CONSIDERATIONS REGARDING THE OPTIMUM DESIGN OF PRESTRESSED ELEMENTS

Transcription

1 Bullein of e Transilvania Universiy of Braşov CIBv 5 Vol. 8 (57) Special Issue No. - 5 CONSIDERTIONS REGRDING THE OPTIU DESIGN OF PRESTRESSED ELEENTS D. PRECUPNU C. PRECUPNU bsrac: Engineering educaion in our universiies ackles e eory of presressed elemens as par of e sudies of reinforced concree. However, e presressing problem as a muc more general naure. I is known a in e case of nonomogenous elemens, during e elasic-linear beaviour, i is no possible o reac e inegral sreng capaciy in eac maerial. Tis disadvanage may be removed by presressing e maerial wi iger sreng. Tus, we obain presressed seel elemens or anoer combinaion of wo differen maerials. Tis paper presens e general eory of e presressed elemens, using e equivalen secion meod. Key words: engineering educaion, presressed elemens, nonomogeneous elemens, sreng capaciy, ig sreng.. Inroducion I is known a by presressing srucures we can obain an opimum disribuion of e sresses and srains. Te resul of is process is an economic design for sreng elemens. loug is principle as been known for a very long ime, an engineering calculus of ese srucures as been developed only recenly. Te presressing principle is sown in Figure were i is very easy o observe a by e inroducion of e iniial sress, e sreng capaciy of e presressed elemen is iger an e sreng capaciy of e nonpresressed elemen. Fig.. Presressing principle cademy of Tecnical Sciences of Romania Cosace Negruzzi Naional College of Iassy

2 8 Bullein of e Transilvania Universiy of Brasov Vol. 8 (57) Special Issue No. - 5 Te more e value of e inroduced sresses grows, e iger is sreng capaciy becomes. Tis observaion is limied by e sabiliy condiion of e elemen during presressing [3]. Tis disadvanage may by removed by applying sep by sep presressing (Figure ), bu, in is case, i is necessary o ave permanen service loads. In our counry e presressing meod was applied mainly for e reinforcemen of old srucures. For insance, a Saligny s bridge over e Danube, by loading e canilevers of e main span (Figure 3) we obained e reverse deformaion of e bridge. On is deformed posiion we reinforced e flanges of e russes from e main span. nnuling e load, e supplemenary reinforcemen will work even under is own weig. Fig.. Presressing sep by sep Bridge Fig. 3. Saligny s bridge over e Danube river

3 D. PRECUPNU e al.: Consideraions regarding e opimum design of presressed Presressing Sysem Te presressing may be obained using: - ie bars or - varied meods of execuion. Presressing by Tie-Bars Le us consider a beam aving a ie-bar on is boom face (Figure 4) [].. e inroduce effor in e ie bar. On e cross secion we ave e diagram. x i Fig. 4. Beam wi ie-bar. On is sae we apply e eernal forces. Te sresses are: ( ) ( ) 3. Opimizaion Condiion a) Remark: > a is: > (ie-bar mus be fixed on e fares fibbers) b) omogeneous sress sae ie-bar carry ou all e ensions e cross secion of e beam is subjeced o compression. (bu pay aenion o is sabiliy)

4 84 Bullein of e Transilvania Universiy of Brasov Vol. 8 (57) Special Issue No. - 5 Sreng condiions - a e presressing e ie-bars: - a e service sae: R R, R, and a e ie-bar ends: R R 4. Te Equivalen Secion eod Le us consider e presressed beam, aving any cross secion (Figure 5). Te sresses diagrams are: Fig. 5. Presressed beam. Diagrams e define a secion wic as: - e area equal wi acual area of e beam ; - insead of ie bar, we ave an area e. e, I is named a equivalen secion o acual secion of e beam. Remark Te cenroid of is equivalen secion is: y Ge e y Ge I I I Ge is siuaed on e neural as of e diagram, wic means a e equivalen secion is subjeced o plane bending []. So, a, insed of e presressed cross secion we can consider e equivalen secion wic, being subjeced o plane bending, e calculus of e acual beam may be subsiued by e calculus a plane bending of e equivalen secion (Figure 6).

5 D. PRECUPNU e al.: Consideraions regarding e opimum design of presressed Calculus Sage Fig. 6. Equivalen secion In funcion of σ /σ we deermine neural as. From condiion a G e o be on is as i resuls e. e ave e equivalen secion [4]. By an usual bending compuing we design e equivalen secion: z eq.sec, z eq. sec z( ) e deermine e equivalen coefficien α, and resuls: and if: - is condiion is saisfied a limi ( ) nearby o e calculus is sopped, - conrary, we modify and repea e calculus. e deermine e leng and e posiion of e ie-bar. For double T secions e calculus is easier: ( ) - we consider an opimum equivalen secion (Fig 7) e,,( eq e ) e deermine e oal effor of ie-bar: e verify e beam a e ie-bar presressing: - we find solving e sysem - i resuls = - we verify e beam: i Fig. 7. Opimum equivalen secion and furer, we follow e same calculaion.

6 86 Bullein of e Transilvania Universiy of Brasov Vol. 8 (57) Special Issue No Conclusions References Te paper presens a new and easy meod for design of presressed elemens using e equivalen principle beween e sreng capaciy of presressed secion and sreng capaciy of nonpresressed secion. Tis meod as wo main advanages: a more rapid calculus and e possibiliy o obain e opimum soluion. In is manner we eliminae e sep by sep calculus applying in e known meod by wic i is very difficul o arrive o an opimum soluion in e design of ese srucures.. aeescu, D.: Special seel consrucions. Tecnical Ediure, 96.. Juncan, N.: Conribuions o e sudy of presressed seel russes. In: PD Tesis, Cluj-Napoca, România, Precupanu, D.: Fas meod regarding e calcululus of possressed seel beams. In: I.P.I. Bullein, 97, fascicle Precupanu, D.: Opimum sape of double T secion. In: I.P.I. Bullein, 973, fascicle 3-4.