Pre-Stressed Concrete

5000. Concrete Structures and Construction 5200. Prestressed Concrete

•Reinforced Concrete • Objective and Scope 5100 – Provide introductory level review of analysis and • Prestressed Concrete 5200 design of prestressed concrete structures – Present and discuss •Reinforcing Bars, Reinforcing Details & Tolerances 5300 • Pre and Post Tensioning Systems •Concrete Containments, Modular Construction & • Introduction to Analysis & design of Prestressed Beams 5400 Mass Concrete

5500 • Durability, NDE & Masonry

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5200. Prestressed Concrete 5200. Prestressed Concrete

5210 • 5210 ‐ Pre and Post Tensioning Systems 5210 • 5210 ‐ Pre and Post Tensioning Systems

5220 • 5220 ‐ Introduction to Analysis & design of 5220 • 5220 ‐ Introduction to Analysis & design of Prestressed Beams Prestressed Beams

BMA Engineering, Inc. – 5000 3 BMA Engineering, Inc. – 5000 4 5210 ‐ Pre and Post Tensioning Systems Prestressed Concrete

• What is prestressing?

Prestressing is a methdhod of reifinforc ing concrete. The concrete is prestressed to counteract the applie d ldloads diduring the anticipated service life of the member.

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Prestressed Concrete Reinforced Concrete Under Flexural Loading

BMA Engineering, Inc. – 5000 7 BMA Engineering, Inc. – 5000 8 Reinforced Concrete – Cont’d Stress in Prestressed Reinforcement

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Axially vs Eccentrically Placed Stress Transfer to Concrete Section PtPrestressed RifReinforcemen t

BMA Engineering, Inc. – 5000 11 BMA Engineering, Inc. – 5000 12 Combined Stresses Due to Prestress + External Pre vs Post‐Tensioned Concrete LdiLoading Pre‐Tensioning: Steel tendons are stressed prior to concrete placement, usually at a precast plant remote from the construction site.

Precast, prestressed concrete elements are transported to the construction site.

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Pre‐Tensioned Concrete Pre‐Tensioning

Pre‐Tensioning: • The process may involve four steps: Steel tendons are stressed prior to concrete – (1)PlacePlace tendons in some prescribed pattern on placement, usually at a precast plant remote the casting bed between two anchorages from the construction site. • ACI 18.5.1: Tension not to exceed 94% of the specified yield strength, but not greater than the lesser of 80% of the specified tensile Precast, prestressed concrete elements are strength of the tendons and the maximum transported to the construction site. value recommended by the manufacturer of the prestressing tendons or anchorages

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– (2) Assemble formwork for concrete if not already – (4) The pretensioned member may be removed in place and pour the concrete. Steam curing and from the casting bed and placed in storage and high early strength Type III Portland cement may later transported to the job site. Only on very be used to accelerate curing large scale projects can the building of a casting yard at the job site be justified – (3) The concrete bonds and attains sufficient strength usually within 24 hours at which time the tendons might be cut from their anchorages

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A Completed Single T Member being Loaded on A Pretensioning Plant a TkTruck

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Post‐Tensioning: • Post‐tensioning becomes practical when: Steel tendons are stressed after the concrete – A structure needs to be fabricated in sections to has been placed and gained sufficient strength limit the weight and the sections are joined later at the construction site by post‐tensioning – Members are too large to be pretensioned and shipped to the site – When a desired cable profile cannot be produced in a pretensioning plant or when the tendons have to be stressed in stages

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Post‐Tensioning Post‐Tensioning (Cont’d)

• Post‐tensioning may involve the following four stepssteps: – (3) If not already in place, tendons are placed in the tubes and placed in tension by jacking against an abutment or end plate – (1) Place flexible hollow metal or plastic tubes at specified locations in the concrete formwork. In some cases the complete tendon assembly – (4) Tendons may be bonded or unbondedunbonded.. If the including tendons, end plate and anchorage may tendons are to be bonded, pppump grout into the be placed in the formwork tendon tubes. Protective coating may be applied – (()2) Pour concrete and allow to cure to the end anchorages

BMA Engineering, Inc. – 5000 23 BMA Engineering, Inc. – 5000 24 History History (Cont’d)

• The concept of prestressing has been used for • The theory was further advanced in the early 1900’s centuries and linear prestressing of beams, slabs and planks – Wooden barrels made by tightening metal bands or ropes began in Europe about 1928 around barrel staves • Modern development of prestressed concrete • General concepts were first formulated in Germany attributed to Eugene Freyssinet of France (1928) & the U.S. in the period 1885 – 1890 • The first major application of linear prestressing in • Applications were limited because high strength steel the U.S. was in 1949 – 1950 was not availa ble – the Walnut Lane Bridge in Philadelphia • The first patent for prestressed concrete ‐ P.H. • The first post‐tensioning in U.S. building construction Jackson of San Francisco in 1886 was in the mid to late 1950s

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Advantages & Disadvantages History (Cont’d)

• In the 1960s, post‐tensioned box girder bridges were • Advantages widely used in California and other Western states – Smaller members to support the same loads, or same size member can be used for longer spans • The use of post‐tensioned nuclear containment also – Crack‐free under working loads (prevents water penetration and began in the 1960s corrosion, better aesthetics, less maintenance) – Total deflections are reduced because of camber produced by prestressing. Also because the full cross‐section is crack free and • The 1970s saw the emergence of new applications effective, prestressed member tend to have greater stiffness – Post‐tensioned foundations for single and multi‐family – Higher capacity to absorb energy (impact resistance) and high fatigue resistance due to low steel stress variation as a result of the high initial residences on expansive and compressible soils pretension – Prestressed rock and soil anchors

BMA Engineering, Inc. – 5000 27 BMA Engineering, Inc. – 5000 28 Advantages & Disadvantages Post‐Tensioning Systems (Cont’d) • Disadvantages • Three basic types of post‐tensioning tendons

– Higher strength concrete and steel are required – More complicated formwork may be required – UbUnbon ddded TdTendons – End anchorages and bearing plates are usually required • Standard – Closer control required in manufacture and closer control of every • Encapsulated phase of construction is required – Labor costs are higher – Bonded Tendons – Additiona l conditions must be chhkdecked in ddiesign, such as stresses – External Tendons when prestressing forces are first applied and stresses after loss of prestress

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Post‐Tensioning Systems Unbonded Tendon

• Unbonded single strand tendons are the most widely used in • A tendon in which the prestressing steel is prevented from buildings and parking structures bonding, and is free to move, relative to the surrounding concrete • They consist of 7‐wire strands. Most commonly used sizes are 050.5” dia strands • The prestressing force can only be transfdferred to the concrete through the anchorage

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• Single strand • Extruded plastic sheathing (HDPE or PP) • Corrosion inhibiting coating (grease or wax) • Ductile iron anchors & hardened steel wedges • Supported by chairs and bolsters • Fully encapsulated in aggressive environments

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7‐Wire Strand Manufacture New Strand

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Encapsulated Tendons Post‐Tensioning Systems ‐ Bonded Tendons

• Strand or bar • Typically multiple strands • Steel or plastic duct • Grouted • Specially designed anchors

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Schematic representation of a typical bonded tendon

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Duct Bar Tendon

• Round, oval, or flat • Uncoated, galvanized, or coated metal, or various types of plastic • Minimum Diameter: – PTI: 225% of strand cross‐section area (250% for Pull‐Through Method – AASHTO: 250% – Single Bar Tendons: Bar diameter + 0.25 in.

BMA Engineering, Inc. – 5000 43 BMA Engineering, Inc. – 5000 44 Post‐Tensioning Systems ‐ Unbonded vs. Multi‐Strand Stressing Equipment BddBonded • Multi‐strand stressing jacks – tend to be heavier and • Unbonded proprietary – Economical – Greater layout flexibility – Force transmitted solely by the anchors – Total force limited by anchor spacing – Retrofit openings require more care – Replaceable – Simple stressing equipment

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Post‐Tensioning Systems ‐ Unbonded vs. Post‐Tensioning Systems ‐ External Tendons BddBonded (Cont’d) • Bonded • Unbonded bar or strand – Can be more costly due to duct placement & grouting • Outside of the concrete structural member – Force transmitted by anchors and bond to concrete • Straight or harped profile – Greater total force can be applied – Strain compatibility with concrete • Can be grouted, sheathed, encased in grease – Openings less difficult or wax – Minimizes need for non‐prestressed reinforcement • Special case: cable stays – More complex stressing equipment required

BMA Engineering, Inc. – 5000 47 BMA Engineering, Inc. – 5000 48 Post‐Tensioning Systems ‐ External Tendons Tendon Sweep (Cont’d) • An external tendon inside a bridge box girder

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Post‐Tensioning Applications ‐ Mat Foundations Post‐Tensioning Applications ‐ Mat Foundations (Cont’d)

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Clean Strands Mark Tendons

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• A hydraulic jack pushes directly against an anchorage imbedded in the hardened

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Burn Tendon Ends Hydraulic Shear

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5220 ‐ Introduction to Analysis & design of 5200. Prestressed Concrete PdPrestressed Beams

5210 • 5210 ‐ Pre and Post Tensioning Systems • Chapter 18 and other provisions of the ACI code not specifically excluded (18.1.3) apply to prestressed concrete 5220 • 5220 ‐ Introduction to Analysis & design of Prestressed Beams • Design Assumptions – Section 18.3.3 defines three classes of prestressed

flexural members based on ft (extreme fiber stress in tension in the precompressed tensile zone, computed using gross sectional properties, psi) as follows:

BMA Engineering, Inc. – 5000 63 BMA Engineering, Inc. – 5000 64 Analysis & Design – Prestressed Concrete Serviceability Design Requirements (Cont’d) • Design Assumptions:

(a) Uncracked Class U: ft ≤ 757.5 √f´c

(b) TitiTransition Class T: 757.5 √f´c < ft ≤ 12 √f´c

()(c) CCkdracked Class C: ft > 12 √f´c

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Permissible Stresses in Prestressing Steel Permissible Stresses in Prestressing Steel (Cont’d)

• The permissible tensile stresses in all types of ppgrestressing b. Immediately after prestress transfer:..0.82fpy but not greater than 0.74fpu

steel, in terms of the specified minimum tensile strength fpu, are summarized in 18.5.1 as follows: Low‐relaxation wire and strands (fpy = 0.90fpu)………………...... 0.74fpu

(a) Due to tendon jacking force: …….0.94fpy but not greater than 0.80fpu Stress‐relieved wire and strands, and plain bars (fpy = 0.85fpu) ...... 0.70fpu

Low‐relaxation wire and strands (fpy = 0.90fpu) ……………………………0.80fpu Defdformed bars (fpy = 0.80f pu) ...... 0.66f pu

Stress‐relieved wire and strands, and plain bars)(fpy = 0.85fpu)..0.80fpu

Defdformed bars (ASTM A722) (fpy = 0.80f)fpu)…………………….………..0.75 fpu c. Post‐tensioning tendons, at anchorages and couplers, immediately after tendon anchorage ..... …………………………………………………………………..0.70fpu

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• The code commentary (Section 18.6) points to – Friction Losses several references on how to compute prestress losses • CttiComputation of ffitiriction losses is covered in ACI • Formulas are available for calculating 18.6.2. When the tendon is tensioned, the – Elas tic Shor ten ing of CCtoncrete friction losses computed can be checked with reasonable accuracy by comparing the – Creep of Concrete measured tendon elongation and the – Shkhrinkage of Concrete prestressing force applied by the tensioning jack – Relaxation of Tendons

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Flexural Strength Flexural Strength (Cont’d) ‐ Notations

• Flexural strength of prestressed members is calculated fps = stress in prestressed reinforcement at nominal using the same assumptions as non prestressed strength psi members dp = distance from extreme compression fiber to • Flexural strength is defined as ultimate concrete strain centroid of prestressed reinforcement, in. of 0.003 and substituting f (stress in prestressed ps ρρ = ratio of prestressed reinforcement = Aps / bdp reinforcement at nominal strength psi) for fy ω = ρ fy / f´c • To avoid lengthy fps calculations based on strains ω´= ρ´f / f´ compatiblbility, the code provides approximate y c Equations 18.3, 18.4 and 18.5 fpu = specified tensile strength of prestressing steel, psi

BMA Engineering, Inc. – 5000 71 BMA Engineering, Inc. – 5000 72 Flexural Strength (Cont’d) ‐ Notations Flexural Strength (Cont’d) – Bonded Tendons

γp = factor for type of prestressing steel

= 0550.55 for fpy / fpu ≥ 0800.80 (deformed bars)

= 0.40 for fpy / fpu ≥ 0.85 (stress – relieved wire and strands, and plain bars)

= 0.28 for fpy / fpu ≥ 0.90 (low –relaxation wire and strands).

fpy = specified yield strength of prestressing steel, psi.

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Flexural Strength (Cont’d) – Bonded Tendons Flexural Strength (Cont’d) – Unbonded Tendons

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For fully prestressed members Eq. 18 – 3 reduces to:

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Flexural Strength (Cont’d) Limits for Reinforcement of Flexural Members ( ACI 18.8 ) With the value of fps known, the nominal moment strength of a rectangular section or a flanged section where the stress • The classifications of tension‐controlled, transition, or block is within the compression flange, can be calculated as compression controlled and the appropriate ф factors follows: also apply to prestressed concrete • The code provides in Section 18.8.2 provisions analogous to 10.5 for non prestressed members, to ensure adequate cracking and significant deflections before failure • The code requires adequate reinforcement to ddlevelop a design moment strength at least equal to 1.2 times the cracking moment strength

BMA Engineering, Inc. – 5000 79 BMA Engineering, Inc. – 5000 80 Limits for Reinforcement of Flexural Members Stress Conditions for Evaluating Cracking ( ACI 18.8 ) (Cont’d) Moment SShtrength ‐ NiNotations

• Adequate reinforcement to develop a design moment Aps = aaearea of pr estressed reeoceeinforcement in teesensile zooene

strength at least equal to 1.2 times the cracking moment Ac = area of precast member strength, that is, Sb = section modulus for bottom of precast member фM ≥ 1.2 M n cr Sc = section modulus for bottom of composite member where M is computed by elastic theory using a cr Pse = effective prestress force modulus of rupture equal to 7.5 √f´c e= eccentricity of prestress force • The provision of 18.8.2 is waived (based on experience) Md = dead load moment of composite member for (()a) Two‐way, unbddbonded post‐titensione d sllbabs; and (b) M = additional moment to cause a stress in bottom Flexural members with shear and flexural strength at a least twice that required by 929.2 fiber equal to modulus of rupture fr

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Cracking Moment Cracking Moment (Cont’d)

The cracking moment Mcr for a prestressed member is determined by summing all the moments that will cause a stress in the bottom fiber equal to

the modulus of rupture fr. Referring to the figure shown below for an unshored prestressed composite member and taking compression as negative and tension as positive:

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• The A minimum area of bonded reinforcement • Provisions are same as nonprestressed members shall be provided in all flexural members with • Prestressing strains have to be accounted for unbonded tendons as required by 18.9.2 and 18.9.3. compression members with an average concrete • Except as provided in 18.9.3, minimum area stress due to prestressing of less than 225 psi, of bonded reinforcement shall be computed by minimum nonprestressed reinforcement must be provided (18.11.2.1) As = 0.004A (18‐6) ct • For compression members with an average concrete where Act is area of that part of cross section between stress due to prestressing equal to or greater than 225 the flexural tension face and center of gravity of gross psi, 18.11.2.2 requires that all prestressing tendons be section enclosed by spirals or lateral ties, except for walls

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Prestressed Compression Members (Cont’d) Prestressed Compression Members (Cont’d)

• Since columns are primarily compression members, • Prestressing may also be used to neutralize dead creating additional compression by prestressing will not weight tensile stresses and there by prevent damage be desirable in most cases of slender precast members during construction • Columns in some exceptional cases are prestressed when buckling strongly influences the mode of failure. • Prestressing of piles prevents damage during the PtPrestressi ng is sometimes used on long sldlender columns driving operation. Prestressing prevents damage from that carry large bending moment and small axial load to transient‐tensile stresses generated by the stress eliminate cracking so that the whole cross section will waves from impact with the pile driver hammer be available to resist bending, ie, P‐delta effect is decreased and axial capacity of column is increased

BMA Engineering, Inc. – 5000 87 BMA Engineering, Inc. – 5000 88 Shear Strength for Prestressed Members Example—Flexural Strength of a Prestressed ( ACI 11.1) MbMember

• The design of shear reinforcement for prestressed Problem members is the same as for reinforced nonprestressed Calculate the nominal concrete members, except that Vc is computed differently and another minimum shear moment strength of the reinforcement requirement applies (11.4.6.4) prestressed member shown

• The code permits a slightly wider spacing of (3/4)h f ′ = 5000 psi (d(instead of d/2 ) for prestressed members, because c fpu = 270,000 psi (low-relaxation the shear crack inclination is flatter in prestressed strands; fpy = 0.90fpu) members

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Example—Flexural Strength of a Prestressed Example—Flexural Strength of a Prestressed MbMember MbMember

Solution Solution (Cont’d) • Calculate stress in prestressed reinforcement at nominal ● Calculate nominal moment strength strength using approximate value for fps. For a fully prestressed member, Eq. (18‐3) reduces to: −Compute the depth of the compression block:

BMA Engineering, Inc. – 5000 91 BMA Engineering, Inc. – 5000 92 Example—Flexural Strength of a Prestressed Example—Flexural Strength of Prestressed MbMember Member Based on Strain Compatibility

Solution (Cont’d) Problem The rectangular beam section shown below is reinforced with a • Check if tension controlled combination of prestressed and nonprestressed strands. Calculate the nominal moment strength using the strain compatibility (moment‐curvature) method.

fc′ = 5000 psi

fpu = 270,000 psi (low‐relaxation strand; fpy = 0.9fpu)

Eps = 28,500 kiksi

jacking stress = 0.74fpu Assume calculated losses = 31.7 ksi

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Example—Flexural Strength of Prestressed Example—Flexural Strength of Prestressed Member Based on Strain Compatibility Member Based on Strain Compatibility Solution Solution (Cont’ d) • Calculate effective strain in prestressing steel

ε = (0.74fpu ‐ losses)/Eps = (0.74 X 270 ‐ 31.7)/28,500 = 0.0059 • Draw strain diagram at nominal moment strength, dfiddefined by the maximum concrete compressive strain of 0.003 and an assumed distance to the neutral axis,

c. For fc′ = 5000, β1 = 0080.80 (see Figure, next slide)

BMA Engineering, Inc. – 5000 95 BMA Engineering, Inc. – 5000 96 Example—Flexural Strength of Prestressed Example—Flexural Strength of Prestressed Member Based on Strain Compatibility MbMember BdBased on Strai n Compa tibility Solution (Cont’d) Solution (Cont’ d) Stress-Strain Curve for Grade 270, Low Relaxation Strand • Obtain equilibrium of horizontal forces The “strain line” drawn above from point 0 must be located to obtain equilibrium of horizontal forces:

C = T1 + T2

To compute T1 and T2, strains ε1 and ε2 are used with the stress‐strain relation for the strand to determine

the corresponding stresses f1 and f2 (see Figure, next slide). Equilibrium is obtained using an iterative procedure

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Example—Flexural Strength of Prestressed Example—Flexural Strength of Prestressed Member Based on Strain Compatibility Member Based on Strain Compatibility Solution (Cont’ d) Solution (Cont’ d)

• Equilibrium is obtained using the following iterative g. Check equilibrium using C = T1 + T2 procedure h. If C < T1 + T2, increase c, or vice versa and return a. Assume c (location of neutral axis) to step b of this procedure. Repeat until b. Compute ε1 and ε2 satis fac tory convergence is achieve d. c. Obtain f1 and f2 from the equations at the bottom Estimate a neutral axis location for first trial. Estimate stressed of stress – strain figure (previous slide) strand at 260 ksi, unstressed strand at 200 ksi.

d. Compute a = β1c T = ΣApsfs = 0.306 (200) + 0.612 (260) = 220 kips = C

e. Compute C = 0085.85 fc′ ab a = C/(0.85 ›b) = 220/(0.85 5 12) = 4432.32 in.

f. Compute T1 and T2 c = a/β1 = 4.32/0.80 = 5.4 in. Use c = 5.4 in. for first try BMA Engineering, Inc. – 5000 99 BMA Engineering, Inc. – 5000 100 Example—Flexural Strength of Prestressed Example—Flexural Strength of Prestressed Member Based on Strain Compatibility Member Based on Strain Compatibility Solution (()Cont’d) Solution (Cont’ d) • The following table summarizes the iterations • Calculate nominal moment strength required to solve this problem:

Using C = 228.5 kips, T1 = 67 kips and T2 = 162 kips, the nominal moment strength can be calculated as

follows by taking moments about T2:

Mn = {[(d2 –a/2) C] ‐ [(d2 –d1) T1]}/12 = {[(22 – (4. 48/2) 228.5] – [(22 – 20) 67]}/12 = 365 ft‐kips

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5200. Prestressed Concrete • Objective and Scope Met – Provideed introductory level review of analysis and design of prestressed concrete structures – Presented and discussed • Pre and Post Tensioning Systems • Introduction to Analysis & design of Prestressed Beams

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