Objectives: To study the effect of Relative Rigidity of soil interaction behaviour on the rectangular plates.Methods: Analysis was done for a rectangular footing subjected to the eccentric concentrated load in the longitudinal direction up to the middle one third of its longer span dimension, the loss of contact phenomena was analyzed by the finite element method using ANSYS 12.0 software and the Critical Relative Rigidity (CRR) values i.e. the relative rigidity (RR) at which the soil medium just starts experiencing loss of contact with the footing were obtained for various L/B (1.2 to 2.0) ratios up to the two way distribution. Findings: With the increase in the eccentricity of concentrated load the CRR values were decreased and as the L/B ratio increases, the CRR values increased. Improvements: Effect of Relative Rigidity of soil interaction behaviour concept can be extended to different types of plates like square, circular, and loss of contact phenomena should be analysed.

1. http://www.iaeme.com/IJCIET/index.asp 426 editor@iaeme.com
International Journal of Civil Engineering and Technology (IJCIET)
Volume 8, Issue 1, January 2017, pp. 426–430, Article ID: IJCIET_08_01_048
Available online at http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=1
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
EFFECT OF CONCENTRATED ECCENTRIC LOAD
IN LONGITUDINAL DIRECTION OF
RECTANGULAR PLATES ON ELASTIC
FOUNDATION
Sahithi. G
PG Student, Civil Engineering Department,
K L University, Vaddeswaram-522502, A. P, India
Ranga Rao.V
Professor, Civil Engineering Department,
K L University, Vaddeswaram-522502, A. P, India
ABSTRACT
Objectives: To study the effect of Relative Rigidity of soil interaction behaviour on the
rectangular plates.Methods: Analysis was done for a rectangular footing subjected to the
eccentric concentrated load in the longitudinal direction up to the middle one third of its
longer span dimension, the loss of contact phenomena was analyzed by the finite element
method using ANSYS 12.0 software and the Critical Relative Rigidity (CRR) values i.e. the
relative rigidity (RR) at which the soil medium just starts experiencing loss of contact with
the footing were obtained for various L/B (1.2 to 2.0) ratios up to the two way distribution.
Findings: With the increase in the eccentricity of concentrated load the CRR values were
decreased and as the L/B ratio increases, the CRR values increased. Improvements: Effect
of Relative Rigidity of soil interaction behaviour concept can be extended to different types
of plates like square, circular, and loss of contact phenomena should be analysed.
Key words: Relative Rigidity, Critical Relative Rigidity, Rectangular Footing, soil structure
interaction, loss of contact.
Cite this Article: Sahithi. G and Ranga Rao.V, Effect of Concentrated Eccentric Load In
Longitudinal Direction of Rectangular Plates On Elastic Foundation. International Journal
of Civil Engineering and Technology, 8(1), 2017, pp. 426–430.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=1
1. INTRODUCTION
The design of foundations is to be conferred more consideration as there is a great deal of
advancement done in the design of the super-structure. The General design of footing considers that
the footing will be in full contact with soil, but does not happen when a slight footing is lying on a
hard stratum. Loss of contact emerges when the footing is having lesser rigidity than the soil rigidity.
So if the soil interaction studies are considered, it will prompt lessening of the safety factor. The
analysis has done on the effect of the lift-off on the response of circular plate for different loads1,2
, a

2. Effect of Concentrated Eccentric Load In Longitudinal Direction of Rectangular Plates On Elastic
Foundation
http://www.iaeme.com/IJCIET/index.asp 427 editor@iaeme.com
three parameter mathematical model for the analysis of plates on elastic foundations. With the basic
assumption, based on which Winkler’s model is developed, as the entire soil medium can be
considered as springs supporting the footing and the springs are not interconnected to each other.
The springs can carry only the vertical force3
. The conclusion that the contact region is independent
of the level of loading when only one type of loading is applied on circular footings resting on the
sand bed4,5
. They got a partial contact factor as low as 0.571 for a single type of loading. The contact
region changed as the load increased. So this was contradictory to the analytical results presented by
the previous investigators6,7
.
2. METHODOLOGY
To incorporate both the footing and soil properties directly the following equation is adopted
Where
RR Relative Rigidity
Ks Modulus of the sub grade reaction
L footing length
E modulus of elasticity of footing
B footing length in shorter direction
2.1. MODELING AND ANALYSIS USING FINITE ELEMENT METHOD
Analysis is done for a rectangular plates of different L/B Ratios varying from 1.2 to 2 considering
the two way distribution and by selecting the suitable element for the analysis that is shell 63 of the
footings resting on soils of different modulus of sub-grade reaction subjected to the eccentric
concentrated load in the longitudinal direction up to the middle one third of its longer span dimension
, and the thickness of footing is assumed as 300mm and edge length for meshing is considered as
100mm as there no further change in the deflection if the mesh length is reduced than 100 mm and
concentrated load of 500KN is imposed on the plate,analysis is carried out and the vertical
displacement is obtained, shown in Figure 1.
Figure 1 Modeled Rectangular Plate using ANSYS

3. Sahithi. G and Ranga Rao.V
http://www.iaeme.com/IJCIET/index.asp 428 editor@iaeme.com
3. RESULTS AND DISCUSSION
The results that are obtained from the analysis of a rectangular plate using the ANSYS12.0 software
are show in Figure 2. Model calculations are done by taking a Rectangular Footing of size
3.6m×3m(l/b=1.2),4.2m×3m(l/b=1.4),4.8m×3m(l/b=1.6),5.4m×3(l/b=1.8),6m×3m(l/b=2.0) and the
poisons ratio is 0.15 and the thickness Of Footing is assumed as 300mm; RR=100 and assume a
concentrated load of 500kN.The following graphs are plotted from the obtained CRR values by the
analysis in ANSYS 12.0 software, shown in Figure 3.
Figure 2 Vertical Displacement of the plate
Figure 3 C.R.R vs. e/L ratio for a particular L/B Ratio
From Figure 3. it is observed that as the eccentricity of concentrated load increases in the
longitudinal direction, the C.R.R value decreases by 79.5% (for L/B=1.2), 80.32% (for L/B=1.4),
76.4% (for L/B=1.6), 81.75% (For L/B=1.8) 82.22 % (for L/B=2.0), this is because as the L/B ratio
is kept constant the footing rigidity is also constant. If the eccentricity increases there is every chance
of loss of contact to bring to the contact with the soil, Soil rigidity should be reduced hence the
Critical Relative Rigidity (C.R.R) reduces. The comparison between C.R.R and L/B ratio for a

4. Effect of Concentrated Eccentric Load In Longitudinal Direction of Rectangular Plates On Elastic
Foundation
http://www.iaeme.com/IJCIET/index.asp 429 editor@iaeme.com
particular e/L Ratio are show in Figure 4, for a particular eccentricity in the longitudinal direction as
L/B ratio is increasing the CRR value is also increasing by 55%( for e-0),47.6%( for e-0.028),42.7%(
for0.055),39.25%( for e-0.083),37.3%( for e-0.0111),34.14%( for e-0.0139),0%( for e-0.167)this is
because as the L/B ratio rigidity of footing increases hence to have loss of contact the soil RR should
be increased so the CRR is increasing.
Figure 4 C.R.R vs. L/B ratio for a particular e/L Ratio
CONCLUSIONS
Following conclusions have been drawn
• In the longitudinal direction the Critical relative rigidity value decreases for a particular L/B ratio
varying from 1.2 to 2.0 considering the two way distribution with increase in eccentricity.
• As the L/B Ratio is increasing from 1.2 to 2.0 the C.R.R values also increase for a particular
eccentricity.
• For a eccentricity in the longitudinal direction varying from 0 to 0.167 for a particular L/B ratio from
1.2 to 2.0 the reduction in the percentage of C.R.R is from 79.5% to 82.22%.
• For a particular eccentricity as the L/B ratio is increasing from 1.2 to 2.0 the percentage increase in
the C.R.R values in the range of 55% to 34.14%.
• When eccentric concentrated load in the longitudinal direction is applied at the middle one third of
its longer span dimension always a loss of contact will occur.

5. Sahithi. G and Ranga Rao.V
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