Proceedma« of the 7th International Working Conference on Stored-product Protectum - Volume 2

Design of 24-m span hyperbolic shell slab and its applicationin the construction of grain depots

Feng Tianmm1

Abstract

The 24-m span hyperbolic shell slab IS a space thin-wallstructure that integrates mathematical model, high-strengthsteel and high-grade concrete mto one body. It IS a new-typeroof member with slab and truss combmed into one piece. Ithas begun to be used in the construction of storehouses mthe gram industry. Practice has proved that this new- typeroof member features rational structure and advancedtechmcal and economic indices, and has achieved goodresul ts m use

Design of Hyperbolic Shell Slab

Design principle

(1) The length of hyperbohc shell slab (24 meters) IS muchlarger than the WIdth (3 meters) The longitudinalstructure IS designed accordmg to the ordinary pre-stressed concrete girder member, the curve in crosssection IS a parabola, and the transverse reinforcementusually only needs to be arranged according to theconstruction.

(2) The calculation diagram of hyperbohc shell slab roofstorehouse IS the same as that of the storehouse by usmgroof truss plus roof boarding as roof, their transversesections are all calculated according to the bent frame.The hyperbohc shell slab roof conforms to theassumption that it has a cross girder with unlimitedrigidity and has rehable lunged connection With wallingcolumn head. It is considered that the longitudinalaction of connectmg hinged beam and tnmmer beam canbe calcula ted according to the frame.

(3) The hyperbolic shell slab roof can bear partial horizontalforce transmitted by the gable, the gable column head ISregarded as an Immovable lunged support, andhorizontal tension brace shall be provided for the edgeshell slab at the slab bottom and gable column head.

1 Beijing Gram Engmeenng Design Institute

Geometrical figure of hyperbolic shell slab

Curved surface equation:_ x2 _ y!:..

Z - t, a2 fy b2

Where, taking a = 1485mm, b950mm, fy = 250mm

12000mm, fa: =

Fig. 1. Geometncal figure of slab

To determine curve surface equation means to select anappropnate two-way curvature. The main straight motherline which passes through the origin of coordinate lies in arational position in terms of ItS x-coordmate at the slab end.The pre-stressed reinforcement will be arranged evenly inparallel along the two sides of main straight mother line,making the gravity of pre-stressed reinforcement versus thelongi tudmal curvihnear aXIS vary along the parabola, andmaking it be proportional to the bending moment diagramunder the action of evenly distnbuted load.The equation of the cross section central line parabola IS:

x2Z = fa: 2aWhere, i;= 950mm, the vertical thickness of slab varies

along WIth the parabola, the rule of vanation IS:

x2tx = toO + 2")aWhere, "IS an introduced parameter, taking

A = ta - to taking to = 70mm, t; = 140mmto

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Proceedings of the 7 th Internaiumal Working Conference on Stored-product Protection - Volume 2

z

fx

Fig. 2. The cross section of the shell slab

The advantage of variation of slab tluckness IS: makingthe concrete area of compressed zone enlarged, also beingable to improve the longitudinal and transverse rigidity, thuscreating the condition for designmg a large-span hyperbolicshell slab. The elimination of flange bnngs aboutconvenience for fabrication, stacking and transportation.

Load and material

The dead weight IS 2. 33kN/m2 , the live load IS 0.5kN/m2, and considering that It will act as a thermal insulatinglayer and waterproof layer, It should be added WIth 1. OkN/nr'.C40 fine stone concrete IS adopted, stones used for

makmg concrete are m a two-stage allocation, 1. e. 5-13mm IS approximately 30 %, 13 - 25mm IS approximately70%, medium-coarse yellow sand IS adopted, It IS strictlyforbidden to use additive that will corrode thereinforcement.Use twisted steel wire with 1>1 10.75 (1 x 3 x cp5) fptk =

1570N/mm2 as pre-stressed reinforcement, and use Class-Ireinforcement or cold drawn low-carbon steel wire asreinforcement of longitudinal and transverse construction.Tension control stress aeon = 0.72 fptk, when pre-stressed

reinforcement is loosened, the concrete grade reaches ~0.75 fe' use two beams of oxygen to cut pre-stressedreinforcement alternatrvely. After the tension IS released,the shell slab WIll automatically arch and eject from themold.

A Case History of Applicationof Hyperbolic Shell Slab

Beijing Gram & Feed Depot IS situated in Niushan Town ofShunyi County. In the depot, the flat story bm for packedgrain adopts 3 x 24-m pre-stressed hyperbolic shell slab ofdouble span and 26-m slab length as the roof, four bins use160 slabs m total, amountmg to 12500 square meters, theproject was completed and put into use by 1992

The selection of roof scheme

In the past years, gram system (especially gram

1600

x

storehouse) was always built uniformly as a flat-story binwith a span below 18 meters. Along with the development ofreform and openmg- up, the demand for adopting economicaland convenient new type bm and the demand by constructionuruts for building large span flat-story bin have been growinggreater and greater, thus the selection of roof scheme hasbecome a problem of utmost importance.The usually adopted roof schemes are pre-stressed

reinforced concrete roof truss plus large roof boarding, steelroof truss plus large roof boarding, and pre-stressedreinforced concrete folded plate. The above-mentionedstructural forms of roof truss plus large boardmg all haveObVIOUSdisadvantages. For instance, the very height of rooftruss with 24-m span already reaches 2.5 meters, when thebottom chord of roof truss IS 6 meters, the eaves height ISnearly 9 meters. The effective utilization ratio of buildingspace IS too low. The rigidity of pre-stressed reinforcedconcrete folded plate itself IS poor, and the transport andhoisting are qurte difficult. Specialized construction companywas required to fabncate, transport and hoist, which resultsm much higher cost. Compared to these, the hyperbolicshell slab is a more feasible scheme. Through demonstrationin many ways, It has the following advantages:(1) The slab has an artistic shape, self-balance for

supenmposed load, and good stability. The slab shape ishelpful to roof dramage, the slab joint IS at the slabridge, which facilitates waterproofmg treatment.Compared to the large roof boarding, the slab jointdecreases by third-fifth, and the mtegrity is also better.

(2) The structural height is small, and the slab bottomheight IS the very eaves height. Compared to the rooftruss plus large roof boardmg, the eaves height canlower by more than two meters, thus reducmg theheight of enclosure walling, so the utilization ratio ofspace is high.

(3) There IS only one member - hyperbolic shell slab, andthe slab space ngidrty IS great. The roof does notrequire to be provided with steel brace, thus saving thequantity of steel to be used.

(4) The covenng thickness IS enlarged, the average reducedthickness of roof truss plus large roof boarding is 8 - 9em concrete, while the actual boarding thickness is only2 .5cm The reduced thickness of pre-stressedhyperbolic slab IS 9. 3cm while the actual thmnest placeof the slab IS 7cm, which IS helpful to waterproofmg andthermal insulation

(5) Force transmission IS Simple. The hyperbolic shell slabtransmits a load directly to the walhng or column, whilethe roof truss plus large roof boarding transmits a loadfrom the boarding to roof truss that transmits the load tothe walling or column. The load transmitted to thewallmg or column by a hyperbolic shell slab is a linearload, while the load transmitted to the walling or

Proceedmqe of the 7th International Working Conference on Stored-product Protection - Volume 2

column by the roof truss is a concentrated force. Theproblem of local bearing must be considered for thewallmg at roof truss support, thereby the method ofwork is also different. Moreover, the hyperbohc shellslab can have multi-point connection With the lowerbracmg structure As counted by two pomts for eachslab end, each six meters of spacmg has a four-pointconnection, while the roof truss has only one point atthe end. Therefore the connection of hyperbohc shellslab is more reliable and more effective With respect toearthquake resistance.

(6) The roof truss plus large roof boardmg (24-m span)must use concrete bent frame structural system andmdependent column base, while the hyperbolic shellslab used as roof boardmg can use bnck-and-remforcedconcrete masonry construction and stnp foundation.The reason is that the hnear load transmitted by the slabmakes the walhng evenly in force, the bearing area islarge, and there is rehable connection between slab andwallmg. Additional advantageous condition is that theenclosure height of walhng is reduced, and thecorresponding dead weight of structure is lighter.

(7) According to the current Beijing estimates quota(1992 ), an analysis and companson is made for thedirect cost of 3 x 24-m hyperbohc slab The direct costof one square meter of hyperbohc slab system is lowerthan that of reinforced concrete roof truss plus largeroof boardmg by more than 10%, and is lower than thatof steel roof truss plus large roof boardmg by more than40%. The direct cost of hyperbohc shell slab is about102 yuan/in", yet without countmg the saved cost ofthe upper structure from foundation due to hyperbohcshell slab.

(8) Hyperbolic shell slab is generally prefabncated on theconstruction site, and hoisted and assembled on the veryplace, thus savmg a considerable sum of transportationexpenses.

Conclusions

Compared to the traditional system of roof truss and beam-

slab structure, the hyperbolic shell slab has better economicresults and supenor structural behavior. After the projectwas completed and put mto use, the relevant leaders andpersons in charge of capital construction of vanous gramdepots went to visit it one after another, and they all gave ita full affirmation and praise. In the planned constructionprojects such as Lishuiqiao Grain Depot, Beijmg GramCenter Depot (a World Bank loan project}, and HaidianNational Gram Reserve Depot, this roof form will beadopted As proved by the actual use m a few years past,the project having adopted the structural design ofhyperbolic shell slab is successful, and it can be said that mthe construction of gram depots from now on, It has played ademonstrative role to some extent.It should be pomted out that the hyperbohc shell slab roof

structure With slab and truss combined into one piece hasmany advantages. However, there are some mmuteproblems m the design and construction yet to be furtherstudied and solved. Nevertheless, along with thedissemmation and use of pre-stressed hyperbohc shell slab mthe construction of storehouses m the gram sector, people'srecognition of it will be contmuously deepemng, and thisstructural member pre-stressed hyperbolic shell slab and itsstructural system Willsurely be improved day by day.

References

Architecture Research Institute of Mimstry of MetallurgicalIndustry, 1973. Hyperbohc shell slab roof (in Chmese).Metallurgical Industry, 1, 26

Ge Lianfu, 1975 Application of pre-stressed hyperbolicshell slab and dISCUSSIonof some problems thereof.Metallurgical Architecture, 5, 31Foundamental construction committee of Zhejiang province,1980 Calculation of 24m x 15m prestressed saddle-shapedshell slab. Prestressed building bloch design andcmstruction, pubhshed by Architecture Industry Pubhc ofChina, 178 -184.Fen Lei, 1990. Bnef introduction of 27m span saddle-shapedshell slab project at Luhe Flour Mill. Prestress TechnologyNewsletter, 10, 4.

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