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Date Created: 10/29/15
A Design Example for a Rectangular Concrete Tank PCA Design Method CVEN 48304434 University of Colorado Boulder Spring Semester 2008 Prepared by Ben Blackard The Portland Cement Association PCA has publications for designing rectangular and circular tanks Some of the design provisions differ from that of the American Concrete Institute ACI speci cations Many in the industry use these PCA design concepts so we will adapt them for our calculations as well Much of the PCA publication is comprised of tables of coefficients for calculating moment and shear in twoway slabs These tables should simplify the calculations We will refer to the PCA Rectangular Concrete Tanks design manual as PCAR and the circular tank design manual as PCAC An additional safety factor is used for the loads called the Sanitation Coefficient we will denote it with SC for brevity Note that this notation is not an industry standard The purpose of the sanitation coefficient is to indirectly reduce the stress and thus the strain in the steel reinforcing The result is lower strain in the concrete and thus less cracking The ultimate load will be multiplied by SC which has different values for different calculations 13 for exure SC 165 for direct tension hoop tensile stress in reinforcing 10 shear provided by concrete 13 for shear beyond that provided by concrete Another change is the uid load factor is 17 rather than 14 as stated in the ACI specification For the purposes of this class the following load combinations and factors will be used Mu 1314D 17F 16H for exure Pu 16514D 17F 16H for direct tension hoop tensile stress in reinforcing Pu 1014D 17F 16H for direct compression hoop compression stress in concrete Vu 1014D 17F 16H shear provided by concrete Vu 1314D 17F 16H for shear beyond that provided by concrete D dead load F uid pressure H earth pressure 39 Concrete Tank Design Example An open top concrete tank is to have three chambers each measuring 20 gtlt60 as shown The wall height is 17 The tank will be partially underground the grade level is 10 below the top of the tank The highest groundwater table is expected to be 4 below grade The uid level inside the tank is 15 60 2039 l l 2039 l 2039 3500 psi fy 60000 psi soil bearing capacity 2700 psf Walls above the groundwater table should be designed using a lateral earth pressure equivalent to that developed by a uid weighing 45 pcf below the groundwater table use 95 pcf Due to the settlement characteristics of the soil it is recommended that the bearing pressure be kept as constant as possible for the full tank loading scenario Assume the density of the uid in the tank is 63 pcf Interior Wall Design Boundary condition case 3 in chapter 2 of PCAR will be used for determining the applied moments to the tank walls pages 217 thru 222 Consider the 15 water depth to be the height of the wall free w a 3 2 g b q fixed a15 b60 ba40 q15 63 pcf945 psf From page 218 of PCAR the maximum vertical moment coefficient is 149 looking at the Mx table This moment occurs at the centerbottom of the wall Similarly the My table gives a maximum horizontal moment coefficient of 99 located at the top ends of the wall For the moment calculations qu 1317945 pcf 2089 psf Mu moment coefficient gtlt qu gtlt a21000 Vertical Moment coef 149 MH 70034 lbftft Horizontal Moment coef 99 MH 46533 lbftft The maximum shear in the wall is obtained from the maximum shear coefficient from page 217 of PCAR in this case Cs 050 The wall will be designed for the concrete to resist the entire shear force For the shear calculation qu 1017945 pcf 1607 psf vu Cs gtlt qu gtlta 0501607 psf15 12053 lbft Note The moment in the wall varies considerably for different locations in the wall The reinforcing could differ at several locations for a highly efficient design The thickness of the wall could also vary either tapering the wall or stepping the wall However for the sake of time the reinforcing will be kept consistent for the entire wall One design for the vertical moments and the other for the horizontal moments This is a common practice in engineering Time is not only saved for the design engineer but also the detailers and construction crew saves time as compared to a more complicated design This design philosophy is entitled to change if substantial material savings could be realized and if time permits Vertical Flexure Design of Interior Wall try a 14 thick wall with 2 clear concrete cover and 8 bars 6 design a 1 wide vertical strip of wall bw12 d 14 2 bardia2115 Agl681n2 re 3500 psi fy 60000 psi As 158 in2 AS f y 31241n c 5508510 M 09 A f d m 8678981binft72325lb l s y 2 MH 70034 lbftft Mn 72325 lbftft minimum exural steel AC1 35006 1051 M s As 2 Amiquot 046 in2 exure steel As 158 inz 3 I c H1 H who AC1 35006 1051 bw d s AS 2 Amiquot 0408 in2 exure steel As 158 inz 3 minimum vertical wall steel ACI 35006 1432 0003gtltAg S As 3 Asmin 0504 in2 total steel As 316 ml minimum steel for temperature and shrinkage ACI 35006 1432 0005gtltAg S As 3 Asmin 084 in2 total steel As 316 inz maximum exural steel 00019125181 bw df AC1 318 1033 Amax 258 in2 exure steel As 158 inz f 0003E y fy Horizontal Flexure Design of Interior Wall The wall is 14 thick place the horizontal bars inside of the vertical bars Try 8 bars 8 bW 12 d 14 2 vertical bar dia bar dia2 105 Ag 168 in2 PC 3500 psi fy 60000 psi As 1185 in2 A fy c 2343 in Blbw085f Mn 09 As fy d 51239 c 6081741binft 50681 lbftft Mu 46533 lbftft Mn 50681 lbftft minimum exural steel AC1 35006 1051 M s As 2 Am 042 in2 exure steel As 11851112 VH1 3 f39 ACI 35006 1051 bw d S As 3 Asmin 0248 in2 exure steel AS 1185 ml 3 minimum vertical wall steel ACI 35006 1432 0003 gtltAg S As 3 Asmin 0504 in2 total steel As 237 ml minimum steel for temperature and shrinkage ACI 35006 1432 0005gtltAg S As 3 Asmin 084 in2 total steel As 237 inz maximum exural steel AC1 318 1033 Amax w 2357 in2 exure steel As 11851112 0003E yfy s Shear Capacity 1 wide strip either way bw12 d115 fc3500 psi V 2J3de 163281bft design shear strength Vn 075VC 12246 lbft Vu 12053 lbft Vn 122461bft Long Exterior Wall The Long exterior wall has the same geometry as the interior wall A simple demonstration shows that the effect of the interior uid is signi cantly greater than the exterior soil and groundwater The long exterior wall will take the same design as the interior walls interior exterior 10 ft 15 ft grade R1 4 ft groundwater R2 E R3 3 ft q1 12 13 interior q1131715 63 pcf 2089 psf R1 0515 QI 156681bft d115 3 5 moment R1gtltd1 78340 lbftft exterior qz 13167 45 pcf 656 psf R2 057 Z 22961bft d2 7 3 2334 q3 13173 50 pcf 332 psf R3 053 3 498 lbft d3 3 3 1 moment szdz R3gtltd3 5857 lbftft Short Exterior Wall Design As with the long exterior walls the effect of the internal uid pressure will be greater than that of the exterior soil and groundwater pressure As a result the wall will be designed for the interior uid pressure free w a 3 2 g b q fixed a 15 b20 ba 133 ql5 63 pcf945 psf The coefficients for ba 15 are larger than those for ba 125 Conservatively the tables for ba 15 will be used From page 220 of PCAR the maximum vertical moment coef cient is 61 This moment occurs at the centerbottom of the wall Similarly the maximum horizontal moment coef cient is 44 located near the top ends of the wall For the moment calculations qu 1317945 pcf 2089 psf Mu moment coef cient gtlt qu gtlt a21000 Vertical Moment coef 61 MH 28672 lbftft Horizontal Moment coef 44 MH 20682 lbftft The maximum shear in the wall is obtained from the maximum shear coef cient from page 217 of PCAR in this case Cs 040 The wall will be designed for the concrete to resist the entire shear force For the shear calculation qu 1017945 pcf 1607 psf Vu Cs gtlt qu gtlta 0401607 psf15 96421bft Vertical Flexure Design for the Short Exterior Wall Keep the wall thickness at 14 with 2 clear concrete cover and 6 bars 8 bW 12 d 14 2 bar dia2 11625 Ag 168 in2 PC 3500 psi fy 60000 psi As 066 in2 A fy c 1305 in Blbw085f Mn 09 As fy d 51239 c 3945481binft 328791bftft Mu 28672 lbftft Mn 32879 lbftft minimum exural steel AC1 35006 1051 M s As 2 Amquot 0465 in2 exure steel As 066 inz VH1 3 f39 AC1 35006 1051 bw d s As 2 Amquot 0413 in2 exure steel As 066 inz 3 minimum vertical wall steel ACI 35006 1432 0003 gtltAg S As 3 Asmin 0504 in2 total steel As 132 ml minimum steel for temperature and shrinkage ACI 35006 1432 0005gtltAg S As 3 Asmin 084 in2 total steel As 132 inz maximum exural steel AC1 318 1033 Amax w 2609 in2 exure steel As 066 inz 0003E yjty s Horizontal Flexure Design for the Short Exterior Wall The wall is 14 thick place the horizontal bars inside of the vertical bars The interior walls and long exterior walls have horizontal a spacing of 8 In order to accommodate rebar splices keep the spacing for the horizontal steel at 8 Try 5 bars 8 bW 12 d 14 2 vertical bar dia bar dia2 106875 Ag 168 in2 PC 3500 psi fy 60000 psi As 0465 in2 A f c4 09191n 5408540 Mn 09 As fy d 2585511binft 215461bftft Mu 20682 lbftft Mn 21546 lbftft minimum exural steel AC1 35006 1051 M s A f 2 Am 0428 in2 exure steel As 04651n2 Y L H 0 AC1 35006 1051 bw d S As 3 Asmin 0374 in2 exure steel AS 0465 inz fy minimum vertical wall steel ACI 35006 1432 0003 gtltAg S As 3 Ami 0504 in2 total steel As 093 inz minimum steel for temperature and shrinkage ACI 35006 1432 0005 gtltAg S As 3 Asmin 084 in2 total steel As 093 inz maximum exural steel AC1 318 1033 Amax W 2357 in2 exure steel As 04651n2 0003 yf E Y s Shear Capacity 1 wide strip either way bw12 d11625 fc3500 psi V z bwd 165051bft design shear strength Vn 075VC 12378 lbft Vu 9642 lbft Vn 12378 lbft Slab Design One of the criteria for slab design is that it must be able to resist the moment from the bottom of the wall As a first approximation assume the slab to be 14quot thick Mu Mu Another scenario is uplift from groundwater The tank in an empty state along with a high groundwater table can experience severe uplift on the oor slab In this example the groundwater table is then 3 117 above the bottom of the 14quot thick slab The approximate dimensions of the slab are 60 X 20 The slab will be designed as a oneway flexure member spanning in the short direction Consider a 1 wide strip of slab with an ultimate load wu from the water pressure below the slab v 20 O 2039 O 20 O The water pressure pushing upward is reduced by the weight of the slab The water pressure is multiplied by a factor of 17 and the dead weight of the concrete is multiplied by a factor of 09 The sanitation coefficient is 13 for exure and 10 for shear provided the concrete will resist all of the shear force wu 131762 pcf4 17 ft1 09150 pcfl4 12l 3671bft Mu 01167367 lbft20 ft2 17132 lbftft from continuous beam tables Vu 10170617367 lbft20 7699 lb Note that this moment is significantly smaller than the moment at the bottom of the long walls The design of the slab in the short direction will be the same as that of the walls in the vertical direction 8 bars 6 top and bottom faces of the slab Also note that the shear is considerably less than in the walls thus the 14 thick slab is adequate for the shear strength The slab in the long span direction is mainly taking moment from the bottom of the short exterior walls The same design will be used in this direction as the vertical reinforcing for the short exterior walls 6 bars 8 top and bottom faces Flotation ACI 350R404 section 312 gives a criterion for otation of the tank under high groundwater water conditions 125 S Dead hoad Uplift Total weight of tank W 60 14 14ul 20 14u 20 14Hl 20 ll 41 slab 6466 6233 1166 4699 ft3 4 long walls 46233 17 1166 4942 ft3 total volume 12019 ft3 6 short walls 620 17 1 166 2378 ft3 total weight oftank 12019 ft3150 pcf 1802850 lb uplift pressure 62 pcf4 17 ft 2585 psf uplift area 6466 6233 4031 ft3 uplift force 1042014 lb Dead Load Uplift 173 Bearing on Soil total weight oftank 1802850 lb weight of uid 320 60 15 63 pcf 3402000 1b total weight 5204850 1b footprint area 4031 ft3 soil pressure 1291 psf soil capacity 2700 psf