PCI Fundamentals of Prestressed Concrete of Prestressed Concrete Design
Design of Prestressed Concrete -
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AHSANULLAH UNIVERSITY OF SCIENCE AND TECHNOLOGY
DEPERTMENT OF CIVIL ENGINEERING
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Presented byS. M. Rahat
Rahman
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Continuous Beam
TOPIC
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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
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Advantage and Disadvantage of Continuous Prestress beam over
Simply Supported BeamAdvantages :
1. Reduce the depth and cross-sectional area2. Reduce the self-weight which adds to the total
capacity of the member
Disadvantage:
3. More frictional loss in continuous beam4. Shortening of continuous beam under prestress may
produce excess lateral force and moment in the supporting member .
5. Concurrence of maximum moment and shear over support
6. Difficulties in achieving continuity for precast elements
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METHODS OF ACHIEVING
CONTINUITY1/23/2014
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• Higher resistance
to stress
• Longer spans
USING CURVED CABLES
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• 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 .
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Cross Sectional Change Of a Continuos Beam
Figure : Jamuna Bridge 1/23/2014
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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.
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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
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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
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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
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LOAD BALANCING METHOD
TOPIC
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• It’s the third principal of Prestressed Concrete.
• Developed by T.Y Lin & Ned H. Burns
HISTORY
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• Taking concrete as a free body.
• Replacing tendons with forces or moments along the span.
MAIN CONCEPT
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Illustration of CONCEPT
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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
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CONCEPT
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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
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CONCEPT
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• For Prestressed load moment at mid-span = P*h
• So the produced moment should be , M=P*h
CONCEPT
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CONCEPT
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• 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
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Cable Layout
TOPIC
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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
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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.
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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.
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Layouts for Pretensioned Beams
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Layouts for posttensioned beams
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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.
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Cable profiles
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THANK YOU
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