Design of Prestressed Concrete - <topic>
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Topic is related to Continuous Beam, Load Balancing Method and Cable Layout of Prestressed Concrete
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Design of Prestressed Concrete - <topic>
- 1. DEPERTMENT OF CIVIL ENGINEERING 1/23/2014 1
- 2. 1/23/2014 2
- 4. Continuous Beams A continuous beam is a statically indeterminate multi span beam on hinged support. The end spans may be cantilever, may be freely supported or fixed supported. Beams are made continuous over the supports to increase structural integrity. Figure : Jamuna Bridge 1/23/2014 4
- 5. Advantage and Disadvantage of Continuous Prestress beam over Simply Supported BeamAdvantages : 1. Reduce the depth and cross-sectional area 2. Reduce the self-weight which adds to the total capacity of the member Disadvantage: 1. More frictional loss in continuous beam 2. Shortening of continuous beam under prestress may produce excess lateral force and moment in the supporting member . 3. Concurrence of maximum moment and shear over support 4. Difficulties in achieving continuity for precast elements 1/23/2014 5
- 7. • Higher resistance to stress • Longer spans USING CURVED CABLES 1/23/2014 7
- 8. • Wide web is necessary • Large anchorage blocks • Skilled workmen USING STRAIGHT CABLES Curved tendon can be replaced by straight tendon but behavior is same due to cross sectional change . 1/23/2014 8
- 9. Cross Sectional Change Of a Continuos Beam Figure : Jamuna Bridge 1/23/2014 9
- 10. Assumption for Continuous Prestress Concrete Beam The eccentricity of the prestressing cables are small compared to the length of the members. e < L Frictional loss of prestress is neglected. Same tendon should run through the entire length of the member. 1/23/2014 10
- 11. Determining the Resisting Moment for Continuous Beam Step 1 : Plot the primary moment diagram for the entire continuous beam as produced only by prestress eccentricity , as if there were no support to the beam Step 2 : Plot the shear diagram Step 3 : Plot the loading diagram Step 4 : Plot the moment diagram corresponding to the loading diagram considering all supports 1/23/2014 11
- 12. Primary Moment : In simple beam , the moment is produced due to tendon variation is called primary moment. Secondary Moment : In continuous beam , moment produced due to internal reaction is called secondary moment . Primary and Secondary Moment 1/23/2014 12
- 13. 1. PRIMARY MOMENT DIAGRAM DUE TO PRESTRESS CONSIDERING NO SUPPORT 2. SHEAR DIAGRAM TO PRIMARY MOMENT 3. LOADING DIAGRAM FOR SHEAR 4. RESULTING MOMENT DIAGRAM DUE TO PRESTRESS 1/23/2014 13
- 15. • It’s the third principal of Prestressed Concrete. • Developed by T.Y Lin & Ned H. Burns HISTORY 1/23/2014 15
- 16. • Taking concrete as a free body. • Replacing tendons with forces or moments along the span. MAIN CONCEPT 1/23/2014 16
- 18. CONCEPT • For Prestressed load moment at mid-span = P*h • For Hypotheoritcal load moment at mid- span = w2L²/8 • Now both are equal. • At last the result is w2 = 8Ph/L² 1/23/2014 18
- 20. CONCEPT • For Prestressed load , moment at mid-span = P*h • For Hypotheoritcal load , moment at mid span = w2 L/4 • Now both are equal. • At last the result is , w2 =4Ph/L 1/23/2014 20
- 22. • For Prestressed load moment at mid-span = P*h • So the produced moment should be , M=P*h CONCEPT 1/23/2014 22
- 24. • Continuous beam act as a simply supported beam • After Load balancing method it is act as a non- prestressed continuous beam. • For analysis only consider unbalanced portion. CONCEPT 1/23/2014 24
- 26. Contents • Cable layout • Simple Beam Layout • Layouts for pretensioned beams • Layouts for posttensioned beams • Cable profiles • Cantilever beam layout • Single cantilevers beam layout • Double cantilevers beam layout 1/23/2014 26
- 27. Cable Layout The schematic arrangement of a group of tendons is called Cable Layout. Tendon : A stretched element used in a concrete member for the purpose of prestressing. 1/23/2014 27
- 28. Simple Beam Layout Controlled by Two Critical Sections : The Maximum Moment : The maximum moment section is controlled by two loading stage : 1) The initial stage 2) The working-load stage The End Section : The end sections are controlled by the area. 1/23/2014 28
- 29. Layouts for Pretensioned Beams 1/23/2014 29
- 30. Layouts for posttensioned beams 1/23/2014 30
- 31. Cable profiles The method is intended for simple beams. It also applicable for complicated layouts, such as complicated and continuous layouts. The method is a graphical one ; giving limiting zone within which the c.g.s. must pass in order that no tensile stresses will be produced. Compressive stresses in concrete are not checked by this method. 1/23/2014 31
Editor's Notes
- The design of statically determinate beams is relatively straightforward; the engineer can work on the basis of the design of individual cross-sections. A number of complications arise when the structure is indeterminate which means that the designer has to consider, not only a critical section, but also the behavior of the beam as a whole. Beams are made continuous over the supports to increase structural integrity. A continuous beam provides an alternate load path in the case of failure at a section. In regions with high seismic risk, continuous beams and frames are preferred in buildings and bridges. A continuous beam is a statically indeterminate structure. A continuous beam is a statically indeterminate multi span beam on hinged support. The end spans may be cantilever, may be freely supported or fixed supported.
- Advantages : Reduce the depth and cross-sectional area Reduce the self-weight which adds to the total capacity of the member Disadvantage: More frictional loss in continuous beam Shortening of continuous beam under prestress may produce excess lateral force and moment in the supporting member . Concurrence of maximum moment and shear over support Difficulties in achieving continuity for precast elements
- Higher resistance to stress Longer spans
- Wide web necessary Large anchorage blocks Skilled workmen High strength threaded rods
- The eccentricity of the prestressing cables are small compared to the length of the members e < L Frictional loss of prestress is neglected Same tendon should run through the entire length of the member
- Step 1 : Plot the primary moment diagram for the entire continuous beam as produced only by prestress eccentricity , as if there were no support to the beam Step 2 : Plot the shear diagram Step 3 : Plot the loading diagram Step 4 : Plot the moment diagram corresponding to the loading diagram considering all supports
- Primary Moment : In simple beam , the moment is produced due to tendon variation is called primary moment. Secondary Moment : In continuous beam , moment produced due to internal reaction is called secondary moment .
- Controlled by Two Critical Sections : The Maximum Moment : The maximum moment section is controlled by two loading stage : 1) The initial stage at transfer with minimum moment acting on the beam 2) The working-load stage with maximum design Moment The End Section : The end sections are controlled by the area required for shear resistance, bearing plates, anchorage spacing and jacking clearances.
- The method is intended for simple beams. It also serves as an introduction to the solution of more complicated layouts, such as complicated and continuous layouts, where cable location cannot be easily determined by inspection. The method is a graphical one ; giving limiting zone within which the c.g.s. must pass in order that no tensile stresses will be produced. Compressive stresses in concrete are not checked by this method. It is assumed that the layout of concrete sections and the area of prestressing steel have already been determined.