Clause 7.6.2 provides empirical formulas to estimate the fundamental natural period Ta of a building for the equivalent static method. Different formulas apply for moment resisting frames (bare frame) and buildings with shear walls or bracing. The computed Ta is used to read Sa/g from the response spectrum.
Key Requirements
•For bare RC MRF buildings: Ta = 0.075 h^0.75
•For bare steel MRF buildings: Ta = 0.085 h^0.75
•For buildings with RC structural walls: Ta = 0.075 h^0.75 / √Aw
•Aw = total effective area of shear walls in the first storey
•h is the height of building in metres from the base
•For buildings with braced frames: Ta = 0.085 h^0.75
•All other buildings including moment-resisting frame with infill panels: Ta = 0.09 h / √d, where d is the base dimension along the direction of lateral force
Formulas
Ta = 0.075 h^0.75
Approximate fundamental period for bare RC moment resisting frame buildings
Ta = Approximate fundamental natural period in secondsh = Height of building in metres from base to top
Ta = 0.085 h^0.75
Approximate fundamental period for bare steel moment resisting frame buildings
Ta = Approximate fundamental natural period in secondsh = Height of building in metres from base to top
Ta = 0.075 h^0.75 / √Aw
Approximate fundamental period for buildings with RC structural walls
Ta = Approximate fundamental natural period in secondsh = Height of building in metresAw = Total effective area of structural walls in the first storey in m², where Aw = Σ[Awi × (0.2 + (Lwi/h))²], Awi = effective cross-sectional area of wall i, Lwi = length of wall i
Ta = 0.09 h / √d
Approximate fundamental period for all other buildings (frames with infill, masonry, etc.)
Ta = Approximate fundamental natural period in secondsh = Height of building in metresd = Base dimension of the building in metres along the direction of lateral force
Practical Notes
✓The bare frame formula (0.075h^0.75) gives a longer period and hence lower Sa/g — but this is only valid for truly bare frames without significant infill
✓For typical Indian construction with masonry infill, use Ta = 0.09h/√d — this gives a shorter period and higher design forces
✓A 10-storey RC frame (h ≈ 30 m) has Ta ≈ 0.075 × 30^0.75 ≈ 0.96 s as bare frame, but may be 0.6-0.7 s with infill
✓Dynamic analysis may give a different period — Cl. 7.7.5 requires that the base shear from dynamic analysis not be less than that from the equivalent static method
Common Mistakes
⚠Using the bare frame formula for buildings with significant masonry infill — infill stiffens the building and reduces the period
⚠Measuring height h from ground level instead of from the structural base (which may be below ground if there are basement levels with lateral restraint)
⚠Not recalculating Ta when adding or removing shear walls during design iteration
⚠Using Ta from dynamic analysis without checking the minimum base shear requirement of Cl. 7.7.5