RectangularTanks Approximate Analysis

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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
Deep Tanks: Rectangular sections
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
Deep Tanks: Rectangular sections
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: Rectangular sections
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: Rectangular sections
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: Rectangular sections
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
Deep Tanks: Rectangular sections
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
C) Medium Moderate Tanks
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
C) Medium Moderate Tanks
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.
C) Medium Moderate Tanks
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 twoway slabs.
Grashof, Marcus, or Egyptian code coefficient can be used to evaluate loads transferred in each direction.
C) Medium Moderate Tanks
Approach 2: The Strip MethodLoad distribution of twoway 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
C) Medium Moderate Tanks
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
Direct tension reinf.
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
Direct tension reinf.
.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
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 (1520cm) and minimum reinforcement min=0.0018 .
Tanks Directly Built on the Ground
Tanks Directly Built on the Ground
f1f2
l