Seismic Base Shear (V = Cs W)
Also known as seismic base shear · equivalent lateral force · V equals Cs W · seismic response coefficient · earthquake design force · static lateral force procedure
Worked example: C_s = 0.10 on 8000 kN → 800 kN base shear — press Try an example to run it live, then adjust anything.
Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!
Seismic Base Shear (V = Cs W) explained
The equivalent lateral force procedure replaces an earthquake with a single static push at the base equal to a fraction of the building's weight. That fraction is , and multiplying it by the effective seismic weight gives the base shear the lateral system must be designed to carry. A 8000 kN building with is designed for 800 kN of lateral force. Notice what drives it: weight, not area or occupancy. Mass is what an earthquake grabs hold of, which is why lightweight roofing and lightweight concrete buy seismic capacity directly, and why a heavy tile roof on an unreinforced wall is such a lethal combination.
is a code quantity, not a physical one. It bundles the design spectral acceleration for the site, the fundamental period of the building, the importance factor , and — most significantly — the response modification factor , which divides the elastic demand down by a factor of up to 8 to credit the ductility and energy dissipation of the chosen structural system. The honest reading is that a code-designed building is expected to yield in a design earthquake and to be damaged; the target is that it not collapse and that people get out. A special moment frame gets a large and a light design force in exchange for detailing that guarantees it can hinge without breaking. An ordinary shear wall gets a small and a big force.
The limits matter. The equivalent lateral force procedure only applies to regular, reasonably short structures; a tall or irregular building needs a modal response spectrum analysis, because higher modes and torsion redistribute the force in ways a single static push cannot represent. is also bounded above and below by code equations, and the lower bound frequently governs on low-seismicity sites. Once you have V, you still have to distribute it up the height, where it goes as roughly — so most of the force lands near the top, not spread evenly.
Seismic Base Shear (V = Cs W) formula
- = Seismic base shear (N)
- = Seismic response coefficient
- = Effective seismic weight (N)
Missing one of these? Work it out first, then come back
- Seismic base shear — Shear Flow (q = VQ/I), Transverse Shear Stress (τ = VQ/Ib)
- Effective seismic weight — Bearing Stress on a Pin or Bolt (σ = P/dt), Shear Flow (q = VQ/I)