ENVIRONMENTAL ENGINEERING CONCRETE STRUCTURESCE 498 Design ProjectSeptember 26, 2006

OUTLINEINTRODUCTION

PERFORMANCE CRITERIA

DESIGN LOADS AND CONDITIONS

STRUCTURAL DESIGN

CONCRETE MIX DESIGN

ADDITIONAL CRITERIA

INTRODUCTIONWhy concrete?Concrete is particularly suited for this application because it will not warp or undergo change in dimensionsWhen properly designed and placed it is nearly impermeable and extremely resistant to corrosionHas good resistance to natural and processing chemicalsEconomical 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 tanksNo prestressed tanks

INTRODUCTIONHow 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 installedCompared to these loads, the actual live loads are smallImpact 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 stressesComplicated 3D FEM analysis are not required. Simple analysis using tabulated results in handbooks etc.

PERFORMANCE CRITERIAWhat 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 segregationCrack width is minimizedAdequate reinforcing steel is usedImpervious protective coating or barriers can also be usedThis is not as economical and dependable as the approach of mix design, stress & crack control, and adequate reinforcem.

PERFORMANCE CRITERIAHow 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 curingUse 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

PERFORMANCE CRITERIAHow to increase durability?Concrete should be resistant to the actions of chemicals, alternate wetting and drying, and freeze-thaw cyclesAir-entrainment in the concrete mix helps improve durability. Add air-entrainment agentsReinforcement must have adequate cover to prevent corrosionAdd good quality fly-ash or pozzolansUse moderately sulphate-resistant cement

DESIGN LOADS AND CONDITIONSAll 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 IBCContent loadsRaw Sewage 63 lb/ft3Grit from grit chamber .. 110 lb/ft3Digested sludge aerobic. 65 lb/ft3Digested sludge anerobic 70 lb/ft3For other numbers see ACI 350. Live loadsCatwalks etc 100 lb/ft2Heavy equipment room 300 lb/ft2

DESIGN LOADS AND CONDITIONSWhen using the LRFD (strength or limit states design approach), the load factors and combinations from ACI 318 can be used directly with one major adjustmentThe load factors for both the lateral earth pressure H and the lateral liquid pressure F should be taken as 1.7The 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 UIn calculations for reinforcement in direct tension, including hoop tension, the required strength should be 1.65 UThe required design strength for reinforcement in shear should be calculated as fVs> 1.3 (Vu-fVc)For compression use 1.0 U

STRUCTURAL DESIGNLarge 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 tensionWalls supporting both interior water loads and exterior soil pressure must be designed to support the full effects of each load individuallyCannot use one load to minimize the other, because sometimes the tank is empty.

STRUCTURAL DESIGNLarge 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 crackingThe 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 courseIt contains tabulated coefficients for calculating stress distributions etc. for different boundary conditions and can be used directly for designIt also includes some calculation and design examples

STRUCTURAL DESIGNReinforced 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 barsMaximum bar spacing should not exceed 12 in.

The amount of shrinkage and temperature reinforcement is a function of the distance between joints in the directionShrinkage and temperature reinforcement should not be less thank the ratios given in Figure 2.5 or ACI 350The reinforcement should not be spaced more than 12 in. and should be divided equally between the two surfaces

STRUCTURAL DESIGNFigure showing minimum shrinkage reinforcement and table showing minimum cover for reinforcement required

STRUCTURAL DESIGNIn order to prevent leakage, the strain in the tension reinforcement has to be limitedThe 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

STRUCTURAL DESIGNServiceability for normal exposuresFor 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.

STRUCTURAL DESIGNImpact, vibration, and torque issuesWhen heavy machines are involved, an appropriate impact factor of 1.25 can be used in the designMost of the mechanical equipment such as scrapers, clarifiers, flocculators, etc. are slow moving and will not cause structural vibrationsMachines that cause vibration problems are forced-draft fans and centrifuges for dewatering clarifier sludge or digester sludgeThe 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

STRUCTURAL DESIGNTo 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 1.5Methods 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 columnThis column must be designed to resist the torque shear without undergoing failure

MATERIAL DESIGNThe cement should conform to:Portland cement ASTM C150, Types I, IA, II, IIA, .Blended hydraulic cement ASTM C595Expansive hydraulic cement ASTM C845They 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 usedBut, pozzolan content not exceed 25% by weight of cementitous materials

MATERIAL DESIGNThe air entraining admixture should conform to ASTM C260Improves resistant to freeze-thaw cyclesImproves workability and less shrinkageIf chemical admixtures are used, they should meet ASTM C494. The use of water reducing admixtures is recommendedThe maximum water-soluble chloride ion content, expressed as a % of cement, contributed by all ingredients of the concrete mix should not exceed 0.10%

MATERIAL DESIGNMix proportioning all material should be proportioned to produce a well-graded mix of high density and workability28 day compressive strength of 3500 psi where the concrete is not exposed to severe weather and freeze-thaw28 day compressive strength of 4000 psi where the concrete is exposed to severe weather and freeze-thawType of cement as mentioned earlierMaximum water-cement ratio = 0.45If pozzolan is used, the maximum water-cement + pozzolan ratio should be 0.45Minimum cementitious material content1.5 in. aggregate max 517 lb/yd31 in. aggregate max 536 lb/yd30.75 in. aggregate max 564 lb/yd3

MATERIAL DESIGNAir entrainment requirements 5.5 1 % for 1.5 in. aggregate6.0 1 % for 1.0 or 0.75 in. aggregateSlump requirements1 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 coatMoist or membrane curing should commence immediately after form removal

ADDITIONAL CRITERIAConcrete 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 corrosionReinforcement embedded in quality concrete is well protected against corrosive chemicalsThere are only special cases where additional protective coatings or barriers are requiredThe 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

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

ENVIRONMENTAL ENGINEERING CONCRETE STRUCTURESCE 498 Design ProjectNovember 16, 21, 2006

OUTLINEINTRODUCTION

LOADING CONDITIONS

DESIGN METHOD

WALL THICKNESS

REINFORCEMENT

CRACK CONTROL

INTRODUCTIONConventionally reinforced circular concrete tanks have been used extensively. They will be the focus of our lecture todayStructural 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 distributionProper spacing and detailing of construction jointsUse of quality concrete placed using proper construction proceduresA thorough review of the latest report by ACI 350 is important for understanding the design of tanks.

LOADING CONDITIONSThe 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

LOADING CONDITIONSThe 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.

DESIGN METHODSTwo approaches exist for the design of RC membersStrength design, and allowable stress design.Strength design is the most commonly adopted procedure for conventional buildingsThe 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.

Design MethodsService 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 levelThe computed stresses serve as the indices of performance of the structure.

DESIGN METHODSThe load combinations to determine the required strength (U) are given in ACI 318. ACI 350 requires two modificationsModification 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 overflowModification 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 UWhere, sanitary coefficient = 1.3 for flexure, 1.65 for direct tension, and 1.3 for shear beyond the capacity provided by the concrete.

WALL THICKNESSThe 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:

WALL THICKNESSEffects of shrinkageFigure 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.

WALL THICKNESSThe 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 equilibriumConcrete tensile stress is fcs = xCEcSteel compressive stress is fss= (1-x)CEsSection force equilibrium. So, rfss=fcsSolve for x from above equation for force equilibriumThe resulting stresses are:fss=CEs[1/(1+nr)]and fcs=CEs[r/(1+nr)]

The concrete stress due to an applied ring or hoop tension of T will be equal to:T * Ec/(EcAc+EsAs) = T * 1/[Ac+nAs] = T/[Ac(1+nr)]

The total concrete tension stress = [CEsAs + T]/[Ac+nAs]

WALL THICKNESSThe 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 As=T/fs and realize Ac=12tSubstitute in equation on previous slide to calculate tension stress in the concrete. Limit the max. concrete tension stress to fc = 0.1 fcThen, the wall thickness can be calculated as t = [CEs+fsnfc]/[12fcfs]* TThis formula can be used to estimate the wall thicknessThe values of C, coefficient of shrinkage for RC is in the range of 0.0002 to 0.0004. Use the value of C=0.0003Assume fs= allowable steel tension =18000 psiTherefore, wall thickness t=0.0003 T

WALL THICKNESSThe 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 = [CEs+fs]/[Acfs+nT]*TFor the case of T=24,000 lb, n=8, Es=29*106 psi, C=0.0003 and Ac=12 x 10 = 120 in3If 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.

REINFORCEMENTThe 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 effectsThe amount of temperature and shrinkage reinforcement is dependent on the length between construction joints

REINFORCEMENTThe 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 barsThe 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 318Chapter 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.

CRACK CONTROLCrack widths must be minimized in tank walls to prevent leakage and corrosion of reinforcementA criterion for flexural crack width is provided in ACI 318. This is based on the Gergely-Lutz equation z=fs(dcA)1/3Where z = quantity limiting distribution of flexural re-bardc = 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.

CRACK CONTROLIn 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 computedFor ACI 350, z has a limiting value of 115 k/in. For severe environmental exposures, z = 95 k/in.

ANALYSIS OF VARIOUS TANKSWall with fixed base and free top; triangular loadWall with hinged base and free top; triangular load and trapezoidal loadWall with shear applied at topWall with shear applied at baseWall with moment applied at topWall with moment applied at base

CIRCULAR TANK ANALYSISIn 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, assumeHeight = H = 20 ft.Diameter of inside = D = 54 ft.Weight of liquid = w = 62.5 lb/ft3Shrinkage coefficient = C = 0.0003Elasticity of steel = Es = 29 x 106 psiRatio of Es/Ec = n = 8Concrete compressive strength = fc = 4000 psiYield strength of reinforcement = fy = 60,000 psi

CIRCULAR TANK ANALYSISIt 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 AppendixEach 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.)

Table A-5 showing the ring tension values

Table A-7, A-12 showing the moment and shear

CIRCULAR TANK ANALYSISIn 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/Dt=9.0wu 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/ft3Therefore, wu HR = 175.3 x 20 x 54/2 = 94, 662 lb/ft3The 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

CIRCULAR TANK ANALYSISA 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 displacementFigure compares the ring tension for tanks with free sliding base, fixed base, and hinged base.

CIRCULAR TANK ANALYSISWhich 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 checkThe maximum tensile stress in the concrete under service loads including the effects of shrinkage isfc = [CEsAs + Tmax, unfactored]/[Ac+nAs] = 272 psi < 400 psiTherefore, adequate

CIRCULAR TANK ANALYSISThe 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/ft3Therefore wuH3 = 138.1 x 203 = 1,104,800 ft-lb/ftThe computed moments along the height are shown in the Table.The figure includes the moment for both the hinged and fix conditions

CIRCULAR TANK ANALYSISThe 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 designDepending 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 w=0.0278Required As = w bdfc/fy = 0.167 in2

CIRCULAR TANK ANALYSISr=0.167/(12 x 7.5) = 0.00189rmin = 200/Fy = 0.0033 > 0.00189Use #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 fc=4000 psi is Vc = 2 (fc)0.5 bwd = 11,384 kipsTherefore, f Vc = 0.85 x 11,284 = 9676 kipsThe applied shear is given by multiplying wu H2 with the coefficient from Table A-12The 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 kipsApplied shear = Vu = 0.092 x wuH2 = 3912 kips < fVc

RECTANGULAR TANK DESIGNThe cylindrical shape is structurally best suited for tank construction, but rectangular tanks are frequently preferred for specific purposesRectangular tanks can be used instead of circular tanks when the footprint needs to be reducedRectangular 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 tanksThe behavior of circular tanks is axisymmetric. That is the reason for our analysis of only unit width of the tankThe ring tension in circular tanks was uniform around the circumference

RECTANGULAR TANK DESIGNThe design of rectangular tanks is very similar in concept to the design of circular tanksThe 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.

RECTANGULAR TANK DESIGNThe 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 processThe lifting force of the water pressure is resisted by the weight of the tank and the weight of soil on top of the slab

RECTANGULAR TANK BEHAVIORMx = 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).

RECTANGULAR TANK BEHAVIORMxy 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 equationsMx=(Mx Coeff.) x q a2/1000My=(My Coeff.) x q a2/1000Mz=(Mz Coeff.) x q a2/1000Mxy=(Mxy Coeff.) x q a2/1000Myz=(Myz Coeff.) x q a2/1000These 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.

RECTANGULAR TANK BEHAVIORThe 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 reinforcementThe Principal of Minimum Resistance may be used for determining the equivalent orthogonal moments for designWhere positive moments produce tension:Mtx = Mx + |Mxy|Mty = My + |Mxy|However, if the calculated Mtx < 0, then Mtx=0 and Mty=My + |Mxy2/Mx| > 0If the calculated Mty < 0Then Mty = 0 and Mtx = Mx + |Mxy2/My| > 0Similar equations for where negative moments produce tension