The Islamic University Of Gaza Department Of Civil Engineering
The Islamic University of GazaDepartment of Civil EngineeringDesign of Rectangular Concrete Tanks
RECTANGULAR TANK DESIGN The cylindrical shape is structurally bestsuited for tank construction, but rectangulartanks are frequently preferred for specificpurposes Easy formwork and construction processRectangular tanks are used where partitions ortanks with more than one cell are needed.
RECTANGULAR TANK DESIGN The behavior of rectangular tanks isdifferent from the behavior of circular tanks The behavior of circular tanks is axi-symmetric.That is the reason for the analysis to use onlyunit width of the tankThe ring tension in circular tanks was uniformaround the circumference
RECTANGULAR TANK DESIGN The design of rectangular tanks is verysimilar in concept to the design of circulartanks The loading combinations are the same. Themodifications for the liquid pressure loadingfactor and the sanitary coefficient are the same.The major differences are the calculatedmoments, shears, and tensions in therectangular tank walls.
RECTANGULAR TANK DESIGN The requirements for durability are the same forrectangular and circular tanks.The requirements for reinforcement (minimumor otherwise) are very similar to those forcircular tanks.The loading conditions that must be consideredfor the design are similar to those for circulartanks.
RECTANGULAR TANK DESIGN The restraint condition at the base is needed todetermine deflection, shears and bendingmoments for loading conditions. Base restraint conditions considered in the publicationinclude both hinged and fixed edges.However, in reality, neither of these two extremesactually exist.It is important that the designer understand the degreeof restraint provided by the reinforcing bars thatextends into the footing from the tank wall.If the designer is unsure, both extremes should beinvestigated.
RECTANGULAR TANK DESIGN Buoyancy forces must be considered in the designprocess The lifting force of the water pressure is resisted by theweight of the tank and the weight of soil on top of theslab
Plate Analysis Results This chapter gives the coefficients of deflections Cd,Shear Cs and moments (Mx, My, Mxy) for plates withdifferent end conditions. Results are provided from FEManalysis of two dimensional plates subjected to our-ofplane loads.The Slabs was assumed to act as a thin plate.For square tanks the moment coefficient can be takendirectly from the tables in chapter 2.For rectangular tank, adjustments must be made toaccount for redistribution for bending moments toadjacent walls.The design coefficient for rectangular tanks are given inchapter3
Tank Analysis Results This chapter gives the coefficients of deflections Cd andmoments (Mx, My, Mxy). The design are based on FEManalysis of tanks.The shear coefficient Cs given in chapter 2 may be usedfor design of rectangular tanks.The effect of tension force, if significant should berecognized.
RECTANGULAR TANK BEHAVIORMx moment per unit width about the x-axisstretching the fibers in the y direction when theplate is in the x-y plane. This momentdetermines the steel in the y (vertical direction).My moment per unit width about the y-axisstretching the fibers in the x direction when theplate is in the x-y plane. This momentdetermines the steel in the x or z (horizontaldirection).yMz moment per unit width about the z-axiszstretching the fibers in the y direction when theplate is in the y-z plane. This moment determinesthe steel in the y (vertical direction).yx
RECTANGULAR TANK BEHAVIOR Mxy or Myz torsion or twisting moments for plate or wall in the x-yand y-z planes, respectively. All these moments can be computed using the equations2 Mx (Mx Coeff.) x q a /10002 My (My Coeff.) x q a /10002 Mz (Mz Coeff.) x q a /10002 Mxy (Mxy Coeff.) x q a /1000Myz (Myz Coeff.) x q a2/1000These coefficients are presented in Tables of Chapter 2 and 3 forrectangular tanksThe shear in one wall becomes axial tension in the adjacent wall.Follow force equilibrium.
RECTANGULAR TANK BEHAVIOR The twisting moment effects such as Mxy may be used toadd to the effects of orthogonal moments Mx and My forthe purpose of determining the steel reinforcementThe Principal of Minimum Resistance may be used fordetermining the equivalent orthogonal moments for design Where positive moments produce tension: Mtx Mx Mxy Mty My Mxy However, if the calculated Mtx 0, If the calculated Mty 0 then Mtx 0 and Mty My Mxy2/Mx 0Then Mty 0 and Mtx Mx Mxy2/My 0Similar equations for where negative moments producetension
RECTANGULAR TANK BEHAVIOR Where negative 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 0 Then Mty 0 and Mtx Mx - Mxy2/My 0
Moment coefficient for Slabs with various edgeConditions
MultiCell TankCorner of Multicell Tank:Moment coefficients from chapter 3, designated as Lcoefficients, apply to outer or L shaped corners ofmulti-cell tanks.
MultiCell TankThree wall forming T-Shape: If the continuous wall, or top of the T, is part of the long sidesof two adjacent rectangular cells, the moment in the continuouswall at the intersection is maximum when both cells are filled.The intersection is then fixed and moment coefficients,designated as F coefficients, can be taken from Tables ofchapter 2.
MultiCell TankThree wall forming T-Shape: If the continuous wall is part of the short sides of two adjacentrectangular cells, moment at one side of the intersection ismaximum, when the cell on that side is filled while the othercell is empty.For this loading condition the magnitude of moment will besomewhere between the L coefficients and the F coefficients.
MultiCell TankThree wall forming T-Shape:If the unloaded third wall of the unit is disregarded, or itsstiffness considered negligible, moments in the loaded wallswould be the same L coefficients. If the third wall is assumed to have infinite stiffness, thecorner is fixed and the F coefficients apply. The intermediate value representing more nearly the truecondition can be obtained by the formula.nEnd Moments L L F n 2where n: number of adjacent unloaded walls
MultiCell Tank
MultiCell TankIntersecting Walls: If intersecting walls are the walls of square cells,moments at the intersection are maximum when anytwo cells are filled and the F coefficients in Tables 1,2, or 3 apply because there is no rotation of the joint. If the cells are rectangular, moments in the longer ofthe intersecting walls will be maximum when twocells on the same side of the wall under considerationare filled, and again the F coefficients apply.
MultiCell TankIntersecting Walls: Maximum moments in theshorter walls adjacent tothe intersection occurwhen diagonally oppositecells are filled, and for thiscondition the LCoefficients apply.
Example 1Design of Single-Cell Rectangular Tank The tank shown has a clear height of a 3m. horizontalinside dimensions are b 9.0 m and c 6.0 m.Height of the soil against wall is 1.5m.Assume f c 300kg / cm 2 and f y 4200kg / cm 2 The tank will consider fixed at the base and free atAEthe top in this example.C
Example 1 (Design of Rectangular Tank) Design of Wall for Loading Condition 1 (Leakage Test) Design for Shear Forces (Top Free anbd bottom Fixed) According to Case 3 for : b/a 3.0 and c/a 2.0 (Page 2-17)
Example 1 (Design of Rectangular Tank) Assume the wall thickness is 30 cmCheck for shear at bottom of the wallV C s q a 0.5 1 3 3 4.5tonV u 1.4 V 1.4 4.5 6.3ton V c 0.75 f c (b )(d ) 0.53 0.75 300(100)(24.3) /1000 16.7 ton V ud 30 5 1.4 / 2 24.3cm
Example 1 (Design of Rectangular Tank) Check for shear at side edge of the long wallV C s q a 0.37 1 3 3 3.33ton V u 1.4 V 1.4 3.33 4.67tonThis wall is subjected to tensile forces due to shear in the shortwallShear in the short wallV C s q a 0.27 1 3 3 2.43tonV u 1.4 V 1.4 2.43 3.4ton N V c 1 35Ag f c (b )(d ) 3.4 1000 0.53 0.75 1 300(100)(24.3) /1000 35 35 100 16.3ton V u
Example 1 (Design of Rectangular Tank) Note when design of Wall for Loading Condition 3 (coverin place) (Top hinged and bottom fixed) Case 4 page 2-23 for the shear coefficient is smaller thanprevious case.
Example 1 (Design of Rectangular Tank) Design of Wall for Loading Condition 1 (Leakage Test) Design for Vertical Reinforcement (Mx) Moments are in ton.m if coefficients are multiplied byqa2/1000 3*9/1000 0.027Moment coefficients taken from Table 5-1 for b/a 3 and c/a 2For Sanitary Structures Required Strength S d factored load S d U f ySd 1.0 fsfactored loadwhere : unfactored load0.9 420f s 165 from diagramSd 1.61.4 165M ux 1.6 1.4 0.027 M x Coef . 0.0605 M x Coef .
Example 1 (Design of Rectangular Tank)
Example 1 (Design of Rectangular Tank) Vertical Bending Reinforcement: Inside Reinforcement (Mu -7.8 t.m) The required reinforcing of the interior face of the wall isM ux 0.0605 129 7.8 ton .m0.85(300) 2.61(10)5 (7.8) 1 1 0.0036 min4200 100(24.3) 2 (300) A s 0.0036 100 24.3 8.75 cm 2 / mUse 8 12 mm/m on the inside of the wall. Outside Reinforcement (Mu -7.8 t.m)M ux 0.0605 10 0.605 ton .mThis maximum positive moment is very small and will controlled byminimum reinforcement.38
Example 1 (Design of Rectangular Tank) Design for Horizontal Reinforcement (My) Horizontal Bending Reinforcement: Inside ReinforcementM ux 0.0605 78 4.7 ton .m0.85(300) 2.61(10)5 (4.7) 1 1 0.0021 min24200 100(24.3) (300) A s 0.0033 100 24.3 8.0 cm 2 / mUse 8 12 mm/m on the inside of the wall. Outside ReinforcementM ux 0.0605 24 1.45ton .mThis maximum positive moment is very small and will controlled byminimum reinforcement.39
Example 1 (Design of Rectangular Tank) Note when design of Wall for Loading Condition 3 (coverin place) (Top hinged and bottom fixed) Case 4 page 3-39 for the moment coefficient is smaller thanprevious case.
Example 1 (Design of Rectangular Tank)30 cm10 cm8 12/m3m8 12/m7.5cmSlab Reinforcement DetailsWalls Reinforcement Details41
Example 1 (Design of Rectangular Tank) Design for Uplift force under Loading Condition 3The weight of the slab and walls as well as the soil resting on the footingprojection must be capable of resisting the upward force of water. Weight of the TankWalls height length thickness 2.5 t/m3 3 (9 9 6 6) 0.3 2.5 67.5 tonBottom slab length width thickness 2.5 t/m3 (9 0.6) (6 0.6) 0.3 2.5 47.5 tonTop slab length width thickness 2.5 t/m3 (9) (6) 0.3 2.5 40.5 tonSoil on footing overhang soil area soil height 1.2 t/m3 [(9.6 6.6)-(9 6)] 1 1.2 11.2 tonTotal Resisting Load 67.5 47.5 40.5 11.2 166.7 ton42
Example 1 (Design of Rectangular Tank) Design for Uplift force under Loading Condition 3 Buoyancy ForceBuoyancy Force Bottom slab area water pressure (9.6 6.6) 1 1.3 82.4 tonAssume the soil is 1m above the base slab.Factor of Safety Total resisting Load/Buoyancy Force 166.7 /82.4 2.043
Example 1 (Design of Roof Slab) Design of Roof SlabIt is assumed that the tank has a simply supported roofThe slab is designed using plate analysis result of case 10chapter 2 with a/b 9/6 1.5 page 2-62For Positive Moment along short spanCoef. Mtx Coef. Mx Coef. Mxy for ve B.M. along short span44
Example 1 (Design of Rectangular Tank)For Positive Moment along long spanCoef. Mty Coef. My Coef. Mxy for ve B.M. along long span45
Example 1 (Design of Rectangular Tank)For Negative Moment along short spanCoef. Mtx Coef. Mx - Coef. Mxy for -ve B.M. along short spanif Mtx 0 then Mtx 046
Example 1 (Design of Rectangular Tank)For Negative Moment along long spanCoef. Mty Coef. My - Coef. Mxy for -ve B.M. along long spanif Mtx 0 then Mtx 047
Example 1 (Design of Rectangular Tank) Steel in short direction Positive moment at centerM tx coef . qu a 2M tx ,1000qu S d 1.2 DL 1.6 LL Maximun M tx coef . 78qu 1.6 1.2 0.3 1 2.5 1.6 0.1 1.7t / mM 1.6 78 1.7 (6) 2 / 1000 7.6 t .m / m DL factors of 1.2 for slab own weightLL assumed to be 100 kg/m20.85(300) 2.61(10)5 (7.6) 1 1 0.0034 min4200 100(24.3) 2 (300) A s 0.0034 100 24.3 8.26 cm 2 / mUse 8 12 mm/m for bottom Reinforcement48
Example 1 (Design of Rectangular Tank) Steel in long direction Positive moment at centerM tx coef . qu a 2M tx ,Maximun M tx coef . 511000M 1.6 51 1.7 (6) 2 / 1000 5.0t .m / md 30 5 1.2 0.6 23.20.85(300) 2.61(10)5 (5.0) 1 1 0.0025 min24200 100(23.2) (300) A s 0.0033 100 23.2 7.7 cm 2 / mUse 8 12 mm/m for bottom Reinforcement49
Example 1 (Design of Rectangular Tank) Moment near corners Maximum Mtx and Mty Coef. 49M tx coef . qu a 2M tx ,Maximun M tx coef . 491000M 1.6 51 1.7 (6) 2 / 1000 4.8t .m / md 30 5 1.2 0.6 23.20.85(300) 2.61(10)5 (4.8) 1 1 0.0024 min24200 100(23.2) (300) A s 0.0033 100 23.2 7.7 cm 2 / mUse 8 12 mm/m for bottom Reinforcement50
Example 1 (Design of Rectangular Tank)8 12/m8 12/m8 12/m8 12/m1.5m25cmSlab Reinforcement Details51
Two-Cell Tank, Long Center Wall The tank in Figure consists of two adjacent cells, each withthe same inside dimensions as the single cell tank (a clearheight of a 3m. Horizontal inside dimensions are b 9.0m and c 3.0 m). The top is considered free.
Two-Cell Tank, Long Center Wall The tank consists of four L-shaped and two T-shaped units.The Bending moments in the walls of multicell tanks areapproximately the same as in single tank, except at locationsof where more than two walls intersect.The same coefficients of single-cell tank can be directly usedexcept at the T-shaped wall intersections.L-(L-F)/3 coefficient are applicable for the three intersectingwalls of the two T-intersectionsThe coefficient are determined as follow: Determine the BM Coef. In two-cell as if it were twoindependent tanks.Determine L and F factors to be used in adjustment of BM coef.at T-shapedAdjust bending moment coef. At T-shaped wall locations.
Two-Cell Tank, Long Center Wall Determine the BM Coef. as if it were two independent Tanks The BM coef. Are determined using table on page 3-30. Forb/a 3 and c/a 1 are given as follow:BM coef. (Mx)for single-Cell-Tank –Long outer Wall
Two-Cell Tank, Long Center WallBM coef. (My) for single-Cell-Tank –Long outer WallBM coef. (Mx) for single-Cell-Tank –short outer Wall
Two-Cell Tank, Long Center WallBM coef. (My) for single-Cell-Tank –short outer WallBM coef. (Mx) for single-Cell-Tank –Center Wall
Two-Cell Tank, Long Center WallBM coef. (My) for single-Cell-Tank –Center Wall
Two-Cell Tank, Long Center Wall Determine L & F factor to adjust BM for at T-shape wall location The L and F factors are required to determine the bendingmoment coefficient taking into account that the tank is multicell.L-factors for short wall for b/a 3 & c/a 1are taken from page 330 and F factors for b/a 1are taken from page 2-21 of chapter 2.L-factors for center wall b/a 3 & c/a 1are taken from page 3-30.and F factors for b/a 3are taken from page 2-18 of chapter 2.Note that coef is not needed for long outer wall since it not haveintersection with more than one wall.
Two-Cell Tank, Long Center WallL and F factors for short outer WallL and F factors for center Wall
Two-Cell Tank, Long Center Wall Adjust bending moment coef at T-shaped intersections Coef. L-(L-F)/3L and F factors for center Wall
Two-Cell Tank, Short Center Wall The tank in Figure consists of two cells with the sameinside dimensions as the cells in the two-cell tank withthe short center wall. (a clear height of a 3m.Horizontal inside dimensions are b 4.5 m and c 6.0m).
Two-Cell Tank, Long Center Wall Determine the BM Coef. As if it were two independent Tanks The BM coef. Are determined using table on page 3-31. Forb/a 2 and c/a 1.5 are given as follow:BM coef. (Mx)for single-Cell-Tank – 6m Long outer Wall
Two-Cell Tank, Long Center WallBM coef. (My) for single-Cell-Tank – 6 m Long outer WallBM coef. (Mx) for single-Cell-Tank –4.5 Long Wall
Two-Cell Tank, Long Center WallBM coef. (My) for single-Cell-Tank –4.5 Long WallBM coef. (Mx) for single-Cell-Tank – Center Wall
Two-Cell Tank, Long Center WallBM coef. (Mx) for single-Cell-Tank – Center Wall Determine L & F factor to adjust BM for at T-shape wall location The L and F factors are required to determine the bendingmoment coefficient taking into account that the tank is multicell.L-factors for short wall for are taken from page 3-31 and Ffactors for b/a 2 and b/a 1.5 are taken from page 2-19 and 2-20respectively.
Two-Cell Tank, Long Center WallL and F factors for 4.5m WallL and F factors for center 6m Wall
Two-Cell Tank, Long Center Wall Adjust bending moment coef at T-shaped intersections Coef F for Col. 1 and Col 2Coef. L-(L-F)/3 for Col. 3and 4 L and F factors for center Wall
Two-Cell Tank, Short Center Wall6m8m
Details at Bottom EdgeAll tables except one are based on the assumption that the bottomedge is hinged. It is believed that this assumption in general iscloser to the actual condition than that of a fixed edge. Consider first the detail in Fig. 9, which shows the wallsupported on a relatively narrow continuous wall footing,
Details at Bottom Edge In Fig. 9 the condition of restraint at the bottom of the footingis somewhere between hinged and fixed but much closer tohinged than to fixed.The base slab in Fig. 9 is placed on top of the wall footing andthe bearing surface is brushed with a heavy coat of asphalt tobreak the adhesion and reduce friction between slab andfooting.The vertical joint between slab and wall should be madewatertight. A joint width of 2.5 cm at the bottom is consideredadequate.A waterstop may not be needed in the construction joints whenthe vertical joint is made watertight
Details at Bottom Edge In Fig. 10 a continuous concrete base slab is provided eitherfor transmitting the load coming down through the wall or forupward hydrostatic pressure.In either case, the slab deflects upward in the middle and tendsto rotate the wall base in Fig. 10 in a counterclockwrsedirection.
Details at Bottom Edge The wall therefore is not fixed at the bottom edge and it isdifficult to predict the degree of restraintThe waterstop must then be placed off center as indicated.Provision for transmitting shear through direct bearing can bemade by inserting a key as in Fig. 9 or by a shear ledge as inFig. 10.At top of wall the detail in Fig. 10 may be applied except thatthe waterstop and the shear key are not essential. The mainthing is to prevent moments from being transmitted from thetop of the slab into the wall because the wall is not designedfor such moments.
Tanks Directly Built on GroundTanks on Fill or Soft Weak Soil The stress on the soil due to weight of the tank and water isgenerally low ( 0.6 kg/cm2 for a depth of water of 5m)But it is not recommended to construct a tank directly onunconsolidated soil of fill due to serious differentialsettlement.Soft weak clayey layers and similar soils may consolidate tobig values even under small stresses.It is recommended to support the tank on columns and isolatedor strip footings if the stiff soil layers are at a reasonable depthfrom the ground surface (see Figure 1).
Tanks Directly Built on GroundTanks on Fill or Soft Weak Soil It is recommended to support the tank on columns and isolatedor strip footings if the stiff soil l
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 .
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