Seismic P-Delta Stability Coefficient (ASCE 7-22 12.8.7)
Whether second-order (P-delta) effects can be ignored, must be amplified, or make the story unstable.
Example
You enter
- Gravity load at/above story Px (kip) 400
- Design story drift delta (in) 2.75
- Importance factor Ie 1
- Seismic story shear Vx (kip) 80
- Story height hsx (in) 144
- Deflection amplification Cd 5.5
- Shear demand/capacity ratio beta (default 1.0) 1
You get
- Stability coefficient theta 0.01736
- Maximum theta_max 0.091
Details, formula, and sources
theta = Px delta Ie / (Vx hsx Cd): below 0.10 neglect P-delta, up to theta_max = min(0.5/(beta Cd), 0.25) amplify by 1/(1-theta), above it the story is potentially unstable. Px 400 kip, Delta 2.75 in, Vx 80 kip -> theta 0.017, neglect; a soft story at theta 0.19 must be redesigned. A design aid; the engineer of record governs.
theta = Px delta Ie / (Vx hsx Cd); theta_max = min(0.5/(beta Cd), 0.25); neglect <= 0.10, amplify 1/(1-theta) up to theta_max, unstable above.
The ASCE 7-22 12.8.7 P-delta stability coefficient and its limits, by name.
The stability-coefficient P-delta check is the published ASCE 7 second-order procedure.
Estimate. AHJ and licensed professional govern.
Field names used by the API: px_kip, delta_in, ie, vx_kip, hsx_in, cd, beta, theta, theta_max
- Stability coefficient theta = Px delta Ie / (Vx hsx Cd)ASCE 7-22 12.8.7
- Maximum theta_max = min(0.5/(beta Cd), 0.25)ASCE 7-22 Eq. 12.8-17
- Thresholds neglect <= 0.10, amplify by 1/(1-theta), unstable above theta_maxASCE 7-22