rectangulartanks approximate analysis

Design of Rectangular Concrete TanksApproximate Analysis

The Islamic University of GazaDepartment of Civil Engineering

Design of Rectangular Concrete Tanks

In closed rectangular tanks with sliding base, the full water pressure is resisted horizontally

Deep Tanks

Where H/L>2 and H/B >2 The effect of fixation of the wall will be limited to a

small part at the base The rest of the wall will resist water pressure

horizontally by closed frame action

H

LB

(3/4H)

H

Deep Tanks: Square sections

It is assumed that the maximum internal pressure take place at ¾ H from the top or 1m from the bottom whichever greater

2

2

at support12

at center24

C

m

pLM

pLM

Dire2

34

ct Tension :

Where:

pLT

p H

Mc

Mm

For rectangular tank in which L/B<2 or the tanks are designed as continuous frame subjected to maximum pressure at H/4 from the bottom

The bottom H/4 is designed as a cantilever

Mc

M1m

M2m

L

B(3/4H)

H

Deep Tanks: Rectangular sections

It is assumed that the maximum internal pressure take place at ¾ H from the top

2 2

2

1

2 2

at support12

8

2 224

C

m c

pM L LB B

pLM M

p L LB B

Mc

M1m

M2m

L

B


2

2 22 2 2

8 24m cpB pM M B LB L

Direct Tension in long Wall

Direct Tension in short Wall

Where

2

3

2

:4

pBT

pLT

p H


For rectangular tank in which L/B>2 The long wall are designed as a cantilever The short walls as a slab fixed supported on the long walls The bottom H/4 portion of the short wall is designed as a

cantilever.


Deep Tanks with L/B >2

3

For Long Wall

Dire

634

ct T2

3n

2

ensio

4

baseHM

BT H

BT H

R=H/2

M=H3/6

H


Deep Tanks with L/B >2

2

sup

2

3

34 12

34 24

1 12 4

For Short Walla) Horizontal Moment

a) Vertical Moment

96

3 4

port

center

H BM

H BM

H H HM H

wH2/12

+

-

wH2/24

(3/4H)

H


Deep Tanks with L/B >2 Direct TensionIt is assumed that the end one meter width of the long wall

contribute to direct tension on the short wall

Direct Tension Short Wall

1T H


B) Shallow Tanks

Where H/L and H/B <1/2The water pressure is resisted by vertical action as follows: a) Cantilever walls

Wall fixed to the floor and free at top may act as simple cantilever walls (suitable for H<3 m)

Tension in the floor = Reaction at the base

Free cantilever of height H and supported on the two sides of their length L must be treated as a slab supported on three sides (if L<4 H)

R=H/2

M=H3/6

H

B) Shallow Tanks

b) Wall simply supported at top and fixed at Bottom Wall act as one way slab and resist water pressure in vertical

direction (suitable for H<4.5 m)

R=0.4H

M=H3/15

H

R=0.1H

H3/15

H3/33.5 +

B) Shallow Tanks

c) Wall fixed at top and fixed at Bottom

R=0.35H

M=H3/20

H

R=0.15H

M=H3/20

M=H3/20

M=H3/20

H3/46.6

+

-

C) Medium Moderate Tanks

In moderate or medium tanks where

The water pressure is resisted by vertical and horizontal actionDifferent approximate methods is used to determine the

internal distribution Some of them:a) Approach 1: Deep tank actionb) Approach 2: Strip method (coefficient method)c) General theory of flat plate.

0.5 & 2H HL B


Approach 1: Deep tank actionFor rectangular tank in which L/B<2 or if L/H<2 the tanks are

designed as continuous frame subjected to maximum pressure at H/4 from the bottom

The bottom H/4 is designed as a cantilever

Mc

M1m

M2m

L

B(3/4H)

H


Approach 1: Deep tank actionFor rectangular tank in which L/B>2

The long wall are designed as a cantilever The short walls as a slab fixed supported on the long walls The bottom H/4 portion of the short wall is designed as a

cantilever.


Approach 2: The Strip Method This method gives approximate solution for

rectangular flat plates of constant thickness, supported in four sides and subjected to uniform hydrostatic pressure

Walls and floors supported on four sides and having L/B<2 are treated as two-way slabs.

Grashof, Marcus, or Egyptian code coefficient can be used to evaluate loads transferred in each direction.


Approach 2: The Strip MethodLoad distribution of two-way slabs subjected to triangular

loading is approximately the same as uniform load.

p=pv + ph

Where:p: hydrostatic pressure at specific depthpv: Pressure resisted in the vertical directionph: Pressure resisted in the horizontal direction

Pv Ph

H/4

3H/4


Approach 2: The Strip Method The fixed Moment at bottom due to pressure resisted

vertically

The shear at a

The shear at b is evaluated from equilibrium The moments due to horizontal pressure are evaluated as

discussed before at (3H/4)

2 2

15 117f V hH HM P P

10 540v hH HRa P P

Pv Ph

H/4

3H/4

a

b

Ra

Design of section subjected to eccentric load

If the resultant stress on the liquid side is compression the section is to be designed as ordinary RC cracked section

If the resultant stress on the liquid side is tension the section must have Adequate resistance of cracking Adequate strength

+ve for tension -ve for compression

'2

6 2

r

c

My N fI btM N f

bt bt

Design of section subjected to eccentric tension

Reinforcement for direct tension can be added to reinforcement required to resist bending using strength design method.

'u u uM M P e

Pu

Mu

Pu

Mu’

e

Example 1

0.5 & 2

/ 6 / 5 1.2 2

H HL B

L B

5m

6m

The tank is moderate tank and we will apply the deep tank approach

The tank walls are designed as continuous frame subjected to pressure varying from zero at the top to max. at H/4. The lower H/4 is designed as cantilever

Example 1

2 2 2 2

2 2

1

6 6 5 5 2.58312 12

3 / 4

2.583 3 / 4 3.4 6.59 . /

6 2.583 1.917 4.89 . /8 8

Direct tension in the Wall34 2

3 51 3.4 6.375 /4 2

C

c

m c

p pM L LB B p

p H

M t m m

pL pM M p p t m m

BT H

T t m

LongWall

Mc

M1m

M2m 5m6m

Example 1

2 2

2

6.59 . /

5 2.583 0.542 1.38 . /8 8

Direct tension in the Wall34 2

3 61 3.4 7.6

Sho

5

rtWa

/4

l

2

l

c

m c

M t m m

pL pM M p p t m m

LT H

T t m

Mc

M1m

M2m 5m6m

Example 1

22

52

2

5

Check the Wall thickness against cracking t=40cm

In long wa

Let wall 6 2 300 34.6 /

6 6.59 106.375 100026.3 /

40 100 1ll:

In short

00 40

6 6.59 107.65 100040 10

wall:0 100 4

tb tb

tb tb

tb

T Mf f kg cmbt bt

f kg cm f

f

2

2 26.6 /0

tbkg cm f

Example 1

2

'

40 5 0.7 34.3

5 .7 14.32

6.375 1000 1.7 1.65 4.73 /0.9 4200

14.36.59 1.7 1.3 6.37 1.7 1.310

Direct tension reinf.

a) Horizontal Reinf. -ve. moment r

0

einf.

Long Wall Reinforcement

sy

u

d cmhe cm

TA cm mf

M

5

2

2

12.55 . /

2.61 10 12.550.85 300 1 1 0.002884200 100 34.3 300

0.00288 100 34.3 9.88 /st

t m m

A cm m

d=34.3cm

40cme=14.3

Example 1

'

5

2

2

2

14.34.89 1.7 1.3 6.37 1.7 1.3 8.79 . /100

2.61 10 8.790.85 300 1 1 0.0024200 100 34.3 300

0.002 100 34.3 6.86 /

+ve. moment reinf.

Inside rein 9.88 4.73 14.61 / 16f.Outide rei

@12.5nf

u

st

M t m m

A cm m

cm m cm

26.86 4.73 11.59 / 14. @12.5cm m cm

Example 1

'

5

min2

2,min

0.851.7 1.3 0.5 3.4 0.85 0.9 . /3

2.61 10 0.90.85 300 1 1 0.000224200 100 34.3 300

0.0006 100

b) Verti

40 2.4 /use 5 8mm/m for inside and outside v

cal rein

ertical rein

f

.

.

f

u

st

M t m m

A cm m

(3/4H)

3.4

0.85

2.55

Example 1

2

'

min

,min


a) Horizontal Reinf.+ve. moment reinf

7.65 1000 1.7 1.65 5.67 /0.9 4200

14.31.38 1.7 1.3 7.65 1.7 1.3 0.63 . /100

0.00014

0.00

.

Short Wall Reinforcement

sy

u

st

TA cm mf

M t m m

A

2

2

06 100 40 2.4 /

Outside horizontal reinf.= 2.4+5.67=8.07 / [email protected]

use 5 8mm/m for inside and outside vertical reinf.b) Vertical Reinf.

cm m

cm m use cm

d=34.3cm

40cme=14.3

Example 2

/ 11.25 / 5 2.25 2L B

5m

6m

The long walls are designed as a cantilever and the short wall as a slab fixed supported on the long walls. The bottom H/4 portion of the short wall is designed as a cantilever.

Example 2

23

2

1 3.46.55 . /

6 63Direct tension T= 3 / 4 3.4 5 / 2 6


.3754 2

6.375 1000 1.7 1.65 4.73 /0.9 4200

use 5 8mm/m for inside and o

u

Long Wall Reinforcement

base

sy

HM t m m

BH ton

TA cm mf

'

2

tside horizontal reinf.

6.55 1.7 1.3 14.48 . / 0.00334

0.00334 100 34.3 11.45

a) Vertical R

/ [email protected]

einf.

u

st

M t m m

A cm m use cm

Example 2

22

support

22

32

3 3 / 4 3.4 5 /12 5.31 . /4 12

3 3 / 4 3.4 5 / 24 2.65 . /4 24

3.4 / 96 0.41 . /95

Direct

Horizonta

tension T

l directio

=

n. Short Wall Reinforcement

center

base

BM H t m m

BM H t m m

HM t m m

2

Direct tension reinf. 1 3.4

3.4 1000 1.7 1.65 2.52 /0.9 4200s

y

H ton

TA cm mf

Example 2

'

'

'

14.35.31 1.7 1.3 3.4 1.7 1.3 10.66 . /10014.32.65 1.7 1.3 3.4 1.7 1.3 4.78 . /100

0.41 1.

a) Horizontal Reinf.

b) Vertical Reinf7 1.3 0.91 ..

/

Short Wall Reinforcement

ve

ve

vertical

M t m m

M t m m

M t m m

Tanks Directly Built on the Ground In tanks directly built on the ground, three cases may exist:

Tanks on weak soils or fill Tanks on rigid foundation Tank on compressible soils

Tanks on Weak Soils or Fill The stress on the soil due to the weight of the tank and water is

generally low (6t/m2 for depth of water of 5 m), but in spite of that fact, it is not recommended to construct a tank directly on unconsolidated fill as this may expose the tank to differential settlement due to nonhomogeneous nature of the fill.

Strip footing, Pile footing, or raft are possible solution depend on the soil characteristics at variable depth.

Tanks Directly Built on the Ground Tanks on Rigid Foundations

If we assume that a tank is supported on a rigid foundation then the vertical reaction of the wall will be resisted by the area beneath it, while bending moment M will deflect the floor in a length l beyond which no deformation or bending moments are created.

Deformation due to M will be balanced by the weight of liquid and the floor w 2

At distance 0 2 /24 6wl Mll l M w

EI EI

l

lM

Tanks Directly Built on the Ground Tanks on Rigid Foundations

The part length l of the floor is designed for bending moment M plus axial tensile force equals to the reaction at the base.

The middle part of the floor slab is designed for axial tension force with minimum thickness provide water tightness (15-20cm) and minimum reinforcement min=0.0018 .

Tanks Directly Built on the Ground

Tanks Directly Built on the Ground

f1f2

l

rectangulartanks approximate analysis

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