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1The Islamic University of GazaDepartment of Civil EngineeringAnalysis of Reinforced Concrete SilosDr. Mohammed Arafa2Concrete SilosDr. Mohammed Arafa3Silo or Bunker ?) 1.5) 1.5 for circular silos 1.5 for rectangular silosa H Ab H DH a>>>Empirical approximation are preferred by many engineers. Tow such approximation are:The present ACI 313 Silos standard, however, uses the same method for both silos and bunkersDr. Mohammed Arafa4Design of SilosSlipformed silos are constructed using a typically 4 ft. (1.2 m) high continuously moving form. Jumpformed silos are constructed using three typically 4 ft. (1.2 m) high fixed forms. The bottom lift is jumped to the top position after the concrete hardens sufficiently. hopper is the sloping, walled portion at the bottom of a silo.Stave silos are silos assembled from small precast concrete units called staves, usually tongued and grooved, and held together by exterior adjustable steel hoops.Dr. Mohammed Arafa5Properties of Granular Materials Dr. Mohammed Arafa6Vertical Pressure'/'1 kY RRq ek (= WhereR = ratio of area to perimeter of horizontal cross section of storage space = weight per unit volume for stored material` = coefficient of friction between stored material and wall or hopper surface1 sin k = Dr. Mohammed Arafa7Hydraulic Radius RFor Circular silos R=D/4For polygonal silos R=D/4for a circular shape of equivalent area.For square silos a or shorter wall of rectangular silos use R=a/4For the long wall b of rectangular silos use R=a`/4where a` is the length of side of an imaginary square silo 2' abaa b=+Dr. Mohammed Arafa8Horizontal Pressure and Vertical FrictionHorizontal Pressurep kq =Vertical friction per unit length of wall perimeter( )V Y q R = Note: `, k vary, the following combinations shall be used with maximum:(1) Minimum ` and minimum k for maximum vertical pressure q.(2) Minimum ` and maximum k for maximum lateral pressure p.(3) Maximum ` and maximum k for maximum vertical friction force VDr. Mohammed Arafa9Pressures and loads for hoppers0 y yq q h = +( ) ( )2 2tantan 'tan tan 'sin cos 1 sin cosyn n nn y n yqP and V PorP q k and V q k = =+= + = The initial pressure normal to the hopper surface at depth hybelow top of hopper shall be the larger of:Dr. Mohammed Arafa10Square and rectangular siloHorizontal Forces Due to Stored Material( )( ),,2 for wall 2 for wall a b desb a desF p b aF p a b==Dr. Mohammed Arafa11Regular Polygonal siloHorizontal Forces Due to Stored Material( )sin21 cosdesT p a | |= |\ .Dr. Mohammed Arafa12Sections with combined tension and bending( ) ( )Small eccentricity ''2' '''' ''uuu us sy yM he dFF e F eA Af d d f d d = < = = Dr. Mohammed Arafa13hopper TypesDr. Mohammed Arafa14Properties of Granular Materials Dr. Mohammed Arafa15Over pressure Factor cdPdesign = 1.7 x Cdx PinitialDr. Mohammed Arafa16Earthquake forcesEarthquake loads may affect stability and strength. The UBC or IBC may be used. Seismic forces are assumed to act in any horizontal direction, but vertical acceleration forces are usually neglected. In computing lateral seismic force The reduction of lateral force is allowed because of energy loss through inter-granular movement and particle-to-particle friction in the stored material. ACI 313 use not less 80% of the weight of the stored material as an effective live load, from which to determine seismic forces. Dr. Mohammed Arafa17Wind forces Wind may affect the stability of empty silos, particularly tall, narrow silos or silos group. Foundation pressure and column stresses, however, may be worse with wind acting on the full silo. Wind load reduction may be applied for cylindrical shape may be applied to single circular for cylindrical The pressures shall be not less than required by the local building code for the locality and height zone in question. Wind pressure distributions shall take into account adjacent silos or structures.Dr. Mohammed Arafa18Thermal LoadsTemperature and shrinkage steel requirement of ACI 318 apply to silos. In addition, hot stored materials may cause thermal stresses too high to be ignored. The approximate method illustrated below was developed specifically for cement storage silos. In this method:Tensile strength of the concrete is neglectedWall temperatures are assumed to vary only radially.Dr. Mohammed Arafa19Thermal LoadsIn building, the usual practice is to ignore a certain amount of inside-outside temperature difference (80oF or 27oC for silos).( )212 1c ctE hM T= ( ) ( )0 080 270.084.09 0.08o oi t itT T T F K T T C KhKh = = =+Dr. Mohammed Arafa20Additional Steel due to Temperature GradientThe additional horizontal steel Astto resist moment due temperature gradient should be located near the colder face. In singly reinforced walls, it should be added to the main hoop steel, ordinarily near the outer face. In doubly reinforced walls, the entire amount Astshould be added to the outside layerDr. Mohammed Arafa21Minimum wall thickness The thickness of silo or stacking tube walls shall be not less than 6 in. (150 mm) for cast-in-place concrete, nor less than 2 in. (50 mm) for precast concrete. The following formula can also be used in service loadingshf f=100f fs s cts ct E nt T+ Dr. Mohammed Arafa22Crack Widththe design crack width computed at 2.5 bar diameter from the center of bar (dc = 2.5 bar diameter ) shall not exceed 0.010 in. (0.25 mm). The design crack width (inch) shall be computed by:Dr. Mohammed Arafa30.0001 s cw f d A =23Load factors and strength reduction factors Load factors for silo or stacking tube design shall conform to those specified in ACI 318. The weight of and pressures due to stored material shall be considered as live load.For concrete cast in stationary forms, strength reduction factors, , shall be as given in ACI 318. For slip forming, unless continuous inspection is provided, strength reduction factors given in ACI 318 shall be multiplied by 0.95.Dr. Mohammed Arafa24Allowable ultimate Compressive loadThe compressive axial load strength per unit area for walls in which buckling (including local buckling) does not control shall be computed by'0.55nw cP f =Dr. Mohammed Arafa25Additional Load at OpeningsFlat BottomThe simplest flat bottom is a slab of uniform thickness. The flat bottom may also be a ribbed slab or beam-slab system. For a slab without hopper-forming fill, the design loads are dead load and pressure, qdescomputed at the top of the slab.. 1.4 1.7u desW DL q = +With earthquake vertical friction at the wall is assumed to be zero, so that the ultimate vertical pressure on the bottom is:( )0.75 1.4 1.7uW DL H = +Slab Shear stresses should be checked. Dr. Mohammed Arafa26Additional Load at Openings2 21.7 1.44sin sin sin1.72sinsin cosy gLmutunq D WWFD Dq DFq p P q ( (= + + ( ( (= ( = = +Conical hopperDr. Mohammed Arafa27Additional Load at OpeningsPyramidal hopper( )( ),,1.7 1.4sin1.7 1.4sina L a a des b gmauab L b b des b gmbubc W A q c WFac W A q c WFb+ +=+ +=, ,1.7 sin and 1.7 sin2 2tau b des a tbu a des bb aF q F q | | | |= = | |\ . \ .Dr. Mohammed Arafa28Additional Load at OpeningsPyramidal hopperDr. Mohammed Arafa29Circular Concrete Ring-Beam and Column System Supporting a Steel HopperSilo-Bottom: Steel hopper supported on concrete ring BeamRing-beam cross SectionDr. Mohammed Arafa30Circular Concrete Ring-Beam and Column System Supporting a Steel Hoppercos sin1.7 1.7mu mux y beamF FF and F w = = +The WSD uniform torsional moment isMt= Fme The Cross sectional Area of the ring Beam is2 21 12rb aA ab = Dr. Mohammed Arafa31Circular Concrete Ring-Beam and Column System Supporting a Steel HopperRing-beam cross Section2 21 12rb aA ab = ( )( )( )( )21 1 2 2 1 221 1 2 2 1 2/ 2 / 2 / 3/ 2 / 2 / 3rrab a b b bxAb a a b a ayA = =2ra yb A a==The Cross sectional Area of the ring Beam isCoordinate of the centroid measured from the origin O are:An equivalent rectangle of height a and b is substituted for the pentagonDr. Mohammed Arafa32Circular Concrete Ring-Beam and Column System Supporting a Steel HopperDr. Mohammed Arafa33Details and placement of reinforcementWhere slipforming is to be used, reinforcement arrangement and details shall be as simple as practical to facilitate placing and inspection during construction.Reinforcement shall be provided to resist all bending moments, including those due to continuity at wall intersections, alone or in combination with axial and shear forces.Horizontal ties shall be provided as required to resist forces that tend to separate adjoining silos of monolithically cast silo groups.In no case shall the total horizontal reinforcement area be less than 0.0025 times the gross concrete area per unit height of wall.Dr. Mohammed Arafa34Details and placement of reinforcementVertical reinforcement in the silo wall shall be (10 diameter) bars or larger, The minimum ratio of vertical reinforcement to gross concrete area shall be not less than 0.0020. Horizontal spacing of vertical bars shall not exceed 18 in. (450 mm) for exterior walls nor 24 in. (600 mm) for interior walls of monolithically cast silo groups. Vertical steel shall be provided to resist wall bending moment at the junction of walls with silo roofs and bottoms. Dr. Mohammed Arafa35Miscellaneous Reinforcement DetailsDr. Mohammed Arafa36Miscellaneous Reinforcement DetailsDr. Mohammed Arafa37Typical Conical hopper Reinforcement with circular BeamDr. Mohammed Araf