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SECTION 7: PRESTRESSED CONCRETE DESIGN

TABLE OF CONTENTS

7

7.1--SCOPE ..................................................................................................................................................................................7-1 7.2--DEFINITIONS .....................................................................................................................................................................7-1 7.3--NOTATION..........................................................................................................................................................................7-1 7.4--MATERIALS .......................................................................................................................................................................7-2 7.5--DESIGN................................................................................................................................................................................7-3 7.5.1--Method of Design.......................................................................................................................................................7-3 7.5.2--Concrete Strength.......................................................................................................................................................7-3 7.6--ALLOWABLE STRESSES.................................................................................................................................................7-3 7.6.1--Concrete......................................................................................................................................................................7-3 7.6.2--Prestressing Tendons..................................................................................................................................................7-3 7.7--LOSS OF PRESTRESS .......................................................................................................................................................7-4 7.8--STRENGTH REQUIREMENTS.........................................................................................................................................7-4 7.8.1--Design Flexural Strength ...........................................................................................................................................7-4 7.8.2--Design Shear Strength................................................................................................................................................7-5 7.8.3--Design Torsional Strength .........................................................................................................................................7-6 7.8.4--Combined Shear and Torsion ....................................................................................................................................7-7 7.9--DEVELOPMENT OF PRESTRESSING STRAND ..........................................................................................................7-7 7.9.1--Development Length..................................................................................................................................................7-7 7.9.2--Transfer Length..........................................................................................................................................................7-7 7.10--DURABILITY....................................................................................................................................................................7-8 7.10.1--General .....................................................................................................................................................................7-8 7.10.2--Concrete Cover.........................................................................................................................................................7-8 7.11--MANUFACTURING TOLERANCES .............................................................................................................................7-8 7.12--INSPECTION.....................................................................................................................................................................7-9 7.13--REFERENCES ...................................................................................................................................................................7-9

7-i

SECTION 7:

PRESTRESSED CONCRETE DESIGN

7.1--SCOPE This Section specifies design provisions for prestressed concrete members. Additional required design provisions, such as those noted in the commentary of this Section, shall be obtained from the LRFD Bridge Design Specifications.

7.2--DEFINITIONS Cracking Moment--A bending moment that produces a tensile stress greater than the sum of induced compression plus the tensile strength of the concrete resulting in tensile cracks on the tension face of the pole. Development Length--Length of embedded tendon required to develop the design strength of prestressing tendons at a critical section. Effective Prestress--Stress remaining in prestressing tendons after all losses have occurred, excluding effects of dead load and superimposed load. Post-Tensioning--Method of prestressing in which tendons are tensioned after concrete has hardened. Precast Concrete--Structural concrete element cast elsewhere than its final position in the structure. Prestressed Concrete--Structural concrete in which internal stresses have been introduced to reduce potential tensile stresses in concrete resulting from loads. Pretensioning--Method of prestressing in which tendons are tensioned before concrete is placed. Reinforcement--Steel material, including reinforcing bar and excluding prestressing tendons. Spiral Reinforcement--Continuously wound reinforcement in the form of a cylindrical helix. Strength, Design--Nominal strength multiplied by a strength reduction factor. Strength, Nominal--Strength of a member or cross-section before application of any strength reduction factors. Strength, Required--Strength of a member or cross-section required to resist factored loads. Tendon--Steel element, such as wire, bar, or strand, or a bundle of such elements, used to impart a prestress to concrete. Transfer--Act of transferring stress in prestressing tendons from jacks or pretensioning bed to concrete member. 7.3--NOTATION Av b bw d db fc f ci

fc

= = = = = = = =

area of the shear reinforcement (mm2, in.2) width of compression face of the member (mm, in.) width of the web (mm, in.) the distance from the extreme compression fiber to the centroid of longitudinal tension reinforcement (mm, in.) nominal diameter of pretensioning strand (mm, in.) specified 28-day design compressive strength of concrete (MPa, psi) c ompressive strength of concrete at time of initial prestress (MPa, psi) square root of specified compressive strength of concrete (MPa, psi)

7-1

7-2

STANDARD SPECIFICATIONS FOR STRUCTURAL SUPPORTS FOR HIGHWAY SIGNS, LUMINAIRES, AND TRAFFIC SIGNALS

fci

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

square root of compressive strength of concrete at time of initial prestress (MPa, psi) effective compressive stress in concrete due to prestress (MPa, psi) stress in prestressed reinforcement at nominal strength (MPa, psi) specified tensile strength of prestressing tendon (MPa, psi) specified yield strength of prestressing tendon (MPa, psi) effective stress in prestressed reinforcement (after allowance for all prestress losses) (MPa, psi) tensile strength of concrete (MPa, psi) specified yield strength of nonprestressed reinforcement (MPa, psi) moment of inertia of the cross-section (mm4, in.4) polar moment of inertia (mm4, in.4) development length of prestressing strand (mm, in.) moment due to load (N-mm, lb-in.) moment due to handling loads (N-mm, lb-in.) nominal moment strength of a section (N-mm, lb-in.) factored moment at section (N-mm, lb-in.) moment of area above the centroid (mm3, in.3) outside radius of section (mm, in.) spacing between shear reinforcement (mm, in.) wall thickness (mm, in.) torsional load (N-mm, lb-in.) nominal torsional strength at a section (N-mm, lb-in.) factored torsional moment (N-mm, lb-in.) shear load (N, lb) nominal shear strength provided by the concrete (N, lb) nominal shear strength (N, lb) nominal shear strength provided by reinforcement (N, lb) factored shear force (N, lb) shorter overall dimension of rectangular part of cross-section (mm, in.) longer overall dimension of rectangular part of cross-section (mm, in.) factor, as defined in Article 7.8.3 strength reduction factor

fpc fps fpu fpy fse Ft fy I J Ld M M Mn Mu Q ro s t T Tn Tu V Vc Vn Vs Vu x y

7.4--MATERIALS All materials and testing shall conform to the current editions of the appropriate standards included in the Standard Specifications for Transportation Materials and Methods of Sampling and Testing and/or from the American Society for Testing and Materials.

SECTION 7: PRESTRESSED CONCRETE DESIGN

7-3

7.5--DESIGN 7.5.1--Method of Design Design of prestressed concrete members shall be based on the allowable stresses and ultimate strength requirements of this Section. Working stresses resulting from prestress forces and Group I load combination (dead load) are investigated using an allowable stress design approach. Extreme loadings of Group II and Group III load combinations, which include wind and ice, are based on ultimate strength design.

7.5.2--Concrete Strength The minimum 28-day compressive strength f'c shall be 35 MPa (5000 psi). 7.6--ALLOWABLE STRESSES 7.6.1--Concrete Allowable stresses in concrete shall be in accordance with Table 7-1.

Table 7-1--Allowable Stresses in Concrete

Load Condition Pretensioned members at prestress transfer (before timedependent prestress losses) Post-tensioned members at prestress transfer (before timedependent prestress losses) Dead load--Group I load combination (after allowance for all prestress losses)

Allowable Compressive Stress (MPa, psi) 0.60 f ci 0.55 f ci 0.45 f c

Allowable Tensile Stress (MPa, psi)

0.25 fci (MPa)

3 fci

(psi)

0.25 fci (MPa) (psi) 3 f ci

0

7.6.2--Prestressing Tendons Tensile stress in prestressing tendons shall not exceed the following: a. due to tendon jacking force: 0.94fpy, but not greater than the lesser of 0.80fpu and the maximum value recommended by the manufacturer of prestressing tendons or anchorages; immediately after prestress but not greater than 0.74fpu; and transfer: 0.82fpy, The allowable stresses for prestressing tendons are in accordance with the Building Code Requirements for Structural Concrete for use with low-relaxation wire and strands, ordinary tendons (i.e., wire, strands, and bars), and bar tendons. Specifications for prestressing strand and wire are given in ASTM A 416 and A 421, respectively. Lowrelaxation wire and strand tendons meeting the requirements of ASTM A 416 and A 421 are commonly used for prestressed concrete poles. Low-relaxation tendons are recognized for their higher yield strength and reduced prestress losses.

b. c.

post-tensioning tendons, at anchorages and couplers, immediately after tendon anchor-age: 0.70fpu.

7-4

STANDARD SPECIFICATIONS FOR STRUCTURAL SUPPORTS FOR HIGHWAY SIGNS, LUMINAIRES, AND TRAFFIC SIGNALS

7.7--LOSS OF PRESTRESS Loss of prestress shall be considered in the design of pretensioned and post-tensioned members. A detailed analysis of losses is not necessary except for unusual situations where deflections could become critical. Lump sum estimate of losses may be used if supported by research data. Depending on the materials used, total prestress loss is usually between 15 percent and 25 percent. Reasonably accurate methods for calculation of prestress loss, such as that prescribed in the LRFD Bridge Design Specifications, Article 5.9.5, "Loss of Prestress," can be used for a better estimate of losses in lieu of using lump sum estimates. To determine the effective prestress fse losses due to anchorage seating, elastic shortening, creep of concrete, shrinkage of concrete, and relaxation of steel should be considered. Losses due to anchorage seating and elastic shortening are instantaneous, whereas losses due to creep, shrinkage, and relaxation are time-dependent. It should be recognized that the time-dependent losses resulting from creep and relaxation are also interdependent. This renders the exact calculation of prestress losses very difficult. However, undue refinement is seldom warranted or even possible at the design stage, because many of the component factors are either unknown or beyond the control of the Designer. Actual losses, greater or smaller than the computed values, have little effect on the design strength of the member, but they could affect service load behavior (i.e., deflections, camber, cracking load).

7.8--STRENGTH REQUIREMENTS 7.8.1--Design Flexural Strength The flexural design of the section shall be based on: Mu Mn where: = 0.9 and:

M u = 1.3M

(7-1)

(7-2)

Equations for the nominal flexural resistance, Mn, are given in the LRFD Bridge Design Specifications for rectangular prestressed or partially prestressed members. For other cross-sections, Mn may be determined by strain compatibility analysis based on the assumptions specified in Article 5.7.2 of the LRFD Bridge Design Specifications. Where the applicability of analysis methods is uncertain, ultimate strength may be determined by approved tests on full-scale sections.

(7-3)

and M is the moment due to Group II or Group III load combination. For handling loads, Mn 1.5M (7-4)

where M is the maximum moment expected during handling and erection of the member under its own weight and any attachments.

SECTION 7: PRESTRESSED CONCRETE DESIGN

7-5

7.8.2--Design Shear Strength The following shear strength requirement shall be satisfied: Vu Vn where: = 0.85

Vu = 1.3V Vn = Vc + Vs

(7-5)

(7-6) (7-7) (7-8)

and V is applied shear due to Group II or Group III load combination. For square and rectangular prestressed concrete members with effective prestress force not less than 40 percent of the tensile strength of the flexural reinforcement, Vc may be computed as:

V d Vc = 0.05 fc + 4.8 u bw d (N) Mu

V d Vc = 0.6 fc + 700 u bw d (lb) Mu

(7-9)

But, Vc need not be less than:

0.17 fc bw d , N,

( 2 fc bw d , lb), nor shall it be greater than

0.42 fc bw d , N,

( 5 fc bw d , lb). The quantity Vud/Mu shall not be greater than 1.0 where Mu is the factored moment occurring simultaneously with Vu at the section considered. The quantity d in the term Vud/Mu shall be the distance from the extreme compression fiber to the centroid of prestressed reinforcement.

7-6

STANDARD SPECIFICATIONS FOR STRUCTURAL SUPPORTS FOR HIGHWAY SIGNS, LUMINAIRES, AND TRAFFIC SIGNALS

For hollow circular prestressed members, Vc may be computed as:

Vc = Ft 2 + Ft f pc Q 2 It

The nominal shear strength of concrete is calculated based on elastic analysis and the assumption that cracking will occur when the principal stress reaches:

0.33 f c , MPa 4 fc , psi .

(

)

(7-10) (MPa) (psi) (7-11)

where:

Ft = 0.33 fc Ft = 4 fc

The shear force Vs contributed by the steel may be computed as:

Vs = Av f y d s

(7-12)

Design yield strength of shear reinforcement shall not exceed 415 MPa (60 000 psi). 7.8.3--Design Torsional Strength The following torsional strength requirement shall be satisfied:

Tu Tn

(7-13)

where:

= 0.85

(7-14)

and:

Tu = 1.3T

(7-15)

and T is the applied torsional moment due to Group II or Group III load combination. The value of Tn for a square or rectangular cross-section may be calculated using the following equation:

Tn = 0.5 fc 1 + 10 f pc fc

2 x y

(N-mm)

(7-16)

Tn = 6 fc 1 +

10 f pc fc

2 x y

(lb-in.)

where:

= 0.35 0.75 + b d For circular cross-sections:

(7-17)

SECTION 7: PRESTRESSED CONCRETE DESIGN

7-7

Tn =

J ro

Ft2 + Ft f pc

(7-18)

where:

Ft = 0.33 fc Ft = 4 fc

(MPa) (psi)

(7-19)

7.8.4--Combined Shear and Torsion For members subjected to flexural shear and torsion, the following interaction equation may be used to represent the strength of the member:

Vu Tu + 1.0 Vn Tn

2 2

(7-20)

7.9--DEVELOPMENT OF PRESTRESSING STRAND 7.9.1--Development Length Three- and seven-wire pretensioning strand shall be bonded beyond the critical section for a development length, Ld, of not less than:

2 d Ld = f ps - f se b 3 6.9

The expression for the development length, Ld, may be rewritten as:

Ld = f se d db + f ps - f se b 20.7 6.9

(mm)

(7-21)

(

)

(mm)

(C7-1)

2 d Ld = f ps - f se b 3 1000

(in.)

Ld =

f se db db + f ps - f se (in.) 3000 1000

(

)

The first term represents the transfer length of the strand (i.e., the distance over which the strand must be bonded to the concrete to develop the prestress fse in the strand). The second term represents the additional length over which the strand must be bonded so that a stress fps may develop in the strand at nominal strength of the member (ACI 318-95).

7.9.2--Transfer Length The transfer length of the prestressing tendons shall be considered at ends of members. The prestress force shall be assumed to vary linearly from zero at end of tendon to a maximum at a distance from end of tendon equal to the transfer length, assumed to be 50 diameters for strand and 100 diameters for single wire.

7-8

STANDARD SPECIFICATIONS FOR STRUCTURAL SUPPORTS FOR HIGHWAY SIGNS, LUMINAIRES, AND TRAFFIC SIGNALS

7.10--DURABILITY 7.10.1--General Concrete structures shall be designed to provide protection of the prestressing tendons and reinforcing steel against corrosion throughout the life of the structure. Aggregates from sources known to have experienced alkali­ silica reactions shall be prohibited. Portland cement with low alkali content, less than 0.6 percent, should be specified to ensure long-term durability. Additional requirements may be specified for structures in highly corrosive environments. Such requirements may include the use of special concrete additives, coatings, epoxy-coated strand, or increase in concrete cover. 7.10.2--Concrete Cover The minimum clear concrete cover for prestressed and nonprestressed reinforcement shall be as follows: a. b. 19 mm (3/4 in.) for centrifugally cast poles, and 25 mm (1 in.) for static cast poles. Severe corrosive environments include exposure to deicing salt, water or airborne sea salt, and airborne chemicals in heavy industrial areas. The centrifugal casting process results in a highly consolidated concrete that is denser than normal concrete, and hence the reduction in cover requirements for centrifugally cast (spun) poles.

Cover may be reduced to 13 mm (1/2 in.) for street lighting poles. For prestressed concrete structures exposed to severe corrosive environments, the minimum cover shall be increased by 50 percent. 7.11--MANUFACTURING TOLERANCES The following manufacturing tolerances shall apply: a. Length shall vary by no more than 50 mm (2 in.), or 25 mm plus 20 mm per 10 m (1 in. plus 1/4 in. per 10 ft) in length, whichever is greater. Outside diameter shall vary by no more than 6 mm (1/4 in.) for spun poles. For static cast poles, tolerance shall not vary in cross-section dimensions for less than 600 mm (24 in.), ±10 mm (±3/8 in.); 600 mm (24 in.) to 900 mm (36 in.), ±13 mm (±1/2 in.); over 900 mm (36 in.), ±16 mm (±5/8 in.). Wall thickness shall be not less than ­12 percent of the design thickness or 6 mm (1/4 in.), whichever is greater. Deviation from longitudinal axis shall vary no more than 20 mm per 10 m (1/4 in. per 10 ft) of length, applicable for the entire length or any segment thereof. Mass shall vary no more than 10 percent of the design mass. End squareness shall vary no more than 0.042 mm/mm (±1/2 in. per 1 ft) of diameter. For poles with base plates, more stringent requirements shall be specified.

b.

c. d.

e. f.

SECTION 7: PRESTRESSED CONCRETE DESIGN

7-9

g.

Longitudinal reinforcement shall vary no more than 6 mm (1/4 in.) for individual elements, and no more than 3 mm (1/8 in.) for the centroid of a group. Circumferential wire spacing shall be a maximum of 100 mm (4 in.), except at the ends (measured from either the top or bottom to a distance of 300 mm [1 ft]), where the maximum spacing shall be 25 mm (1 in.). Circumferential wire shall be within 40 mm (1 1/2 in.) of its specified location, except at the ends (measured from either top or bottom to a distance of 300 mm [1 ft]) where the spacing location shall be within ±6 mm (±1/4 in.). The number of spirals of cold-drawn circumferential wire along any 1.5 m (5 ft) of length shall not be less than required by design.

h.

7.12--INSPECTION The quality of materials, the process of manufacture, and the finished poles shall be subjected to inspection and approval by the Owner, the Designer, or both. Inspection records shall include quality and proportions of concrete materials and strength of concrete; placement of reinforcement, mixing, placing, and curing of concrete; and tensioning prestressing tendons. 7.13--REFERENCES AASHTO. 1996. Standard Specifications for Highway Bridges, Nth Edition, HB-N. American Association of State Highway and Transportation Officials, Washington, DC. AASHTO. 1998. AASHTO LRFD Bridge Design Specifications, Second Edition, LRFDUS-2 and LRFDSI-2. American Association of State Highway and Transportation Officials, Washington, DC. AASHTO. 1998. Standard Specifications for Transportation Materials and Methods of Sampling and Testing, Nth Edition, HM-N. American Association of State Highway and Transportation Officials, Washington, DC. ACI. 1995. Building Code Requirements for Structural Concrete, ACI 318-95. American Concrete Institute, Farmington Hills, MI. ASTM. 1998. "Standard Specification for General Requirements for Prestressed Concrete Poles Statically Cast," ASTM C935-95. In Annual Book of ASTM Standards. American Society for Testing and Materials, West Conshohocken, PA, pp. X­ Y. ASTM. 1998. "Standard Specification for Spun Cast Prestressed Concrete Poles," ASTM C1089-98. In Annual Book of ASTM Standards. American Society for Testing and Materials, West Conshohocken, PA, pp. X­Y. ASCE/PCI Joint Committee on Concrete Poles. 1997. "Guide for the Design of Prestressed Concrete Poles--Final Draft," PCI Journal. American Society of Civil Engineers and Precast/Prestressed Concrete Institute, City, ST, November/December 1997, pp. X­Y). PCI. 1992. PCI Design Handbook--Precast and Prestressed Concrete, Fourth Edition. Precast/Prestressed Concrete Institute, Chicago, IL.

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