In seismic design, one of the most commonly misunderstood topics is the fundamental period of a building and how it affects base shear calculations. ASCE 7 provides guidance through both empirical formulas and analytical modeling, but how do we reconcile the two—and what’s allowed?

Let’s break it down.

1. Two Types of Periods in ASCE 7

Empirical Period Ta
A simplified formula based on building height and structural system:
Ta=Ct.hn^x
This is quick and conservative but does not account for actual stiffness or cracking in your structure.
Analytical Period T
Derived from structural analysis software (like ETABS) using cracked stiffness models that reflect realistic behavior.

2. Can You Use the Analytical Period?

Yes! ASCE 7 allows the use of the analytical period as long as it doesn’t exceed a certain upper limit:

T≤Cu⋅Ta

Where Cu is a coefficient that depends on the site seismicity (specifically S1, the 1-second spectral acceleration). The higher the seismicity, the lower the allowed multiplier Cu. This is to prevent engineers from underestimating base shear on soft or hazardous sites.

3. What is Cu?

Cu acts like a “speed limit” for the period. It ensures that even if your model is very flexible (e.g., because of cracking), you don't go beyond what ASCE considers safe.

Here's a simplified table:

S1 (Spectral Acceleration)	Cu
≤ 0.1	1.7
0.3	1.5
≥ 0.6	1.2

4. Why Is the Empirical Period So Short?

Because it's based on historical data from code-conforming buildings with typical stiffness—not on modern, flexible structures. It doesn’t consider real-world issues like:

Cracked concrete stiffness
Irregular geometry
Actual mass and stiffness distribution

That’s why the empirical period tends to be much shorter than what your ETABS model gives.

5. Final Takeaways

The empirical period is always conservative—safe to use but may overestimate base shear.
The analytical period is allowed—as long as it's capped at Cu⋅Ta.
Using the analytical period makes sense when your model reflects real stiffness (e.g., cracked sections), especially for cost-effective or drift-sensitive designs.
Never use the design spectrum SD1 to find Cu. Always use the MCE-level S1=Fv⋅S1, MCE.

Bonus Tip:

You can use the analytical period to check drift or performance criteria, even if it’s above the Cu⋅Ta—just don’t use it to calculate base shear.

Understanding Seismic Period Limits in ASCE 7: Empirical vs. Analytical Periods