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Prestressed composite beams
The document discusses composite construction using precast prestressed concrete beams and cast-in-situ concrete. It describes how the two elements act compositely after the in-situ concrete hardens. Composite beams can be constructed as either propped or unpropped. Propped construction involves supporting the precast beam during casting to relieve it of the wet concrete weight, while unpropped construction allows stresses to develop under self-weight. Design and analysis of composite beams involves calculating stresses and deflections considering composite action. Differential shrinkage between precast and in-situ concrete also induces stresses.
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Prestressed composite beams
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- 2. 02/06/18 SPK-PSG Collegeof Technology 2 • A composite beam is one whose cross-section consists of two or more elements of different materials, acting together while carrying some or all of the loads • Composite prestressed concrete consists of precast prestressed beams and cast insitu concrete. • The insitu portion is not usually prestressed and therefore, often consists of lower grade concrete provided with ordinary reinforcement. • After the insitu concrete has hardened, the two elements perform as one. • Depending on the stiffness, the precast member can be designed to carry the weight of the in situ concrete or can be propped, so that it carries only its self-weight during casting. Composite beam
- 3. • In lattercase, the props are removed when the concrete has hardened and the weight of insitu topping is then carried by the composite action. 02/06/18 SPK-PSG College of Technology 3
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- 5. Advantages…. • Economical • Lesstime consuming • Reduction in the false work and shoring cost • No need of formwork and scaffoldings • CIPC slab provides continuity at the ends of elements over adjacent spans • Provides stability to girders 02/06/18 SPK-PSG College of Technology 5
- 6. Types of composite construction Propped Construction The dead load stress developed in the precast prestressed units can be minimized by propping them while casting the concrete in situ. Unpropped Construction If the precast units are not propped while placing the in situ concrete, stresses are developed in the unit due to the self- weight of the member and the dead weight of the in situ concrete. 02/06/18 SPK-PSG College of Technology 6
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- 8. Analysis and Design……. •Analysis Problem – Given data • Sectional properties • Length of the member • Load conditions – Result • Internal stresses or forces • Design problem – Given data • Length of the member • Load conditions • Forces or stresses – Result • Sections to be checked for its adequacy 02/06/18 SPK-PSG College of Technology 8
- 9. Analysis of compositesections for concrete stresses • The flexural stresses are calculated using elastic analysis. • Let the flexural stress be denoted as f, the bending moment M and section modulus or elastic modulus Z, then • Bending moment is computed from the self weight of the precast unit and the weight of wet cast in situ slab concrete in case of unpropped construction. • On the other hand, in propped construction, the weight of concrete is not considered as the propping of the beam relieves the weight of the wet concrete in the situ slab. 02/06/18 SPK-PSG College of Technology 9 Z M f ±=
- 10. Problem-1 • A precastpretensioned beam of rectangular section has a breadth of 100 mm and a depth of 200 mm. the beam with an effective span of 5 m is prestressed by tendons with their centroids coinciding with the bottom kern. The initial force in the tendons is 150 kN. The loss of prestress may be assumed to be 15 percent. The beam is incorporated in a composite T – beam by casting a top flange of breadth 400 mm and thickness 40 mm. if the composite beam supports a live load of 8 kN/m2 . Calculate the resultant stresses developed in the precast and insitu concrete assuming the pretensioned beam as: (a) Unpropped, (b) propped during the casting of the slab. Assume the same modulus of elasticity for concrete in precast beam and insitu cast slab. 02/06/18 SPK-PSG College of Technology 10
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- 15. Differential Shrinkage • Incomposite construction, the precast prestressed beams are resisting the applied loads along with the cast In situ slab. • Precast elements were placed earlier, creep and shrinkage would have already taken place. • The wet concrete of slab is laid over the precast unit, and the shrinkage and creep continues. • The magnitude of the tensile force is computed as Nsh=ξcs Ec Ai where Nsh = Magnitude ξcs = Shrinkage strain Ec = Modulus of elasticity of insitu concrete Ai = Cross sectional area 02/06/18 SPK-PSG College of Technology 15
- 16. • This tensileforce is balanced by a compressive force applied at the centriod of equal magnitude. • The force applied at the cast in situ slab causes a direct force acting at the centriod of the composite section together with a bending moment. 02/06/18 SPK-PSG College of Technology 16
- 17. • The formulaeto compute the stresses due to differential shrinkage are as follows Stress at the top fibre of the slab Stress at the bottom fibre of the slab Stress at the top fibre of the beam Stress at the bottom fibre of the beam 02/06/18 SPK-PSG College of Technology 17 f Z M A P tc s −+= f Z M A P bc s −+= Jc s Z M A P += bc s Z M A P −=
- 18. 02/06/18 SPK-PSG Collegeof Technology 18 sP M f tZbZ JZ cA Direct compressive force and bending moment section moduli at top, junction and bottom of the precast beam Area of composite beam Uniform tensile stress at centre of the slab Where,
- 19. Problem-2 A composite beamof rectangular section is made of inverted T-beam having a slab thickness of 150 mm and width of 1000 mm. the rib size in 150 mm x 850 mm. The in situ concrete slab has EC = 30kN/m2 and the thickness of cast in situ slab is 1000 mm. If the differential shrinkage in 100 x 10-6 units, estimate the shrinkage stress developed in the precast and cast in situ units. 02/06/18 SPK-PSG College of Technology 19
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- 21. Deflections of composite beams •The estimation of deflections at service loads essentially depends on two factors i.e, the stages of loading and the difference in modulus of elasticity of precast concrete unit and the cast in situ slab. • Unpropped Construction- Deflections are computed using sectional properties and modulus of elasticity of the precast unit. Loads are due to prestress, self weight of beam and the weight of the cast in situ slab. • Propped Construction- The composite beam section properties are used to determine the deflections due to live load and self weight of the cast in situ slab. Note- If different grades of concrete are used in cast in situ slab and precast beam, then equivalent second moment of area is to be used in computations. 02/06/18 SPK-PSG College of Technology 21
- 22. Design of compositebeams of precast unit and cast in situ slab In design of composite beams, the moment of resistance of precast prestressed unit is increased by the addition of cast in situ slab. Two possibilities are A prestressed beam of known size is to be added with a cast in situ slab. A prestressed section is to be designed for a composite section of known size. Section modulus of composite action 02/06/18 SPK-PSG College of Technology 22 ( ) ( ) −−− ≥ min 1 MMffZ MZ Z twctb b bc ηη
- 23. Section modulus ofcomposite action Where, Zbc= section modulus at the bottom fiber of composite section Zb= section modulus at the bottom fiber of precast beam M1= moment acting on composite beam M= moment acting on precast beam Mmin= minimum moment η= loss ratio fct,ftw= compressive stress at transfer and tensile stress at working load. 02/06/18 SPK-PSG College of Technology 23 ( ) ( ) −−− ≥ min 1 MMffZ MZ Z twctb b bc ηη
- 24. 02/06/18 SPK-PSG Collegeof Technology 24 ++≥ bcb tw Z M Z Mf f ηηη inf −≥ t tt Z M ff min sup The minimum prestressing force P is computed from the following expression ( ) ( )bt tb ZZ ZfZfA P + + = supint and the eccentricity of the prestressing force is ( ) ( )tb bt ZfZfA ffZZ e supint supint + − = finf ,fsup =stress in concrete at the bottom and top of section respectively Zt ,Zb = section moduli at the top and bottom of section respectively Also
- 25. Problem-3 Design a compositeslab for the bridge deck using a standard invested T section. The top flange is 250 mm wide and 100 mm thick. The bottom flange is 500 mm wide and 250 mm thick. The web thickness is 100 mm and the overall depth of the inverted T-section is 655 mm. The bridge deck has to support a characteristic imposed load of 50 kN/m2 over an effective span of 12 m. Grade 40 concrete is specified for the precast pretensioned T section with a compressive strength at transfer of 36 N/mm2 . Concrete of grade 30 is used for the insitu part. Determine the minimum prestress necessary and check for safety under serviceability limit state. Section properties: Area = 180500 mm2 , position of centroid = 220 mm from the soffit.I = 81.1 x 108 mm4 , Zt = 18.7 x 106 mm3 , Zb = 37 x 106 mm3 . Loss ratio = 0.8, Mmin = 0. 02/06/18 SPK-PSG College of Technology 25
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- 29. References • Prestressed concrete-K.U.Muthu,Azmi Ibrahim, Maganti Janardhana and M.Vijayanad (Based on IS 1343-2012) • Design of prestressed concrete structures- T.Y.Lin and NED.H.Burns. • Fundamentals of Prestressed Concrete –N.C.Sinha and S.K.Roy • Prestressed concrete –N.Rajagopalan • Prestressed Concrete- N.Krishna Raju • Reinforced concrete –Limit State Design-Ashok K Jain • IS 1343-2012-Prestressed Concrete Code of Practice 02/06/18 SPK-PSG College of Technology 29
- 30. Thanks for listening Allthe best 02/06/18 SPK-PSG College of Technology 30