 CHAPTER 3
METHODOLOGY
3.1 General

This chapter describes the analytical performance of the behavior of G+6 storied building when it is subjected to seismic loading in hard rock or hilly terrain region in Zone ?. The method of analysis performed is Linear Dynamic method of analysis in STAAD Pro, where analysis of any type of structure can be done easily. This method is also known as Response Spectrum analysis. This approach permits the multiple modes of response of a building to be taken into consideration (in the frequency domain). All Structural parameters are kept constant only by varying the Slope and Plan Orientation with Respect to the Flat Surface with Global Direction of propagation of the seismic wave.
3.2 Response Parameters calculation as per IS 1893:2002
The Response spectrum analysis, one of the most widely used dynamic analysis procedures to analysis a building. While the performing response spectrum analysis in STAAD Pro, the design lateral forces at each floor and in each mode is calculated by STAAD in Accordance with the IS:1893(part 1): 2002
Qik = Ak * ?ik *Pk * Wi (from clause 7.8.4.5c and 7.8.4.5d)
Where
Ak = Design’ horizontal acceleration spectrum value as per 6.4.’2 using the natural period of vibration (Tk ) of mode k.

Step 1: The value of Ak and Wi has to be defined by user.

Ahk =Z I Sa2 R g Where
Z = Zone factor, From Table 2 (clause 6.4.2)
I = Importance Factor, From Table 6 (clause 6.4.2)
Sa/g = Average response acceleration coefficient for rock or soil sites as given by Fig 2. From Table 3 based on appropriate natural period and damping of structure (clause 6.4.2)
R= Response reduction factor, From Table 7 (clause 6.4.2)
g = acceleration due to gravity
The design horizontal seismic coefficient Ah for various modes are calculated from above and input is given as STAAD parameter in definition command.

STAAD uses the following procedure to generate the lateral seismic loads
We have to specify the value for Z/2 x I/R as factor for input spectrum, and then the program calculates the time period. By default STAAD calculates first six modes of vibrations unless specified.

Then the program calculates Sa/g value for each mode utilizing time period and damping for each mode
Then the program calculates the design horizontal acceleration spectrum Ak for different modes.

Step 2: And ?ik , Pk values are calculated by STAAD .

For the mode participation factor for different mode of vibrations and peak lateral seismic force at each floor in each mode is ascertained. All response quantities for each mode are calculated.
Where as in Response spectrum analysis, the peak response quantities are obtained by using following methods as per IS: 1893(part1):2002
Square root of sum of squares (SRSS)
Complete quadratic combination (CQC)
The peak response quantities like member forces, displacements, storey forces, storey shears and base reactions are combined as per Complete Quadratic Combination (CQC) method.

?=i=1rj=1r?????j Where,
r = Number of modes being considered,
?? = Cross-modal coefficient,
?i = Response quantity in mode i (including sign), and
?j = Response quantity in mode i (including sign).

??=8?2(1+?)?1.5(1+?2)2+4?2?(1+?)2 ? = Modal damping ratio (in fraction) as specified in 7.8.2.1,
? = Frequency ratio = ? / ?i
?i = Circular frequency in ith mode, and
?j = Circular frequency in jth mode.

Alternatively, the peak response quantities may be combined as follows
If the building does not have closely-spaced modes, then the peak response quantity (?) due to all modes considered shall be obtained as

Where,
?k = Absolute value of quantity in mode k
r = Number of modes being considered.

If the building has a few closely-spaced modes, then the peak response quantity (?*) due to these modes shall be obtained as

Where the summation is for the closely-spaced modes only. This peak response quantity due to the closely spaced modes (?*) is then combined with those of the remaining well-separated modes by the method described in 7.8.4.4 (a).

Step 3: The modal mass (Mk) of mode k is given by

Where
g = Acceleration due to gravity,
?ik = Mode shape coefficient at floor i in mode k
Wi = Seismic weight of floor i.

Step 4: Modal Participation Factors (Pk ) of mode k is given by:

Storey Shear Force in Each mode – The peak shear force ( Vik ) acting in storey i in mode k is given by

Lateral Forces at Each Storey Due to All Modes Considered – The design lateral forces. Froof and Fi at roof and at floor i:

3.3 Structural modeling
3.3.1 Geometry of the Structure:
All the analyses are performed with the help of STAAD Pro using the seismic parameters As per the IS : 1893 (Part 1): 2002.

A G + 6 Structure Resting on different Sloping Conditions is considered for analysis.

Fig. Structure modeling in STAAD Pro
Mainly the analysis is carried out by two parts
The orientation of Building with Respect to the Propagation of Seismic wave is considered as 00, 100, 200, 300, 400, 450, 500 , 600 , 700 , 800 , 900 .

The building is resting on Sloped terrain with varying slopes of 00, 20, 40, 60, 80, 100, 120, 140.

With all the 88 possible cases are analyzed by using Response spectrum analysis in STAAD Pro
The orientation of Building with Respect to the Propagation of Seismic wave is follows

Plan [email protected] 0 0 Plan Orientation @ 100

Plan Orientation @ 200 Plan Orientation @ 300

Plan Orientation @ 400 Plan Orientation @ 450

Plan Orientation @ 500 Plan Orientation @ 600
Plan Orientation @ 700 Plan Orientation @ 800

Plan Orientation @ 900
The different Sloping profiles are as follows

Elevation view @ ground slope 00 Elevation view @ ground slope 20

Elevation view @ ground slope 40 Elevation view @ ground slope 60

Elevation view @ ground slope 80 Elevation view @ ground slope 100
Elevation view @ ground slope 120 Elevation view @ ground slope 140
3.3.2 Sectional and material properties of the Structure

Member Shape Size (B x D) in m
Beam Rectangular 0.3 x 0.6
Column Circular 0.6
3.4 Loads and details
Live Load 0.75 KN/m2
Density of RCC 23.5 KN/m3
Density of Brick 20 KN/m3
Wall thickness
External
Internal 0.23 m
0.115 m
Slab thickness 0.150 m
Wall Load (External) 11.04 KN/m
Wall Load (Internal) 5.52 KN/m
Floor finish 1 KN/m2
Height of each floor 3 m
Height of Plinth 1.5 m
Earthquake Zone V
Soil type Hard
Damping Ratio 5 %
Importance factor 1
Response reduction factor(As per IS:1893(part1);2002 5
Type of structure Special Moment Resisting Frame
Self weight of slab
Thickness of Slab = 0.15 m
Density of Concrete = 25 KN/m3
Self weight of Slab = Thickness of Slab x Density of Concrete
= 0.15 x 25
= 3.75 KN/m2
Floor finish Load = 1 KN/m2
Total slab weight at floor level = 4.75 KN/m2
Width of the Outer wall = 0.23 m
Width of the Inner wall = 0.115 m
Height of floor = 3m
Wall Weight (Outer) = Thickness of wall x Height of wall x Density of brick wall
= 0.23 x (3 – 0.6) x 20
= 11.04 KN/m
Wall Weight (Inner) = Thickness of wall x Height of wall x Density of brick wall
= 0.115 x (3 – 0.6) x 20
= 5.52 KN/m
Parapet Wall Weight = Thickness of wall x Height of wall x Density of brick wall
= 0.115 x 0.9 x 20
= 2.07 KN/m