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Design of Water Tanks:
Part (1)
Prof. Dr. Hamed Hadhoud
Cairo University Prof. Dr. Hamed Hadhoud
1
Cairo University Prof. Dr. Hamed Hadhoud
Types of Tanks
Elevated Tanks
Resting on Soil & Underground Tanks 2
Tank Walls
Walls
Shallow Medium Deep
L
H
L
H
L
H
L/H ≥ 2 H/L ≥ 2 L/H <2 & L/H >0.5
Cairo University Prof. Dr. Hamed Hadhoud
3
Shallow Walls
L
H
• L/H ≥ 2 (for same continuity conditions, or for different continuity conditions) where m is the continuity factor • Loads are transmitted in the vertical direction
gwH
Total Pressure
gwH
Vertical Strip
0.0
Horizontal Strip
Cairo University Prof. Dr. Hamed Hadhoud
1 m
4
2/ HmLm HL
Deep Walls
• H/L ≥ 2 (for same continuity conditions, or for different continuity cond.) where m is the continuity factor
• Loads are transmitted in the horizontal direction • Due to the fixation of the wall to the floor, the
lower portion of the wall doesn’t deflect horizontally resulting in transmitting part of the load in the vertical direction
gwH
Total Pressure
gwH
Vertical Strip Horizontal Strip
L
H H/4
gwH
H/4
Hwg4
3
H/4
Cairo University Prof. Dr. Hamed Hadhoud
5
2/ LmHm LH
Medium Walls
• L/H <2 & L/H >0.5 (for same continuity conditions, or for different continuity cond.)
• Loads are transmitted in both horizontal and vertical directions
• Due to the fixation of the wall to the floor, the lower portion of the wall doesn’t deflect horizontally resulting in transmitting part of the horizontal load in the vertical direction
gwH
Total Pressure Vertical Strip Horizontal Strip
H/4 hP
4
3
H/4
L
H
Pv Ph Pv Ph Ph
Grashoff Tables a and b
or use equations
Pv= a gw H (or b gw H) Ph= b gw H (or a gw H)
Cairo University Prof. Dr. Hamed Hadhoud
44
4
44
4
,
,
LmHm
HmdirLfactorload
LmHm
LmdirHfactorload
LH
H
LH
L
6
HmLmr HL / LmHmror LH /
5.0/&2/ HmLmHmLm HLHL
Tank Floors
gwH
tf
DL = gw tf + floor finishes LL = gw H wf= DL + LL
L1
L2
Grashoff Tables a and b
wa= a wf (in the short direction) wb= b wf (in the long direction)
Or use equations
Cairo University Prof. Dr. Hamed Hadhoud
4
22
4
11
4
112
4
22
4
11
4
221
LmLm
LmdirLinfactorload
LmLm
LmdirLinfactorload
7
2211 / LmLmr 1122 / LmLmror
Continuity Factors
8
Cairo University Prof. Dr. Hamed Hadhoud
End 1 End 2 Factor (m)
Continuous Continuous 0.76
Continuous Hinged 0.87
Continuous Free 1.76
Horizontal Beam
Roof Slab
Free
Statical System of Tank Walls
9
Cairo University Prof. Dr. Hamed Hadhoud
Cantilever H ≤ 3 m
Hinged @ top H ≤ 4 m
Fixed @ top H ≤ 5 m
Horizontal Beam
Roof Slab
tie
tie
tie
Column
Analysis & Design of Elevated
Rectangular Tanks: Vertical Sections
10
Cairo University Prof. Dr. Hamed Hadhoud
1.0 m 1.0 m
w2 w3
w1
w2 w3
w1
OR Top horizontal beam
Case of Cantilever Wall
11
Cairo University Prof. Dr. Hamed Hadhoud
w2 w3
w1
Statically Determinate
BMD
NFD
+
+ +
Case of Wall Hinged @ Top
(Analysis using 3M Equation)
12
Cairo University Prof. Dr. Hamed Hadhoud
w2 w3
w1
A
B C
D Twice Statically Indeterminate From Symmetry: MB = MC
Applying 3M equation @B
)(6)()(20 21 rrLMLHM BB H
L
35045
3
3
3
2
1
HwHwr
24
3
1
2
Lwr
Get MB
HR
Hw
HwM AB
6
4
6
2
32
2Get RA
RA
BMD
MB
Case of Wall Hinged @ Top
(Analysis using Moment Distribution Method)
13
Cairo University Prof. Dr. Hamed Hadhoud
w2 w3
w1
A
B C
D
H
L
HR
Hw
HwM AB
6
4
6
2
32
2Get RA
RA
BMD
MB
Joint B
Member BA BC
K 0.75 I/L 0.5 I/L
D.F.
F.E.M. MBA MBC
Balance M. -(MBA+MBC)*DBA -(MBA+MBC)*DBC
Carry Over M. 0 0
Moment FM1+ Balance M + 0 FM2+ Balance M + 0
BCBA
BABA
KK
KD
BCBA
BCBC
KK
KD
Case K Carry over factor
Fixed-Fixed
K=I/L 0.5
Fixed-Hinged
K=0.75 I/L 0.0
Symmetrical K=0.5 I/L 0.0
Cairo University Prof. Dr. Hamed Hadhoud
Case of Wall Hinged @ Top
(Analysis using Moment Distribution Method)
Fixed-end Moments
14 w= g h 15
3hg
20
3hg
117
3hg
124
3hg
Case of Wall Hinged @ Top
15
Cairo University Prof. Dr. Hamed Hadhoud
w2 w3
w1
A
B C
D Maximum Positive BM in the wall @ point of zero shear
XH
wXR
Q
A2
2
1
0H
L
Get X
Get Mm
RA
X
RA
X
H
w2
32
1 2 XX
H
wXXRM Am
Maximum Positive BM in the floor
BMD
MB
Mm
Mf
Bf MLw
M 8
2
1
Case of Wall Hinged @ Top
16
Cairo University Prof. Dr. Hamed Hadhoud
w2 w3
w1
A
B C
D Tension Force @ floor
Af R
Hw
HwT
2
4
2
3
2H
L
Get Tf
Get T,wallmax
RA
2, 1
max
LwwallT
Maximum Tension Force @ wall bottom
NFD
T,wallmax
Tf
+ + +
Get Tm
H
XwallTTm max,
Tension Force @ wall section with max. +ve BM
Case of Wall Hinged @ Top
17
Cairo University Prof. Dr. Hamed Hadhoud
A
B C
D
Critical sections
1
2
3 4
Section Type M N
1 Air-Side Section Mm Tm
2 Water-Side Section MB T,wall max
3 Water-Side Section MB Tf
4 Air-Side Section Mf Tf
Analysis & Design of Elevated
Rectangular Tanks: Horizontal Sections
18
Cairo University Prof. Dr. Hamed Hadhoud
Consider a strip @ H/4 from wall bottom From symmetry once-statically indeterminate
p1
p1
p2 p2
L1
L2
H/4 p
24246)()(2
3
22
3
112211
LpLpLMLLMML
Get M
2&
2
222
111
LpT
LpT
B.M.D.
M M
M M
1 3
2
4
Design critical sections; 2&3 Water-side 1&4 Air-side
1T 1T
2T
2T
Design of walls as deep beams
(in-plane action)
Cairo University Prof. Dr. Hamed Hadhoud
L
H
• The Tank walls will act as beams carrying the tank floor gravity load
• Those beams are usually deep beams • Check the condition for the deep beam
beamcontinuousforL
H
beamsimpleforL
H
4.0
8.0
19
L
H
L
Design of walls as deep beams
(in-plane action)
Cairo University Prof. Dr. Hamed Hadhoud
min,
87.0
@37.0
@43.0
86.0
S
s
y
US
CT
UU
CT
CT
CT
CT
Af
TA
y
MT
caseanyinHywhere
momentnegativebeamcontinuousforLy
momentpositivebeamcontinuousforLy
beamssimpleforLy
g
20
Design of walls as deep beams
(in-plane action)
Cairo University Prof. Dr. Hamed Hadhoud
21
Detailing
Cairo University Prof. Dr. Hamed Hadhoud
22
Vertical Section
Deep Beam RFt
Water stop (@ construction joint)
Detailing
Cairo University Prof. Dr. Hamed Hadhoud
23
Vertical Section
Deep Beam RFt
Water stop (@ construction joint)
Detailing
Cairo University Prof. Dr. Hamed Hadhoud
24
Vertical Section
Deep Beam RFt
Detailing
Cairo University Prof. Dr. Hamed Hadhoud
25
Vertical Section
Deep Beam RFt
Detailing
Cairo University Prof. Dr. Hamed Hadhoud
26
Vertical Section
Deep Beam RFt
Detailing
Cairo University Prof. Dr. Hamed Hadhoud
27
Vertical Section
Deep Beam RFt
Detailing
Cairo University Prof. Dr. Hamed Hadhoud
28
Horizontal Section
Detailing
Cairo University Prof. Dr. Hamed Hadhoud
29
Horizontal Section
Example (1)
Cairo University Prof. Dr. Hamed Hadhoud
30
Design and give full details for the conduit shown below
Loads
Cairo University Prof. Dr. Hamed Hadhoud
31
Straining Actions
Cairo University Prof. Dr. Hamed Hadhoud
32
Vertical Strip:
Floor Longitudinal Strip:
Vertical Strip
Floor Longitudinal Strip
Design of Critical Sections
Cairo University Prof. Dr. Hamed Hadhoud
33
Design of section (1):
Design of Critical Sections
Cairo University Prof. Dr. Hamed Hadhoud
34
Design of section (2):
34
Design of Critical Sections
Cairo University Prof. Dr. Hamed Hadhoud
35
Design of section (3):
35
Design of Critical Sections
Cairo University Prof. Dr. Hamed Hadhoud
36
Design of section (4):
1.5*18.5= 27.8
7.8
421 27.8
Design of Critical Sections
Cairo University Prof. Dr. Hamed Hadhoud
37
Design of beam action of wall:
Own weight= 25*0.3*2= 15 kN/m’
Floor load=24.5*2*0.79= 38.7 kN/m’
Wu= 1.5*(15+38.7)= 80.6 kN/m’
beamDeepL
H 4.0
5
2
my
mm
Lymomentnegative
my
mm
Lymomentpositive
mHy
CT
CT
CT
CT
CT
74.1
74.185.1537.0
37.0@
74.1
74.115.2543.0
43.0@
74.187.0
mkNLw
M
mkNLw
M
UveU
UveU
.9.16712
56.80
12
.5.20110
56.80
1022
max,
22
max,
momentnegativeforSame
usemmA
mmf
TA
kNy
MT
S
s
y
US
CT
U
veU
184900
308
15.1
360
10005.96
5.9674.1
9.167
2
min,
2
g
Reinforcement Details
Cairo University Prof. Dr. Hamed Hadhoud
38
418 418
Example (2)
Cairo University Prof. Dr. Hamed Hadhoud
39
Calculate bending moments and normal forces due to the shown water pressures using both 3M equation and moment distribution methods (tf=tw=0.3 m)
5 m
5 m
50kN/m2
60 kN/m2
Using 3M equation
Cairo University Prof. Dr. Hamed Hadhoud
40
5m
5m
50kN/m2
60 kN/m2
A D
B C
Twice Statically Indeterminate From Symmetry: MB = MC
Applying 3M equation @B
mkNM
MM
B
BB
.33.108
)24
560
45
550(6)5()55(20
33
kNR
RM
A
AB
20
56
550 2
Using moment distribution method
Cairo University Prof. Dr. Hamed Hadhoud
41
Joint B
Member BA BC
K 0.75 I/L 0.5 I/L
D.F.
F.E.M.
Balance M. -(83.33-125)*0.6 = 25
-(83.33-125)*0.4= 16,67
Carry Over M. 0 0
Moment 108.33 -108.33
6.0
5.075.0
75.0
BCBA
BABA
KK
KD
4.0
5.075.0
5.0
BCBA
BCBC
KK
KD
33.83
15
550 2
BAM
mkN
M BC
.125
12
560 2
kNRRM AAB 2056
550 2
5m
5m
50kN/m2
60 kN/m2
A D
B C
0.0 BABC MM
0.0 BABC MM