ENVIRONMENTAL ENGINEERING CONCRETE STRUCTURES

1
ENVIRONMENTAL ENGINEERING CONCRETE STRUCTURES

• CE 498 Design Project
• September 26, 2006

2
OUTLINE

• INTRODUCTION
• PERFORMANCE CRITERIA
• DESIGN LOADS AND CONDITIONS
• STRUCTURAL DESIGN
• CONCRETE MIX DESIGN
• ADDITIONAL CRITERIA

3
INTRODUCTION

• Why concrete?
• Concrete is particularly suited for this
  application because it will not warp or undergo
  change in dimensions
• When properly designed and placed it is nearly
  impermeable and extremely resistant to corrosion
• Has good resistance to natural and processing
  chemicals
• Economical but requires significant quality
  control
• What type of structure?
• Our focus will be conventionally reinforced
  cast-in-place or precast concrete structures
• Basically rectangular and/or circular tanks
• No prestressed tanks

4
INTRODUCTION

• How should we calculate loads?
• Design loads determined from the depth and unit
  weight of retained material (liquid or solid),
  the external soil pressure, and the equipment to
  be installed
• Compared to these loads, the actual live loads
  are small
• Impact and dynamical loads from some equipments
• What type of analysis should be done?
• The analysis must be accurate to obtain a
  reasonable picture of the stress distribution
  in the structure, particularly the tension
  stresses
• Complicated 3D FEM analysis are not required.
  Simple analysis using tabulated results in
  handbooks etc.

5
PERFORMANCE CRITERIA

• What are the objective of the design?
• The structure must be designed such that it is
  watertight, with minimum leakage or loss of
  contained volume.
• The structure must be durable it must last for
  several years without undergoing deterioration
• How do you get a watertight structure?
• Concrete mix design is well-proportioned and it
  is well consolidated without segregation
• Crack width is minimized
• Adequate reinforcing steel is used
• Impervious protective coating or barriers can
  also be used
• This is not as economical and dependable as the
  approach of mix design, stress crack control,
  and adequate reinforcem.

6
PERFORMANCE CRITERIA

• How to design the concrete mix?
• The concrete mix can be designed to have low
  permeability by using low water-cement ratio and
  extended periods of moist curing
• Use water reducing agents and pozzolans to reduce
  permeability.
• How to reduce cracking?
• Cracking can be minimized by proper design,
  distribution of reinforcement, and joint spacing.
• Shrinkage cracking can be minimized by using
  joint design and shrinkage reinforcement
  distributed uniformly

7
PERFORMANCE CRITERIA

• How to increase durability?
• Concrete should be resistant to the actions of
  chemicals, alternate wetting and drying, and
  freeze-thaw cycles
• Air-entrainment in the concrete mix helps improve
  durability. Add air-entrainment agents
• Reinforcement must have adequate cover to prevent
  corrosion
• Add good quality fly-ash or pozzolans
• Use moderately sulphate-resistant cement

8
DESIGN LOADS AND CONDITIONS

• All the loads for the structure design can be
  obtained from ASCE 7 (2006), which is the
  standard for minimum design loads for building
  structures endorsed by IBC
• Content loads
• Raw Sewage 63 lb/ft3
• Grit from grit chamber .. 110 lb/ft3
• Digested sludge aerobic. 65 lb/ft3
• Digested sludge anerobic 70 lb/ft3
• For other numbers see ACI 350.
• Live loads
• Catwalks etc 100 lb/ft2
• Heavy equipment room 300 lb/ft2

9
DESIGN LOADS AND CONDITIONS

• When using the LRFD (strength or limit states
  design approach), the load factors and
  combinations from ACI 318 can be used directly
  with one major adjustment
• The load factors for both the lateral earth
  pressure H and the lateral liquid pressure F
  should be taken as 1.7
• The factored load combination U as prescribed in
  ACI 318 must be increased by durability
  coefficients developed from crack width
  calculation methods
• In calculations for reinforcement in flexure, the
  required strength should be 1.3 U
• In calculations for reinforcement in direct
  tension, including hoop tension, the required
  strength should be 1.65 U
• The required design strength for reinforcement in
  shear should be calculated as fVsgt 1.3 (Vu-fVc)
• For compression use 1.0 U

10
STRUCTURAL DESIGN

• Large reinforced concrete reservoirs on
  compressible soil may be considered as beams on
  elastic foundations.
• Sidewalls of rectangular tanks and reservoirs can
  be designed as either (a) cantilever walls fixed
  at the bottom, or (b) walls supported at two or
  more edges.
• Circular tanks normally resist the pressure from
  contents by ring tension
• Walls supporting both interior water loads and
  exterior soil pressure must be designed to
  support the full effects of each load
  individually
• Cannot use one load to minimize the other,
  because sometimes the tank is empty.

11
STRUCTURAL DESIGN

• Large diameter tanks expand and contract
  appreciably as they are filled and drained.
• The connection between wall and footing should
  either permit these movements or be strong enough
  to resist them without cracking
• The analysis of rectangular wall panels supported
  at three or four sides is explained in detail in
  the PCA publication that is available in the
  library and on hold for the course
• It contains tabulated coefficients for
  calculating stress distributions etc. for
  different boundary conditions and can be used
  directly for design
• It also includes some calculation and design
  examples

12
STRUCTURAL DESIGN

• Reinforced concrete walls at least 10 ft. high
  that are in contact with liquids should have a
  minimum thickness of 12 in.
• The minimum thickness of any minor member is 6
  in., and when 2 in. cover is required then it is
  at least 8 in.
• For crack control, it is preferable to use a
  large number of small diameter bars for main
  reinforcement rather than an equal are of larger
  bars
• Maximum bar spacing should not exceed 12 in.
• The amount of shrinkage and temperature
  reinforcement is a function of the distance
  between joints in the direction
• Shrinkage and temperature reinforcement should
  not be less thank the ratios given in Figure 2.5
  or ACI 350
• The reinforcement should not be spaced more than
  12 in. and should be divided equally between the
  two surfaces

13
STRUCTURAL DESIGN

• Figure showing minimum shrinkage reinforcement
  and table showing minimum cover for reinforcement
  required

14
STRUCTURAL DESIGN

• In order to prevent leakage, the strain in the
  tension reinforcement has to be limited
• The strain in the reinforcing bars is transferred
  to the surrounding concrete, which cracks.
• Hence, minimizing the stress and strain in the
  reinforcing bar will minimize cracking in the
  concrete.
• Additionally, distributing the tension
  reinforcement will engage a greater area of the
  concrete in carrying the strain, which will
  reduce cracking even more.
• The strength design requires the use of loads,
  load combinations and durability coefficients
  presented earlier

15
STRUCTURAL DESIGN

• Serviceability for normal exposures
• For flexural reinforcement located in one layer,
  the quantity Z (crack control factor of ACI)
  should not exceed 115 kips/in.
• The designer can use the basic Gergley-Lutz
  equation for crack width for one way flexural
  members.
• The reinforcement for two-way flexural member may
  be proportioned in each direction using the above
  recommendation too.
• Alternate design by the working stress method
  with allowable stress values given and tabulated
  in ACI 350. Do not recommend this method for us.

16
STRUCTURAL DESIGN

• Impact, vibration, and torque issues
• When heavy machines are involved, an appropriate
  impact factor of 1.25 can be used in the design
• Most of the mechanical equipment such as
  scrapers, clarifiers, flocculators, etc. are slow
  moving and will not cause structural vibrations
• Machines that cause vibration problems are
  forced-draft fans and centrifuges for dewatering
  clarifier sludge or digester sludge
• The key to successful dynamic design is to make
  sure that the natural frequency of the support
  structure is significantly different from
  frequency of disturbing force

17
STRUCTURAL DESIGN

• To minimize resonant vibrations, ratio of the
  natural frequency of the structure to the
  frequency of the disturbing force must not be in
  the range of 0.5 to 1.5.
• It should preferably be greater than 1.5
• Methods for computing the structure frequency are
  presented in ACI 350 (please review if needed)
• Torque is produced in most clarifiers where the
  entire mechanism is supported on a central column
• This column must be designed to resist the torque
  shear without undergoing failure

18
MATERIAL DESIGN

• The cement should conform to
• Portland cement ASTM C150, Types I, IA, II, IIA,
  .
• Blended hydraulic cement ASTM C595
• Expansive hydraulic cement ASTM C845
• They cannot be used interchangeably in the same
  structure
• Sulfate-resistant cement must have C3A content
  not exceeding 8. This is required for concrete
  exposed to moderate sulfate acctak (150 to 1000
  ppm)
• Portland blast furnace slab cement (C595 may be
  used)
• Portland pozzolan cement (C595 IP) can also be
  used
• But, pozzolan content not exceed 25 by weight of
  cementitous materials

19
MATERIAL DESIGN

• The air entraining admixture should conform to
  ASTM C260
• Improves resistant to freeze-thaw cycles
• Improves workability and less shrinkage
• If chemical admixtures are used, they should meet
  ASTM C494. The use of water reducing admixtures
  is recommended
• The maximum water-soluble chloride ion content,
  expressed as a of cement, contributed by all
  ingredients of the concrete mix should not exceed
  0.10

20
MATERIAL DESIGN

• Mix proportioning all material should be
  proportioned to produce a well-graded mix of high
  density and workability
• 28 day compressive strength of 3500 psi where the
  concrete is not exposed to severe weather and
  freeze-thaw
• 28 day compressive strength of 4000 psi where the
  concrete is exposed to severe weather and
  freeze-thaw
• Type of cement as mentioned earlier
• Maximum water-cement ratio 0.45
• If pozzolan is used, the maximum water-cement
  pozzolan ratio should be 0.45
• Minimum cementitious material content
• 1.5 in. aggregate max 517 lb/yd3
• 1 in. aggregate max 536 lb/yd3
• 0.75 in. aggregate max 564 lb/yd3

21
MATERIAL DESIGN

• Air entrainment requirements
• 5.5 1 for 1.5 in. aggregate
• 6.0 1 for 1.0 or 0.75 in. aggregate
• Slump requirements
• 1 in. minimum and 4 in. maximum
• Concrete placement according to ACI 350 (read
  when you get a chance)
• Curing using sprinkling, ponding, using moisture
  retaining covers, or applying a liquid
  membrane-forming compound seal coat
• Moist or membrane curing should commence
  immediately after form removal

22
ADDITIONAL CRITERIA

• Concrete made with proper material design will be
  dense, watertight, and resistant to most chemical
  attack. Under ordinary service conditions, it
  does not require additional protection against
  chemical deterioration or corrosion
• Reinforcement embedded in quality concrete is
  well protected against corrosive chemicals
• There are only special cases where additional
  protective coatings or barriers are required
• The steel bars must be epoxy coated (ASTM A775)
• In special cases, where H2S evolves in a stagnant
  unventilated environment that is difficult or
  uneconomical to correct or clean regularly, a
  coating may be required

23
REFERENCES

• ACI 350 (1989)
• Books on reserve in the library
• Emails from Jeffrey Ballard, structural engineer,
  HNTB. He will visit to talk with us soon.

24
ENVIRONMENTAL ENGINEERING CONCRETE STRUCTURES

• CE 498 Design Project
• November 16, 21, 2006

25
OUTLINE

• INTRODUCTION
• LOADING CONDITIONS
• DESIGN METHOD
• WALL THICKNESS
• REINFORCEMENT
• CRACK CONTROL

26
INTRODUCTION

• Conventionally reinforced circular concrete tanks
  have been used extensively. They will be the
  focus of our lecture today
• Structural design must focus on both the strength
  and serviceability. The tank must withstand
  applied loads without cracks that would permit
  leakage.
• This is achieved by
• Providing proper reinforcement and distribution
• Proper spacing and detailing of construction
  joints
• Use of quality concrete placed using proper
  construction procedures
• A thorough review of the latest report by ACI 350
  is important for understanding the design of
  tanks.

27
LOADING CONDITIONS

• The tank must be designed to withstand the loads
  that it will be subjected to during many years of
  use. Additionally, the loads during construction
  must also be considered.
• Loading conditions for partially buried tank.
• The tank must be designed and detailed to
  withstand the forces from each of these loading
  conditions

28
LOADING CONDITIONS

• The tank may also be subjected to uplift forces
  from hydrostatic pressure at the bottom when
  empty.
• It is important to consider all possible loading
  conditions on the structure.
• Full effects of the soil loads and water pressure
  must be designed for without using them to
  minimize the effects of each other.
• The effects of water table must be considered for
  the design loading conditions.

29
DESIGN METHODS

• Two approaches exist for the design of RC members
• Strength design, and allowable stress design.
• Strength design is the most commonly adopted
  procedure for conventional buildings
• The use of strength design was considered
  inappropriate due to the lack of reliable
  assessment of crack widths at service loads.
• Advances in this area of knowledge in the last
  two decades has led to the acceptance of strength
  design methods
• The recommendations for strength design suggest
  inflated load factors to control service load
  crack widths in the range of 0.004 0.008 in.

30
Design Methods

• Service state analyses of RC structures should
  include computations of crack widths and their
  long term effects on the structure durability and
  functional performance.
• The current approach for RC design include
  computations done by a modified form of elastic
  analysis for composite reinforced steel/concrete
  systems.
• The effects of creep, shrinkage, volume changes,
  and temperature are well known at service level
• The computed stresses serve as the indices of
  performance of the structure.

31
DESIGN METHODS

• The load combinations to determine the required
  strength (U) are given in ACI 318. ACI 350
  requires two modifications
• Modification 1 the load factor for lateral
  liquid pressure is taken as 1.7 rather than 1.4.
  This may be over conservative due to the fact
  that tanks are filled to the top only during leak
  testing or accidental overflow
• Modification 2 The members must be designed to
  meet the required strength. The ACI required
  strength U must be increased by multiplying with
  a sanitary coefficient
• The increased design loads provide more
  conservative design with less cracking.
• Required strength Sanitary coefficient X U
• Where, sanitary coefficient 1.3 for flexure,
  1.65 for direct tension, and 1.3 for shear beyond
  the capacity provided by the concrete.

32
WALL THICKNESS

• The walls of circular tanks are subjected to ring
  or hoop tension due to the internal pressure and
  restraint to concrete shrinkage.
• Any significant cracking in the tank is
  unacceptable.
• The tensile stress in the concrete (due to ring
  tension from pressure and shrinkage) has to kept
  at a minimum to prevent excessive cracking.
• The concrete tension strength will be assumed 10
  fc in this document.
• RC walls 10 ft. or higher shall have a minimum
  thickness of 12 in.
• The concrete wall thickness will be calculated as
  follows

33
WALL THICKNESS

• Effects of shrinkage
• Figure 2(a) shows a block of concrete with a
  re-bar. The block height is 1 ft, t corresponds
  to the wall thickness, the steel area is As, and
  the steel percentage is r.
• Figure 2(b) shows the behavior of the block
  assuming that the re-bar is absent. The block
  will shorten due to shrinkage. C is the shrinkage
  per unit length.
• Figure 2(c) shows the behavior of the block when
  the re-bar is present. The re-bar restrains some
  shortening.
• The difference in length between Fig.2(b) and
  2(c) is xC, an unknown quantity.

34
WALL THICKNESS

• The re-bar restrains shrinkage of the concrete.
  As a result, the concrete is subjected to
  tension, the re-bar to compression, but the
  section is in force equilibrium
• Concrete tensile stress is fcs xCEc
• Steel compressive stress is fss (1-x)CEs
• Section force equilibrium. So, rfssfcs
• Solve for x from above equation for force
  equilibrium
• The resulting stresses are
• fssCEs1/(1nr) and fcsCEsr/(1nr)
• The concrete stress due to an applied ring or
  hoop tension of T will be equal to
• T Ec/(EcAcEsAs) T 1/AcnAs
  T/Ac(1nr)
• The total concrete tension stress CEsAs
  T/AcnAs

35
WALL THICKNESS

• The usual procedure in tank design is to provide
  horizontal steel As for all the ring tension at
  an allowable stress fs as though designing for a
  cracked section.
• Assume AsT/fs and realize Ac12t
• Substitute in equation on previous slide to
  calculate tension stress in the concrete.
• Limit the max. concrete tension stress to fc
  0.1 fc
• Then, the wall thickness can be calculated as
• t CEsfsnfc/12fcfs T
• This formula can be used to estimate the wall
  thickness
• The values of C, coefficient of shrinkage for RC
  is in the range of 0.0002 to 0.0004.
• Use the value of C0.0003
• Assume fs allowable steel tension 18000 psi
• Therefore, wall thickness t0.0003 T

36
WALL THICKNESS

• The allowable steel stress fs should not be made
  too small. Low fs will actually tend to increase
  the concrete stress and potential cracking.
• For example, the concrete stress fc
  CEsfs/AcfsnTT
• For the case of T24,000 lb, n8, Es29106 psi,
  C0.0003 and Ac12 x 10 120 in3
• If the allowable steel stress is reduced from
  20,000 psi to 10,000 psi, the resulting concrete
  stress is increased from 266 psi to 322 psi.
• Desirable to use a higher allowable steel stress.

37
REINFORCEMENT

• The amount size and spacing of reinforcement has
  a great effect on the extent of cracking.
• The amount must be sufficient for strength and
  serviceability including temperature and
  shrinkage effects
• The amount of temperature and shrinkage
  reinforcement is dependent on the length between
  construction joints

38
REINFORCEMENT

• The size of re-bars should be chosen recognizing
  that cracking can be better controlled by using
  larger number of small diameter bars rather than
  fewer large diameter bars
• The size of reinforcing bars should not exceed
  11. Spacing of re-bars should be limited to a
  maximum of 12 in. Concrete cover should be at
  least 2 in.
• In circular tanks the locations of horizontal
  splices should be staggered by not less than one
  lap length or 3 ft.
• Reinforcement splices should confirm to ACI 318
• Chapter 12 of ACI 318 for determining splice
  lengths.
• The length depends on the class of splice, clear
  cover, clear distance between adjacent bars, and
  the size of the bar, concrete used, bar coating
  etc.

39
CRACK CONTROL

• Crack widths must be minimized in tank walls to
  prevent leakage and corrosion of reinforcement
• A criterion for flexural crack width is provided
  in ACI 318. This is based on the Gergely-Lutz
  equation zfs(dcA)1/3
• Where z quantity limiting distribution of
  flexural re-bar
• dc concrete cover measured from extreme tension
  fiber to center of bar located closest.
• A effective tension area of concrete
  surrounding the flexural tension reinforcement
  having the same centroid as the reinforcement,
  divided by the number of bars.

40
CRACK CONTROL

• In ACI 350, the cover is taken equal to 2.0 in.
  for any cover greater than 2.0 in.
• Rearranging the equation and solving for the
  maximum bar spacing give max spacing z3/(2 dc2
  fs3)
• Using the limiting value of z given by ACI 350,
  the maximum bar spacing can be computed
• For ACI 350, z has a limiting value of 115 k/in.
• For severe environmental exposures, z 95 k/in.

41
ANALYSIS OF VARIOUS TANKS

• Wall with fixed base and free top triangular
  load
• Wall with hinged base and free top triangular
  load and trapezoidal load
• Wall with shear applied at top
• Wall with shear applied at base
• Wall with moment applied at top
• Wall with moment applied at base

42
CIRCULAR TANK ANALYSIS

• In practice, it would be rare that a base would
  be fixed against rotation and such an assumption
  would lead to an improperly designed wall.
• For the tank structure, assume
• Height H 20 ft.
• Diameter of inside D 54 ft.
• Weight of liquid w 62.5 lb/ft3
• Shrinkage coefficient C 0.0003
• Elasticity of steel Es 29 x 106 psi
• Ratio of Es/Ec n 8
• Concrete compressive strength fc 4000 psi
• Yield strength of reinforcement fy 60,000 psi

43
CIRCULAR TANK ANALYSIS

• It is difficult to predict the behavior of the
  subgrade and its effect upon restraint at the
  base. But, it is more reasonable to assume that
  the base is hinged rather than fixed, which
  results in more conservative design.
• For a wall with a hinged base and free top, the
  coefficients to determine the ring tension,
  moments, and shears in the tank wall are shown in
  Tables A-5, A-7, and A-12 of the Appendix
• Each of these tables, presents the results as
  functions of H2/Dt, which is a parameter.
• The values of thickness t cannot be calculated
  till the ring tension T is calculated.
• Assume, thickness t 10 in.
• Therefore, H2/Dt (202)/(54 x 10/12) 8.89
  (approx. 9 in.)

44
Table A-5 showing the ring tension values
45
Table A-7, A-12 showing the moment and shear
46
CIRCULAR TANK ANALYSIS

• In these tables, 0.0 H corresponds to the top of
  the tank, and 1.0 H corresponds to the bottom of
  the tank.
• The ring tension per foot of height is computed
  by multiplying wu HR by the coefficients in Table
  A-5 for the values of H2/Dt9.0
• wu for the case of ring tension is computed as
• wu sanitary coefficient x (1.7 x Lateral
  Forces)wu 1.65 x (1.7 x 62.5) 175.3 lb/ft3
• Therefore, wu HR 175.3 x 20 x 54/2 94, 662
  lb/ft3
• The value of wu HR corresponds to the behavior
  where the base is free to slide. Since, it cannot
  do that, the value of wu HR must be multiplied by
  coefficients from Table A-5

47
CIRCULAR TANK ANALYSIS

• A plus sign indicates tension, so there is a
  slight compression at the top, but it is very
  small.
• The ring tension is zero at the base since it is
  assumed that the base has no radial displacement
• Figure compares the ring tension for tanks with
  free sliding base, fixed base, and hinged base.

48
CIRCULAR TANK ANALYSIS

• Which case is conservative? (Fixed or hinged
  base)
• The amount of ring steel required is given by
• As maximum ring tension / (0.9 Fy)
• As 67494/(0.9 60000) 1.25 in2/ft.
• Therefore at 0.7H use 6bars spaced at 8 in. on
  center in two curtains.
• Resulting As 1.32in2/ft.
• The reinforcement along the height of the wall
  can be determined similarly, but it is better to
  have the same bar and spacing.
• Concrete cracking check
• The maximum tensile stress in the concrete under
  service loads including the effects of shrinkage
  is
• fc CEsAs Tmax, unfactored/AcnAs 272
  psi lt 400 psi
• Therefore, adequate

49
CIRCULAR TANK ANALYSIS

• The moments in vertical wall strips that are
  considered 1 ft. wide are computed by multiplying
  wuH3 by the coefficients from table A-7.
• The value of wu for flexure sanitary
  coefficient x (1.7 x lateral forces)
• Therefore, wu 1.3 x 1.7 x 62.5 138.1 lb/ft3
• Therefore wuH3 138.1 x 203 1,104,800 ft-lb/ft
• The computed moments along the height are shown
  in the Table.
• The figure includes the moment for both the
  hinged and fix conditions

50
CIRCULAR TANK ANALYSIS

• The actual restraint is somewhere in between
  fixed and hinged, but probably closer to hinged.
• For the exterior face, the hinged condition
  provides a conservative although not wasteful
  design
• Depending on the fixity of the base, reinforcing
  may be required to resist moment on the interior
  face at the lower portion of the wall.
• The required reinforcement for the outside face
  of the wall for a maximum moment of 5,524
  ft-lb/ft. is
• Mu/(f fc bd2) 0.0273 (where d t cover
  dbar/2)
• From the standard design aid of Appendix A, take
  the value of 0.0273 and obtain a value for w from
  the Table.
• Obtain w0.0278
• Required As w bdfc/fy 0.167 in2

51
CIRCULAR TANK ANALYSIS

• r0.167/(12 x 7.5) 0.00189
• rmin 200/Fy 0.0033 gt 0.00189
• Use 5 bars at the maximum allowable spacing of
  12 in.
• As 0.31 in2 and r 0.0035
• The shear capacity of a 10 in. wall with fc4000
  psi is
• Vc 2 (fc)0.5 bwd 11,384 kips
• Therefore, f Vc 0.85 x 11,284 9676 kips
• The applied shear is given by multiplying wu H2
  with the coefficient from Table A-12
• The value of wu is determined with sanitary
  coefficient 1.0 (assuming that no steel rft.
  will be needed)
• wuH2 1.0 x 1.7 x 62.5 x 202 42,520 kips
• Applied shear Vu 0.092 x wuH2 3912 kips lt
  fVc

52
RECTANGULAR TANK DESIGN

• The cylindrical shape is structurally best suited
  for tank construction, but rectangular tanks are
  frequently preferred for specific purposes
• Rectangular tanks can be used instead of circular
  tanks when the footprint needs to be reduced
• Rectangular tanks are used where partitions or
  tanks with more than one cell are needed.
• The behavior of rectangular tanks is different
  from the behavior of circular tanks
• The behavior of circular tanks is axisymmetric.
  That is the reason for our analysis of only unit
  width of the tank
• The ring tension in circular tanks was uniform
  around the circumference

53
RECTANGULAR TANK DESIGN

• The design of rectangular tanks is very similar
  in concept to the design of circular tanks
• The loading combinations are the same. The
  modifications for the liquid pressure loading
  factor and the sanitary coefficient are the same.
  
• The major differences are the calculated moments,
  shears, and tensions in the rectangular tank
  walls.
• The requirements for durability are the same for
  rectangular and circular tanks. This is related
  to crack width control, which is achieved using
  the Gergely Lutz parameter z.
• The requirements for reinforcement (minimum or
  otherwise) are very similar to those for circular
  tanks.
• The loading conditions that must be considered
  for the design are similar to those for circular
  tanks.

54
RECTANGULAR TANK DESIGN

• The restraint condition at the base is needed to
  determine deflection, shears and bending moments
  for loading conditions.
• Base restraint conditions considered in the
  publication include both hinged and fixed edges.
• However, in reality, neither of these two
  extremes actually exist.
• It is important that the designer understand the
  degree of restraint provided by the reinforcing
  that extends into the footing from the tank wall.
  
• If the designer is unsure, both extremes should
  be investigated.
• Buoyancy Forces must be considered in the design
  process
• The lifting force of the water pressure is
  resisted by the weight of the tank and the weight
  of soil on top of the slab

55
RECTANGULAR TANK BEHAVIOR
Mx moment per unit width about the x-axis
stretching the fibers in the y direction when the
plate is in the x-y plane. This moment determines
the steel in the y (vertical direction).
My moment per unit width about the y-axis
stretching the fibers in the x direction when the
plate is in the x-y plane. This moment determines
the steel in the x (horizontal direction).
Mz moment per unit width about the z-axis
stretching the fibers in the y direction when the
plate is in the y-z plane. This moment determines
the steel in the y (vertical direction).
56
RECTANGULAR TANK BEHAVIOR

• Mxy or Myz torsion or twisting moments for
  plate or wall in the x-y and y-z planes,
  respectively.
• All these moments can be computed using the
  equations
• Mx(Mx Coeff.) x q a2/1000
• My(My Coeff.) x q a2/1000
• Mz(Mz Coeff.) x q a2/1000
• Mxy(Mxy Coeff.) x q a2/1000
• Myz(Myz Coeff.) x q a2/1000
• These coefficients are presented in Tables 2 and
  3 for rectangular tanks
• The shear in one wall becomes axial tension in
  the adjacent wall. Follow force equilibrium -
  explain in class.

57
RECTANGULAR TANK BEHAVIOR

• The twisting moment effects such as Mxy may be
  used to add to the effects of orthogonal moments
  Mx and My for the purpose of determining the
  steel reinforcement
• The Principal of Minimum Resistance may be used
  for determining the equivalent orthogonal moments
  for design
• Where positive moments produce tension
• Mtx Mx Mxy
• Mty My Mxy
• However, if the calculated Mtx lt 0,
• then Mtx0 and MtyMy Mxy2/Mx gt 0
• If the calculated Mty lt 0
• Then Mty 0 and Mtx Mx Mxy2/My gt 0
• Similar equations for where negative moments
  produce tension