G.17.4.2.1.3 Define Lateral (Push) Loading
The mathematical model directly incorporating the nonlinear load-deformation characteristics of individual components and elements of the building shall be subjected to monotonically increasing lateral loads representing inertia forces in an earthquake until a target displacement is exceeded.
A static, nonlinear pushover analysis usually requires multiple analyses cases. The first pushover load case is gravity load applied to the structure. The rest of the load cases may apply different lateral loads in terms of push load increments, whatever the case may be.
A pushover case may start from zero initial conditions or it may start from the results at the end of a previous pushover case. Thus, the gravity load case starts from zero initial conditions. The first lateral load case will start from the end of the gravity load case, the second lateral load case will start from the end of the first lateral load case, and so on until the target displacement is exceeded.
The lateral loads shall be applied in both positive and negative directions since it may lead to different results for asymmetric structures.
Lateral Loading Pattern
Lateral loads should be applied in predetermined patterns that represent predominant distributions of lateral inertial loads during earthquake response.
Distribution of lateral load must be applied to the structure when performing a pushover analysis.
Typically push load is defined in any one of the following:
- User defined static load pattern
- User defined base shear to be distributed vertically
Incremental push load ΔP is calculated by using any of the following two methods:
- You define Push load. In other words, you specify the incremental push load pattern on the structure by defining lateral load at nodes.
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Or, you define the base shear which is distributed laterally as per methods described in Section 1.4.1. The lateral load at each floor is again divided by the number of load step increment to get actual push load incremental load. Thus:
whereΔP = V/N - V
= - Lateral load distributed from user defined base shear.
- N
= - Total number of load step
The actual load acting on the structure at any load step i = ΔPi = ΔP · Spi
where- Spi
= - Stiffness Parameter at ith iteration
= Slope of the capacity curve at (i-1)th iteration / Initial slope of the capacity curve
During linear stage (i.e., all members in the structure are linear), the stiffness parameter is 1.0. Whenever any member becomes nonlinear the stiffness parameter decreases since slope of the capacity curve becomes less than that during elastic stage. Thus, actual lateral load acting on the nonlinear structure at any load increment stage is less than that during linear stage.