Approximate Fundamental Period Ta (ASCE 7 §12.8.2.1)
The approximate fundamental period Ta of a building, the input a seismic base-shear calculation needs.
Example
You enter
- Structural system steel_mrf
- Structural height hn, base to roof (ft) 120
- SD1, 1-second (g) -- optional, for the Cu Ta cap 0.6
You get
- Approximate period Ta 1.290 s
- Cu ta (s) 1.806
Details, formula, and sources
ASCE 7 §12.8.2.1 Ta = Ct hn^x, hn the structural height (base to roof, ft), Ct/x from Table 12.8-2: steel moment frames 0.028/0.8, concrete moment frames 0.016/0.9, steel EBF/BRBF 0.03/0.75, all other systems 0.02/0.75. A 120 ft steel moment frame gives Ta 1.29 s; a 48 ft other-system building 0.36 s. Ta is conservative (a shorter period lands higher on the spectrum); a period from a rational analysis may be used but not over Cu Ta (Table 12.8-1, from SD1) -- enter SD1 to see that cap. A licensed engineer governs.
Ta = Ct hn^x. Table 12.8-2: steel MRF 0.028/0.8, concrete MRF 0.016/0.9, steel EBF/BRBF 0.03/0.75, other 0.02/0.75. Cu Ta upper limit from Table 12.8-1 (SD1).
The ASCE 7 §12.8.2.1 approximate fundamental period Ta = Ct hn^x, with the Table 12.8-2 coefficients and the Table 12.8-1 Cu upper-limit factor, by name.
The approximate-period equation and the Ct/x and Cu tables are stated in ASCE 7 §12.8.2.1; the arithmetic is public. The structural height and SD1 are the user's own site/design inputs.
Estimate. AHJ and licensed professional govern.
Field names used by the API: system, hn_ft, sd1, ta_s, cu_ta_s
- Approximate period Ta = Ct hn^x (hn base-to-roof structural height, ft)ASCE 7 §12.8.2.1 Eq. 12.8-7
- System coefficients steel MRF 0.028/0.8; concrete MRF 0.016/0.9; EBF/BRBF 0.03/0.75; other 0.02/0.75ASCE 7 Table 12.8-2
- Cu Ta cap a computed T may be used up to Cu Ta; Cu 1.7 (SD1 <= 0.1) to 1.4 (SD1 >= 0.4)ASCE 7 Table 12.8-1