Öngerilmeli omega kesitli köprü kirişlerinin optimizasyonu
Öngerilmeli omega kesitli köprü kirişlerinin optimizasyonu
Dosyalar
Tarih
1996
Yazarlar
Onbaşı, Erkan
Süreli Yayın başlığı
Süreli Yayın ISSN
Cilt Başlığı
Yayınevi
Fen Bilimleri Enstitüsü
Özet
Araştırmada üç adet tipik omega kirişi incelenmiştir. Kirişlerin hangi açıklıkta en efektif kullanılacağı araştırılmıştır. Araştırmanın ilerleyen bölümlerinde 1.20 m yüksekliğindeki kiriş TİP 1, 1.70 m yüksekliğindeki kiriş TİP II, 2.00 m yükseklideki kiriş TİP III olarak anılacaktır. Kirişlerin öngerme donatısı gereksinimlerini daha çok eğilme tesirleri belirlediği için, bu konu ağırlıklı olarak irdelenmiştir. TİP I kirişi 14 m - 28 m arasında, TİP II kirişi 20 m - 34 m arasında, TİP III kirişi de 28 m ile 34 m arasında ikişer metrelik artımlarla ele alınmıştır, emniyet gerilmeleri yöntemiyle gerilme durumları incelenmiş, limit durumda taşıma kapasiteleri araştırılmıştır. Farklı sünme ve farklı rötre'den doğan gerilmeler ihmal edilemeyecek mertebede olduklarından bu tesirler de göz önünde bulundurulmuştur. 20 m açıklıklı TIP I kirişte, 28 m açıklıklı TİP II kirişte ve 32 m açıklıklı TİP III kirişte öngerme donatısının artmasıyla öngerme kayıplarının değişimi incelenmiştir. TİP I, TİP II, TİP III kirişlerinin öngerme donatısı miktarlarına göre moment taşıma kapasitelerinin nasıl değiştiği, diyagram şeklinde sunulmuştur. Tüm kirişlerin öngerme hesaplarını göstermek imkansız olduğu için örnek olarak 20 m açıklıklı TİP I kirişinin çözümü ayrıntılı olarak verilmiştir. Her kiriş, gerilme durumları araştırılırken kesitte hiç bir durumda çekme gerilmesi kalmayacak şekilde ve müsade edilen çekme gerilmesi aşılmayacak şekilde iki dunumda göz önüne alınmıştır. Ara değerler yer problemi nedeniyle gösterilmemiştir.
The first aplications of precast pretensioned bridge structures began aproximately in 1930's but in our country only in 1980's. After the highways become importance the use of precat pretentioned members are increased. Standart shaped beams are investigated. In this calculation three typs of standart omega shaped beams researched in two different ways. As first way, the calculations are made so thet the stresses at final stage are under the permissible stresses and as second way the calculations are made so thet at final stage no tension stresses remain in the sections. The results are given for the first way. The 1.20 m high omega shaped beam is called as TYP I, the 1.70 m high omega shaped beam is called as TYP II, the 2.00 m high omega shaped beam is called as TYP III. Midsection of 7YP i Figure 1 Midsection of TYP II FIgur» 2 XIII Midsection of TVP III Fîgure 3 The span length varies between 14 m and 38m with 2 m increasments. The width of the bridge is assumed as 10.5 m common in highway bridges, with 2 m culvert on the right sight and 1 m culvert on the left sight and a 25 cm high cast in situ slab. Precast concrete is B45, cast in situ slab concrete and precast fasia concrete is B30. Reinforcing steel is, grade 60 ( yield strength = 420 MN/m2 ) and prestressing steel is, St 1724 low relaxation 7 wire 0.6 inch strands. The supports are elastomeric bearings and the structural system is taken as simply supported system. Precast beam dead load, cast in situ slab weight, superimposed dead load are taken as dead loads. Two lane standart lane load and live load at construction stage are taken as live loads. The stress investigations are made in four levels as shown in figure 4. The serviceability requirements are searched for all systems. Calculation results are sumerized in tables at chapter 7,8,9. As an example are the calculations of 20 m long TYP I beam given. copo copu Figure XIV The variation of prestress losses by increasing prestressing reinforcement due to creep, elastic shortening, shrinkage, relaxation and thermal treatment effects are calculated for TYP I beam at 20 m span length, for TYP Ilbeam at 28 m span length, for TYP III beam at 32 m span length and as diagrams given in diagram 1,2 and 3. The ultimate moment capacities for all three typ precast beams are calculated and as diagrams given in diagram 4,5 and 6. Because of the importance of differential shrinkage and differential creep in composite beams, these effects are included in the stress investigation part of the calculations and the results are summerized in tables. A method for crack width control at manufacturing is given at Appendix A. Prestressing Reinforcement Area ( cm2 ) Diagram 1: Prestress Losses Variation Diagram For TYP I Beam at 20 m Span Length O vo -H VO r» rf ?-« r-i Prestressing Reinforcement Area ( cm2 ) Diagram 2 : Prestress Losses Variation Diagram For TYP II Beam at 28 m Span Length XV o o Prestressing Reinforcement Area (cm2 ) Diagram 3 : Prestress Losses Variation Diagram For TYP III Beam at 32 m Span Length 8,0 y 7,0 - 6,0 - 5,0 - 4,0 3,0 2,0 1,0 0,0 ?fl oe ? *Ti ~* m of Prestressing Reinforcement Area ( cm2 ) Diagram 4 : Ultimate Moment Capacity Variation of TYP I Beam XVI 14.0 O e u E o S 20,0 S 3 O O» o* "3- r-ı o 3 S 3 "i f~. fi t-- r-ı oo vo r- t-- Prestressing Reinforcement Area ( cm2 ) Diagram 5 : Ultimate Moment Capacity Variation of TYP II Beam 18,0 - 2,0 0,0 C-l oo" f"l Prestressing Reinforcem ent Area ( cm2 ) Diagram 6 : Ultimate Moment Capacity Variation of TYP III Beam XVII İn accordance with the researches we can say for the TYP I beam ; TYP I beam is effective to use between 18 m and 24 m span lengths. Under 18m span length, the stresses are under the permissible stresses but we must add bonded reinforcement for the crack limiting considerations. Over 26 m span length, the compressive stresses at section C-C reaches the permissible compressive stresses. Prestressing reinforcement over 67 cm2 decreases the ultimate moment capacity and the compressive stresses reaches over the permissible compresstion stress, that means, TYP I beam is not usable for over 28 m span length. The prestress reinforcement requirements between the mentioned span lengths can be taken from the tables in Chapter 7,8,9. TYP II beam is effective to use between 24 m and 32 m span lengths. Under 24m span length, the stresses are under the permissible stresses but we must add bonded reinforcement for the crack limiting considerations. Over 28 m span length the tension stresses by manufacturing stage at the support zone passes over the permissible tension stress. İn this section we must take comprestion reinforcement into account and the crack widths must be checked. Over 34 m span length the comprestion stresses at manufacturing stage in section C- C passes over the permissible comprestion stress and so we reach the ultimate capacity of TYP II beam. TYP III beam is effective to use between 28 m and 34 m span lengths. Over 32 m span length the tension stresses by manufacturing stage at section C-C passes over the permissible tension stress. İn these sections we must add compresstion reinforcement and check the crack widths. Over 34 m span length,the high value of reinforcement indice causes much comprestion reinforcement, which can not be placed in the flange section. Thats why we can not use the TYP III beam over 34 m span lengths. The low performance of the TYP III beam is caused by the small flange width of the sections. And this effects the ultimate moment capacity negative. İn general we can say that the TYP HI beam is not suitable for 10.5 m wide bridges. If we compare the two ways of analysis we recover that for the second way the requirements of prestressing reinforcemet are approximately, 10 cm2 higher for TYP I, 12 cm2 higher for TYP II and 17 cm2 higher for TYP III than for the first way of analysis. And we must take into account approximately 15 percent more prestressing losses than in the first way of analysies. After all these researches it appeared that, C-C sections at manufacturing stage are the most critical sections. To prevent the objections in this section and to use the beams in longer span lengths, it can be suggested to surround the prestressing strains with a tube or to oil the prestressing strains at the support zone, to tense the prestressing strains with an angle, or at least to enlarge the sections C-C and B-B
The first aplications of precast pretensioned bridge structures began aproximately in 1930's but in our country only in 1980's. After the highways become importance the use of precat pretentioned members are increased. Standart shaped beams are investigated. In this calculation three typs of standart omega shaped beams researched in two different ways. As first way, the calculations are made so thet the stresses at final stage are under the permissible stresses and as second way the calculations are made so thet at final stage no tension stresses remain in the sections. The results are given for the first way. The 1.20 m high omega shaped beam is called as TYP I, the 1.70 m high omega shaped beam is called as TYP II, the 2.00 m high omega shaped beam is called as TYP III. Midsection of 7YP i Figure 1 Midsection of TYP II FIgur» 2 XIII Midsection of TVP III Fîgure 3 The span length varies between 14 m and 38m with 2 m increasments. The width of the bridge is assumed as 10.5 m common in highway bridges, with 2 m culvert on the right sight and 1 m culvert on the left sight and a 25 cm high cast in situ slab. Precast concrete is B45, cast in situ slab concrete and precast fasia concrete is B30. Reinforcing steel is, grade 60 ( yield strength = 420 MN/m2 ) and prestressing steel is, St 1724 low relaxation 7 wire 0.6 inch strands. The supports are elastomeric bearings and the structural system is taken as simply supported system. Precast beam dead load, cast in situ slab weight, superimposed dead load are taken as dead loads. Two lane standart lane load and live load at construction stage are taken as live loads. The stress investigations are made in four levels as shown in figure 4. The serviceability requirements are searched for all systems. Calculation results are sumerized in tables at chapter 7,8,9. As an example are the calculations of 20 m long TYP I beam given. copo copu Figure XIV The variation of prestress losses by increasing prestressing reinforcement due to creep, elastic shortening, shrinkage, relaxation and thermal treatment effects are calculated for TYP I beam at 20 m span length, for TYP Ilbeam at 28 m span length, for TYP III beam at 32 m span length and as diagrams given in diagram 1,2 and 3. The ultimate moment capacities for all three typ precast beams are calculated and as diagrams given in diagram 4,5 and 6. Because of the importance of differential shrinkage and differential creep in composite beams, these effects are included in the stress investigation part of the calculations and the results are summerized in tables. A method for crack width control at manufacturing is given at Appendix A. Prestressing Reinforcement Area ( cm2 ) Diagram 1: Prestress Losses Variation Diagram For TYP I Beam at 20 m Span Length O vo -H VO r» rf ?-« r-i Prestressing Reinforcement Area ( cm2 ) Diagram 2 : Prestress Losses Variation Diagram For TYP II Beam at 28 m Span Length XV o o Prestressing Reinforcement Area (cm2 ) Diagram 3 : Prestress Losses Variation Diagram For TYP III Beam at 32 m Span Length 8,0 y 7,0 - 6,0 - 5,0 - 4,0 3,0 2,0 1,0 0,0 ?fl oe ? *Ti ~* m of Prestressing Reinforcement Area ( cm2 ) Diagram 4 : Ultimate Moment Capacity Variation of TYP I Beam XVI 14.0 O e u E o S 20,0 S 3 O O» o* "3- r-ı o 3 S 3 "i f~. fi t-- r-ı oo vo r- t-- Prestressing Reinforcement Area ( cm2 ) Diagram 5 : Ultimate Moment Capacity Variation of TYP II Beam 18,0 - 2,0 0,0 C-l oo" f"l Prestressing Reinforcem ent Area ( cm2 ) Diagram 6 : Ultimate Moment Capacity Variation of TYP III Beam XVII İn accordance with the researches we can say for the TYP I beam ; TYP I beam is effective to use between 18 m and 24 m span lengths. Under 18m span length, the stresses are under the permissible stresses but we must add bonded reinforcement for the crack limiting considerations. Over 26 m span length, the compressive stresses at section C-C reaches the permissible compressive stresses. Prestressing reinforcement over 67 cm2 decreases the ultimate moment capacity and the compressive stresses reaches over the permissible compresstion stress, that means, TYP I beam is not usable for over 28 m span length. The prestress reinforcement requirements between the mentioned span lengths can be taken from the tables in Chapter 7,8,9. TYP II beam is effective to use between 24 m and 32 m span lengths. Under 24m span length, the stresses are under the permissible stresses but we must add bonded reinforcement for the crack limiting considerations. Over 28 m span length the tension stresses by manufacturing stage at the support zone passes over the permissible tension stress. İn this section we must take comprestion reinforcement into account and the crack widths must be checked. Over 34 m span length the comprestion stresses at manufacturing stage in section C- C passes over the permissible comprestion stress and so we reach the ultimate capacity of TYP II beam. TYP III beam is effective to use between 28 m and 34 m span lengths. Over 32 m span length the tension stresses by manufacturing stage at section C-C passes over the permissible tension stress. İn these sections we must add compresstion reinforcement and check the crack widths. Over 34 m span length,the high value of reinforcement indice causes much comprestion reinforcement, which can not be placed in the flange section. Thats why we can not use the TYP III beam over 34 m span lengths. The low performance of the TYP III beam is caused by the small flange width of the sections. And this effects the ultimate moment capacity negative. İn general we can say that the TYP HI beam is not suitable for 10.5 m wide bridges. If we compare the two ways of analysis we recover that for the second way the requirements of prestressing reinforcemet are approximately, 10 cm2 higher for TYP I, 12 cm2 higher for TYP II and 17 cm2 higher for TYP III than for the first way of analysis. And we must take into account approximately 15 percent more prestressing losses than in the first way of analysies. After all these researches it appeared that, C-C sections at manufacturing stage are the most critical sections. To prevent the objections in this section and to use the beams in longer span lengths, it can be suggested to surround the prestressing strains with a tube or to oil the prestressing strains at the support zone, to tense the prestressing strains with an angle, or at least to enlarge the sections C-C and B-B
Açıklama
Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1996
Anahtar kelimeler
Kirişler,
Optimizasyon,
Beams,
Optimization