effects of soil structure interaction on cylindrical water ... · effects of soil structure...

The Indian Concrete Journal September 201656

POINT OF VIEW POINT OF VIEW

Effects of soil structure interaction on cylindrical water tanksVirendra P. Dehadrai and R.K. Ingle

The recommendations of codes IS 3370:2009 and IS 3370:1967 as regards to consideration of the end condition of cylindrical wall are conflicting. Vichare and Inamdar have given analytical solutions for tanks resting on deformable soils. These cylindrical tanks are analysed using FEM and the results are validated. In this paper cylindrical tanks of various sizes (

a) (

values)

,

i. Cylindrical Wall with

(i.e. H=3.5, D=20 and t=0.25m)

ii. Cylindrical Wall with

. (i.e. H=3.5, D=13 and t=0.175m)

iii. Cylindrical Wall with

(i.e. H=3.5, D=10 and t=0.15m)

iv. Cylindrical Wall with

(i.e. H=3.5, D=6 and t=0.15m) The analysis is performed for tanks with

= 2.45,5.4,8.61 and 13.61, however only the

results for wall of the tank with

= 5.4 are presented in Figure 2 for hoop force and moment.

= 5.4

= 5.4

values) and with/without toe are analysed to arrive at variation in wall and base slab forces due to change in foundation stiffness. Effect of soil structure interaction (SSI) on base of the tank with variation in modulus of subgrade reaction in plan is also presented.

1. IntRoDuctIonThe analysis of water retaining structures are generally done mainly using coefficients given in PCA [1] and IS 3370 [2], which consider standard boundary conditions at the bottom of wall i.e. hinged or fixed. Considering the approximation involved, the method of continuity analysis was promoted by Jain & Jaikrishna [3] and A S Arya [4]. It is interesting to see the recommendations of IS 3370:2009 [5] and IS 3370:1967 [2] as regards to consideration of the end condition of cylindrical wall as verbatim given below, which are conflicting;

IS 3370:1967 mentions (vide Cl 5.4.b of Part II) that “It is difficult to restrict rotation or settlement of the base slab and it is advisable to provide vertical reinforcement as if the walls were fully fixed at the base, in addition to the reinforcement required to resist horizontal ring tension for hinged at base conditions of walls, unless the appropriate amount of fixity at the base is established by analysis with due consideration to the dimensions of the base slab, the type of joint between the wall and slab and, where applicable, the type of soil supporting the base slab.” Also ( vide Cl 3.1.2 of Part IV) it mentions that “It may be difficult to predict the behaviour of the sub grade and its effect upon the restraint at the base, but it is more reasonable to assume that the base is hinged than fixed, and the hinge-based assumption gives a safer design.”

IS 3370:2009 on other hand mention (vide Cl 6.4.b of Part II) “Unless the extent of fixity at the base is established by analysis with due consideration to the dimensions of the base slab, the type of joint between the wall and slab and the type of soil supporting the base slab it is advisable to assume wall to be fully fixed at the base.”

Vichare and Inamdar [6] have given analytical solutions for tanks resting on deformable soils. They have combined results given by Timoshenko and Krieger [7], which give complete solution for the circular plate on elastic foundation with results provided by Kelkar and Sewell [8] incorporating flexibility of raft into calculation of design forces for a circular water tank. Involved formulas are arrived at to find the forces in wall and base slab. This numerical problem is validated by FEM using a reputed software.

To verify the wall behaviour of cylindrical tank resting on deformable soils, it was proposed to study the cylindrical water tank with and without toe for various configurations (varying

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

, where “H” is height , “D” is the diameter and “t” is thickness of cylindrical wall) resting on uniform strata of soil stiffness (k) 20, 60, 100, 160 and 200 MPa/m (abbreviated as 20K, 60K, 100K, 160K and 200K). The tank is analysed by Finite Element Analysis (FEA). These models are also analysed for wall hinged at base and fixed at base cases for comparison purpose. The results of Hoop and Vertical Moment in wall and moments in base slab for various soil stiffness k, are presented. Tanks are considered as resting on ground or underground and hence analysis for three cases i.e water inside, soil outside and both water inside along with soil outside are considered. The self-weight of tank is considered in all the cases as acting downward. Site conditions may require placing tank on soils of varying stiffness. Therefore the effect of the varying soil stiffness below tank base on forces in wall is also studied and results are presented.

The Indian Concrete Journal September 2016 57

POINT OF VIEW

2. AnAlysIs of cylInDRIcAl tAnKs on unIfoRm soIl stRAtAFor validation of the FEM, a cylindrical ground water tank as considered by Vichare and Inamdar [6] is considered and the results were validated. The results are in agreement. Annexure A gives the comparison of results. After validation of the procedure, cylindrical tanks of different configurations as given below are considered and the results are presented for tanks without and with toe. (Figure 1).

Cylindrical Wall with

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 2.45 (i.e. H = 3.5, D = 20 and t = 0.25 m)


a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 5.4 (i.e. H = 3.5, D = 13 and t = 0.175 m)


a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 8.16 (i.e. H=3.5, D=10 and t = 0.15 m)


a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 13.61 (i.e. H=3.5, D=6 and t = 0.15 m)

The results with and without toe when tank is full are presented below.

i.

ii.

iii.

iv.

2.1 Tank with water inside without toe

The analysis is performed for tanks with

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 2.45, 5.4, 8.61 and 13.61, however only the results for wall of the tank with

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 5.4 are presented in Figure 2 for hoop force and moment. The moments in base slab are presented in Table 1 for the same tank.

From the above results the following observation are summarised,

It is evident from the above studies that the effect of SSI in cylindrical wall forces is predominant because of downward concentrated self-weight of wall acting around periphery of the tank and non-uniform pressure on soil.

i.

Table 1. Moment in base slab for tank without toe (kN-m)

2.45

5.4

8.16

13.61

Soil stiffness (MPa/m)

20 60 100 160 200

-ve +ve -ve +ve -ve +ve -ve +ve -ve +ve

2.45 6.8 6.3 2.3 5.9 0.4 6.0 (+1.18) 6.19 (+1.88) 6.18

5.4 3.9 3.4 1.3 3.0 0.3 3.1 (+0.63) 2.99 (+1.02) 2.87

8.16 3.4 1.2 1.5 2.1 0.7 2.1 0.42 2.02 (+0.26) 1.92

13.16 4.4 2.0 2.7 1.8 2.0 1.6 1.44 1.51 1.47 1.54

(-ve Moment – Tension at bottom of slab near wall, +ve Moment – Tension at top of slab)



For tanks without toe, the response of the cylindrical tank wall on elastic foundation is nearer to boundary condition of wall hinged at base. It is seen that the bending moment causing tension on water face at base is absent for soil stiffness values from k=20 (soft strata) to 200 MPa/m (hard strata).

For moment in wall, values obtained by considering wall as hinged form the upper bound except for tanks on very soft soils with soil stiffness k=20 to 60 MPa/m, and at top where moments are negligible.

From the studies with various configurations of the tanks it is evident that the variation in hoop and bending moment in wall due to SSI cannot be correlated with shape and size of the tank i.e.

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

value. As such SSI needs to be done for all the cylindrical tanks without toe.

It is presumed that the hoop and bending moment forces results will lie between two boundary conditions i.e. fixed base and hinged base. The results shows that for the cylindrical tanks resting on soft soils having stiffness less than 60 MPa/m, the hoop tension and bending moment at center is more than hinged base case.

From the results it can be seen that there is significant change in the design force values for wall and base slab as the founding soil stiffness is changed.

As soil stiffness increase, moment in base slab near wall due to water load increases and that due to self-weight decreases. As such the combination forces due

ii.

iii.

iv.

v.

vi.

vii.

to water and self weight vary, changing –ve and +ve moments in base slab based on the soil stiffness

2.2 Tank with water inside with toe

It is evident from the above that the effect of SSI in cylindrical wall forces is predominant because of self-weight of wall acting around periphery of the tank. The effect is more pronounced for smaller tanks where more deflection around the wall inflicts more hoop tension in wall, than wall hinged condition. Here it was proposed to check the effect of extension of the base slab beyond wall as toe. The analysis is presented for on ground tanks and underground tanks considering toe extension as shown in Figure 1b.

On-ground tanks (With tank full – no soil outside)

The effect of extension of toe on wall will depend on the extent of extension beyond wall. For evaluating the effect, tank with

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 5.4 is presented for two cases with Extension of toe of 300 mm and 450 mm beyond wall. The results are presented in Figures 3 and 4 for 300 and 450 extensions. The moments in base slab are presented in Table 2. Similar studies are done for tanks with

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 2.45 with toe extension of 450 mm, 8.16 & 13.61 with toe extension of 300 mm.

From these results the following observation are made.

There is considerable effect of extent of toe extension on wall forces.

Hoop in wall is less affected than Moment in wall due to extension of the toe.

i.

ii.


POINT OF VIEW

For tanks with toe, the response of the cylindrical tank wall resting on deformable soils is in between wall hinged and fixed at base.

For hoop force in wall, values obtained by considering wall as hinged forms the upper bound and for moments, the fixed end condition moment forms upper bound.

It will be seen that variation in the design force values as the soil stiffness is changed (SSI effect) is reduced considerably with toe extension.

The moments in base slab inside tank reduces as the soil stiffness increases. This is not observed in tanks without toe as the SSI effect is pronounced.

2.3 Underground tanks (With tank empty – soil outside)

To study effect of SSI on underground tanks, the tanks with toe as shown in Figure 5, are analysed with earth load on toe and active earth pressure on wall in addition to self-weight of the tank.

The results are presented in Figures 6 and 7 for 450 extension of toe for tank with

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 5.4.

iii.

iv.

v.

vi.

Table 2. Moment in base slab for on ground tank with toe (kN-m)

2.45

5.4

8.16

13.61

/ Toe extension (mm)

Soil stiffness

20K 60K 100K 160K 200K

Near wall +ve Near wall +ve Near wall +ve Near wall +ve Near wall +ve


2.45/450 4.34 1.51 2.32 4.68 2.88 2.62 4.88 3.41 2.53 5.11 3.82 2.32 5.23 3.99 2.18

5.4/300 1.91 0.49 1.24 2.05 1.34 1.31 2.13 1.68 1.2 2.23 1.95 1.04 2.28 2.06 0.94

5.4/450 3.73 1.37 0.44 2.98 1.5 1.16 3.82 1.60 0.55 3.85 1.67 0.595 3.87 1.71 0.61

8.16/ 300 1.76 0.44 .59 1.83 .836 .62 1.88 1 .54 1.93 1.13 .449 1.96 1.19 .39

13.16/300 1.67 -.14 0.14 1.7 .123 .28 1.72 .22 .29 1.73 0.308 .276 1.74 .34 .27



The moments in base slab are tabulated in Table 3. From the above study following observations are seen,

For underground tanks with toe, the response of the cylindrical tank wall resting on deformable soils is not bounded between wall hinged and fixed at base.

The bending moment in cylindrical wall of underground tank on elastic foundation is more than bending moment in wall hinged/fixed at base.

Substantial moment causing tension on earth face of wall at bottom is observed for underground tanks resting of elastic foundation. This implies that for walls of underground tanks, minimum reinforcement shall be given on both surfaces.

As the soil stiffness increases moment in base slab inside tank reduces.

i.

ii.

iii.

iv.

3. AnAlysIs of cylInDRIcAl tAnKs on VARyIng soIl stRAtA

Many times the site conditions require tanks to be resting on soils of varying stiffness. Two tanks with

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 2.45 and 13.61 without and with toe are considered. The larger tank (

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 2.45) is rested on two types of varying soil stiffness,

Soil stiffness varies as 20, 120 and 200 MPa/m (Figure 8a)- TYPE 1

Soil stiffness varies as 20 and 200 MPa/m (Figure 8b)- TYPE 2

Whereas smaller tank (

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 13.61) is rested on varying soil stiffness TYPE 2 only. The variation of maximum force values (Vertical moment (M), Hoop force (Nø ), Vertical Reaction (Rv) and circumferential moment (Mø)) for larger tank without toe with variation of soil stiffness is presented in Table 4 and for smaller tank in Table 5.

i.

ii.

Table 3. Moment in base slab for underground tank with toe, tank empty (kN-m)

2.45

5.4

8.16

13.61

/ Toe extension (mm)

Soil stiffness “MPa / m”

20 20 20 20 20

Near wall +ve Near wall +ve Near wall +ve Near wall +ve Near wall +ve


2.45/450 -2 -22 -8 -1 -15 -5 -1 -13 -5 -1 -11 -4 -1 -10 -4

5.4/300 -1 -12 -4 -1 -8 -3 -1 -7 -3 -1 -6 -2 -1 -6 -2

5.4/450 -2 -13 -5 -1 -9 -4 -1 -7 -3 -1 -6 -2 0 -6 -2

8.16/300 -1 -10 -4 -1 -6 -3 -1 -5 -2 0 -5 -2 0 -4 -2

13.16/300 -1 -10 -4 0 -6 -3 0 -5 -2 0 -4 -2 0 -4 -2

Table 4. Maximum force values in wall for tank with

2.45

5.4

8.16

13.61

= 2.45 (without toe) for uniform soil stiffness 20 to 200 MPa/m and on soil with varying stiffness

Soil stiffness(MPa/m)

M(kN-m)

Nø (kN)

Rv (kN)

Mø (kN-m)

Type 1 16 203 74 4

Type 2 17 203 100 4

20 10 189 20 4

60 8 170 20 2

100 8 163 20 2

160 7 158 20 1

200 7 155 20 1

Fixed 17 113 20 3

Pinned 8 167 20 2


POINT OF VIEW

Table 6 and 7 gives variation of maximum force values for larger and smaller tank respectively for tank with toe with variation of soil stiffness

From the above, following observation are summarised.

For tanks resting on soil of varying stiffness, the axi-symmetric disposition of forces as seen in tank resting on soil of uniform stiffness gets disturbed, which means a careful attention is warranted to study forces at different location on wall circumference.

The maximum hoop force in wall of tank placed on soil of varying stiffness for larger tank (

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 2.45) increases by 21.56% over the maximum hoop for Pinned base condition.

The maximum compression in wall of tank placed on soil of varying stiffness for larger tank (

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 2.45) increases by 400% over the compression of wall of tank placed on uniform soil stiffness. This is very significant and will need proper consideration while designing the wall footing.

Vertical moment value in wall of tank placed on soil of varying stiffness for larger tank (

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 2.45) is close to value for fixed base condition.

Circumferential moment value in wall of tank placed on soil of varying stiffness for larger tank (

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 2.45) is close to values for fixed base condition

The maximum hoop force in wall of tank placed on soil of varying stiffness for smaller tank (

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 13.61)

i.

ii.

iii.

iv.

v.

vi.


2.45

5.4

8.16

13.61

= 13.61 (without toe) for soil stiffness 20 to 200 MPa/m and on soil with varying stiffness


M(kN-m)

Nø (kN)

Rv (kN)

Mø (kN-m)

Type 2 9 123 55 3

20 4 103 12 2

60 2 93 12 2

100 2 89 12 0

160 2 86 12 0

200 2 84 12 0

Fixed 4 72 12 1

Pinned 2 84 12 0


2.45

5.4

8.16

13.61

= 2.45 (with toe) for soil stiffness 20 to 200 MPa/m and on soil with varying stiffness


M(kN-m)

Nø (kN)

Rv (kN)

Mø (kN-m)

Type 1 18 158 85 4

Type 2 20 160 113 4

20 12 127 20 2

60 12 126 20 3

100 12 125 20 3

160 12 125 20 3

200 12 125 20 3

Fixed 17 113 20 3

Pinned 8 167 20 2

increases by 46.6% over the maximum hoop for Pinned base condition.

The maximum compression in wall of tank placed on soil of varying stiffness for smaller tank (

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 13.61) increases by 356% over the compression of wall of tank placed on uniform soil stiffness. This is very significant and will need proper consideration while designing the wall footing.

. Vertical moment value in wall of tank placed on soil of varying stiffness for smaller tank (

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 13.61) increases by 128 % over the maximum Vertical moment for Fixed base condition.

vii.

viii.


2.45

5.4

8.16

13.61

= 13.61 (with toe) for soil stiffness 20 to 200 MPa/m and on soil with varying stiffness


M(kN-m)

Nø (kN)

Rv (kN)

Mø (kN-m)

Type 2 5.1 93.4 57.4 2.6

20 2.1 76.4 12.0 0.4

60 2.4 75.6 12.0 0.5

100 2.5 75.2 12.0 0.5

160 2.6 75.0 12.0 0.5

200 2.6 74.8 12.0 0.6

Fixed 3.9 71.9 12.0 0.8

Pinned 1.8 83.9 12.1 0.4



Circumferential moment value in wall of tank placed on soil of varying stiffness for smaller tank (

a) (

values)

,


(i.e. H=3.5, D=20 and t=0.25m)


. (i.e. H=3.5, D=13 and t=0.175m)


(i.e. H=3.5, D=10 and t=0.15m)






= 5.4

= 5.4

= 13.61 ) increases by 250 % over the maximum Circumferential moment for Fixed base condition.

4. conclusIonsThe analysis of water retaining structures is very critical as it need to be designed for limited crack width. Proper analysis helps in designing these structures for full utilization of their complete life. The conclusions drawn here will help in preparing proper mathematical model for analysis of water retaining structures and understanding the effect of SSI.

The suggestion of IS 3370:2009 to assume cylindrical wall fixed at base may lead to design of wall seriously deficient in hoop resistance.

The behavior of cylindrical tank wall on elastic foundation for almost all practical structures lies between wall hinged at base and wall fixed at base, when base slab is extended beyond wall. Thus it is a good practice to provide wall with wall footing to reduce the effect of SSI.

When tanks are without toe due to pronounced effect of SSI, the moments in base slab as soil stiffness vary change unpredictably. When the tanks are provided with toe, the base slab moments inside tank reduce as soil stiffness increases.

Design of wall for hoop considering wall hinged at base and for moment considering wall fixed at base will lead to conservative design.

ix.

i.

ii.

iii.

iv.

When the tank rests on soil of varying stiffness there is increase in hoop (20 to 50%) over pinned base condition and vertical moment (lesser for bigger tanks to 400% for smaller tanks) over fixed base condition.

For the tank resting on soil of varying stiffness the axi symmetric force disposition in wall gets disturbed warranting careful consideration along circumference of wall. Different sizes of wall footing along circumference will be required to negate SSI effect in such cases.

References

Portland Cement Association (PCA),Circular concrete tanks without prestressing, PCA, Skokie, Ill.

_____ Indian Standard for Concrete Structures for Storage of Liquids – Code of Practice. Part 1 – General Requirement. Part 2 – Reinforced Concrete Structures.Part 4- Design Tables, IS: 3370 (Part 1,2&4) : 1967, Bureau of Indian Standards, New Delhi.

Jai Krishna, Jain O P, Plain & Reinforces Concrete, Vol I, II, Eighth Edition, Reprint 2007, Nem Chand & Bros, Roorkee, India, 2007.

Arya A S, Data for Analysis and Design of Circular Shell Structures 1-4,Indian Concrete Journal, June 1970

_____Indian Standard for Concrete Structures for Storage of Liquids – Code of Practice. Part 1 – General Requirement. Part 2 – Reinforced Concrete Structures. IS: 3370 (Part 1&2) : 2009, Bureau of Indian Standards, New Delhi.

Vichare S and Inamdar M M, An Analytical Solution For Cylindrical Concrete Tank On Deformable Soil, International Journal of Advanced Structural Engineering, Vol. 2, No. 1, Pages 69-90, July 2010

Timoshenko, S., Woinowsky-Krieger, S., Theory of Plates and Shells, 2nd Edition, McGraw-Hill Book Co., New-York,1959.

Kelkar, V. S. and Sewell, R. T. Fundamentals of the Analysis and Design of Shell Structures, Prentice-Hall Inc., Eaglewood Cliffs, NJ, USA.1987.

v.

vi.

1.

2.

3.

4.

5.

6.

7.

8.

Dr R.K. Ingle is Professor in the Department of Applied Mechanics, Visvesvaraya National Institute of Technology, Nagpur. His research interest is bridges, water tanks, towers and multi storeyed buildings.

Virendra P. Dehadrai holds a BE from VRCE Nagpur; M Tech from IIT Mumbai; pursuing his PhD at VNIT Nagpur. He is Director of M/s Aquades Structural Consultants (P) Ltd, Nagpur, involved into RCC designs, specializing in design of water supply structures. His areas of interest are design of water supply structures, multi-storey structures and earthquake engineering.


POINT OF VIEW

Table A1. Results of FEM, maximum forces M (kN-m) Nø (kN) Moment in base slab

(kN-m)

3.6 143 3.37

AnnEXuRE A

Comparison of results from Vichare and Inamdar with FEM software

effects of soil structure interaction on cylindrical water ... · effects of soil structure...

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