Two-Stage Seismic Analysis for Tall Buildings with Podium or Basement

In the seismic design of tall buildings with podiums or basements, the structure typically consists of a flexible tower built over a stiff, low-rise podium. Due to the significant difference in stiffness and dynamic response between these two parts, a special analytical approach known as the 'two-stage analysis' is permitted by ASCE 7-16. This method separates the seismic analysis of the flexible tower from the stiff podium for more accurate and economical design.

Why Two-Stage Analysis is Important

When a podium is extremely stiff compared to the tower, most of the building’s modal mass will be concentrated in the tower. This causes the modal participation from the podium to be negligible in response spectrum analysis (MRSA). If a combined analysis is performed, the stiffness of the podium can artificially increase the system stiffness and result in underestimation of seismic base shear for the tower. The two-stage method ensures that the seismic demand is appropriately distributed and allows for a clearer understanding of how the tower responds independently.

Code Provision (ASCE 7-16 Section 12.2.3.2)

ASCE 7-16 allows the use of the two-stage analysis procedure if the following conditions are met:

- The stiffness of the lower portion (podium or basement) is at least ten times the stiffness of the upper portion (tower).

- The effective period of the entire structure is less than 1.1 times the period of the upper (tower) portion alone.

Seismic Analysis Methods for Tower and Podium

- The upper flexible portion (tower) shall be analyzed independently using the Equivalent Lateral Force (ELF) procedure or Modal Response Spectrum Analysis (MRSA), depending on its height and regularity.- The lower stiff portion (podium or basement) is then analyzed using the ELF procedure, including the gravity loads and seismic forces transferred from the tower.- The tower’s base shear is applied as a lateral load to the podium at the interface level.

R / ρ Ratio Adjustment Between Tower and Podium

The forces transmitted from the tower to the podium (including those resisted by backstay walls or frames) must be amplified to account for the differences in ductility between the systems. The code recommends adjusting the transferred force by:  

  F_transfer = V_tower × Scale_Factor

Scale_Factor = (R/ρ)_tower / (R/ρ)_podium > 1.0

Where:- V_tower = Seismic base shear from tower analysis- R_tower = Response modification factor of the tower system- R_podium = Response modification factor of the podium system- ρ = Redundancy factor (typically 1.0 or 1.3)

Diaphragm Backstay Forces

In many designs, the tower’s lateral-force-resisting elements (e.g., shear walls or frames) do not align directly with the podium walls. In such cases, the floor diaphragm at the interface level acts as a horizontal beam to transfer lateral loads to the podium elements. This behavior is referred to as 'backstay action'. The diaphragm must be designed to have sufficient in-plane strength and stiffness to resist these backstay forces and to prevent excessive deformation or failure.

Numerical Example

Assume the following:- Tower base shear (V_tower) = 3000 kN- R_tower = 5.0 (e.g., dual system with SMRF + shear wall)- R_podium = 3.0 (e.g., ordinary RC moment frame)- ρ = 1.3

Then, the amplified force transferred to the podium is:    F_transfer = 3000 × (3.0 / (5.0 × 1.3)) = 3000 × 0.4615 = 1384.6 kNThis force is applied laterally at the interface level and must be resisted by the podium's LFRS. The diaphragm must also transfer this force horizontally to the podium walls or frames through backstay action.