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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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