Progressive Loading and Analysis of RC-Plane Framed …ijifr.com/pdfsave/17-04-2015306V2-E8-027.pdfstructural elements subjected to general static vertical loading ... with beam footing

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Original Paper Paper

International Journal of Informative & Futuristic Research ISSN (Online): 2347-1697

Volume 2 Issue 8 April 2015

Abstract

A rational approach to the design of structures resting on soil media should take into account both deformation characteristics of the soil and flexibility of the structures. The analytical treatment of such interaction problems invariably requires a certain amount of mathematical and computational effort involving classical theories of elasticity or plasticity or both. In the conventional method of analysis of Reinforced cement concrete open plane framed structures, the base of the structure is assumed to be fixed. i.e., the flexibility of soil and foundation are ignored. However the foundation and soil material will have flexibility. The type of analysis which considers the flexibility characteristics of foundation and soil is called ‘Interaction Analysis’. Interpretation of interaction results have been achieved in the past by the adoption of relative stiffness ratios for the different components of the total system. The flexural rigidities of the superstructure, foundation elements and stiffness of the soil have been identified as evaluating parameters which assist the interpretation of interaction results. Hear, an attempt has been made to find out the variation in axial forces and moment of the structural elements subjected to general static vertical loading condition over a viable practical ranges of relative stiffness ratios between ‘Superstructure to soil’ and Foundation to soil’ by using Winkler spring model for interaction analysis. Interaction analysis with progressive loading is carried out in the same order to find out the variation. Further, an attempt has been made to arrive at the practical ranges of relative stiffness to be adopted to minimize the variation of axial forces and moments in the structural members.

Progressive Loading and Analysis of

RC-Plane Framed Structures Paper ID IJIFR/ V2/ E8/ 027 Page No. 2475-2486 Research Area Civil Engineering

Key Words Deformation, Flexibility, Interaction analysis, Stiffness, Foundation

SreeKeshava K.S 1 Assistant Professor, Department Of Civil Engineering, Jyothy Institute Of Technology - Bangalore

Dr. B.V.Venkatasubramanya2 Head Of Department, Department Of Civil Engineering, Jyothy Institute Of Technology - Bangalore

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ISSN (Online): 2347-1697 International Journal of Informative & Futuristic Research (IJIFR)

Volume - 2, Issue - 8, March 2015 20th Edition, Page No: 2475-2486

SreeKeshava K.S., Dr. B.V.Venkatasubramanya :: Progressive Loading and Analysis of RC-Plane Framed Structures

1. Introduction

Reinforced cement concrete open plane frames (i.e., without considering the infilling walls)

are quite common building structures used for residential flats, commercial complexes and other

public utility buildings. In the conventional method of analysis of these structures, the load

distribution within the building frame is calculated on the assumption that the base of the structure is

fixed allowing no relative displacements between the columns, resulting in uniform or varying soil

pressure distribution. This loading is then used to calculate foundation settlements assuming the

structure to be compatible with the soil settlement profile. The above two assumptions are quite

contradictory. Though in the traditional design methods no relative settlements between the column

footings are allowed, the varying subsurface and loading conditions introduce differential

settlements as had been observed by earlier field and theoretical investigations. Since, unequal

settlements occur in most of the cases, secondary stresses are induced in every member of framed

structure. The ratio of secondary forces and the member end forces obtained in the structure

analyzed under conditions of fully fixity may be described as “Interaction Effects”.

The influence of interaction between a framed structure and the foundation-soil system

beneath it, on the distribution of load between the Columns and the differential settlements, has been

described by many Writers, e.g., Lee and Brown. However in most cases, it has been assumed that

the frame is complete before loading commences, although much of the loading may be applied

progressively during construction. Heil and Goschy both analyze progressive loading, but do not

attempt to quantify the differences between the effect of progressive Loading and loading of the

completed frame. Hence, soil, foundation and superstructure constitute one interacting system and

these are not independent component. Interaction between a framed structure interaction along with

the foundation and the soil below are known to influence the distribution of loads among columns

and the differential settlements of the structure.

Unlike the structural materials viz, concrete and steel, the properties of which are

predictable to an acceptable degree of accuracy, the properties of soil system are often difficult to

access, soil being a natural geological material. Thus it has been customary to assign large factor of

safety to soil stresses when compared to those of superstructure. In such a situation, the soil stresses

generally do not cross the “Elastic range” except probably in the small overstressed zones. Hence in

the present analysis the soil system is assumed to be elastic state. Within the ambit of linear

elasticity, the soil system has been variously modeled, yet the four most common adopted models

are; Winkler springs, two parameters model, Half-Space continuum, Layered continuum. Of these

the layered continuum model establishes the exact distribution of stress and strain within the soil

system. However, the theoretical formulations implicit in such problems are difficult and only a few

closed form solutions are available and only a few closed form solutions are available. As a result,

the first two models, namely Winkler springs and half-space continuums are widely used because of

their simplicity.

Figure-1: Winkler spring Model

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The Winkler spring model is the most convenient representation of soil support in the domain of

linear elasticity for framed structure-soil interaction analyses. The closeness of the analytical results

obtained using this model with those corresponding to the elastic half-space continuum has been

investigated in the past for foundation beams. The findings, however, are not applicable to framed

structures founded on beam or strip footings. Moreover, the past investigations employ the concept

of characteristic length which does not adequately account for the stiffness contribution of the

superstructure. A framed structure on beam foundation can be described parametrically by the ratios

of stiffness‟s of superstructure and foundation beams to that of soil. For a practical range of soil

allowable pressures, the ranges of these relative stiffness ratios have been established.

2. Relative Stiffness

The flexible nature of the foundation, the superstructure and the supporting soil medium has great

influence on the behaviour of framed structures. The flexural rigidities of the superstructure and

foundation elements and the stiffness of the soil have been identified as indices for devising

parameters, which assists the interpretation of interaction results, by many earlier investigations.

Currently, the ratios of stiffness of superstructure to soil exist in as parameter for interaction

analysis. While it is generally recognized that these ratios have wide limits few comprehensive

studies have been made to define these limits for different types of structures resting over a wide

range of soils. In this paper, the feasible range of these ratios of stiffness all demarcated for plane

framed reinforced concrete building structure with beam footing resting on soils in which shallow

foundations are feasible.

Absolute stiffness of superstructure, soil and foundation is

Brown and Yu (1986) made the studies on load sequence and soil structure interaction. They used

relative stiffness between „superstructure and soil (Kbs) as the parameters for studying the columns

loads transferred to the foundations, and the differential settlements in the foundation.

The absolute stiffness of the superstructure (Kb), foundation (Kf) have been defined as,

= nE / …..(1)

= E / …. (2)

Ks = Es / (1- ) ….. (3)

Where, n = total number of storeys

E =flexural rigidity of the floor beam

l =length of the bay or floor beam

L=length of the foundation = n,l

n ,= number of bays.

The relative stiffness‟s between the superstructure and soil ( ) and between foundation and soil

( ) have been defined as

= / ------------ (3)

= (16/ )( / ) -------------(4)

The interaction analysis has been carried out over a range of varying between 0.001 to 0.01 and

0.01 to 0.1 respectively. These resemble the factors proposed by sommer (1965) but are more

elegant and convenient to adopt as indices of structures soil interaction.

The absolute stiffness of the soil Ks can be related to the allowable bearing pressure Qa as Ks =

120 QaB KN/ …....………. (5)

Where, B= width of foundation in meters.

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2.1 Modulus Of Elasticity And Poisson’s Ratio

The modulus of elasticity (Es) is often determined from unconfined triaxial or odemetric

compression tests. Plate load tests and pressure meters tests may also be used to determine the in situ

modulus elasticity of the soil. The modulus of elasticity increases with increase in confining stresses.

For the case where the initial stresses is an isotropic state of stress, the modulus of elasticity

increases approximately as Where varies from 0.1 to 1.0 an average value of =1/2. Owing to the

dependence of Es on the void ratio and the difficulty of obtaining undisturbed sample of granular

soils, it is especially difficult to measure the modulus of elasticity of granular soil reliably. The

modulus of elasticity of cohesive soil has been found to be comparatively insensitive to the effects

confining stress. However the Es of the cohesive soils is found to vary with the void ratio and also

depends on the moisture contents. A comparison of the results of field settlements with those

computed using unconfined compressive test data indicate that the laboratory Es value

underestimates the field Es by a considerable amount (bowles 1977).

Table-2.1: Typical range of values for Poisson’s (after Bowles, 1977)

Type of soil

Clay-saturated 0.4-0.5

Clay-Unsaturated 0.1-0.3

Sandy Clay 0.2-0.3

Silt 0.3-0.35

Sand dense 0.2-0.4

Coarse 0.15

Fine 0.25

2.2 Modulus Of Subgrade Reaction (Ks)

It is based on the suggestion given by Bowles in 1977.this method is presented on the assumption

that allowable soil pressure is based on some maximum amount of deformation (Si) including on a

factor of safety (Fs). Thus modulus of sub grade reaction is

K‟s = (Fs) Qa / Si

For a settlement of 0.0254m and factor of safety 3, K‟s can be taken as

K‟s= 120 Qa KN/

Typical values for modulus of sub grade reaction are given in table-2.The allowable bearing pressure

of soil (Qa) generally lies between 50KN/ to 200KN/ .The soil stiffness is accounted in terms

of elastic modulus Es and Poisson‟s ratio Vs or in terms of modulus of sub grade reaction K‟s. This

section is primarily concerned with a brief examination of the above factors.

Table-2.2:Typical values for the modulus of sub grade reaction KN/m3 (After Bowles, 1977)

Soil Range of K’s

Loose sand 4700-15700

Medium Sand 9430-78500

Dense Sand 62840-125670

Clayey sand 31420-78550

Silty Sand 21560-47130

Clayey Soil <4 11780-23560

4< <8 23560-47130

8< >47130

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2.3 Relative Stifness Between Superstructure And Soil (Kbs)

Reinforced cement concrete open plane framed structures are quite common in building structures,

used for residential flats, commercial complexes and other public utility buildings. In this type of

structure, the superstructure floor beams, which are built monolithic with floor slabs, usually have a

higher rigidity than the supporting columns. The filters walls are not rigidly connected to the

supporting beam and do not contribute much to their rigidity. The framed structures of residential

and commercial complexes are subjected to live loads ranging between 2 Kpa to 5 Kpa, and the span

of floor slabs generally ranges between 3m and 10m. Depending on the interframe spacing (s),

which also lies between 3m and 10m, the loading on the superstructure floor beams ranges between

22.5KN/m for small interframe spacing with filler walls. For super structure floor beam, the

span/depth ratio (l/d) usually varies between 10 and 20, and the depth/width ratio(d/b)lies between 1

and 3. The allowable bearing pressure of soil (Qa) generally lies between 50KN/ to 200KN/ .

The absolute stiffness of soil Ks can be related to the allowable bearing pressure Qa as

Ks = 120 QaB KN/ Where B=width of foundation in meters

For beam or strip footing, in order to avoid over lapping of the foundations of adjoining frame, the

maximum foundation width may not exceed 2/3 of the interframe spacing(s), hence the economics

of a raft foundation needs to be examined. The maximum number of floors feasible is governed

mainly by the allowable soil pressure and to some extent it also depends on the interframe spacing.

As the interframe spacing is increased, the number of floors feasible shows a decreasing trend for

lighter live loads on floor beams, whereas for heavier live loads on floor beams, the maximum

number of floors shows an increasing trend. The practical ranges can be obtained using equations

1,2 and 3.

2.4 Relative Stiffness Between Foundation And Soil ( )

The absolute stiffness of foundation, soil and the relative stiffness between foundation and soil are

defined according to the equations 4, 5 &6 respectively. The maximum width of the foundation

beam (B) is restricted to a maximum value of S/2 where S is the inter frame spacing. The span/depth

ratio (l/D) for the foundation beam of the bay can be taken as equal to that of floor beams as between

10 and 20. The depth/width ratio (D/B) of the foundation beam generally lies between 0.15 to 0.5.

The value of depends on the following parameters

Allowable pressure ( )

Length of bay (l)

Length of bay/depth ratio (l/D) of foundation beam.

Number of bays ( )

The number of bays has a greater effect on the value of than other factors. The value of

decreases with increase in allowable soil pressure and bay span, a trend, which is contrary to the

variation of . It is seen from the table that 3.8 to3.10 that for one bay frame lies between

0.001 and 0.785.It has been shown that the maximum interaction effect is felt only in end

bays(Venkatasubramanya 1989).Hence, for an interaction analysis a three-storey structure is found

to be ideal.

3. Problem Considered And Method Of Analysis

The interaction analysis is carried out considering the frame and soil as parts of the single

compatible unit, the soil is represented by Winkler spring model. The bending moments, shear

forces and axial forces of the beam and column elements of the bottom and top storey elements with

different allowable bearing capacities of the soil media are obtained using STAAD-Pro package. The

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analysis is carried out for the frame with different stages of construction with proper loadings and

also carried out with conventional method which is usual practiced method of construction and these

cases covering the practical ranges of and (0.005 to 0.1).

A three bay, three-storied symmetrical R.C open plane frame having a bay span of 5m and storey

heights of 4m for ground floor and 3m each for first and second floor has been considered. The

modulus of elasticity of concrete is assumed to be 2.2E+07 KN/m2. The moment of inertia of floor

beams and of the columns has been taken as the same so that there is better redistribution of

moments and forces. In the present study dead load of 15 KN/m is considered on the superstructure

beams also the form work is taken as 6 KN/m and live load on floor and roof is taken as 12 and 10

KN/m is applied in proper order. The superstructure rest on a soil media whose allowable bearing

pressure range is 50- 200 KN/m2. The member properties as per codal provisions for a span length

of 8m, the beam dimension as 0.3X0.75m (inclusive of slab thickness) and column dimension as

0.45X0.45m respectively.

The other set of analysis is carried out by considering the relative stiffness and are found to

depend on many parameters i,e. E, , , and . By varying any of these parameters or some of

the parameters together, the required practical ranges of and can be obtained. For the given

soil (known and ) the required practical ranges of and can be obtained by

proportioning different geometrical sizes ( and ) for the foundation and superstructure beams or

for given the structure required ranges of and can be obtained by varying the parameters

and . The former procedure has been adopted here. For the frame and soil selected the absolute

stiffness values of frame. Foundation and soil components are given by,

= nE /

=3*2.2* * /

=50925.93 KN/ = E /

=2.2* * /

=1060.9569

Ks = 120 Qa*B=120*150*1.0= 18000 KN/

The relative stiffness ratio between foundation and soil and between superstructure and soil,

= / , / 18000=2.829

= (16/ )( / ) = (16*1060.9569 / ( )

= 0.3

Tables 3.1 and 3.2 gives the values of moment of inertia and to be adopted for obtaining the

desired range of and . The entire analysis is carried out for a range of and between

0.005 and 0.1.

Table-3.1: Sectional properties of foundation Beam.

Moment of Inertia

= /0.3

Area of Beam (A*f) Width of Beam

foundation, B

0.005 0.01666 0.581 1.0

0.01 0.033 0.734 1.0

0.1 0.333 1.58 1.0

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Table-3.2: Sectional properties of floor beam and column.

4. Analysis Of Results The maximum bending moments in the superstructure and foundation beams, and axial forces in

column members obtained from interaction analysis. The effect of stages of construction on the

interaction result are compared in terms of a moment increse ratio, axial force increse ratio and shear

force increse ratio is defined as

Moment increse ratio= [ ( ) / ]*100

Axial force increse ratio=[ ( / ]*100

Shear force increse ratiio=[ ( ]*100 Where,

, , = Maximum bending moment, axial force and Shear force from sum of stages of

construction.

, , = Maximum bending moment, axial force and shear force from conventional method

of construction.

4.1 Axial force in End Column of Ground Floor

The effect of axial force in end column of ground floor is computed for progressive loading and

conventional method and the axial force ratio is plotted shown in figure 4.1(a).The maximum axial

force difference ratio is found to be increase with Kbs value but vary inversely with Kfs. It is seen

from the graph that for most of ranges of Kfs the difference ratio increases for all ranges of Kbs.

When the foundation is flexible I,e. 0.01 Kfs 0.005 the variation is found to be maximum for all

values of Kbs, at the other hand for relatively rigid foundations I,e. 0.1 Kfs 0.01 the variation is

minimum for all Kbs. For relatively rigid structures resting on flexible foundation, the maximum

axial force difference ratio is found to be 13.38% and the same decrease to be 5.17% if the

foundation is relatively rigid.

Moment of Inertia

= /2.829

Width of beam ‘b’ Depth of beam ‘d’

0.005 1.76* 0.230 0.45

0.01 3.53* 0.300 0.52

0.1 0.050 0.450 0.98

Figures 4.1 (a, b): Axial force variations in End and Central column of Ground Floor

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4.2 Axial force in central Column of Ground Floor

The effect of axial force in central column of ground floor is computed for progressive loading and

conventional method loading and the axial force ratio is plotted in figure 4.1 (b). The maximum

axial force difference ratio is found to be increase with Kbs value but vary inversely with Kfs. For

relatively rigid structures resting on relatively rigid foundations, the maximum axial force difference

ratio is found to be 2.33% and the same increases to be 3.6% if the foundation is relatively flexible.

Similarly, for structure that are relatively flexible, resting on relatively flexible foundations the

maximum axial force difference ratio is found to be 2.3% and the same decreases to 1.92%, if the

foundation is relatively rigid. The axial force obtained by progressive loading is higher compare

with conventional method of interaction analysis.

4.3 Shear force in exterior beam of ground Floor

The effect of shear force in exterior beam of ground floor is computed for progressive loading and

conventional method loading. The shear force difference ratio is plotted in figure 4.3 (a). The shear

force obtained by conventional method is higher compare with progressive loading of interaction

analysis. The maximum shear force difference ratio is found to be 3.95% for relatively rigid

structures resting on flexible foundation. The same is increases to 4.27%, if the foundation becomes

relatively rigid.

(a) (b)

Figures 4.3 (a, b): Shear force & bending moment variations in Exterior Beam of Ground Floor

4.4 Bending moment in Exterior Beam of Ground Floor

The effect of bending moment in exterior beam of ground floor is computed for progressive loading

and conventional method. The bending moment difference ratio is plotted in figure 4.3(b).The

moment difference ratio is found to be increase in Kbs value but the same is found to vary inversely

with Kfs.It is seen from the graph that for most of ranges of Kfs the difference ratio increases for all

ranges of Kbs. When the foundation is flexible i,e. 0.01 Kfs 0.005 the variation is found to be

maximum for all values of Kbs, at the other hand for relatively rigid foundations i,e. 0.1 Kfs 0.01

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the variation is minimum for all KbsWhen the superstructure is relatively regid and the foundation is

relatively flexible the maximum moment difference ratio is found to be 22.70% and the same is

increses to 29.49%, as the foundation becomes relatively rigid. Hence, to minimise the variation, the

foundation is made to be relatively rigid and the super structure to be relatively flexible.

4.5 Bending moment in Interior Beam of Ground Floor

The effect of bending moment in Interior beam of ground floor is computed for progressive loading

and conventional method and difference ratio is plotted in figure 4.5(a). The moment difference ratio

is found to be decrease with increase in Kbs value but the same is found to vary inversely with Kfs.

It is seen from the graph that for most of ranges of Kfs the difference ratio increases for all ranges of

Kbs. When the foundation is flexible I.e. 0.01 Kfs 0.005 the variation is found to be minimum for

all values of Kbs, at the other hand for relatively rigid foundations I,e. 0.1 Kfs 0.01 the variation is

maximumfor all Kbs.When the foundation is flexible and the super structure is rigid variation is

monimum is found to be 0.09%, and it increses to 2.47%, when the foundation is relatively rigid.

Also, for relatively flexible superstructure (i,e 0.005 Kbs 0.01) the variation is minimum for all

Kfs and ismaximum when super structure is rigid (I,e.0.01 Kfs 0.005).For relatively flexible super

structures variation is 2.38% and is decreases to 0.65% when the super structure is rigid.

(a) (b)

Figures 4.5 (a, b)-Bending moment variations in interior Beam of Ground and Top Floor

4.6 Bending moment in Interior Beam of Top Floor

The effect of bending moment in interior beam of top floor is computed for progressive loading and

conventional method difference ratio is plotted in figure 4.5 (b). The moment obtained by

conventional method is higher compare with progressive loading of interaction analysis. The

moment difference ratio is found to be increase in Kbs value but the same is found to decrease with

increase in Kfs. For relatively flexible superstructure resting on relatively flexible foundation, the

0

0.5

1

1.5

2

2.5

3

0.0050.05

Kbs=0.005

Kbs=0.01

Kbs=0.1

Kfs per

cen

tag

e o

f B

end

ing

mo

men

t v

ari

ati

on

0

3

6

9

12

0.0050.05

Kbs=0.005

Kbs=0.01

Kbs=0.1

Kfs p

ercen

tag

e o

f b

end

ing

mo

men

t v

ari

ati

on

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6

10

14

18

22

26

30

0.0050.05

Kbs=0.005

Kbs=0.01

Kbs=0.1

Kfs

per

cen

tag

e o

f b

end

ing

mo

men

t v

ari

ati

on

-1

2

5

8

11

0.0050.05

Kbs=0.005

Kbs=0.01

Kbs=0.1

Kfs

per

cen

tag

e o

f b

end

ing

mo

men

t v

ari

ati

on

maximum moment ratio is found to be about 10.70% and the same decreases to 1.63%, if the

foundation becomes relatively rigid.

4.7 Bending moment in end of Exterior Beam foundation

The effect of bending moment in end of exterior beam is computed for progressive loading and

conventional method difference ratio is plotted in figure-4.8 (a). It is seen from the graph that for

most of ranges of Kfs the difference ratio increases for all ranges of Kbs. When the foundation is

flexible I,e. 0.01 Kfs 0.005 the variation is found to be maximum for all values of Kbs, at the

other hand for relatively rigid foundations I,e. 0.1 Kfs 0.01 the variation is minimum for all

Kbs.The sagging moment seen at exterior (end of column support). When the super structure is

relatively rigid and the foundation is relatively flexible, the maximum moment difference ratio is

16.40%, the same is decreases to 7.22%, if the foundation becomes relatively rigid. The moment

obtained by conventional method is higher compare with progressive loading of interaction analysis.

4.8 Bending moment in end of Interior Beam foundation

The effect of bending moment in end of interior beam is computed for progressive loading and

conventional method difference ratio is plotted in figure-4.8 (b).The sagging moment seen at interior

(end of column support).for a relatively flexible superstructure resting on relatively flexible

foundation, the maximum moment difference ratio is found to be 10.52% and the same is decreases

to about 4.07%, if the foundation becomes relatively rigid. The moment obtained by progressive

loading is higher compare with conventional method of interaction analysis.

Figure-4.8 (a) Figure-4.8 (b)

Figures 4.8(a, b) : Bending moment variations in End of Exterior and Interior beam of foundation

4.9 Hogging Moment in Centre of Interior Beam of Foundation

The effect of bending moment in center of interior beam is computed for progressive

loading and conventional method difference ratio is plotted in figure-4.9(a).The moment

obtained by progressive loading is higher compare with conventional method of interaction

analysis Maximum Hogging moment in foundation beam increases with increase in Kfs

value but is found to vary inversly with Kbs.For the structure which are relatively flexible

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rest on foundation which are relatively flexible the moment difference ratio is found to be

27.75% and same decreases to 22.89%, if foundation becomes relatively rigid.

Figure-4.9(a): Hogging Moment in Centre of Interior Beam of Foundation

5. Conclusions

From the analysis of results the following observations and conclusions can be drawn

I. There will be an enhancement in the design moment values of the floor beams,

foundation beams and columns. The enhancement depends on progressive loading

and rigidity of superstructure and foundation elements.

II. The study shows that, it is important to study the variation in foundation beams and

also in ground storey of columns and floor beams due to the effect of progressive

loading.

III. To minimize the enhancement in moment values, the superstructure elements should

be proportioned that the superstructure becomes relatively flexible (0.005

and foundation becomes relatively rigid (0.01

IV. By making foundation relatively rigid the superstructure moment increse can be

reduced but this will result in the enhancement of foundation moments. So a

judicious proportionimg of superstructure and foundation elements should be made.

References

[1] Brown P.T. and Yu Si K.R. (1986). Load sequence and structure-foundation Interaction. Journal of

Structural Engineering, ASCE. 112(3): 481-488.

[2] Venkatasubramanya B.V (1989) “Framed structure soil interaction with particular reference to partial loss

of and presence of underground voids”. Ph.D Thesis I.I.sc., Bangalore, India.

[3] Agrawal R. and Hora M.S. (2012). Nonlinear interaction behaviour of plane frame-layered soil system

subjected to seismic loading. Structural Engineering and Mechanics. 11(6): 711-734.

[4] Al-Shamrani M.A. and Al-Mashary F.A. (2003). A Simplified Computation of the Interactive Behavior

between Soils and Framed Structures. Engineering Science. 16(1): 37-60.

20

23

26

29

32

35

0.0050.05

Kbs=0.005

Kbs=0.01

Kbs=0.1

Kfs per

cen

tage

of

ben

din

g m

om

ent

var

iati

on

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[5] A. Mandal, D. Moitra, and S.C. Dutta, (2000). Soil-structure interaction on building frame: a small scale

model study, Int. J. Struct., 18(2), 92-108.

[6] Colasanti R.J. and Horvath J.S. (2010). Practical Subgrade Model for Improved Soil-Structure Interaction

Analysis: Software Implementation. Practice Periodical on Structural Design and Construction. 15(4): 1-9.

[7] IS:456-2000, “Code of Practice Plain and Reinforced Concrete” , Bureau of Indian Standards, New Delhi,

India.

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Progressive Loading and Analysis of RC-Plane Framed …ijifr.com/pdfsave/17-04-2015306V2-E8-027.pdfstructural elements subjected to general static vertical loading ... with beam footing