DEPERTMENT OF CIVIL ENGINEERING 1/23/20141

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Continuous Beam TOPIC 1/23/20143

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

Advantage and Disadvantage of Continuous Prestress beam over Simply Supported Beam Advantages : 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 1/23/20145

METHODS OF ACHIEVING CONTINUITY 1/23/20146

Higher resistance to stress Longer spans USING CURVED CABLES 1/23/20147

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. 1/23/20148

Cross Sectional Change Of a Continuos Beam Figure : Jamuna Bridge 1/23/20149

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. 1/23/201410

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 1/23/201411

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 1/23/201412

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 1/23/201413

L OAD B ALANCING M ETHOD TOPIC 1/23/201414

It’s the third principal of Prestressed Concrete. Developed by T.Y Lin & Ned H. Burns H ISTORY 1/23/201415

Taking concrete as a free body. Replacing tendons with forces or moments along the span. M AIN C ONCEPT 1/23/201416

Illustration of C ONCEPT 1/23/201417

C ONCEPT For Prestressed load moment at mid-span = P*h For Hypotheoritcal load moment at mid- span = w 2 L²/8 Now both are equal. At last the result is w 2 = 8Ph/L² 1/23/201418

C ONCEPT 1/23/201419

C ONCEPT For Prestressed load, moment at mid-span = P*h For Hypotheoritcal load, moment at mid span = w 2 L/4 Now both are equal. At last the result is, w 2 =4Ph/L 1/23/201420

C ONCEPT 1/23/201421

For Prestressed load moment at mid-span = P*h So the produced moment should be, M=P*h C ONCEPT 1/23/201422

C ONCEPT 1/23/201423

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. C ONCEPT 1/23/201424

Cable Layout TOPIC 1/23/201425

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 1/23/201426

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. 1/23/201427

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. 1/23/201428

Layouts for Pretensioned Beams 1/23/201429

Layouts for posttensioned beams 1/23/201430

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. 1/23/201431

Cable profiles 1/23/201432

THANK YOU 1/23/201433