Portal Frame · Lateral Drift · Deflected Shape
Simulate lateral sway of a single-bay fixed-base portal frame under a horizontal load. Compute lateral drift, drift ratio, beam-to-column stiffness ratio k, and column base moment — with a live animated deflected-shape diagram showing whether the frame passes H/400 (wind serviceability) or H/200 limits.
The tool uses the approximate portal frame drift formula Δ = PH³/(12EIc) · (2k+1)/(6k+1), where k = (Ib/L)/(Ic/H) is the beam-to-column stiffness ratio. Higher k (stiffer beam) approaches the fixed-beam case; k → 0 (flexible beam) approaches the cantilever case. Column base moments are estimated via the portal method as M ≈ PH/4 per column.
Stiffness ratio: k = (Ib/L)/(Ic/H). Lateral drift: Δ = PH³/(12EIc) · (2k+1)/(6k+1). Drift ratio: Δ/H. Column base moment (portal method): Mcol ≈ PH/4. Drift limits: H/400 (wind serviceability per ASCE 7) and H/200 (typical code maximum). All units converted to inches for consistency.
Use for preliminary sizing of moment-frame lateral systems in buildings when checking wind or seismic drift at the serviceability level. This approximate formula is valid for uniform fixed-base single-story frames; for multi-story frames, irregular frames, or final design, use a full matrix stiffness or FEA analysis. Results are most accurate when k is between 0.1 and 10.
H/400 is a common serviceability limit for inter-story drift under wind loads in commercial buildings, meaning the story sways no more than one four-hundredth of the floor-to-floor height. For a 12 ft story that is 12×12/400 = 0.36 in. ASCE 7 Table 12.12-1 gives seismic drift limits separately as a fraction of story height.
The portal method is a hand-calculation approximation for lateral loads on frames. It assumes an inflection point at mid-height of each column and mid-span of each beam, distributing the lateral shear to columns proportional to their tributary width. Column base moment Mcol ≈ PH/4 is the portal method result for a symmetric single-bay frame.
When the beam is infinitely rigid (k → ∞), both columns deflect in double curvature and Δ → PH³/(24EIc) (double the cantilever stiffness). When the beam is flexible (k → 0), the columns act as independent cantilevers and Δ → PH³/(12EIc). Increasing beam stiffness (larger Ib) always reduces frame drift.
No — this formula applies to single-story, single-bay, fixed-base portal frames. Multi-story frames require the full stiffness matrix method or a finite element analysis. For preliminary multi-story sizing, the portal or cantilever method can be applied story-by-story, but accuracy decreases with irregularity.