24/10/2013

EPM711 – Design of Concrete Structures

Prestressed concrete structures (I)• Basic principles• Prestressing methods and devices• Analysis of sections under service loading

Professor A. J. KapposCivil Engineering Department

City University London, 2013

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What is prestressed concrete?It is concrete, wherein there have been introduced internal stresses of such magnitude and distribution that the stresses resulting from given external loading are counteracted to a certain degree.

In reinforced concrete members the prestress is typically introduced by tensioning the steel reinforcement.

What’s wrong with ordinary (non-prestressed) concrete?Concrete resistance to tensile stresses is low (fctfc/10). Steel is added to concrete to provide resistance to tensile stresses and control cracking.

reinforced concrete members are ‘legally’ cracked under service loading

Problems:Corrosion (of reinforcement), water-tightness ( durability)

Deflections ( functionality), especially in large spans!

Economy (‘useless’ concrete in tension zone, no advantage in using high-strength steel)

Aesthetics(appearance)

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Basic principles of prestressed concrete

• Use of high tensile strength steel alloys producing permanent pre-compressionin areas subjected to tension.

• A fraction of tensile stress is counteracted, thereby reducing the required cross-sectional area of steel reinforcement.

Steel bars being stretched by jacks

R/C beam subjected to concentric prestress force P and service load (g+q) σ1=-P/A + M/W1 (W1=I/y1; M=(g+q)ℓ2/8) (σ1: stress at bottom fibre of the beam section; σ2: stress at top fibre)

R/C beam subjected to concentric prestress force P σ=-P/A (AAc)

cgc: centroid of concrete sectioncgs: centroid of steel section

The prestress force P can eliminate tensile forces resulting from gravity loads, … but has no effect on the moment M,g+q

Basic principles of prestressed concrete - contnd

compression negative

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R/C beam subjected to eccentric prestress force P and service load σ1=-P/A - (Pe)/W + M/W ; for full prestressing: σ1 0

The prestress force P not only eliminates tensile forces resulting from gravity loads, but also reduces (counteracts) the moment M,g+q

the beam can carry higher service loads without cracking!

but: need to control σ1

(-) ΕC2:

R/C beam subjected to eccentric prestress force P σ1=-P/A - (Pe)/W

Basic principles of prestressed concrete - contnd

Loading combinations in Serviceability Limit States (SLS)

Characteristic combination

Quasi-permanent combination (reversible SLS)

Ψ0 = 0.71.0

Ψ2 = 0.30.8

Typical load combination in Ultimate Limit State (ULS)

γG = 1.35, γQ = 1.35

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Objectives of prestressing: To eliminate concrete cracking under service

loading, by ensuring that σg+P+q 0 (fullprestressing)

or: σg+P+q fct (limited prestressing)

alternatively, to control cracking

partial prestressing: σg+P+ψ2q fct(all 3 options are allowed by EC2 that treats reinforced concrete (R/C) and prestressed concrete (PSC) together)

To reduce deflections, by increasing stiffness (EIg>EIcr) and introducing pre-camber

To increase shear strength (favourable effect of prestress force P)

To allow efficient and economic use of high-strength steel

Keeping a constant eccentricity is not the most efficient way to counteract the bending moments M,g+q from service loading

need for tendon profile following more closely the M diagram!

Harped tendon(suitable when a concentrated load is present at midspan)

Draped tendon(parabolic profile, suitable in the usual case of uniform loading)

radius of gyration r=(Ig/Ac)

e

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Methods of prestressinga) Pretensioning (prefabricated elements)b) Post-tensioning

PRETENSIONING:Casting of concrete around reinforcing tendons that have been stressed to the desired degree.

Stages of pretensioning

abutment (bulkhead)

due to bond

Mould

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Advantages of pretensioning suitable for precast members produced in bulk large anchorage devices not necessary

Disadvantages of pretensioning prestressing bed (with stiff abutments) required for the

procedure waiting period in the prestressing bed, before the concrete

attains sufficient strength effectiveness depends critically on quality of bond between

concrete and steel over the transmission length

‘Harping’ of tendons, to obtain eccentricity

harping point

POST-TENSIONING:Reinforcing tendons are stretched by jacks whilst keeping them inserted in conduits (ducts) left pre-hand during curing of concrete in some cases tendons can be external

The ducts are then pumped full of grout to bond steel tightly to the concrete (bonded tendons), or (less often)

are left without grout (unbonded tendons)

conduit

Beam with hollow conduit embeddedin concrete

Hollow cellular beam with intermediate diaphragms

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Stages of the post-tensioning operation:1. Casting of concrete2. Placement of the tendon(s)3. Placement of the anchorage

block and jack 4. Applying tension to the tendons5. Seating of the wedges6. Cutting of the tendons

Hydraulic jack for tensioning cables

Post-tensioning ducts in a box girder

Jacking and anchoring with wedges

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Other anchoring systems:

Multi-plane Anchor

Anchor Plate for PT-Bar

General and local anchor zone in end of I-girder

(spiral reinforcement required to resist bursting forces)

Detailing of anchorage zone:

Grouting filling of duct with a material that provides an anti-corrosive alkaline

environment to the prestressing steel and also a strong bond between the tendon and the surrounding grout

the major part of grout consists of water and cement, with a water-to-cement ratio of about 0.5, together with some water-reducing admixtures, expansion agent and pozzolans

Connections for secondary, vacuum grouting, operations

(grout vents)

Grouting details for a 2-span spliced girder duct system.

Vacuum grout injection

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Advantages of post-tensioning suitable for heavy cast-in-place members waiting period in the casting bed is less transfer of prestress is independent of transmission length

Disadvantage of post-tensioning requirement of anchorage device and grouting

Couplers (for connecting strands or bars) they are located at the junction of the members, e.g. at or near columns in post-tensioned slabs, or piers in post-tensioned bridge decks. couplers are tested to transmit the full capacity of the strands or bars.

Analysis of concrete section under working loads

Unlike R/C, the primary verification of PSC is based on SLS and the assumption of elastic (uncracked) behaviour

Basic objective: maintain favourable stress conditions under different working loads need to check both Mmin and Mmax

Key assumptions: plane sections remain plane (Bernoulli) linear σ – ε relationships bending about a principal axis prestress force P=Pef (after all losses

occurred) changes in σp due to service loads (g, q)

have negligible effect section properties based on gross concrete

cross section (Ac, Ig)

y2

y1

b

eh

rectangular section

I - section

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PSC beam subjected to eccentric prestress force P

Under wmin=g Under wmax=g(+g1)+q

min P required for σ1=0 :

g1: additional dead loads (important in bridges)

(σ1: stress at tension fibre under service load; σ2: stress at compression fibre)

(Wi=I/yi)

for a given P, the eccentrically prestressed beam can carry a max moment

A concentrically prestressed beam can carry

The max |σ2| (top stress) corresponding to Mmax =P(W1/A+e) is:

increase in flexural capacity

which is the same as that for a concentrically prestressed beam!

clear advantage of using eccentric tendons (increased flexural capacity, without increased compression at the top)

However:

The Mmin stage should always be checked along the beam, since stresses close to the beam ends (low Μ) can exceed those at midspan!

prove at home!

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Np(x)=-P(x)cos(a(x))Mp(x)=-yp(x)P(x)sin(a(x))Vp(x)=-P(x)sin(a(x))

PSC beam with parabolic prestressing tendon

forces along the tendon

forces on concrete

forces at section x:

these forces form a self-equilibratingsystem (no reactions at supports)

upward thrust

friction forces (for tensioning at x=0)

e

Load balancing concept (Lin): The upward thrust due to prestressing is equivalent to applying an equivalent (uniform) loading wb that produces M, V, N diagrams counteracting (‘balancing’) those due to gravity loading

Mp=M,b

Vp=V,b

Np=N,b

There are 3 approaches to analysis of PSC sections in flexure:

stress concept (‘basic’ method) [main method used here]

force concept (C-Line method) [not used here]

load balancing method [briefly introduced here]

Mmax = wbℓ2/8 = Pe

wb = 8Pe/ℓ2

deflection at mid-span:

useful concept for draped or harped tendons (not for straight ones!), also for indeterminate structures

diagrams for beam with parabolic tendon(assuming T0)

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References and main sources of figures:Caltrans (California Department of Transport) “Prestress Manual”, Jan. 2005.

Collins, M.P. and Mitchell, D. (1997) Prestressed Concrete Structures. Response Publications, Montreal/Toronto.

FHWA (Federal Highway Administration) “Post-Tensioning Tendon Installation and Grouting Manual”, Washington, DC, 2004.

Mosley, W.H., Hulse, R. and Bungey, J.H. (2012) Reinforced concrete design to Eurocode 2 (EC2) (7th edition), Palgrave Macmillan, Basingstoke.

Menon, D. & Sengupta, A.K., Prestressed Concrete Structures, IIT Madras 2013 http://nptel.iitm.ac.in/courses/IIT-MADRAS/PreStressed_Concrete_Structures/

Nawy, E. (2010) Prestressed Concrete: A Fundamental Approach (5th edition), Prentice Hall-Pearson, New Jersey.

Nilson, A. H. “Design of Prestressed Concrete”, John Wiley & Sons, New York, 1987.

Wikipedia https://en.wikipedia.org/wiki/Prestressed_concrete , 2013