### ANALYSIS OF STRUCTURE

```A Seminar on
SUPERVISED BY
DR.S.K. TIWARI
Associate Professor
SUBMITTED BY
ANKIT SURI
(2010PST125)
DEPARTMENT OF STRUCTURAL ENGINEERING
MALAVIYA NATIONAL INSTITUTE OF TECHNOLOGY, JAIPUR
December 2011
SOIL STRUCTURE INTERACTION
 Soil is a very complex material for the
modeling.
 It is very difficult to model the soil-structure
interaction problem.
 In RCC buildings slab on grade is a very
common construction system e.g. mat
footing
 Very heavy slab loads occur in these
structures.
 For safe and economical design, compute plate
displacement and stresses accurately.
 Difficult to obtain samples for testing producing
results in accordance with ground behavior.
 Necessary to make simplifying assumptions.
SCOPE OF STUDY
 To develop a workable approach for analysis of plates
on elastic foundations.
 Structural Engineers go for simplified assumptions of
rigid foundation
 STAAD Pro is used to incorporate the elasticity of soil
that will provide approximate solutions as close to the
exact solutions.
TYPES OF FOUNDATION MODELS
 The plate-foundation system is idealized as a thin
elastic plate resting on a linearly elastic foundation.
 Various foundation models were given by the
WINKLER MODEL
 Winkler first studied beam on elastic springs
 Model based on the pure bending beam theory.
p = Kw
Here, w = vertical translations of the soil
p = contact pressure
K = modulus of subgrade reaction
 Plates based on Winkler model involve fourth order
differential equation:
4
D ▼ w+ Kw = q
 Here D is the plate flexural rigidity, q is the pressure
on the plate and▼ is the Laplace operator.
 The deformations outside the loaded area were
neglected and taken as zero.
DEFORMATION OF A UNIFORMLY LOADED PLATE
ON TYPICAL WINKLER MODEL
Source : Kerr A. D., "Elastic and visco-elastic foundation models." Journal of
Applied Mechanics, ASCE, 31, 1964. p. 491-498
 Winkler foundation model has two major limitations:
 No interaction between springs is considered.
 The spring constant may depend on a number of
parameters, such as stiffness of beam, geometry of
beam, soil profile, and behavior.
FILONENKO BORODICH MODEL
 Top ends of springs connected to a elastic membrane
stretched to constant tension T.
 It was done to achieve some degree of interaction
between the spring elements,
 Modulus of subgrade reaction is given by
p = Kw – T ▼2 w
FILONENKO-BORODICH FOUNDATION MODEL
Source : Kerr A. D., "Elastic and visco-elastic foundation models." Journal of
Applied Mechanics, ASCE, 31, 1964. p. 491-498
HETENYI MODEL
 Embedded a plate in the three-dimensional case in the
material of the Winkler foundation to accomplish
interaction among springs.
 Assumed that the plate deforms in bending only.
p = Kw + D▼2 ▼2 w
w = vertical translation
D = flexural rigidity of plate.
PASTERNAK FOUNDATION MODEL
 Pasternak assumed shear interactions between spring
elements.
 Connecting the ends of springs to a beam or plate
consisting of incompressible vertical elements, which
can deform only by transverse shear.
p = Kw - G ▼2 w
TIMOSHENKO MODEL
 This model is based on Timoshenko beam theory
 Plane sections still remain plane after bending but are
no longer normal to the longitudinal axis.
 This model considers both the bending and shear
deformations.
 Pressure sustained per unit deformation of subgrade at
specified deformation or pressure level.
 Calculated from plate load test from the plot of q
versus δ
K = q/δ
Here , q = mean bearing pressure
K = modulus of subgrade reaction
δ = mean settlement
PLATE BEARING TEST
Source : Bowles J E., Foundation Analysis and Design, McGraw-Hill, Inc., 1982
DETERMINATION OF MODULUS OF
TERZAGHI
 His work showed that value of k depends upon
dimensions of area acted upon by subgrade reaction.
 He incorporated shape and size effects in his equations
For footings on clay: k = k1 x Bf
For footings on sand : k = k1 *
For rectangular footing on sand of dimensions b x mb:
k = k1*
Where,
k = desired value of modulus of subgrade reaction
k1 = value of k from a plate load test
Bf = footing width
VALUES OF K FOR SLAB ON WINKLER
FOUNDATION
 Boit found that he could obtain a good correlation with the
Winkler model for the maximum moment case by setting
the value of k as follows:
Where,
Es = modulus of elasticity of soil
vs = Poisson’s ratio of the soil
B = modulus of elasticity of the beam
I = moment of inertia of the beam
• Vesic showed that K depends upon the stiffness of the
soil, as well as the stiffness of the structure.
• Vesic’s work extended Boit’s solution by providing the
distribution of deflection, moment, shear and pressure
along the beam.
• He found the continuum solution correlated with the
Winkler model by setting
 Bowles (1982) suggested an indirect method of
approximate estimation of the value of modulus of
 According to him it may be assumed that net ultimate
bearing capacity of a footing occurs at a settlement of
25 mm.
 qnu = cNCSC + γ1DfNqSqrw + 0.5 γ2BN γS γrw’
k =
= 40 qnu
Values of modulus of subgrade reaction
(suggested by Bowles 1982)
Type of Soil
Loose sand
Medium dense sand
Dense sand
Clayey medium dense sand
Silty medium dense sand
Clayey soil : qu < 200 Kpa
200<qu<400 Kpa
qu> 800 Kpa
K (KN/m2/m)
4800 - 16000
9600 - 80000
64000 - 128000
32000 - 80000
24000 - 48000
12000 - 24000
24000 - 48000
>48000
PROBLEM DEFINITION AND STRUCTURAL
MODELLING
 STRUCTURAL MODEL
 Three-dimensional structure is modeled for the
analysis utilizing the STAAD Pro software.
 The plan dimensions of the building are 34.92 m x
16.85 m.
 The Structure has 10 (G+9) stories with height of 3.66 m
each.
 The raft is modeled with the structure.
 The total area of the raft is divided into finite number
of plates.
 The soil under the raft slab is represented by a set of
springs for which the spring constants k, adjusted to
reflect the corresponding soil type.
PLAN OF THE STRUCTURE
3 D VIEW OF STRUCTURE
MEMBER AND RAFT SIZES
 BEAM SIZE - 300mm X 450mm
 COLUMN SIZE – 450mm X 600mm
 RAFT SLAB is divided into finite number of plates
 Approximately 1.0m x 1.0m plates are used.
 Thickness is taken as 600mm.
SUPPORTING SOIL MODELLING IN
 STAAD has a facility for automatic generation of
spring supports specified under the SUPPORT
command.
 The modulus of subgrade reaction constant k for each
soil type is taken as 10,000 kN/m3, 45,000 kN/m3, and
95,000 kN/m3, representing soft, medium, and stiff soil,
respectively
 Self weight of floor slabs = 0.15 x 25 = 3.75 kN/m2
 Weight of floor finish (4 inches thick) = 0.1 x 20 = 2
KN/m2
 Weight of flooring (1 inch thick) = 0.025 x 26.70 (marble)
= 0.6675 KN/m2
 Incidental load due to partition wall = 1.0 KN/m2 (as per
clause 3.1.2 of IS 875 Part II)
 Dead load of wall (230 mm thick) = 19 x 0.23 x 3.66 = 16
kN/m
 Dead load of plaster on wall = 2 x 0.012 x 20 x 3.66 =
1.76 kN/m
 Dead load of parapet wall = 19x0.23 x 1.0 + 2 x 0.012 x
20 x 1.0 = 4.85 kN/m
IMPOSED LOAD (IS: 875 - 1987 PART II)
 The magnitude of minimum imposed load which has
to be considered for the structural safety is provided in
IS: 875 -1987 (part II).
 Here imposed load of intensity 3kN/m2 and 4kN/m2
have been taken as per the code and same is applied in
all floors.
 On the roof it is taken as 1.5kN/m2.
SEISMIC LOAD (IS: 1893 - 2002)
 The total design lateral force or design seismic base shear Vb
is computed in accordance with the IS 1893 (Part I) -2002
Vb = Ah x w
Where
 Calculation of base shear is carried out for structure
located in seismic zone IV.
 Z = 0.24
 I = 1.0 considering the structure is of general category.
 R = 3 for OMRF

ELX
 ELZ
 DL
 LL
Where,
ELX = Earth-quake Load in X-direction
ELZ = Earth-quake Load in Z-direction
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
1.5 (DL + IL)
1.2(DL + IL + ELX)
1.2 (DL + IL - ELX)
1.2 (DL + IL + ELZ)
1.2 (DL + IL - ELZ)
1.5 (DL + ELX)
1.5 (D L - ELX)
1.5 (DL + ELZ)
1.5 (DL - ELZ)
0 .9 DL + 1.5 ELX
0 .9 DL - 1.5 ELX
0 .9 DL + 1.5 ELZ
0 .9 DL - 1.5 ELZ
RESULTS AND CONCLUSIONS
 It has been observed that the stiff stratum at the base
does not change the design forces significantly.
 The bending moments at the base of the columns
soils as compared to the medium and soft soil.
 As the stiffness of the soil strata increased, structure
behavior became closer to that observed for rigid
supports.
BENDING MOMENT FOR EXTERIOR
COLUMNS FOR 1.5(DL+LL) TABLE 7.2
Floor
Level
-1
0
1
2
3
4
5
6
7
8
9
MZ (K=10000
KN/m2/m )
Bottom Top
node node
90.23 -4.288
-23.32 22.61
-23.92 25.44
-27.03 28.09
-30.1 30.87
-32.49 33.19
-34.5 35.07
-36.27 36.56
-38.02 38.25
-38.67 44.27
-27.2 35.55
MZ (K= 45000
KN/m2/m )
Bottom Top
node node
71.75
3.88
-17.78 20.44
-24.08 24.61
-26.73 27.57
-29.44 30.19
-31.66 32.35
-33.55 34.11
-35.19 35.52
-36.76 37.06
-37.32 41.57
-29.11 36.51
MZ (K= 95000
KN/m2/m )
MZ
Bottom Top Bottom Top
node node node node
58.22
7.1
-5.78 14.76
-17.38 21.05 -17.6 23.95
-25.01 25.34 -27.59 27.83
-27.49 28.27 -29.49 30.27
-30.06 30.8 -31.86 32.52
-32.19 32.87 -33.74 34.36
-34.01 34.56 -35.37 35.87
-35.59 35.92 -36.79 37.09
-37.09 37.4 -38.15 38.46
-37.62 41.54 -38.57
42
-30.15 37.59 -32.2 39.96
BENDING MOMENT FOR INTERIOR
COLUMNS FOR 1.5(DL+LL) TABLE 7.4
MZ (K=10000
Floor
Level
-1
0
1
2
3
4
5
6
7
8
9
MZ (K= 45000
KN/m2/m )
KN/m2/m )
Bottom Top Bottom Top
node node node node
-71.34 34.43 -33.93 18.76
-15.57 20.89 -7.82 11.38
-22.85 23.55 -13.44 14.24
-24.69 24.53 -15.45 15.36
-24.51 24.76 -15.47 15.76
-24.68 24.43 -15.78 15.57
-23.99 23.64 -15.22 14.92
-23.17 22.83 -14.52 14.23
-22.52 22.3 -13.95 13.74
-22.14 22.26 -13.76 14.16
-22.33 28.4 -13.06 16.72
MZ (K= 95000
KN/m2/m )
MZ
Bottom Top Bottom Top
node node node node
-20.21 12.95 -1.63
1.91
-6.1
8.85
-2.88
4.27
-10.63 11.57 -5.38
6.65
-12.79 12.74 -7.78
7.84
-12.92 13.22 -8.18
8.53
-13.3 13.12 -8.72
8.57
-12.81 12.52 -8.34
8.08
-12.16 11.88 -7.77
7.53
-11.62 11.41 -7.29
7.08
-11.51 11.99 -7.29
7.96
-10.48 13.48 -5.68
7.42
ABRUPT CHANGE IN BENDING MOMENTS AT THE
BASE FOR FOUNDATIONS ON SOFTER SOILS
 Generally this portion of the structure is not given
consideration in most of the practical designs which
are based on the assumption of rigid support system.
DEFLECTION PROFILE FOR CASE OF
FIXED SUPPORT FIG 6.12 (a) (EQX)
DEFLECTION PROFILE FOR CASE OF
ELASTIC SUPPORT FIG 6.12 (b) (EQX)
 For seismic forces, magnitude of bending moments in
the columns and beams of the structure increase with
the increase in modulus of subgrade reaction.
 The structure on soft soil deflects as a whole body (Fig
7.12.)
 The relative displacements between successive floors
are less for structure on soft soils.
BENDING MOMENTS AT SUPPORT OF BEAM
CONNECTED TO EXTERIOR COLUMN FOR EQX TABLE 7.5
Floor Level
-1
0
1
2
3
4
5
6
7
8
9
MZ
(K=10000
MZ
(K= 45000
MZ
(K= 95000
KN/m2/m )
KN/m2/m )
KN/m2/m )
-66.13
-145.49
-152.31
-146.86
-137.6
-124.37
-106.25
-82.38
-52.20
-14.78
5.16
-82.68
-160.56
-165.77
-159.63
-149.74
-136.00
-117.47
-93.29
-62.87
-25.38
-2.30
-88.7
-165.81
-170.47
-164.04
-153.89
-139.94
-121.25
-96.95
-66.44
-28.94
-4.86
MZ
-98.66
-176.13
-179.92
-172.85
-162.12
-147.7
-128.64
-104.07
-73.34
-35.87
-9.89
BENDING MOMENT FOR INTERIOR COLUMNS FOR EQX
TABLE 7.1
MZ (K=10000
Floor
Level
MZ (K= 45000
KN/m2/m )
KN/m2/m )
Bottom Top Bottom Top
node node node node
MZ (K= 95000
KN/m2/m )
MZ
Bottom Top Bottom Top
node node node node
-1
43.03
58.72
81.58
50.88
96.99
47.59
132.59
43.88
0
124.62
-61.32
133.36
-70.07
136.09
-73.02
142.35
-78.43
1
83.7
-76.61
90.08
-83.36
92.4
-85.72
97.32
-90.48
2
75.24
-76.9
82.02
-83.38
84.37
-85.63
89.07
-90.1
3
69.48
-74.61
75.82
-80.76
78
-82.87
82.35
-87.04
4
62.47
-71.04
68.52
-76.92
70.58
-78.91
74.65
-82.83
5
52.8
-65.42
58.61
-71.08
60.58
-72.99
64.43
-76.72
6
40.32
-57.49
45.93
-62.99
47.82
-64.83
51.5
-68.4
7
24.42
-46.36
29.89
-51.74
31.72
-53.54
35.27
-57.03
8
5.45
-33.09
10.79
-38.33
12.57
-40.04
16
-43.31
9
-18.65
5.33
-13.16
-2.17
-11.31
-4.73
-7.65
-9.76
STOREY DRIFT
 For soft soils very significant increase in displacements
of the structure can occur when subjected to lateral
forces due to earthquake.
 For EQX forces deflection at the top floor was 10 to 12%
more for structure supported on soft soils than that
observed for the case of fixed supports.
Storey drift along exterior column
for EQX
Floor Level
0
1
2
3
4
5
6
7
8
9
Fixed
11.512
23.868
36.398
48.657
60.334
71.903
80.541
88.23
93.7
96.81
K=10000
KN/m2/m
13.667
27.329
41.148
54.682
67.627
79.648
90.357
99.321
106.074
110.536
K= 45000
KN/m2/m
12.402
25.229
38.218
50.93
63.054
74.256
84.144
92.283
98.205
101.792
K= 95000
KN/m2/m
12.111
24.752
37.56
50.09
62.037
73.059
82.77
90.726
96.465
99.861
Storey drift along interior column
for EQX
Floor Level
0
1
2
3
4
5
6
7
8
9
Fixed
11.478
23.76
36.277
48.447
60.111
70.892
80.38
88.116
93.6
96.633
K=10000
KN/m2/m
13.426
26.907
40.559
53.941
66.759
78.677
89.297
98.158
104.766
108.958
K= 45000
KN/m2/m
12.281
24.997
37.883
50.509
62.579
73.754
83.635
91.759
97.628
101.067
K= 95000
KN/m2/m
12.024
24.569
37.288
49.752
61.658
72.672
82.395
90.363
96.078
99.352
MORE BM IN MEMBERS DUE TO
DIFFERENTIAL SETTLEMENT IN SOFT SOILS.
 The softer the soil, the more the differential
settlement.
 This differential settlement resulted in an increase in
bending moments of raft slab.
BENDING MOMENT CONTOURS FOR
been studied.
 The moments in the raft have been affected by the
change in the values of the modulus of subgrade
reaction K, which is responsible for differential
settlement of raft slab.
BM variations in raft slab for K = 10000
BM variations in raft slab for K = 45000
BM variations in raft slab for K = 95000
BM variations in raft slab for K = 10000
BM variations in raft slab for K = 45000
BM variations in raft slab for K = 95000 in
 As the value of modulus of subgrade reaction
decreases the differential settlements increase leading
to an increase in both the hogging and sagging
bending moments.
 The hogging moments produce tension at the top and
can cause the foundation to loose contact with soil.
 Hence due consideration must be given to the elastic
nature of soil in design.
RECOMMENDATIONS
 The soil structure interaction must be considered in
the design of structures.
 At the design stage, specific effort must be made to
find the realistic value of modulus of subgrade
reaction depending on the type of soil, so that we can
get the exact design forces for optimum design
solution.
REFERENCES
 Bowles J E., Foundation Analysis and Design, McGraw-
Hill, Inc., 1982
 Kerr A. D., "Elastic and visco-elastic foundation
models." Journal of Applied Mechanics, ASCE, 31,
1964. p. 491-498.
 Daloglu A. T. and Vallabhan C. V. G., "Values of K for
slab on Winkler foundation" Journal of Geotechnical
and Geo-environmental Engineering, Vol. 126, No.5,
2000 p. 361-371.
 Fwa T.F., Shi X.P. and Tan S.A. , "Use of Pasternak
foundation model in concrete pavement analysis"
Journal of Transportation Engineering, Vol. 122, No.4,
1996 p. 323-328
 Horvath J. S., "Modulus of subgrade reaction: new
perspective," Journal of Geotechnical Engineering,
Vol. 109, No. 12, 1983, p. 1591-1596.
 Liou G. S. and Lai S.C., "Structural analysis model for
mat foundations," Journal of Structural Engineering,
Vol. 122, No.9, 1996. p. 1114-1117.
 Mishra R. C. and Chakrabarti S. K., "Rectangular plates
resting on tensionless elastic foundation: some new
results", Journal of Engineering Mechanics, Vol. 122,
No 4, 1996. p. 385-387.
 Shi X.P., Tan SA and Fwa T.F., "Rectangular thick plate
with free with free edges on Pasternak foundation"
Journal of Engineering Mechanics, Vol. 120, No.5, 19711988.
 STAAD Pro V8i, Structural Analysis and Design
Package, Research Engineers.
 Stavridis L. T., "Simplified analysis of layered soilstructure interaction," Journal of Structural
Engineering, Vol. 128, No.2, 2002. p. 224-230.
 Wang C. M., Xiang Y. and Wang Q., 2001,
"Axisymmetric buckling of reddy circular plates on
Pasternak foundation," Journal of Engineering
Mechanics, Vol. 127, No 3
 Yin J-H., "Comparative modeling study of reinforced
beam on elastic foundation" Journal of Geotechnical
and Geo-environmental Engineering, ASCE, 126(3),
2000. p 265-271.
 IS 875(Part 1): 1987: Indian Standard Code of Practice for




IS 875(Part 2): 1987: Indian Standard Code of Practice for