130617 3 pti edc 130 flexure 55 reduced

8/13/2019 130617 3 PTI EDC 130 Flexure 55 Reduced

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SECTION 3

DESIGN OF POST-TENSIONED COMPONENTS

FOR FLEXURE

DEVELOPED BY THE PTI EDC-130 EDUCATION COMMITTEE

LEAD AUTHOR: TREY HAMILTON, UNIVERSITY OF FLORIDA


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NOTE: MOMENT DIAGRAMCONVENTION

In PT design, it is preferable to draw moment diagrams tothe tensile face of the concrete section. The tensile faceindicates what portion of the beam requires reinforcing forstrength.

When moment is drawn on the tension side, the diagrammatches the general drape of the tendons. The tendonschange their vertical location in the beam to follow thetensile moment diagram. Strands are at the top of thebeam over the support and near the bottom at mid span.

For convenience, the following slides contain momentdiagrams drawn on both the tensile and compressive face,denoted by (T) and (C), in the lower left hand corner. Pleasedelete the slides to suit the presenter's convention.


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OBJECTIVE

1 hour presentation

Flexure design considerations


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PRESTRESSED GIRDERBEHAVIOR

k1DL

Lin and Burns, Design of Prestressed Concrete Structures, 3rdEd., 1981

1.2DL + 1.6LL

DL


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LIMIT STATES AND PRESENTATIONOUTLINE

Load Balancing k1DL

Minimal deflection.Select k1 to balance majority of sustained load.

Service DL + LL Concrete cracking.

Check tension and compressive stresses.

Strength 1.2DL + 1.6LL +1.0Secondary

Ultimate strength.Check Design Flexural Strength (Mn)


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EXAMPLE

Load Balancing > Service Stresses > Design Moment Strength


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DIMENSIONS ANDPROPERTIES


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SECTION PROPERTIES


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LOAD BALANCING

Tendons apply external self-equilibratingtransverse loads to member.

Forces applied through anchorages

The angular change in tendon profile causes atransverse force on the member



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LOAD BALANCING

Transverse forces from tendon balancesstructural dead loads.

Moments caused by the equivalent loads are

equal to internal moments caused byprestressing force



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EQUIVALENT LOAD

Harped Tendoncan be sized and placed such that the upward

force exerted by the tendon at midspan exactly balancesthe

applied concentrated load



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EQUIVALENT LOAD

Parabolic Tendoncan be sized and placed such that the upward

force exerted by the tendon along the length of the member exactly

balancesthe applied uniformly distributed load



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FORMULAS (FROM PTI DESIGN MANUAL?)



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EXAMPLE LOADBALANCING

Determine portion of total dead load balancedby prestressing

wDL= 0.20 klf

superimposed dead load (10psf*20ft)

wsw= 2.06 klfself weight including tributary width of slab



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Including all short and long term

losses



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Prestressing in this example balances ~100% oftotal dead load.

In general, balance 65 to 100% of the self-weight

Balancing in this range does not guaranteethatservice or strength limit states will be met.These must be checked separately



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STRESSES

Section remains uncracked

Stress-strain relationship is linear for bothconcrete and steel

Use superposition to sum stress effect of eachload. Prestressing is just another load.



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CALCULATING STRESSES



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STRESSES

Stresses are typically checked at significantstages

The number of stages varies with the

complexity and type of prestressing.

Stresses are usually calculated for the servicelevel loads imposed (i.e. load factors are equal

to 1.0). This includes the forces imposed by theprestressing.



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PLAIN CONCRETE

Load Balancing > Service Stresses > Design Moment Strength(T)


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ECCENTRIC PRESTRESSING



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ECCENTRIC PRESTRESSINGSTRESSES AT SUPPORT



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VARY TENDON ECCENTRICITY

Harped Tendon follows

moment diagram from

concentrated load

Parabolic Drapefollows

moment diagram from

uniformly distributed load



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STRESSES AT TRANSFER - MIDSPAN

Including friction and elasticlosses



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STRESSES AT TRANSFER FULL LENGTH

Stress in top fiber

Stress in bottom fiber



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STRESSES AT SERVICE - MIDSPAN

Including all short and long termlosses



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STRESSES AT SERVICE FULLLENGTH

Stress in top fiber

Stress in bottom fiber

Transition (7.5 root fc)

Cracked (12 root fc)



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FLEXURAL STRENGTH (MN)ACI 318 indicates that the design moment strength of flexural

members are to be computed by the strength design procedure

used for reinforced concrete with fpsis substituted for fy



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ASSUMPTIONS

Concrete strain capacity = 0.003

Tension concrete ignored

Equivalent stress block for concrete compression

Strain diagram linear

Mild steel: elastic perfectly plastic

Prestressing steel: strain compatibility, or empirical

Perfect bond (for bonded tendons)



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fps- STRESS IN PRESTRESSING STEELAT NOMINAL FLEXURAL STRENGTH

Empirical (bonded and unbonded tendons)

Strain compatibility (bonded only)



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EMPIRICAL BONDED TENDONS

270 ksi

prestressing

strand



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EMPIRICAL BONDED TENDONSNO MILD STEEL


O S O


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BONDED VS. UNBONDEDSYSTEMS

Steel-Concrete force transfer is uniformalong the length

Assume steel strain = concrete strain

(i.e. strain compatibility)

Cracks restrained locally by steelbonded to adjacent concrete


BONDED VS UNBONDED


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BONDED VS UNBONDEDSYSTEMS

Steel-Concrete force transfer occurs atanchor locations

Strain compatibility cannot be assumed

at all sections

Cracks restrained globally by steel strainover the entire tendon length

If sufficient mild reinforcement is not

provided, large cracks are possible



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SPAN-TO-DEPTH 35 OR LESS

SPAN-TO-DEPTH > 35

Careful with units for fse(psi)



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COMBINED PRESTRESSING ANDMILD STEEL

Assume mild steel stress = fy Both tension forces contribute to Mn


STRENGTH REDUCTION


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STRENGTH REDUCTIONFACTOR

Applied to nominal moment strength (Mn) toobtain design strength (Mn)

ranges from 0.6 to 0.9

Determined from strain in extreme tensionsteel (mild or prestressing)

Section is defined as compression controlled,

transition, or tension controlled


STRENGTH REDUCTION


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STRENGTH REDUCTIONFACTOR


DETERMINE FLEXURAL


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DETERMINE FLEXURALSTRENGTH

Is effective prestress sufficient?

Determine fps Use equilibrium to determine:

Depth of stress block a

Nominal moment strength Mn

Determine depth of neutral axis and strain in

outside layer of steel (et) Determine

Compute Mn



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fpsOF BONDED TENDON



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aand



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MN BONDED TENDON



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REINFORCEMENT LIMITS

Members containing bonded tendons musthave sufficient flexural strength to avoid abruptfailure that might be precipitated by cracking.

Members with unbonded tendons are notrequired to satisfy this provision.



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REINFORCEMENT LIMITS



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fps UNBONDED TENDON



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Mn UNBONDED TENDON



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MIN. BONDED REINF.

Members with unbonded tendons must have aminimum area of bonded reinf.

Must be placed as close to the tension face

(precompressed tensile zone) as possible. As= 0.004Act Act area of section in tension



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AS MINIMUM


M UNBONDED TENDON


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Mn UNBONDED TENDONINCORPORATE MILD STEEL

130617 3 pti edc 130 flexure 55 reduced

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