The analysis involves applying horizontal loads, in a prescribed pattern, to the structure incrementally, i.e. pushing the structure and plotting the total applied shear force and associated lateral displacement at each increment, until the structure or collapse condition.
Purpose of Pushover Analysis
It is expected that most buildings rehabilitated in accordance with a standard, would perform within the desired levels when subjected to the design earthquakes. Structures designed according to the existing seismic codes provide minimum safety to preserve life and in a major earthquake, they assure at least gravity-load-bearing elements of non-essential facilities will still function and provide some margin of safety. However, compliance with the standard does not guarantee such performance. They typically do not address performance of non-structural components neither provide differences in performance between different structural systems. This is because it cannot accurately estimate the inelastic strength and deformation of each member due to linear elastic analysis. Although an elastic analysis gives a good indication of elastic capacity of structures and indicates where first yielding will occur, it cannot predict failure mechanisms and account for redistribution of forces during progressive yielding.
To overcome this disadvantages different nonlinear static analysis method is used to estimate the inelastic seismic performance of structures, and as the result, the structural safety can be secured against an earthquake. Inelastic analysis procedures help demonstrate how buildings really work by identifying modes of failure and the potential for progressive collapse. The use of inelastic procedures for design and evaluation helps engineers to understand how structures will behave when subjected to major earthquakes, where it is assumed that the elastic capacity of the structure will be exceeded. This resolves some of the uncertainties associated with code and elastic procedures. The overall capacity of a structure depends on the strength and deformation capacities of the individual components of the structure. In order to determine capacities beyond the elastic limit some form of nonlinear analysis, like Pushover Analysis, is required.
Theory on which it is based
There are two nonlinear procedures using pushover methods:
a) Capacity Spectrum Method,
b) Displacement Coefficient Method.
In STAAD Displacement Coefficient method has been followed.
Displacement Coefficient Method is to find target displacement which is the maximum displacement that the structure is likely to be experienced during the design earthquake. It provides a numerical process for estimating the displacement demand on the structure, by using a bilinear representation of capacity curve and a series of modification factors, or coefficients, to calculate a target displacement. Refer Section 3.3.3.3.2 of FEMA 356: 2000 for detailed description of calculation of target displacement
Lateral load can be applied by following three methods.
Method 1
The vertical distribution of the base shear shall be as specified in this section for all buildings. The lateral load applied at any floor level x shall be determined in accordance with equation (1-8-1) and equation (1-8-2):
F_{x} = C_{vx}V …………………………. (1-8-1)
where
w_{x}h^{k}_{x}
C_{vx} = -------------------- …………………………. (1-8-2)
n
S w_{i}h^{k}_{i}
i = 1
Method 2
A vertical distribution proportional to the shape of the fundamental mode in the direction under consideration is performed. Use of this distribution shall be permitted only when more than 75% of the total mass participates in the fundamental mode in the direction under consideration, and the uniform distribution is also used.
w_{x }F_{x}^{ }
F_{x} = --------------- V
_{ n}
S w_{i }F_{i}
^{ i }^{= 1}
Method 3
A vertical distribution is performed consisting of lateral forces at each level proportional to the total mass at each level .
w_{x }
F_{x} = --------- V
_{n}
S w_{i }
where,
C_{vx} = Vertical distribution factor
k = 2.0 for T 2.5 seconds ≥
= 1.0 for T 0.5 seconds ≤
Linear interpolation shall be used to calculate values of for intermediate values of k for
intermediate values of T.
V = User defined base shear
w_{i} = Portion of the total building weight W located on or assigned to floor level i
w_{x}_{ } = Portion of the total building weight W located on or assigned to floor level x
h_{i}_{ } = Height (in ft) from the base to floor level i
h_{x} = Height (in ft) from the base to floor level x
F_{x }= Amplitude of mode a floor level x