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I JSRD - I nternational Journal for Scientifi c Research & Development| Vol. 3, I ssue 11, 2016 | ISSN (onli ne): 2321-0613

All rights reserved by www.ijsrd.com  389

Linear Static Analysis of Regular Space Frame with & without Fixed

BaseMs. Akshaya Ghalimath1 Mr. Mantesh A.Hatti2 Ms. Sheetal More3 Ms. Chaitrali Jamadar4

1,2,3,4Department of Civil Engineering1,2,3,4A.G. Patil Institutes, Solapur, Solapur University

 Abstract  —  Due to present increase in the world population

 people in this world tends to occupy available location

 present in any zone, which also includes zones falling in the

high seismic zone categories. Commonly designers considerthe building to be fixed at their bases. Flexibility of the soil

causes the decrease in stiffness resulting increasing in the

natural period of the structure. Such increases in the natural

 periods, changes the seismic response of structure hence it

may be an important issue for design consideration. The

 present study provides systematic guideline for determining

the natural periods of frame buildings due to the effect of

soil-flexibility and identification of spring stiffness for linear

 building story and various influential parameters such as

 period, displacement, base shear and column forces haveidentified for both fixed and flexible base has to be studiedfor bare frame for all types of soils.

Key words:   Bare Frame, Fixed Base, Flexible Base, Base

Shear, Period, Displacement, Axial Forces In Column

I.  I NTRODUCTION 

Presently and majority existing of reinforced cement

concrete structure has been a tremendous increase in the

amount of tall stories in modern localities and the structures

do not need the current seismic requirement as they are

 primarily designed for gravity loads only. Since the structure

 being tall and slender are subjected to seismic and wind

load, if the structure is not stiff enough to resist the loadsand vibration cause. Therefore it is important for these

structures to resist lateral forces along with vertical forces.

As waves from an earthquake a reach a structure, they

 produce motion in the structure. This motion depends on the

structure vibration characteristics and the layout of the

structure. For the structure to reach to the motion, it needs to

overcome its own inertia force, which results in an

interaction between the structure and the soil. The extent to

which the structural response changes the characteristics ofearthquake motions observe at the foundation level depends

on the relative mass and stiffness properties of the soil and

the structure. Thus the physical properties of the foundation

medium are an important factor in the earthquake responseof the structure supported on it. The process in which the

response of soil influences the motion of the structure and

the motion of the structure influence the response of the soil

is termed as soil structure interaction.

In the analysis work one model of R.C.C. Space

Frame G+ 10 floors are made to know the realistic behavior

of building during earthquake.

 A.   Bare Frame:

The in-plane stiffness of masonry infill wall is not taken into

account in bare frame. Bare frame will deflect under

horizontal loads by bending in columns and beams .Non-

structural components such as masonry that are subjected toseismic forces are not normally within the design scope of

the structural engineer, whose responsibility is to provide

the seismic safety of the building.

Fig. 1: Bare Frame

II.  THEORETICAL FORMULATION 

 A.  Objective

The main objective of this work is to carry out the effect of bases, types of soil on the seismic behavior of R.C.C.

 building with linear static analysis method.

 B.   Methods of Seismic Analysis

Following Flow chart shows seismic analysis methods used

for Seismic evaluation:

Fig. 2: Seismic Analysis Methods

1)   Linear Static Analysis

Equivalent static analysis is the indirect method of

considering the effect of ground motion and there is

incorporation of dynamic properties of the structure in terms

of fundamental period, response reduction factor, soil type,

seismic zone and importance factor. Equivalent static

analysis were carried out for all the models under the action

of Dead load (DL), Live load (LL) and earthquake load

(EQ) for different load combination as per IS 1893-2002.This method is limited to regular type of structure whose

response is governed by first mode of vibration. As per IS

1893-2002 regular structure up to 40m in height in zone IV

and V and up to 90m in zone II and III can be analyzed by

Time History and Response Spectrum analysis.

2)  SMRF:Special Moment-Resisting Frame, It is a moment- resisting

frame specially detailed to provide ductile behavior and

comply with the requirements given in IS 4326 or IS13920

or SP6.For the analysis and design purpose one model has

 been considered namely as bare frame (S.M.R.F frame).

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 Linear Static Analysis of Regular Space Frame with & without Fixed Base

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III.  DESCRIPTION OF STRUCTURES 

In this paper the study has been carried out for ten Storied 3

Bay 3D RC frame building models with varying soil

conditions. The buildings are located in seismic zone II, III,

IV and V. The bottom storey height is 1.5m and upper floorsheight is taken as 3m for all buildings shown in fig. (3.2) the

 buildings are kept symmetric to avoid torsional response

under pure lateral forces. The Spacing of beam is 3.2 m.

IV.  METHODOLOGY 

Multi storied building with fixed and flexible base subjected

to seismic forces were analyzed under different soil

condition like very soft, soft, medium, sandy, and hard. The

 buildings were analyzed using linear static analysis usingsoftware E-TAB. Seismic analysis was carried out by

following IS1893:2002-PartI. Different response results

were found for fixed and flexible base buildings.

Fig. 3: Plan of frame

Fig. 4: View of frame

Material Properties  Values 

Grade of Concrete  25 N/mm2 

Grade of steel  415 N/mm2 

Modulus of Elasticity of Concrete  25000000 N/mm2 

Modulus of elasticity of steel  200000 N/mm2 

Unit Weight of Concrete  25 KN/m3 

Unit Weight of Brick   20 KN/m3 

Poisson’s Ratio for Concrete  0.2 

Table 1: Material Properties

 A. 

 Material Considered In the Study

The scientist Pais and Kausel (1988) has given different

formulae for calculation of spring stiffness for both 2D and

3D system considering rigid rectangular footing at the

ground surface which are three translational and three

rotational degree of freedom for rigid footing are given in

Table (1) below:

Degree of freedom Pais and kausel (1988)

Translation along z-axis , =   1 − 3.1(

). +1.6 Translation along y-axis , =  

2 − 6.8 (). +0.8(

)+ 1.6 

Translation along x-axis , =   2 − 6.8().

+2.4 

Torsion about z-axis , = 4.25(). +4.06 

Rocking about y-axis , =   1 − 3.73(

). + 0.27 

Rocking about x-axis , =   1 − [3.2(L

B) + 0.8] Table 1: Description

Three translational and three rotational degree of freedom

for rigid footing:

Where

G= E/2(1+ )

G = Shear modulus

E = Modulus Elasticity of SoilL =Length of Rectangular footing

B = width of Rectangular footing=Poisson ratio of soil

V.  A NALYSIS OF RESULTS 

Ten storied building frames with fixed and flexible base

analyzed and designed to understand the behavior under

seismic forces. Various seismic responses were compared

for both the type of building frames.

FIXED FLEXIBLE

VerySoft Soft Medium Hard Sandy

VerySoft Soft Medium Hard Sandy

Period In (Sec) 1.8232 1.8232 1.8232 1.8232 1.8232 2.3066 2.1311 2.1989 1.9801 1.8583

Base Shear

In (KN)

EQX 230.82 230.82 230.82 230.82 230.82 170.19 188.04 147.29 129.96 134.31

EQY 187.13 187.13 187.13 187.13 187.13 146.70 160.09 126.35 107.07 109.64

Displacement(mm) 10 10 10 10 10 20 20 10 10 10

Corner

Column

(Pu) KN 586.50 586.50 586.50 586.50 586.50 1934.9 1860.0 1894.08 926.03 890.83

(Mu3)

KNM15.414 15.414 15.414 15.414 15.414 69.794 66.78 68.24 44.03 42.36

Table 2: ZONE II (Different Parameters for Fixed & Flexible Base of Bare Frame for 3.2

FIXED FLEXIBLE

Very

SoftSoft Medium Hard Sandy

Very

SoftSoft Medium Hard Sandy

Period In (sec) 1.8232 1.8232 1.8232 1.8232 1.8232 2.3066 2.1311 2.1989 1.9801 1.8583Base Shear EQX 230.82 230.82 230.82 230.82 230.82 273.06 300.87 235.67 207.93 214.90

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In (KN) EQY 187.13 187.13 187.13 187.13 187.13 236.66 256.15 202.17 171.31 175.42

Displacement(mm) 10 10 10 10 10 30 30 20 10 10

CornerColumn

(Pu)

KN586.50 586.50 586.50 586.50 586.50 1934.97 1788.04 1894.08 982.36 949.815

(Mu3)

KNM15.414 15.414 15.414 15.414 15.414 69.794 116.34 68.24 46.716 42.365

Table 3: ZONE III (Different Parameters for Fixed & Flexible Base of Bare Frame for 3.2m)

FIXED FLEXIBLEVery

SoftSoft Medium Hard Sandy

Very

SoftSoft Medium Hard Sandy

Period In (sec) 1.8232 1.8232 1.8232 1.8232 1.8232 2.3066 2.1311 2.1989 1.9081 1.8583

Base ShearIn (KN)

EQX 230.82 230.82 230.82 230.82 230.82 407.35 448.85 353.50 311.90 322.36

EQY 187.13 187.13 187.13 187.13 187.13 354.99 384.23 303.25 256.96 263.14

Displacement(mm) 10 10 10 10 10 40 40 30 20 20

Corner

Column

(Pu)

KN586.50 586.50 586.50 586.50 586.50 1922.42 1906.27 1915.07 1651.2 1599.56

(Mu3)

KNM15.414 15.414 15.414 15.414 15.414 160.65 158.49 159.39 106.29 105.14

Table 4: ZONE IV (Different Parameters for Fixed & Flexible Base of Bare Frame for 3.2m)

FIXED FLEXIBLE

VerySoft

Soft Medium Hard SandyVerySoft

Soft Medium Hard Sandy

Period In (sec) 1.8232 1.8232 1.8232 1.8232 1.8232 2.3066 2.1311 2.1989 1.9081 1.8583

Base Shear

In (KN)

EQX 230.82 230.82 230.82 230.82 230.82 614.38 676.95 530.25 466.58 483.53

EQY 187.13 187.13 187.13 187.13 187.13 532.49 576.34 452.41 384.39 394.70

Displacement(mm) 10 10 10 10 10 60 60 50 30 30

Corner

Column

(Pu)

KN586.50 586.50 586.50 586.50 586.50 2079.94 2083.61 2083.87 1779.8 1735.35

(Mu3)

KNM15.414 15.414 15.414 15.414 15.414 225.46 221.74 223.32 141.82 139.65

Table 5: ZONE V (Different Parameters for Fixed & Flexible Base of Bare Frame for 3.2m)

VI. 

CONCLUSION

 Following Conclusion are observed from above study:

1)  The natural time period increases for flexible base ascompared to fixed base for all types of soil for all

seismic zones.

2)  The base shear will be reduces for flexible base as

compared to fixed base for all types of soil in both ‘X

‘and ‘Y’ direction f or II seismic zone.

3)  The values of base shear in X-direction are more than

Y-direction.

4)  The values of natural period and base shear are

increases zone wise i.e. Zone II and Zone V.

5)  The values of top storey displacement increase for

flexible as compared to fixed base.6)  The values of top storey displacement increases zone

wise from Zone II to Zone V for all types of soil.

7)  The values of column forces i.e. axial force increases

for flexible base as compared to fixed base.

8)  Axial force increases zone wise from Zone II to Zone

V for all types of soil.9)  The values of bending moment in the column are more

for flexible base as compared to fixed base.

10)  The values of bending moment in the column are more

for flexible base as compared to fixed base for Zone II

to Zone V for all type of soil.

11)  Lateral loads affects not only natural period, base shear

 but it also affects lateral deflection therefore lateralload and gravity load should be consider.

R EFERENCES [1]  Chopra A.K. 1995. Dynamics of Structures. Prentice

Hall.

[2]  IS 1893-2002 - Bureau of Indian Standards Manak

Bhavan, 9 Bahadur Shah Zafar Marg New Delhi

110002.

[3]  R.M. Jenifer Priyanka Studies on Soil structure

interaction of Multi Storeyed Building with Rigid and

Flexible Foundation ISSN 2250-2459, ISO9001:2008

Certified Journal, Volume 2, and Issue12 December

2012.[4]  Ramesh Baragani Performance Based Seismic

Evaluation G+6 RC Buildings Considering Soil

structure interactions Volume 14 Number 3-Aug 2014.

[5]  S.G Shah Soil structure interaction analysis methods-

State of art-Review Volume 2, No 1, 2010.

[6]  Shiji P.V Effect of Soil Structure Interaction inSeismic Loads of framed Structures, ISSN 2229-5518,

Volume 4, Issue 5, May-2013.

[7]  Stewart, Jonathan Soil structure interaction in building

1: Analytical aspects, 01-01-1999