 displacements are out of scope.
Verification examples #
Verification status: 103 values compared in 8 examples (8 published, 0 hand calculations from the cited equations): 101 within tolerance, 2 recorded deviations. Code basis: the provisions it uses were read in the target edition.
| Example | Source | Values |
|---|---|---|
| 12-story concrete frame, north-south | FEMA P-1051 (2015), pp. 454 to 459, Tables 10-11a, 10-12a | θ per story, accumulated load, drift ratio, Δxe, 0.5/(β Cd) |
| 12-story concrete frame, east-west | FEMA P-1051, p. 460, Table 10-12b | θ per story |
| One-story industrial frame | FEMA P-1051, Example 9.1, pp. 369 to 375 | δx 18 in., allowable 10.28 in., θmax 0.125 |
| 23-story steel building | FEMA P-2192-V1 (2020), Table 4-7, p. 151 | δx, drift ratios both ways, 2 % limit |
| 18-story coupled composite walls | FEMA P-2192-V1, Table 5-5, pp. 197 to 198 | Amplified displacements, largest drift ratio 1.65 % |
FEMA P-2192 is written to ASCE 7-22. FEMA P-1051 is written to ASCE 7-10, whose θ equation is the same as Eq. 12.8-18 by algebra. Two published values are documented differences: θmax of 0.091 in P-1051 is 0.10 here, because ASCE 7-22 adds that θmax need not be taken below 0.10 (the value 0.5/(β Cd) itself agrees); and the θ of 0.069 printed in Example 9.1 does not follow from its printed numbers, which give 0.058. P-1051 p. 459 prints Cd = 5.5 and then "(6.5)" in the line for θ: only 5.5 reproduces its value and its table, so 5.5 is used.
No published example checks the 1/(1 − θ) factor, the division by (1 + θ), the MCE displacement or the separation: those are hand calculations in the tests.