Torsion consideration in IS 1893-2002 seismic analysis
1-Introduction:
Torsion in induced in a floor when there is eccentricity between center of mass through which the resultant of seismic loading at a floor level acts and center of rigidity through which the resultant of the restoring force of the system acts. This is known as natural or inherent torsion of the system and the eccentricity is called the static eccentricity.
In addition to the natural torsion, there is also something called accidental torsion which is considered to account for rotational component of ground motion etc.
The design eccentricity is taken as a combination of static and accidental eccentricities and is given by the following equations.
e_{di} = αe_{si} + βb_{i }--------- (1)
e_{di} = δe_{si} - βb_{i }---------- (2)
e_{di} = Design Eccentricity at the ith floor
e_{si }= Static Eccentricity at the ith floor or the projected distance between the centre of mass and centre of rigidity at the ith floor.
b_{i }=plan dimension of the ith floor normal to the direction of ground motion.
α, β, δ = specified constants in the codes
IS: 1893-2002, as in clause 7.9.2 has specified the following values of contants.
α = 1.5
= 1.0, if 3D dynamic analysis is carried out
β = 0.05
δ = 1
2- Static Seismic Analysis:
The easiest and the effective way to do the static seismic analysis as per IS 1893-2002 with the effect of torsion is to define the Rigid Diaphragms. Once can also manually specify the Master Slave in ZX direction and do a seismic analysis. In both the aforementioned cases, one does not actually need to model the slabs. Thus the last method of doing seismic analysis with torsion is to actually model the slabs.
2.1- Model with Rigid Diaphragms:
When the Rigid Diaphragm is modelled at a specified height, the program identifies the center of mass of the floor at that level based on the mass definition in the Mass Reference Load Case. By default, the Data of the Mass in the Y direction is used to determine the center of mass. In absence of mass data in the Y direction, the masses in the other directions are used.
Once the center of mass is identified the calculated seismic force at that level is applied at the center of mass. The center of rigidity is based on the distribution of the elements that provide lateral stiffness and thus does not need an exclusive determination. Thus the inherent torsion is automatically determined.
However, if the design static eccentricity component of the design eccentricity is greater than the natural static eccentricity (α > 1), then an additional torsional moment of the value of (α-1) e_{si }*Fi is introduced at the center of mass to achieve the full torsion condition. Please refer to the figure below. The value of β*bi*Fi is added or substracted to the additional natural torsion to incorporate the effect of accidental torsion.
2.2- Specifying the values of α, β and δ:
The general format of specifying the seismic loading in STAAD with Rigid Diaphragm is as follows:
LOAD n
1893 LOAD { X | Z } (f_{1}) (DECCENTRICITY f2 ) (ACCIDENTAL f_{3})
The DEC parameter should be used to specify the value of α and δ, represented by the value of f2 in the above command line. The ACC parameter should be used to specify the value of β, represented by the value of f3 in the command line above.
Thus, the equivalent specification for static seismic analysis with design eccentricity represented by equation (1) in section 1 as follows:
LOAD 1
1893 LOAD X 1 DEC 1.5 ACC 0.05_{ }
PERFORM ANALYSIS
CHANGE
Similarly, the equivalent specification for static seismic analysis with design eccentricity represented by equation (2) in section 1 as follows:
LOAD 2
1893 LOAD X 1 DEC 1 ACC -0.05_{ }