ENVIRONMENTAL ENGINEERING CONCRETE STRUCTURES

1
ENVIRONMENTAL ENGINEERING CONCRETE STRUCTURES

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

2
OUTLINE

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

3
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.

4
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

5
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.

6
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.

7
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.

8
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.

9
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

10
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.

11
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

12
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

13
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.

14
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

15
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.

16
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.

17
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.

18
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

19
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

20
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.)

21
Table A-5 showing the ring tension values
22
Table A-7, A-12 showing the moment and shear
23
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

24
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.

25
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

26
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

27
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

28
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

29
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

30
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.

31
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

32
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).
33
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.

34
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