Isis Ec Module 3 - Notes (PDF)

ISIS Educational Module 3:

An Introduction to FRP-Reinforced Concrete

Prepared by ISIS Canada A Canadian ian Netwo twork of Centre tres of Excelle llence www.isiscanada.com Principal Contributor: L.A. Bisby, Ph.D., P.Eng. Department of Civil Engineering, Queen’s University Contributors: M. Ranger and B.K. Williams March 2006

ISIS Education Committee: N. Banthia, University of British Columbia L. Bisby, Queen’s University R. Cheng, University of Alberta R. El-Hacha, University of Calgary G. Fallis, Vector Construction Group R. Hutchinson, Red River College A. A. Mufti, fti, Unive iversit rsity y of Manito itoba K.W. Neale, Université de Sherbrooke J. Newhook, Dalhousie University K. Soudki, University of Waterloo L. Wegner, University of Saskatchewan

ISIS Canada Educational Module No. 3: An Introduction to FRP-Reinforced Concrete

Objectives of This Module The objective of this module is to provide engineering students with an overall awareness of the application and design of fibre reinforced polymer (FRP) reinforcing materials in new concrete structures. It is one of a series of modules on innovative FRP technologies available from ISIS Canada. Further information information on the use of FRPs FRPs in a variety of innovative applications can be found at www.isiscanada.com.. While research into the use of FRP www.isiscanada.com materials as reinforcement for concrete is ongoing, an overall knowledge of currently available FRP reinforcements, and design procedures for their use, is essential for the new generation generation of structural engineers. The problems of the future cannot be solved with the materials and methodologies of the past. The primary objectives of this module are: 1. to provide engineering students with a general awareness of FRP materials and some of their potential uses in civil engineering applications;

2.

to introduce general philosophies and procedures for designing structures with FRP reinforcing materials; 3. to facilitate the use of FRP reinforcing materials in the construction industry; and 4. to provide guidance to students seeking additional information on this topic. The material presented herein is not currently part of a national or international code, but is based mainly on the results of numerous detailed research studies conducted in Canada and around the world. Procedures, material resistance factors, and design equations are based on the recommendations of the ISIS Canada Design Manual No. 3: Reinforcing Concrete Structures with Fibre Reinforced Polymers. As such, this this module should not be used as a design document, and it is intended for educational use only. Future engineers who wish to design FRP-reinforced concrete structures should consult more complete design documents (refer to Section 10 of this document).

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Additional ISIS Educational Modules Available from ISIS Canada ( www.isiscanada.com ) Module 1 – Mechanics Examples Incorporating FRP Materials

Module 6 – 6 – Application & Handling of FRP Reinforcements for Concrete

Nineteen worked mechanics of materials problems problems are presented which incorporate FRP materials. materials. These examples could be used in lectures to demonstrate various mechanics concepts, or could be assigned for assignment or exam exam problems. This module seeks to expose first and second year undergraduates to FRP materials at the introductory level. Mechanics topics covered covered at the elementary level include: equilibrium, stress, strain and deformation, elasticity, plasticity, determinacy, thermal stress and strain, flexure and shear in beams, torsion, composite beams, and deflections.

Important considerations in the handling and application of FRP materials for both reinforcement and strengthening of reinforced concrete structures are presented in detail. Introductory information on FRP materials, their mechanical properties, and their applications in civil engineering applications is provided. Handling and application of FRP materials as internal reinforcement for concrete structures is treated in detail, including discussions on: grades, sizes, and bar identification, handling and storage, placement and assembly, quality control (QC) and quality assurance (QA), and safety precautions. This is followed by information on handling and application of FRP repair materials for concrete structures, including: handling and storage, installation, QC, QA, safety, and maintenance and repair of FRP systems.

Module 2 – Introduction to FRP Composites for Construction FRP materials are discussed in detail at the introductory level. This module seeks to expose undergraduate students to FRP materials such that they have a basic understanding of the components, manufacture, properties, mechanics, durability, and application of FRP materials materials in civil infrastructure applications. applications. A suggested laboratory is included which outlines an experimental procedure for comparing the stress-strain responses of steel versus FRPs in tension, and a sample assignment is provided.

Module 4 – Introduction to FRP-Strengthening of Concrete Structures The use of externally-bonded FRP reinforcement for strengthening concrete structures is is discussed in detail. FRP materials relevant relevant to these applications are first presented, followed by detailed discussions of FRP-strengthening of concrete structures in flexure, shear, and axial compression. A series of worked examples examples are presented, case studies are outlined, and additional, more specialized, applications are introduced. A suggested assignment assignment is provided with worked solutions, and a potential laboratory for strengthening concrete beams in flexure with externally-bonded FRP sheets is outlined.

Module 5 – 5 – Introduction to Structural Health Monitoring The overall motivation behind, and the benefits, design, application, and use of, structural health monitoring (SHM) systems for infrastructure are presented and discussed at the introductory level. The motivation motivation and goals of SHM are are first presented and discussed, followed by descriptions of the various components, categories, and classifications of SHM systems. Typical SHM methodologies are outlined, innovative fibre optic sensor technology is briefly covered, and types of tests which can be carried out using SHM are explained. Finally, a series of SHM case studies is provided to demonstrate four field applications of SHM systems in Canada.

Module 7 – 7 – Introduction to Life Cycle Costing for Innovative Infrastructure Life cycle costing (LCC) is a well-recognized means of guiding design, rehabilitation and on-going management decisions involving infrastructure systems. LCC can be employed to enable and encourage the use of fibre reinforced polymers (FRPs) and fibre optic sensor (FOS) technologies across a broad range of infrastructure applications and circumstances, even where the initial costs of innovations exceed those of conventional alternatives. The objective of this module is to provide undergraduate engineering students with a general awareness of the principles of LCC, particularly as it applies to the use of fibre reinforced polymers (FRPs) and structural health monitoring (SHM) in civil engineering applications.

Module 8 – 8 – Durability of FRP Composites for Construction Fibre reinforced polymers (FRPs), like all engineering materials, are potentially susceptible to a variety of environmental factors that may influence their long-term durability. It is thus important, when contemplating the use of FRP materials in a specific application, that allowance be made for potentially harmful environments and conditions. It is shown in this module that modern FRP materials are extremely durable and that they have tremendous promise in infrastructure applications. The objective of this module is to provide engineering students with an overall awareness and understanding of the various environmental factors that are currently considered significant with respect to the durability of fibre reinforced polymer (FRP) materials in civil engineering applications.

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Section 1

Introduction and Overview WHY USE FRPs? The population of the modern developed world depends on a complex and extensive system of infrastructure for maintaining economic economic prosperity prosperity and quality quality of life. life. The existing public infrastructure of Canada, the United States, Europe, and other countries has suffered from decades of neglect and overuse, leading to the accelerated deterioration of bridges, buildings, and municipal and transportation systems, and resulting in a situation that, if left unchecked, may lead to to a global infrastructure crisis. Much of our infrastructure is unsatisfactory in some respect, and public funds are not generally available for the required replacement of existing structures or construction of new ones.

Fig. 1-1. 1-1. Severe Severely ly c orroded r einforcing steel in th is bridge column h as resulted in spalling of the concrete cover and exposur e of the steel reinforcement.

used in the past, they are looking to newer technologies, such as non-corrosive FRP reinforcement, that will increase the service lives of concrete structures and reduce maintenance costs. FRPs have, in the last ten to fifteen years, emerged as a promising alternative material for reinforcement of concrete structures. FRP materials are non-corrosive and nonmagnetic, and can thus be used to eliminate the corrosion problem invariably encountered with conventional reinforcing steel. steel. In addition, FRPs are are extremely extremely light, versatile, and demonstrate extremely high tensile strength, making them ideal materials for reinforcement of concrete (refer to Figure 1-2).

Fig. 1-2. FRP Reinforcing bars being installed in the conc rete deck of the Salmon River Bridge, British Columbia prior to pouring of the concrete. FRPs FRPs are particularly particularly us eful for reinforc ing concr ete bridge decks which are highly susceptible to corrosion.

One of the primary factors which has led to the current unsatisfactory state of our infrastructure is corrosion of reinforcing steel inside concrete (Fig. 1), which causes the reinforcement to expand, and results in delamination or spalling of concrete, loss of tensile reinforcement, or in some cases failure. Because infrastructure infrastructure owners owners can no longer afford to upgrade and replace existing structures using the same materials and methodologies as have been

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Section 2

FRP Materials This section provides a brief overview of FRP materials and some of their important characteristics and properties when used as reinforcing materials materials for concrete. A more complete discussion of FRP materials and their applications in civil engineering can be obtained from ISIS EC Module 2: FRP Composites for Civil Engineering Applications, or from one of a number currently available composite materials textbooks.

from the combination combination of fibres and matrix. matrix. The reader is is referred to ISIS EC Module 2 (ISIS, 2003) for further information on fibres and matrices.

GENERAL FRP materials, originally developed for use in the automotive and aerospace sectors, have been considered for use as reinforcement of concrete structures since the 1950s. However, it is really only in the last 10 years or so that FRPs have begun to see widespread use in large civil engineering projects, likely due to drastic reductions in FRP material and manufacturing costs, which have made FRPs competitive on an economic basis. Many types and shapes of FRP materials are now available in the the construction industry. industry. For the purposes purposes of tensile reinforcement of concrete, the currently available reinforcing products include unidirectional FRP bars, which have fibres oriented along the axis of the reinforcement only, and orthogonal grids, which have unidirectional bars running in in two (or sometimes sometimes 3) orthogonal orthogonal directions. directions. In this document, the focus is on unidirectional FRP reinforcing bars, since they are the most widely used of the FRP reinforcing products currently available in North America. Also, although although it has been been demonstrated through research that FRP materials can be effectively used for prestressed reinforcement of concrete structures, this is a specialized topic and is beyond the scope of this module. Fig. 2-1 shows various types and shapes of currently available FRP materials.

Fig. 2-1. 2-1. Various t ypes and sh apes of FRPs FRPs used i n the construction industry

Stress [Mpa]

1800-4900

600-3000

fibres

FRP matrix

34-130

0.4 – 4.8

Constituents FRP materials are composed of high strength fibres embedded in a polymer matrix. matrix. The fibres, which have have very small diameters and are generally considered continuous, provide the strength and stiffness of the composite, while the matrix, which has comparatively poor mechanical properties, separates and disperses the fibres. The primary function of the matrix is to transfer loads to the fibres through shear stresses that develop at the fibre-matrix interface, although it is also important for environmental protection of the fibres. In concrete reinforcing applications, the fibres are generally carbon (graphite), glass, or aramid (Kevlar), and the matrices are typically epoxies or vinyl esters. esters. Fig. 2-2 shows typical typical stress-strain stress-strain curves for fibres, matrices, and the FRP materials that result

> 10

Strain [%]

Fig. 2-2. 2-2. Stress-strain Stress-strain relationship s for fibres, matrix , and FRP.

Manufacturing Process Although a variety of techniques can be used to manufacture FRP shapes, a technique called pultrusion pultrusion is used almost exclusively for the manufacture manufacture of FRP reinforcing reinforcing rods. In this technique, continuous strands of the fibres are drawn from creels (spools of fibres) through a resin tank, where they are saturated with resin, pulled through a number of wiper rings, and finally pulled through a heated die. This process simultaneously forms and heat cures the FRP into a

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reinforcing rod. rod. To ensure a strong bond with concrete, a surface treatment is normally applied consisting of a spiral or braided wrap, or a coating of sand embedded in the outer surface of the polymer matrix. matrix. The pultrusion process is illustrated schematically below.

shaping and heating die

creel

puller

resin tank

Fig. 2-3. The pultrusion process.

Fig. 2-4. ISOROD glass FRP reinforcement.

Various FRP reinforcing products are currently available in industry. Figs. 2-4 to 2-6 show some of the different products currently being produced for use in NorthAmerica.

Properties Unidirectional FRP materials used in concrete reinforcing applications are linear elastic up to failure, and they do not exhibit the yielding behaviour that is typically displayed by conventional reinforcing reinforcing steel. This is shown shown in Fig. Fig. 2-7, which demonstrates the significant differences in the tensile behaviour of FRPs as compared with steel. FRP materials generally have much higher strengths than the yield strength of steel, although they do not exhibit yield, and have strains at failure that are are much less. The differences in behaviour between FRPs and steel have important consequences for the design of FRP-reinforced concrete members, as we shall see, since yielding of reinforcement in steel-reinforced concrete members is used implicitly to provide ample warning of impending failure. The specific properties of FRP materials vary a great deal from product to product, and depend on the fibre and matrix type, the fibre volume content, and the orientation of the fibres within the the matrix, among other factors. It is beyond the scope of this module to discuss different FRP reinforcing materials materials in detail. However, Table 2-1 and Fig. Fig. 2-7 give material properties for a number of typical FRP reinforcing products. products. It is thus thus becomes important in the design of FRP-reinforced concrete members to specify which FRP material is to be used and what minimum mechanical properties are required.

TM

Fig. 2-5. Leadlin Leadlin e

carbon FRP reinforcement.

Fig. 2-6. NEFMAC grid-shaped FRP reinforcement.

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Table 2-1. Selected Properties of Typical Currently Available FRP Reinforcing Products Diameter Area Tensile Strength Elastic Modulus Reinforcement Type Designation 2 [mm] [mm ] [MPa] [GPa] Deformed Steel #10 11.3 100 400* 200 V-ROD CFRP Rod 3/8 9.5 71 1431 120 V-ROD GFRP Rod 3/8 9.5 71 765 43 NEFMAC GFRP Grid G10 N/A 79 600 30 NEFMAC CFRP Grid C16 N/A 100 1200 100 NEFMAC AFRP Grid A16 N/A 92 1300 54 TM LEADLINE CFRP Rod -12 113 2255 147 * specified yield strength 2500 Steel ISOROD CFRP ISOROD GFRP NEFMAC GFRP NEFMAC CFRP NEFMAC AFRP TM Leadline CFRP

2000 ] a P 1500 M [ s s e r t 1000 S

500 0 0

1

2

high strength of these materials, they are often competitive on a cost-per-force basis. Furthermore, the excellent durability of FRP reinforcing materials in concrete, which has the potential to increase the service lives of structures while reducing inspection and maintenance costs, makes them cost-effective when the entire life-cycle cost of a structure is considered, rather than the initial construction cost alone. Another often cited potential disadvantage of FRP materials is their relatively low elastic modulus as compared with steel. This means that FRP-reinforced FRP-reinforced concrete concrete members are often controlled by serviceability (deflection) considerations, rather than strength requirements.

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Strain [%]

Fig. 2-7 2-7.. Stress-strain Stress-strain plots for variou s reinforc ing materials

Advantages and Disadvantages FRP materials for use in concrete reinforcing applications have a number of key advantages over conventional reinforcing steel. steel. Some of the most important important advantages include: • FRP materials do not corrode electrochemically, and have demonstrated excellent durability in a number of harsh environmental conditions; • FRP materials have extremely high strength-toweight ratios . FRP materials materials typically weigh weigh less than one fifth the weight of steel, with tensile strengths that can be as much as 8 to 10 times as high; and • FRP materials are electromagnetically inert . This means that they can be used in specialized structures such as buildings to house magnetic resonance imaging (MRI) or sensitive communications equipment, etc. There are, however, some disadvantages to using FRPs, as opposed to conventional reinforcing steel, as reinforcement for concrete. The main disadvantage is the comparatively comparatively high initial cost of FRP FRP materials. materials. Although prices have dropped drastically in recent years, most FRP materials remain more expensive than conventional reinforcing steel on an initial material material cost basis. basis. However, because of the

ADDITIONAL CONSIDERATIONS Coefficient of Thermal Expansion The thermal properties of FRP reinforcing products are substantially different than those of conventional reinforcing steel and concrete, and can also vary a great deal in the longitudinal and and transverse transverse directions. The characteristics characteristics are highly variable among different FRP products, and it is difficult to make generalizations regarding thermal expansion or other properties. properties. The thermal properties of any FRP reinforcing material should be thoroughly investigated before it is used as reinforcement for concrete, since differential thermal expansion of FRPs inside concrete has the potential to cause cracking and spalling of the concrete cover.

Table 2-2. 2-2. Typical Coeffic ients o f Thermal -6 Expansion for FRP FRP Reinforcin Reinforcin g Bars [ 10 /°C] Material Direction Steel GFRP CFRP AF AFRP Longitudinal 11.7 6 to 10 -1 to 0 -6 to –2 Transverse 11.7 21 to 23 22 to 23 60 to 80

Effect of Elevated Temperature or Fire Elevated temperatures, as may be experienced in some industrial settings or in the case of fire, adversely affect the mechanical and bond properties of FRP reinforcing materials in concrete. Thus, special precautions precautions are required

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when FRPs are used in structures where elevated temperatures or fire are concerns. concerns. In most most cases, cases, the temperature or the FRP reinforcement should b e maintained below the glass transition transition temperature (GTT) (GTT) of the polymer polymer matrix. For currently available FRP FRP reinforcing reinforcing products the GTT is generally in the range of 65 to 150°C.

Bond Properties The properties of the bond between FRP reinforcing bars and concrete depend on the surface treatment applied to the FRP reinforcing bar during manufacturing, the mechanical properties of the FRP, and the environmental conditions to which the bar is subjected during during its lifetime. Again, generalizations are difficult to make, although the bond between currently available FRP reinforcing materials and concrete appears equivalent (or superior in some cases) to that between steel steel reinforcement and concrete. concrete. The bond of FRP bars to concrete does not depend on the concrete strength, as it does for steel reinforcement.

Creep and Relaxation When FRP materials are subjected to a constant elevated stress level they can fail fail suddenly and unexpectedly. This type of failure is referred to as creep-rupture and is highly

undesirable. The larger the ratio of the sustained (dead (dead load) stress to the transient (live load) stress in an FRP reinforcing bar, the more likely creep-rupture becomes. Susceptibility to creep rupture is also influenced by UV radiation, high temperature, alkalinity, and weathering. Different FRP types have different susceptibilities to creep-rupture. Carbon FRPs are the least susceptible, followed by aramid aramid FRPs. FRPs. Glass FRPs FRPs are the most susceptible. To protect against against creep-rupture, creep-rupture, the material material resistance factors suggested by ISIS Canada (ISIS, 2001) for FRP reinforcements have been adjusted to account for the effect of sustained sustained load. These resistance resistance factors, Φfrp, are given in Table 3-1.

Durability The durability of FRP reinforcing bars in concrete is a complex topic and research in this area is ongoing. Readers seeking additional information on the durability of FRP materials are encouraged to consult ISIS Educational Module #8, also available from ISIS Canada at www.isiscanada.com.. To date, FRP reinforcing applications www.isiscanada.com in concrete structures have performed well, and no failures due to durability problems have been reported.

Section 3

Design for Flexure PHILOSOPHY AND ASSUMPTIONS The design of FRP-reinforced concrete in Canada should be conducted under the unified limit-states philosophy currently used by the existing design design codes. For buildings, loads and load combinations for FRP-reinforced concrete members should be determined in accordance with CSAS806-02. For bridges, the Canadian Highway Bridge Design Code, CSA-S6-05, CSA-S6-05, should should be used. Serviceability checks for cracking and deflection must also be performed.

Resistance Factors Following the recommendations of ISIS Canada Design Manual No. 3, the material resistance factor for concrete is taken as Φc = 0.60 for buildings, 0.65 for precast concrete, and 0.75 for bridges. bridges. The material material resistance resistance factor for FRPs depends on the type of FRP material, and is based on the variability of material characteristics, the effect of sustained load, and various durability considerations. Table 3-1 provides resistance factors for steel, concrete, and FRP materials as specified by relevant Canadian codes.

Assumptions It is assumed that FRPs are perfectly linear-elastic materials. Thus, failure of an FRP-reinforced section in flexure can be due to FRP FRP rupture or concrete crushing. The ultimate ultimate flexural strength for both of these failure modes can be calculated using a similar methodology as that used for steel-reinforced steel-reinforced sections. Hence, the the following following additional assumptions are required: 1. the failure strain of concrete in compression is 3500 × 10-6; 2. the strain in the concrete at any level is proportional to the distance from the neutral axis (plane sections remain plane); 3. FRPs are linear elastic to failure; 4. concrete compressive stress-strain curve is parabolic and concrete has no strength in tension; 5. perfect bond exists between FRP reinforcement and concrete; and 6. neglect FRPs’ strength in compression.

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Table 3-1. 3-1. Resistanc Resistanc e Facto Facto rs f or FRP Bars Material Notation Factor Building Components: CSA-S806-02 Φc Concrete cast in situ 0.60 Precast concrete 0.65 Φc Steel reinforcement 0.85 Φs Carbon FRP 0.75 Φf Glass FRP 0.75 Φf Aramid FRP 0.75 Φf Bridge Components: CSA-S6-05 Concrete 0.75 Φc Carbon FRP 0.75 Φf Aramid FRP 0.60 Φf Glass FRP 0.50 Φf Stress f frfr

u

E fr fr 1

Strain εfr

Compression failure is the most desirable of the above failure modes. This failure mode is less violent violent than tension failure, and is similar to the failure of an over-reinforced section when using steel reinforcement. Tension failure is less desirable, since tensile rupture of FRP reinforcement will occur with less warning. Tension failure will occur when the reinforcement ratio is below the balanced reinforcement ratio for the section. This failure mode is permissible with certain safeguards.

Balanced Failure As mentioned above, balanced failure will occur when concrete crushing occurs simultaneously with FRP tensile rupture. It is important to remember remember that the balanced failure condition is drastically different for FRP-reinforced concrete than it is for members reinforced with steel. Because FRPs will not yield at the balanced condition, an FRP-reinforced concrete member at the balanced condition will fail suddenly, although accompanied by cracking and a significant amount of deflection. At balanced failure, the strain in the concrete reaches its ultimate value, εcu = 0.0035, while the FRP reinforcement simultaneously reaches its ultimate strain, ε frpu. The ultimate ultimate strain strain of the FRP depends on the specific FRP reinforcing material being used (refer to Table 2-1), and is determined from the FRP ultimate stress, f stress, f frpu, and tensile elastic modulus, E modulus, E frp, using:

u

Fig. 3-1. Assumed stress-strain behaviour of FRP.

ε frpu

=

Stress

f frpu E frp

(Eq. 3-1)

Using strain compatibility, for a rectangular cross-section with a single layer of FRP reinforcement, the distribution of strains across the member can be illustrated as shown in Fig. 3-3a. Thus, the ratio ratio of the balanced balanced neutral axis depth, cb, to the effective depth of the section, d , at the balanced reinforcement ratio, ρ frpb, can be expressed in terms of known quantities as follows:

f’ c c f c c E c c 1

Strain εc

ε’ c c

εcu

Fig. 3-2. 3-2. Assumed stress-strain behaviour of concrete. FAILURE MODES There are three potential flexural failure modes for FRPreinforced concrete sections: • Balanced failure – simultaneous FRP tensile rupture and concrete crushing • Compression failure – concrete crushing prior to FRP tensile rupture • Tension Failure – tensile rupture of the FRP prior to concrete crushing

cb d

=

ε cu ε cu

+ ε frpu

(Eq. 3-2)

To determine the balanced reinforcing ratio, force equilibrium over the cross-section is utilized, and the compressive and tensile stress resultants, C and T , are equated as follows:

= T C =

(Eq. 3-3)

The true distribution of stress in the concrete in the compression zone is non-linear, as shown in Figure 3-3a. However, as is the case for steel-reinforced concrete members, we can replace the non-linear stress distribution with an equivalent equivalent rectangular stress-block. stress-block. To do this, the

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same stress-block parameters, α1 and β 1, are used as those suggested in CSA A23.3-94/CHBDC for steel-reinforced concrete, namely:

= 0.85 − 0.0015 f 'c ≥ 0.67 β 1 = 0.97 − 0.0025 f ' c ≥ 0.67 α 1

(Eq. 3-4) (Eq. 3-5)

β 1c = a

Thus, the compressive stress resultant is:

C = α 1φ c f 'c β 1cb b

(Eq. 3-6)

The tensile stress resultant is determined from the FRP ultimate stress and the cross-sectional area of FRP reinforcement:

=

bd

= α 1 β 1

φ frp A frp f frp α 1φ c f c' b

ε frp

=

⎛ ε cu ⎞ ⎜ ⎟ (Eq. 3-8) ⎜ f frpu ⎝ ε cu + ε frpu ⎠⎟

c

⇒ ε frp = ε cu

For a given FRP-reinforced concrete member, an FRP reinforcement ratio less than ρ frpb will result in tension failure, and an FRP reinforcement ratio greater than ρ frpb will result in compression failure. Next, we will will examine the two potential failure modes that are of practical interest.

β 1d − β 1c β 1c

⇒ f frp = E frp ε cu

φ c f 'c φ frp

(Eq. 3-11)

d − c

(Eq.3-7)

Now, equating the compressive and tensile stress resultants and rearranging, the balanced failure reinforcement ratio, ρ frpb, is obtained:

ρ frpb

=

And from strain compatibility (refer to Fig. 3-3b) we can derive the following:

ε cu

T = φ frp ε frpu E frp A frp

A frpb

A complication in the analysis arises from the fact that FRP reinforcement does not yield, and hence the stress in the FRP at compression failure of the member, f frp, is unknown. Equating the tensile and compressive stress resultants yields:

(Eq. 3-12)

β 1d − a a

Now, substituting Eq. 3-11 into Eq. 3-12, and solving for the stress in the FRP reinforcement at compressive failure, gives: 1 ⎡ ⎤ ' ⎛ 4α 1 β 1φ c f c ⎞ 2 1 ⎢ ⎟ − 1⎥ (Eq. 3-13) f frp = E frp ε cu ⎢⎜1 + ⎥ ⎜ ρ frpφ frp E frpε cu ⎟ 2 ⎠ ⎢⎣⎝ ⎥⎦

Compression Failure If an FRP-reinforced concrete section contains sufficient tensile reinforcement, then failure of the section will be induced by crushing of the concrete in the compression zone before the FRP reaches its ultimate strain. This type of failure is highly unlikely for a T-section in positive bending, since the width of the compression zone, b, is very large, and so only rectangular sections are considered. For the case of compression failure, the strains in the cross-section can be illustrated as shown in Figure 3-3b. Again, the strain in the extreme compression fibre is assumed to be εcu = 0.0035, and the non-linear stress distribution in the concrete can be replaced by the CSA A23.3-94/CHBDC equivalent rectangular stress block (using parameters α1 and β and β 1 as defined previously). The compressive and tensile stress resultants can be determined as follows:

C

=

α 1 φ c f c ' β 1 cb

(Eq. 3-9)

T

= φ frp A frp f frp

(Eq. 3-10)

Once the stress in the FRP reinforcement is known, Eq. 3-11 can be used to determine the depth of the equivalent rectangular stress block, a, and the flexural capacity, M capacity, M r r, can be obtained in a similar fashion as for steel-reinforced concrete:

M r

a ⎞ = φ frp A frp f frp ⎛ ⎜ d − ⎟ ⎝ 2 ⎠

(Eq. 3-14)

NOTE: Rather than using Eq. 3-13 to determine the stress in the FRP at compressive failure, an iterative procedure can be performed using Eqs. 3-9, 3-10, and 3-11 by assuming a neutral axis depth, calculating the compressive and tensile stress resultants using strain compatibility, and checking if C = C = T . If C ≠ T , the neutral axis depth is updated and the procedure is repeated until convergence of the neutral axis depth is achieved within a suitable tolerance.

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α1Φcf’c

b εcu a = β1cb

cb

C

(a) BALANCED FAILURE εc = εcu εfrp = εfrpu

d Afrpb f frpu frpu

εfrpu

T

α1Φcf’c εcu a = β1c

c

C

(b) d

COMPRESSION FAILURE εc = εcu εfrp < εfrpu

Afrp εfrp < εfrpu

f frp frp

T

αΦcf’c εc < εcu a = βc

c

C

(c) TENSION FAILURE εc < εcu εfrp = εfrpu

d Afrp f frpu frpu

εfrpu

Cross-section

Strain Distribution

Stress Distribution

T

Equivalent Stress Distribution

Fig. 3-3. 3-3. Flexural Flexural f ailure mod es for FRP-reinfo FRP-reinfo rced co ncrete beams.

Tension Failure If the FRP reinforcement ratio is less than the balanced failure reinforcement ratio, then the section will fail by FRP tensile rupture before the concrete in the compression zone crushes (Fig. (Fig. 3-3c). This situation situation is different from an under-reinforced concrete member with steel reinforcement in that there is is no yielding of the the FRP. In this case, the

strain in the concrete at failure is less than εcu = 0.0035, and the strain in the FRP reinforcement is given by:

ε frpu

=

f frpu E frp

(Eq. 3-15)

Because the concrete in the compression zone is not at ultimate, the stress distribution in the concrete cannot be

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described using the equivalent rectangular stress block parameters used previously. The α1 and β 1 parameters suggested by CSA A23.3-94/CHBDC are valid only for the case of εc = εcu. Thus, modified stress block parameters parameters are required. These modified parameters, α and β , can be determined either from tabulated values available in ISIS Design Manual No. 3, or from Figs. 3-2 and 3-3 below, which give α and β as as functions of the strain in the concrete for a variety of concrete strengths.

C = αφ c f c' β cb

(Eq. 3-17)

Again, for equilibrium it is required that:

C = = T

(Eq. 3-18)

If the above equation is not satisfied, then a new value of the neutral axis depth is assumed, α and β are are reevaluated, and Eq. 3-18 is checked. This process is repeated in an iterative iterative fashion until Eq. 3-18 is satisfied. For each iteration, iteration, the updated neutral axis depth, c, can be determined using:

c

=

φ frp A frp ε frpu E frp

(Eq. 3-19)

αφ c f c' β b

where α and β are determined at the following concrete strain (from strain compatibility, Fig. 3-3c):

ε c

Fig. 3-2. Equivalent stress-block parameter α for for concrete.

= ε frpu

c

(Eq. 3-20)

d − c

Once the tensile and compressive stress resultants are known, the moment resistance of the member can be determined by taking moments about the compressive stress resultant. Thus:

M r

= φ frp A frp f frpu ⎛ ⎜ d − ⎝

β c ⎞

⎟

2 ⎠

(Eq. 3-21)

Due to the brittle failure associated with failure by rupture of the FRP reinforcement, it is recommended that and additional safety requirement of:

M ≥ 1.5 M r f

(Eq. 3-22)

be applied when failure failure is by tensile tensile rupture of the FRP.

MINIMUM FLEXURAL RESISTANCE

Once α and β have been determined, the tensile and compressive stress resultants can be determined for an assumed value of the neutral axis depth using:

Three criteria are suggested by ISIS Canada Design Manual No. 3 to provide minimum tensile reinforcement for an FRP-reinforced FRP-reinforced concrete member. Failure of a member immediately after cracking, which occurs suddenly and without warning, should be avoided. Thus, the moment resistance of an FRP-reinforced concrete member, M r r, should be at least 50% greater than the cracking moment, M moment, M cr cr . Hence:

T = φ frp A frp f frpu

M r ≥ 1.5M cr

Fig. 3-3. Equivalent stress-block parameter β for concrete.

= φ frp A frp ε frpu E frp

(Eq. 3-16)

(Eq. 3-23)

11


The cracking moment is determined from the modulus of rupture of the concrete, f r r , the moment of inertia of the transformed section, I section, I t t , and the distance from the centroidal axis of the transformed section to the extreme tension fibre, yt , using:

M cr

=

f r I t y t

where f r

= 0.6

f 'c

permitted (refer to Figure 3-4). Members can be easily designed on the basis of the strain in the outermost layer of FRP reinforcing bars by assuming strain compatibility.

(Eq. 3-24)

As the minimum reinforcement condition is usually governed by tensile rupture of the FRP reinforcement, the moment resistance, M r r , must be at least 50% greater than the moment due to the factored loads, M loads, M f . Thus:

M ≥ 1.5 M r f

(Eq. 3-25)

ADDITIONAL CONSIDERATIONS Beams with FRP Rebars in Multiple layers For the case of FRP-reinforced concrete beams with reinforcement in two or more layers, the strain in the outer layer of FRP reinforcement reinforcement is the critical critical strain. This means that “lumping” of reinforcement, as is commonly performed in the analysis of steel-reinforced concrete beams, is not

Fig. 3-4 3-4.. Lumping o f reinforcement is no t permitted.

Beams with Compression Reinforcement FRP reinforcing materials are generally weak in compression. Although these these materials materials may be used as compression reinforcement, their contribution contribution to the flexural strength of FRP-reinforced concrete members should be neglected.

Section 4

Serviceability GENERAL Serviceability considerations, relating both to cracking and to deflection, are crucial factors in the design of FRPreinforced concrete flexural members. FRP reinforcing reinforcing bars generally have much higher strengths than the yield strength of conventional steel reinforcement. reinforcement. However, the modulus modulus of elasticity of FRP materials is generally less than that of reinforcing steel, and this can lead to the formation of large cracks or to unserviceable unserviceable deflections. The result is that, in in many cases, serviceability considerations may control the design of FRP-reinforced FRP-reinforced concrete members.

primarily for aesthetic reasons, as well as to control service load stresses in the reinforcement (to prevent creep-rupture). If there is a need to calculate the crack width at service load levels for an FRP-reinforced concrete member, guidance is available in Section 7.4.1 of ISIS Design Manual No. 3. The limiting crack width for FRP-reinforced members is recommended by CHBDC (CSA, 2005) to be 0.7 mm, except for members subjected to aggressive environments where 0.5 mm is recommended. Alternatively, as a conservative approach, the ISIS design guidelines suggest, to control cracking, that the maximum strain in tensile FRP reinforcement at service should not exceed 0.2%. Thus:

CRACKING In steel-reinforced concrete members, it is necessary to control crack widths both for aesthetic reasons and to prevent corrosion of reinforcing steel. For FRP-reinforced FRP-reinforced members, there is no such corrosion requirement (FRP bars are non-corrosive) and so cracking must be limited

ε frps

≤ 0.002

(Eq. 4-1)

The strain in the FRP at service load levels can be determined using the concept of transformed sections in either cracked or un-cracked sections.

12


If there is a need to calculate the crack width at service load levels for an FRP-reinforced concrete member, guidance is available in Section 7.3.1 of ISIS Design Manual No. 3.

The ratio (l (l n /h) /h) s is the equivalent ratio for steel-reinforced concrete and is obtained from Table 9-1 of CSA A23.3-94.

DEFLECTION

If a member remains uncracked under service loads, then deflection requirements requirements can be checked using the concept of transformed sections. sections. However, if the member is cracked under service load, the effective moment of inertia should be calculated (for a rectangular section) using the following equation, which was empirically derived from test data on FRP-reinforced FRP-reinforced concrete members:

Since the modulus of elasticity of FRP reinforcement is generally substantially lower than for conventional steel reinforcement, FRP-reinforced members typically display significantly more deflection than equivalent steelreinforced members. This means that the minimum thickness (overall member depth) requirements used in CSA A23.3-94 or CSA S6-05 for steel-reinforced concrete are unconservative, and are thus not directly applicable to members reinforced reinforced with FRPs. Furthermore, deflections for FRP-reinforced concrete members must be checked against the requirements of CSA A23.3-94 or CSA S6-05 using the effective moment of inertia, as described below.

MINIMUM THICKNESS For steel-reinforced concrete structures, CSA A23.3-94 recommends span-to-depth ratios for a variety of member types and end conditions to ensure adequate deflection control. For FRP-reinforced FRP-reinforced concrete members, the following equation should be used to ensure similar span to deflection ratios as for steel-reinforced steel-reinforced beams: α d

ε ⎞ ⎛ l n ⎞ = ⎛ l n ⎞ ⎛ ⎜ ⎟ ⎜ ⎟ ⎜⎜ s ⎟⎟ ⎝ h ⎠ frp ⎝ h ⎠ s ⎝ ε frp ⎠

(Eq. 4-2)

where: ℓ n is the member length [mm] h is the member thickness [mm] ε s is the maximum strain allowed in the steel reinforcement in service εfrps is the maximum strain allowed in the FRP reinforcement in service α d d is a dimensionless coefficient taken as 0.50 for a rectangular section

EFFECTIVE MOMENT OF INERTIA

I e

=

I t I cr 2 ⎛ ⎞ ⎛ ⎞ M I cr + ⎜1 − 0.5⎜⎜ cr ⎟⎟ ⎟( I t − I cr ) ⎜ ⎝ M a ⎠ ⎠⎟ ⎝

(Eq. 4-3)

where: I cr cr is the moment of inertia of the cracked section transformed to concrete with concrete in tension ignored, calculated using the Eq. 4-4 below [mm 4] I t t is the moment of inertia of a non-cracked section transformed to concrete [mm4] M cr is the cracking Moment [N·mm] M a is the maximum moment in a member at the load stage at which deflection is being calculated [N·mm]

I cr

=

b(kd ) 3 3

+ n frp A frp d (1 − k ) 2

(Eq. 4-4)

where: b is the width of the compression zone [mm] d is is the effective depth of the section [mm] n frp is the modular ratio E ratio E frp/ E E c The neutral axis depth, kd , can be calculated using the following equation:

k =

⎡− n ρ + ⎣⎢ frp frp

(n

ρ frp )

frp

2

+ 2n frp ρ frp ⎤⎥ (Eq. 4-5) ⎦

where: ρ frp is the FRP reinforcement ratio.

13


Section 5

Deformability In the past, the concept of a balanced section was used to implicitly design steel-reinforced concrete structures for ductile behaviour. behaviour. Traditionally, a balanced section section is one in which the steel reinforcement reaches the yield strain simultaneously with the crushing strain being reached in the concrete. It was recognized that an an under-reinforced design, design, having reinforcement less than the balanced condition, gave ductile behaviour, with very large curvature observed prior to failure. failure. Conversely, an over-reinforced over-reinforced design, with reinforcement above the balanced condition, gave a very safe structure with comparatively less deformation observed prior to failure. Thus, a trade-off between ductility and safety was recognized. Unlike steel, FRP reinforcement has a linear strainstress relationship. relationship. For FRP FRP reinforcement reinforcement there is no plastic phase. However, because of the comparatively low modulus of elasticity of FRP reinforcing materials, an FRPreinforced member will also exhibit sufficiently large curvature at failure. Because of this important difference in the characteristics of FRP reinforcement, in comparison with steel, it is important that issues of deformability and safety be thoroughly investigated. ISIS Canada Design Manual No. 3 suggests that the FRP reinforcement ratio can be less than the balanced FRP

reinforcement ratio, provided that the curvature at service loads is an acceptably low proportion of the curvature at ultimate. This concept is referred to as deformability and can be summarized, for rectangular and T-beams in flexure, by the following equation:

⎛ ψ u M u ⎞ ⎟⎟ ≥ 4 ψ M ⎝ s s ⎠

for rectangular sections

(Eq. 5-1)

⎛ ψ u M u ⎞ ⎟⎟ ≥ 6 ψ M ⎝ s s ⎠

for T-sections

(Eq. 5-1)

DF = ⎜⎜

DF = ⎜⎜

In the previous expressions, ψ u and M and M u are the curvature and moment at ultimate conditions, respectively, and ψ s and M and M s are the curvature and moment at service conditions, but not exceeding the condition where the maximum concrete compressive strain = 0.001. The concept of deformability, while extremely important, is rather complex and is not discussed further. Deformability is discussed in significant detail in Chapter 9 of ISIS Design Manual No. 3.

Section 6

Spacing and Cover Concrete Cover Adequate concrete cover to the FRP-reinforcement is required to prevent cracking due to thermal expansion, swelling from moisture, and to protect the FRP reinforcement from from fire. Due to the wide wide variety of FRP FRP reinforcing products available, it is difficult to make generalizations as to the required concrete cover for various types of FRP reinforcing reinforcin g materials. CHBDC (CSA, 2005) recommends that the minimum clear cover shall be 35 mm with a construction tolerance of ±10 mm. The overall guidelines suggested by ISIS Canada Design Manual No. 3 are as follows;

Table 6-1. 6-1. Cover Cover to Flexural Reinfor cement Exposure Beams Slabs Interior 2.5d b or 40mm 2.5d b or 20mm Exterior 2.5d b or 50mm 2.5d b or 30mm * d b is the bar diameter in mm

CSA-S806-02 provides additional information on concrete cover requirements requirements if fire rating requirements requirements area design consideration.

Bar Spacing To ensure that concrete can be placed properly and that temperature cracking will be avoided, the minimum bar spacing for longitudinal reinforcing bars in FRP-reinforced concrete members should be taken as the maximum of: • 1.4 d b • 1.4 times the maximum aggregate size (MAS) • 30 mm • the concrete cover obtained above The maximum spacing of flexural reinforcement should be taken, in the same manner as suggested by CSA A23.394 for steel-reinforced concrete, as the smaller of: • 5 times the slab thickness • 500 mm

14


Constructability The following are additional considerations which must be accounted for when designing with FRP reinforcement: • All FRP materials should be protected against UV radiation. • Storage and handling requirements for FRPs may vary significantly depending on the specific product being used. • FRPs should not come into contact with reinforcing steel in a structure.

•

FRP reinforcement is light and must be tied, with plastic ties, to formwork to prevent it from floating during concrete placing and vibrating operations. • Care must be taken when vibrating concrete to ensure that the FRP reinforcement is not damaged (plastic protected vibrators vibrators should be used). Additional information on the appropriate handling and application of FRP materials is given in ISIS Educational Module 6.

Section 7

Additional Topics DEVELOPMENT LENGTH AND ANCHORAGE For concrete to be reinforced with FRPs, there must be force transfer from the FRP to the the concrete through through bond. The required development length for FRP reinforcement is dependent on the bond between FRP and concrete, which in turn depends on the bar diameter, surface condition, embedment length, and bar shape. Because the bond of FRP bars to concrete differs depending on the specific FRP reinforcement being used, the development length for any specific product should be determined from experimental tests. Most FRP reinforcement reinforcement manufacturers manufacturers can provide guidance in this regard for any specific FRP product.

members. FRPs have been used successfully as shear reinforcement in full-scale field applications, although the topic is not covered in any significant detail in this manual. If steel stirrups are used in an FRP reinforced concrete member, and the shear design is conducted according to existing standards, such as CSA A23.3-94, then no problems with the shear capacity of the member are expected. Further information on the shear design of concrete members reinforced with FRPs for both flexure and shear can be found in Chapter 11 of ISIS Design Manual No. 3.

FLEXURAL DESIGN AIDS To assist in the flexural design of FRP-reinforced concrete members, ISIS Canada has produced a series of designs aids. The design aids consist of a series series of charts that that were developed for rectangular sections with a specific type of reinforcement in a single single layer. They were developed developed based on the serviceability requirement that the strain in the FRP at service load levels should not exceed ε frp = 0.002, and they can be used for the design of section dimensions and reinforcement details to satisfy both serviceability and ultimate limit limit states requirements. requirements. The design charts have not been included herein, but are available in Chapter 10 of ISIS Design Manual No. 3.

DESIGN FOR SHEAR

Fig. 7-1. CFRP stirrups for shear reinforcement of a prestressed concrete bridge girder.

FRP are widely used in a variety of shapes and configurations for flexural reinforcement of concrete

15


Section 8

Examples EXAMPLE 1 Moment Capacity Analysis of a Rectangular Beam with FRP Reinforcement (Tension Failure) Problem: Calculate the factored moment resistance, M r r, for a precast (φc = 0.65) FRP-reinforced concrete section with the following dimensions:

mm diameter Leadline TM stirrups and that the beam has an interior exposure condition.

Section width Section depth

Concrete compressive strength, f’ strength, f’ c = 35 MPa. ISOROD GFRP tensile strength, f strength, f frpu = 617 MPa ISOROD GFRP tensile modulus, E modulus, E frp = 42 GPa The area of one 12.7 mm bar, A bar, A bar = 129 mm2

b = 350 mm h = 600 mm

The tensile reinforcement consists of eight 12.7 mm diameter GFRP ISOROD bars (bundled in pairs) in a single layer. Assume that the shear reinforcement reinforcement consists consists of 5

Given information:

Solution: 1. Determine the concrete cover and and the effective depth of the section. The required concrete cover to the flexural reinforcement is (Table 6-1):

= (2.5)(12.7) = 32 mm

2.5d b

or 40 mm

Where:

= 0.85 − 0.0015 f 'c = 0.80 β 1 = 0.97 − 0.0025 f ' c = 0.88 α 1

ε frpu

=

f frpu E frp

=

617 42 × 10 3

= 0.0146

(Eq. 3-4) (Eq. 3-5) (Eq. 3-1)

∴ 40 mm governs. 4. Check if the section will fail fail by tension tension failure failure or compression failure. failure. In this case: case:

The effective depth, d , is calculated from:

d = h − cover −

d b 2

= 600 − 40 −

12.7 2

= 554 mm

2. Calculate the FRP FRP reinforcement reinforcement ratio:

ρ frp

=

A frp bd

=

8 ×129 350 × 554

= 0.00532

3. Calculate the balanced FRP reinforcement ratio (Eq. 3-8):

ρ frpb

=

A frpb bd

= α 1 β 1

= 0.80(0.88)

φ c f ' c φ frp f frpu

0.0035 ⎛ ⎞ ⎜ ⎟ 617 ⎝ 0.0035 + 0.0146 ⎠

0.65 35 0.4

⎛ ε cu ⎞ ⎜ ⎟ ⎜ ε cu + ε frpu ⎟ ⎝ ⎠

ρ frp

= 0.00532 < ρ frpb = 0.0125

Therefore, we have TENSION FAILURE, and the strain distribution is as shown in Fig. 9-1. 5. Perform an iterative strain-compatibility strain-compatibility analysis: Assume the neutral axis depth, c = 50 mm. mm. The value of of 50 mm is arbitrary, but is is likely a reasonable first first guess. Now, using strain compatibility:

ε c c

=

ε frpu d − c

which gives:

= 0.0125 16


ε c

= 50

Now we must check for equilibrium of the stress-resultants stress-resultants on the cross-section:

0.0146 554 − 50

= 1448 × 10 −6

C = 206 < T = 255

350 mm εc < εcu

Since C < T , further iteration is is required. We will try increasing (guessing) (guessing) the neutral axis depth to 55 mm. In the same manner as above, the following can be determined:

c

ε c d= 554mm

= 57

0.0146 554 − 57

= 1674 ×10 −6 T = 0.4(8 × 129 )(617 ) = 382 046 N

= 255 kN 0.0146

The stress block parameters, α = 0.80 and β = 0.69, are again determined from from Figs. 3-2 and 3-3. Giving:

Fig. 9-1. Strain compatibility analysis. The tensile stress resultant can be calculated directly using Eq. 3-16:


= 0.4(8 × 129 )(617 ) = 254698 N = 255 kN where Φ frp is determined according to Table 3-1. The compressive stress resultant is more difficult to obtain. It is given by Eq. 3-17:

C = αφ c f c' β cb Because the strain in the extreme concrete compression fibre is less than ultimate, the equivalent rectangular stress block factors, α and β , must be determined from Figs. 3-2 and 3-3. From Fig. 3-2, with a concrete strain of εc = 1448 × 10-6 and interpolating between the curves for 30 and 40 MPa concrete, we find that α = 0.75. Using Fig. 3-3, with the same concrete strain as above, we find β find β = = 0.69. Now, the compressive compressive stress resultant can be obtained:

C = αφ c f c' β cb

= 0.75(0.65)(35)(0.69)(50)(350) = 206 030 N = 206 kN

C = 0.8(0.65)(35)(0.69)(57 )(350) = 2505532 N

= 251 kN C = 251 ≈ T = 255 → OK This time, C and T are approximately equal, and we can continue to determine the moment capacity using Eq. 3-21:

⎛ ⎝

M r = φ frp A frp f frpu ⎜ d −

β c ⎞

⎟

2 ⎠

0.69 × 57 ⎞ = 0.4(8 ×129)(617 )⎛ ⎜ 554 − ⎟ 2 ⎝ ⎠ = 136.1×10 6 N ⋅ mm = 136.1 kN ⋅ m Thus, the moment capacity of the section is 136.1 kN·m. Finally, we must check that the minimum flexural capacity requirements are are satisfied. Using Eq. 3-23:

M r ≥ 1.5M cr The cracking moment is determined using Eq. 3-24:

M cr =

f r I t yt

(0.6 =

)

35 (6.30 × 10 9 ) 302

= 74.0 × 10 6 N ⋅ mm = 74.0 kN ⋅ m where:

17


= 0.6 f 'c I t = transformed section moment of inertia yt = distance from N.A. to extreme tension fibre f r

Thus we have:

M r = 136 kN ⋅ m ≥ 1.5M cr = 1.5 × 74.0 = 111 kN ⋅ m → OK

Thus, the beam has satisfactory capacity to avoid failure upon cracking. The reader should note that the beam in the preceding analysis may not be adequate with regard to serviceability requirements, particularly given that the modulus of ISOROD GFRP reinforcement is less than that of conventional steel reinforcement. Serviceability requirements for cracking and deflection should also be investigated, although they are not covered here.

EXAMPLE 2 Moment Capacity Analysis of a Rectangular Beam with Tension Reinforcement (Compression Failure) Problem: Calculate the factored moment resistance, M r r, for a precast (φc = 0.65) FRP-reinforced concrete section with the following dimensions: Section width Section depth

b = 300 mm h = 500 mm

The tensile reinforcement consists of six #10 ISOROD CFRP bars in a single layer. Assume that the shear reinforcement consists of 5 mm diameter Leadline TM

stirrups and that the beam has an interior exposure condition. Given information: Concrete compressive strength, f’ strength, f’ c = 35 MPa. ISOROD CFRP tensile strength, f strength, f frpu = 1596 MPa ISOROD CFRP tensile modulus, E modulus, E frp = 111 GPa The area of one #10 bar, A bar, A bar = 71 mm2 The diameter of one #10 bar, d bar, d b = 9.3 mm

Solution: 1. Determine the concrete cover and and the effective depth of the section.

ρ frpb

The required concrete cover to the flexural reinforcement is (Table 6-1):

2.5d b

= (2.5)(9.3) = 23 mm or 40 mm

The effective depth, d , is calculated from:

d = h − cover −

d b 2

= 500 − 40 −

9 .3 2

=

A frp bd

=

A frpb

= α 1 β 1

φ c f 'c

Where:

= 455 mm


ρ frp

⎛ ε cu ⎞ ⎜ ⎟ ⎜ ε cu + ε frpu ⎟ bd φ frp f frpu ⎝ ⎠ 0.65 35 ⎛ 0.0035 ⎞ = 0.80(0.88) ⎜ ⎟ 0.8 1596 ⎝ 0.0035 + 0.0144 ⎠ = 0.00245 = 0.245%

=

(6 × 71) = 0.00312 = 0.312% 300(455)


α 1

= 0.85 − 0.0015 f 'c = 0.80

(Eq. 3-4)

β 1

= 0.97 − 0.0025 f 'c = 0.88

(Eq. 3-5)

ε frpu

=

f frpu E frp

=

1596 111× 10 3

= 0.0144

(Eq. 3-1)

4. Check if the section will fail fail by tension tension failure failure or compression failure. failure. In this case: case:

18


ρ frp

= 0.00312 > ρ frpb = 0.00245

7. Determine the flexural capacity, M capacity, M r r (Eq. 3-14):

Therefore, we have COMPRESSION FAILURE, and the strain distribution is as follows:

M r

300 mm εcu = 0.0035

a ⎞ = φ frp A frp f frp ⎛ ⎜ d − ⎟ ⎝ 2 ⎠ 87 ⎞ = 0.8(6 × 71)(1396)⎛ ⎜ 455 − ⎟ 2 ⎠ ⎝ = 196 × 10 6 N ⋅ mm = 196 kN ⋅ m

c

Thus, the moment capacity of the section is 196 kN·m. d= 455 mm

Finally, we must check that the minimum flexural capacity requirements are satisfied. Using Eq. 3-23: 3-23:

M r ≥ 1.5M cr The cracking moment is determined using Eq. 3-24: εfrp < εfrpu

M cr =

Fig. 9-1. Strain compatibility analysis.

f frp

= 0.5(111000 )(0.0035) 1 ⎡⎛ ⎤ 2 ⎞ 4(0.80 )(0.88)(0.65)(35) ⎢⎜⎜1 + ⎟ − 1⎥ ⎢⎝ 3.12 × 10 −3 (0.8)(111000 )(0.0035) ⎠⎟ ⎥ ⎣ ⎦ = 1396 MPa 6. Determine the stress block depth, a (Eq. 3-11):

β 1c = a =

=

φ frp A frp f frp α 1φ c f c'b

0.8(6 × 71)(1387 ) 0.80(0.65)(35)(300 )

= 87 mm

yt

(0.6 =

5. Determine the tensile stress in the FRP reinforcement at compressive failure of the section (Eq. 3-8): 1 ⎡⎛ ⎤ 2 ' ⎞ 4 α β φ f 1 1 c c ⎟ − 1⎥ = 0.5 E frp ε cu ⎢⎜⎜1 + ⎢⎝ ρ frpφ frp E frpε cu ⎠⎟ ⎥ ⎣ ⎦

f r I t

)

35 (3.20 × 10 9 ) 248

= 45.8 × 10 6 N ⋅ mm = 45.8 kN ⋅ m where:

= 0.6 f 'c I t = transformed section moment of inertia yt = distance from N.A. to extreme tension fibre f r

Thus we have:

M r = 196 kN ⋅ m ≥ 1.5M cr = 1.5 × 45.8 = 68.7 kN ⋅ m

→

OK

Thus, the beam has satisfactory capacity to avoid failure upon cracking. The reader should note that the beam in the preceding analysis may not be adequate with regard to serviceability requirements, particularly given that the modulus of ISOROD CFRP reinforcement is less than that of conventional steel reinforcement. Serviceability Serviceability requirements for cracking and deflection should also be investigated, although they are not covered here.

19


Section 9

Field Applications The following case studies provide examples of field applications where FRP reinforcement has been used successfully for reinforcement of concrete. Further information on a variety of additional field applications can be obtained from the ISIS Canada website (www.isiscanada.com www.isiscanada.com). ).

TAYLOR BRIDGE

stainless steel tension bars were used for the connection between the barrier barrier wall and the the deck slab. The bridge incorporates a complex embedded fibre optic structural sensing system that will allow engineers to compare the long-term behaviour of the various materials. This remote monitoring is an important factor in acquiring long-term data on FRPs that is required for widespread acceptance of these materials through national and international codes of practice.

A significant research milestone was achieved on October 8, 1998 when Manitoba’s Department of Highways and Transportation opened the Taylor Bridge in Headingley, Manitoba. The two-lane, 165.1-metre-long structure has four out of 40 precast concrete girders reinforced with carbon FRP stirrups. These girders are also prestressed with carbon FRP cables and bars. Glass FRP reinforcement has been used in portions portions of the barrier walls.

Fig. 10-2. 10-2. Placing Placing the FRP-reinfor FRP-reinfor ced co ncr ete deck of the Taylor Taylor Bri dge.

JOFFRE BRIDGE Fig. 10-1. 10-1. The The Taylor Br idg e, in Headingly Manitoba, Manitoba, during construc tion. As a demonstration project, it was vital the materials be tested under the same conditions as conventional steel reinforcement. Thus only a portion of the bridge was designed using FRPs. Two types of carbon FRP reinforcements were used in the Taylor bridge. Carbon fibre composite cables produced by Tokyo Rope, Japan, were used to pretension two girders, while the other two girders were pretensioned using Leadline bars produced by Mitsubishi Chemical Corporation, Japan. Two of the four FRP-reinforced FRP-reinforced girders were reinforced for shear using carbon FRP stirrups and leadline bars in a rectangular cross section. The other two beams were reinforced for shear using epoxy coated steel reinforcement. The deck slab was reinforced by Leadline bars similar to those used for prestressing. Glass FRP reinforcement produced by Marshall Industries Composites Inc. was used to reinforce a portion of the barrier wall. Double-headed

Early in August of 1997, the province of Québec decided to construct a bridge using carbon FRP reinforcement. The Joffre Bridge, spanning the Saint Francois River, was another contribution to the increasing number of FRPreinforced bridges in Canada. A portion of the Joffre Bridge concrete deck slab is reinforced with carbon FRP, as are portions of the traffic traffic barrier wall and the sidewalk. sidewalk. The bridge is outfitted extensively with various kinds of monitoring instruments including fibre optic sensors embedded within the FRP reinforcement (these are referred to as smart reinforcements). Over 180 monitoring instruments are installed at critical locations in the concrete deck slab and on the steel girders, to monitor the behaviour of the FRP reinforcement under service conditions. The instrumentation is also providing valuable information on long-term performance of the concrete deck slab reinforced with FRP materials.

20


Fig. 10-5. Placement of GFRP and CFRP reinforcement in the Wotton Bridge deck. Fig. 10-3. 10-3. Placement of FRP grid for J off re Bridg e’s concrete deck reinforcement (yellow coils are sensor lead wires).

Fig. 10-6. 10-6. The completed Wott on Br idge.

Fig. 10-4 10-4.. Aerial view of Joffre Brid ge durin g construction.

WOTTON BRIDGE Wotton Bridge, in the municipality of Wotton, Québec, is a single span prestressed concrete girder bridge with a total length of 30.6 metres and a width of 8.9 metres. The deck slab rests on four prestressed concrete girders, spaced at 2.3 metres, with a cantilever slab of one metre on either side. The deck slab is reinforced internally with ISOROD GFRP and CFRP reinforcing bars with diameters of 15 mm and 10 mm respectively. respectively. FRP reinforcement reinforcement is used used both for top top and bottom slab reinforcement.

MORRISTOWN BRIDGE

Fig. 10-7. 10-7. The The GFRP GFRP-reinfor -reinfor ced Morri stow n Bri dge deck just before placement placement of the concrete deck slab.

The Morristown Bridge, in the State of Vermont, USA, is a single-span integral abutment bridge with a total length of 43 metres and a width of 11.3 metres. metres. The deck slab has a thickness of 230 mm and rests on 5 steel girders spaced at 2.4 metres. The deck slab cantilevers cantilevers on either side of the bridge are 0.92 metres in length. Top and bottom deck reinforcement consists of ISOROD GFRP reinforcing bars.

21


Fig. 10-8. Close-up of the Morristown Bridge deck’s GFRP GFRP reinforcement reinforcement just before placement of the concrete (bars (bars were “ bundled” in this application).

Section 10

References and Additional Guidance Additional information information on the use of FRP materials can be obtained in various documents available from ISIS Canada:

• • • • •

ISIS Design Manual No. 4: Strengthening Reinforced Concrete Structures with Externally-Bonded Fiber Reinforced Polymers. ISIS Design Manual No. 5: Prestressing Concrete Structures with FRPs. ISIS Educational Module 1: Mechanics Examples Incorporating FRP Materials. ISIS Educational Module 2: An Introduction to FRP Composites for Construction. ISIS Educational Module 4: An Introduction to FRP-Strengthening of Concrete Structures.

Due to the increasing popularity and use of FRP reinforcements in the concrete construction industry, a number of design recommendations have recently been produced by various organizations for the design of concrete structures with internal FRP reinforcement. The following documents should be consulted for additional information or if design with FRP materials is being contemplated.

• • • •

ISIS Design Manual No. 3: Reinforcing Concrete Structures with Fiber Reinforced Polymers. Published by Intelligent Sensing for Innovative Structures Canada, Winnipeg, MB. 2001 CAN/CSA-S806-02: CAN/CSA-S806-02: Design and Construction of Building components with Fibre Reinforced Polymers. Published by the Canadian Standards Association, Ottawa, ON. 2002. CAN/CSA-S6-05: CAN/CSA-S6-05: Canadian Highway Bridge Design Code. Published by the Canadian Standards Association, Ottawa, ON. 2005. ACI 440.1R-03: Guide for the design and construction Concrete Reinforced Reinforced with FRP Bars. Published by the American Concrete Institute, Farmington Hills, MI. 2003.

Notation A frp

cross-sectional area of FRP reinforcement in tension (mm2)

A frpb

cross-sectional area of FRP reinforcement at the balanced failure condition (mm2)

A frpmin frpmin

minimum area of FRP required (mm2)

a

depth of the equivalent rectangular stress block (mm)

b

width of the compression zone for a rectangular section (mm)

C

compressive stress resultant (N)

22


C n

nominal compressive stress resultant (N)

c

depth of neutral axis (mm)

cb

depth of the neutral axis at the balanced failure condition (mm)

d

effective depth of the section (mm)

d b

diameter of the reinforcement (mm)

E c

elastic modulus of the concrete (MPa)

E frp

elastic modulus of the FRP (MPa)

f ’c

compressive strength of the concrete (MPa)

f frp

stress in the FRP reinforcement at failure (MPa)

f frpu

ultimate tensile strength of the FRP (MPa)

f r r

modulus of rupture of the concrete (MPa)

h

overall member depth (mm)

I cr cr

moment of inertia of the cracked section transformed to concrete with concrete in tension ignored (mm 4)

I t t

moment of inertia of the transformed section (mm4)

ℓ n

member length (mm)

M a

maximum moment in a member at the load stage at which deflection is being calculated (N·mm)

M cr cr

cracking moment of the cross-section (N·mm)

M f

moment due to the factored loads (N·mm)

M r r

factored moment resistance of the cross-section (N·mm)

n frp

modular ratio E ratio E frp/ E E c

T

tensile stress resultant (N)

T n

nominal tensile stress resultant (N)

yt

distance from the centroidal axis of the transformed section to the extreme tension fibre (mm)

α

stress-block parameter for concrete at a strain less than u ltimate

α1

CSA A23.3-94 stress-block parameter for concrete at ultimate

α d

dimensionless coefficient taken as 0.50 for a rectangular section

β

stress-block parameter for concrete at a strain less than ultimate

β 1

CSA A23.3-94 stress-block parameter for concrete at ultimate

εcu

ultimate concrete strain

ε frp

strain in the FRP reinforcement at compression failure

ε frps

strain in the tensile FRP reinforcement at service load

ε frpu

ultimate strain of the FRP in tension

ε s

maximum strain allowed in the reinforcement in service

φ c

material resistance factor for concrete

φ frp

material resistance factor of FRP reinforcement

ρ frpb

balanced failure reinforcement reinforcement ratio ratio

ρ frp

FRP reinforcement ratio

23


Appendix A: Suggested Student Assignment

250 mm

Problem #1: Calculate the factored moment resistance, M r r, in positive bending, for the precast (φ (φ c = 0.65) FRP-reinforced concrete section shown below. Assume that the the beam has an interior interior exposure condition: Material Properties: Concrete Compressive Strength, f’ Strength, f’ c = 45 MPa FRP Ultimate Strength, f Strength, f frpu = 1596 MPa FRP Elastic Modulus, E Modulus, E frp = 111 MPa Area of FRP Bars, A bar = 71 mm2

2 – 9.3 mm diameter carbon ISOROD bars m m 0 0 5

3 – 9.3 mm diameter carbon ISOROD bars

300 mm

Problem #2: Calculate the factored moment resistance, M r r, in positive bending, for the precast (φ (φ c = 0.65) FRP-reinforced concrete section shown below. Assume that the the beam has an interior interior exposure condition: Material Properties: Concrete Compressive Strength, f’ Strength, f’ c = 40 MPa FRP Ultimate Strength, f Strength, f frpu = 2255 MPa FRP Elastic Modulus, E Modulus, E frp = 147 MPa Area of FRP Bars, A bar = 113 mm2

m m 0 0 4

6 – 12 mm diameter TM carbon Leadline bars i n t w o l a er s

24


Appendix B: Assignment Solutions Problem #1:

250 mm

Calculate the factored moment resistance, M r r, in positive bending, for the precast (φ (φ c = 0.65) FRP-reinforced concrete section shown below. Assume that the the beam has an interior interior exposure condition:

2 – 9.3 mm diameter carbon ISOROD bars m m 0 0 5

Material Properties: Concrete Compressive Strength, f’ Strength, f’ c = 45 MPa FRP Ultimate Strength, f Strength, f frpu = 1596 MPa FRP Elastic Modulus, E Modulus, E frp = 111 MPa Area of FRP Bars, A bar = 71 mm2

3 – 9.3 mm diameter carbon ISOROD bars

Solution: 1. First, note that we always always assume FRP reinforcement is ineffective in compression. compression. Thus, we can completely completely ignore the compression reinforcement for the purposes of this problem. Next, determine the concrete cover and the effective depth of the section.

α 1

= 0.85 − 0.0015 f 'c = 0.78

(Eq. 3-4)

β 1

= 0.97 − 0.0025 f 'c = 0.86

(Eq. 3-5)

The required concrete cover to the main reinforcement is (Table 6-1):

ε frpu

= (2.5)(9.3) = 23 mm or 40 mm

2.5d b

The effective depth, d , is thus:

d = h − cover −

d b 2

= 500 − 40 −

ρ frp 9 .3 2

= 455 mm


=

A frp bd

⎛ ε cu ⎞ ⎜ ⎟ ⎜ ε cu + ε frpu ⎟ bd φ frp f frpu ⎝ ⎠ 0.65 45 ⎛ 0.0035 ⎞ = 0.78(0.86 ) ⎜ ⎟ 0.8 1596 ⎝ 0.0035 + 0.0143 ⎠ = 3.02 ×10 −3

=

f frpu E frp

=

1596 111×103

A frpb

= α 1 β 1

φ c f 'c

= 0.0143

(Eq. 3-1)

−3 = 1.87 × 10 < ρ frpb = 3.02 × 10 −3

Therefore, we have TENSION FAILURE, and the strain distribution is as follows: 250 εc < εcu

(3 × 71) = = 1.87 ×10 −3 250(455)


ρ frpb

=


∴ 40 mm cover governs.

ρ frp

Where:

c

d

= 4 5 5 m m

0.0143

25


5. Perform an iterative strain-compatibility strain-compatibility analysis:

Since C ≈ T , further iteration is not required.

Assume the neutral axis depth, c = 60 mm. mm. Using strain strain compatibility:

6. Determine the moment capacity using Eq. 3-21:

ε c c

=

ε frpu d − c

⇒ ε c = 60

0.0143 455 − 60

= 2172 ×10

−6

⎛ ⎝

M r = φ frp A frp f frpu ⎜ d −


where Φ frp is determined according to Table 3-1. The compressive stress resultant obtained using Eq. 3-17:

C = αφ c f c' β cb The strain in the extreme compression fibre is less than ultimate, α and β , must therefore be determined from Figs. 3-2 and 3-3. From Fig. 3-2, 3-2, with a concrete concrete strain of εc = -6 2172 × 10 and interpolating between the curves for 40 and 50 MPa concrete, we find that α = 0.90. Using Fig. 3-3 we find β find β = = 0.70. The compressive stress resultant can be obtained:

C = αφ c f β cb ' c

= 0.90(0.65)(45)(0.70)(60)(250) = 276412 N = 276 kN Check for equilibrium of the stress-resultants on the crosssection:

⎟

2 ⎠

0.70 × 60 ⎞ = 0.8(3 × 71)(1596 )⎛ ⎜ 455 − ⎟ 2 ⎝ ⎠ = 118 ×10 6 N ⋅ mm = 118 kN ⋅ m

The tensile stress resultant can be calculated directly using Eq. 3-16:

= 0.8(3 × 71)(1596 ) = 272000 N = 272 kN

β c ⎞

Thus, the moment capacity of the section is 118 kN·m. 7. Check that the minimum flexural capacity requirements are satisfied. satisfied. Using Eq. 3-23:


M cr =

f r I t yt

(0.6 =

)

45 (2636.88 ×10 6 ) 250

= 42 ×10 6 N ⋅ mm = 42 kN ⋅ m Thus we have:

M r = 118 kN ⋅ m ≥ 1.5M cr = 1.5 × 42 = 63 kN ⋅ m

→

OK

Therefore, the flexural resistance of the carbon FRPreinforced concrete beam is 118 kN·m.

C = 276 ≈ T = 272

26


Problem #2:

300 mm

Calculate the factored moment resistance, M r r, in positive bending, for the precast (φ (φ c = 0.65) FRP-reinforced concrete section shown below. Assume that the the beam has an interior interior exposure condition: m m 0 0 4

Material Properties: Concrete Compressive Strength, f’ Strength, f’ c = 40 MPa FRP Ultimate Strength, f Strength, f frpu = 2255 MPa FRP Elastic Modulus, E Modulus, E frp = 147 MPa Area of FRP Bars, A bar = 113 mm2 Maximum aggregate size, MAS size, MAS = = 14 mm

6 – 12 mm diameter TM carbon Leadline bars i n t w o l a er s

Solution: 1. Determine the concrete cover and and the effective depth of the section. The required concrete cover to the flexural reinforcement is (Table 6-1):

2.5d b

= (2.5)(12) = 30 mm

or 40 mm

The bar spacing requirements dictate that the spacing between layers of reinforcement must be the greater greater of:

1.4d b

= (1.4)(12) = 17 mm ;

ρ frp

ρ frpb

30 mm ; or

d bottom

= h − cover −

2

= 400 − 40 −

12 2

= h − cover − = 400 − 40 −

d b

2 12 2

(6 ×113) = 6.76 ×10 −3 300(334 )

⎛ ε cu ⎞ ⎜ ⎟ ⎜ bd φ frp f frpu ⎝ ε cu + ε frpu ⎠⎟ 0.65 40 ⎛ 0.0035 ⎞ = 0.79(0.87 ) ⎜ ⎟ 0.8 2255 ⎝ 0.0035 + 0.0153 ⎠ = 1.84 ×10 −3

=

A frpb

= α 1 β 1

φ c f 'c

α 1

= 0.85 − 0.0015 f 'c = 0.79

(Eq. 3-4)

β 1

= 0.97 − 0.0025 f 'c = 0.87

(Eq. 3-5)

= 354 mm

The depth to the top layer of reinforcement is:

d top

bd

=

Where:

The effective depth to the bottom layer of reinforcement, d , is (note that we may not “lump” the reinforcement as we would normally do for steel reinforced concrete):

d b

A frp


1.4 MAS = (1.4)(14) = 20 mm ;

the concrete cover of 40 mm → Governs

=

− 40

− 40 = 314 mm

2. Calculate the FRP FRP reinforcement reinforcement ratio (here we we will use the average value of effective depth, THIS STEP ONLY!):

ε frpu

=

f frpu E frp

=

2255 147 × 10 3

= 0.0153

(Eq. 3-1)


ρ frp

−3 = 6.76 ×10 > ρ frpb = 1.84 ×10 −3

Therefore, we have COMPRESSION FAILURE, and the strain distribution is as follows:

27


300 mm εcu = 0.0035

c

m m 0 0 4

d b o t t o m

= 3 5 4 m m

d t o p

= 3 1 4 m m

εfrp,top εfrp,bottom εfrp < εfrpu

5. Assume the neutral axis depth, c = 115 mm (educated guess). 6. Now we must determine the actual stresses in the different layers of FRP reinforcement ( NO LUMPING) and check that the compression and tensile forces are equal. From the strain profile shown above:

ε cu c

=

c

=

d bottom

0.0035 115

= 7274 ×10 −6

ε frp ,top d top

ε frp ,top

= (354 − 104 ) ⋅

= (314 − 104 ) ⋅

0.0035 104

0.0035 104

= 8436 ×10 −6

= 7088 ×10 −6

Now, the tension force is calculated by summing the contributions of both layers of FRP:

−c 0.0035 115

= 6057 ×10

−6

Now, the tension force is calculated by summing the contributions of both layers of FRP:

= φ frp A frp ε frp ,bottom E frp

= 0.8(3 × 113)(7274 × 10 −6 )(147000 ) = 290000 N = 290 kN T top

Since C = 616 ≠ T = 531, we must try a different neutral axis depth. Try c = 104 mm. As before:

ε frp ,bottom

−c

⇒ ε frp,top = (314 − 115)

T bottom

= 0.79(0.65)(40 )(0.87 )(115)(300) = 617000 N = 617 kN

ε frp ,bottom

⇒ ε frp ,bottom = (354 − 115) ε cu

C = α 1φ c f c' β cb

= φ frp A frp ε frp ,top E frp

= 0.8(3 × 113)(6057 ×10 −6 )(147000 ) = 241000 N = 241 kN So the total tensile force is T = = 290 + 241 = 531 kN. Now, the compression force is

T bottom

T top

= 0.8(3 × 113)(8436 ×10 −6 )(147000 ) = 336000 N = 336 kN

= 0.8(3 ×113)(7088 ×10 −6 )(147000 ) = 282000 N = 282 kN

So the total tensile force is T = = 336 + 282 = 618 kN. Now, the compression force is

C = 0.87(0.65)(40 )(0.87 )(104 )(300)

= 613000 N = 613 kN Since C = = 613 ≈ T = = 618, we will use a neutral axis depth of c = 104 mm. 7. We can now determine the flexural capacity, M r r (Eq. 3 14):

28


⎛ ⎝

M r = φ frp A frp ,bottom f frp ,bottom ⎜ d bottom

a − ⎞⎟ 2 ⎠

a ⎞ + φ frp A frp ,top f frp ,top ⎛ ⎜ d top − ⎟ 2 ⎠ ⎝ 104 ⎞ = 336 ×10 3 ⎛ ⎜ 354 − ⎟ 2 ⎠ ⎝ 104 ⎞ + 282 ×103 ⎛ ⎜ 314 − ⎟ 2 ⎠ ⎝ = 175 ×10 6 N ⋅ mm Thus, the moment capacity of the section is 175 kN·m. Finally, we must check that the minimum flexural capacity requirements are are satisfied. Using Eq. 3-23:

M cr =

f r I t yt

⎛ 300 × 4003 ⎞ (0.6 40 )⎜⎜ 12 ⎟⎟ ⎝ ⎠ = 200

= 30.3 ×10 N ⋅ mm 6

Thus we have:

M r = 175 ≥ 1.5M cr = 1.5(30.3) = 45.5 → OK Thus, the beam has satisfactory capacity to avoid failure upon cracking. Therefore, the flexural resistance of the carbon FRPreinforced concrete beam is 175 kN·m.


29


Appendix C: Suggested Laboratory The following laboratory procedure is given as an example of a reinforced concrete laboratory that can be given in conjunction with an undergraduate course on reinforced concrete design, and that includes both conventional reinforcing steel and internal internal FRP reinforcement. reinforcement. Given the wide variety of laboratory and testing facilities available at various Canadian universities, this laboratory is given primarily as an example for professors of what can be done using FRP reinforcement to increase the impact and student understanding of traditional reinforced concrete labs. Inclusion of FRP reinforcement into traditional reinforced concrete laboratories is advantageous for a number of reasons, including: • it introduces students to a new and innovative material which is gaining acceptance within the reinforced concrete industry; • it increases student understanding of the fundamental concepts and assumptions, including serviceability and

deflection, used in reinforced concrete beam design and analysis; • it forces students to consider and understand important mechanics concepts such as elasticity, plasticity, and ductility; and • it exposes students to the state-of-the-art in reinforced concrete design and thus increases student enthusiasm for the course content, subsequently, in many cases, increasing student participation and effort. The laboratory presented herein suggests the use of glass FRP reinforcing bars, ISOROD, manufactured by Pultrall Inc. It is important to recognize recognize that the laboratory procedures can be adapted to include the use of any specific type of FRP reinforcement, and this specific type of reinforcement has been used here only as an example.

Caution: FRP Materials FRPs are linear linear elastic materials. materials. As such, these materials do not display the yielding behaviour observed when testing steel and they provide little warning prior to failure . In addition, beams which fail in shear or due to FRP rupture may fail suddenly and with little warning. It is important

that instructors, students, laboratory demonstrators, and technical staff be made aware of the specific failure modes to be expected when testing FRP materials, and that appropriate safety precautions be taken in addition to those precautions that are normally enforced.

30


Concrete Beam Laboratory OVERVIEW This laboratory is intended to increase students’ understanding of the effects of various amounts and types of internal reinforcement, both steel and fibre reinforced polymer (FRP), on the flexural and shear behaviour of reinforced concrete concrete beams. The laboratory consists of the fabrication and testing of five concrete beams with varying amounts and types of reinforcement. The laboratory illustrates the following important concepts: 1. the flexural and shear behaviour of reinforced concrete beams; 2. under-reinforced versus over-reinforced concrete beams; 3. the effect of shear reinforcement on the load capacity, deflection, ductility, and failure of reinforced concrete beams; 4. the effect of reinforcement type (steel or FRP) on the load capacity, deflection, ductility, and failure of reinforced concrete beams; and 5. the concepts of cracking, yielding, and momentcurvature. The class will be divided into five groups, and each group will be responsible for the fabrication and testing of one of the five beams. Experimental data obtained during during testing for all beams will be made available to all groups for use in writing the laboratory laboratory report. Each group will submit submit one report only, but will comment on the results for all five beams.

Beam Details All beams will be fabricated from concrete with a specified 28-day concrete strength of 35 MPa (compression tests will be conducted to determine the true 28-day strength of the concrete). Steel reinforcement will consist consist of deformed reinforcing bars with a specified yield strength of 400 MPa. FRP reinforcement will consist of glass FRP reinforcing bars with a specified ultimate strength of 691 MPa and a tensile elastic elastic modulus of 40 GPa. GPa. Note that the beams suggested herein are given as an example only, since GFRP bars should not directly contact steel bars in an actual field application of GFRP reinforcement. The five beams to be tested in this laboratory are: 1. an under-reinforced beam without shear reinforcement (steel reinforcing bars); 2. an under-reinforced beam with shear reinforcement (steel reinforcing bars); 3. an over-reinforced beam with shear reinforcement (steel reinforcing bars);

4.

an under-reinforced beam with shear reinforcement (glass FRP reinforcing bars); and 5. an over-reinforced beam with shear reinforcement (glass FRP reinforcing bars). Dimensions and reinforcement details of the beams are given on the following page.

Instrumentation and Testing All beams will be tested in four-point bending to failure, as shown in the figure figure below. Strain gauges will will be mounted on the tensile reinforcement, prior to casting the concrete, and on the concrete compression compression fibre. Load, deflection, deflection, and reinforcement and concrete compressive strain will be measured and recorded during during testing. Cracking patterns patterns will also be marked marked and photographed during during testing. Any significant visual observations will be recorded throughout the tests.

Laboratory Report The laboratory report should consist of the following: 1. A title page giving the group name and number. 2. An abstract, briefly stating the purpose and procedure of the lab and the major conclusions drawn. 3. An introduction providing information on the material properties, beam details, testing setup, instrumentation, procedures, etc. 4. A calculations and analysis section detailing all calculations performed for the the laboratory. laboratory. Where a calculation has been performed more than once only a sample calculation calculation should be provided. A summary of theoretical calculations should be presented in tabular form. 5. An experimental results and discussion section, summarizing the test results obtained for all beams tested. This section should should include photographs and plots showing beam behaviour along with a thorough comparison of theoretical and observed results, and a comparison of the behaviour of the various beams. 6. A conclusion in which the major points of interest from the above sections sections are highlighted. The focus in the conclusion should be on the consequences of the observed behaviour on the practical design of reinforced concrete beams. 7. A list of references. All tests referenced during the course of the laboratory project should be listed using an accepted referencing format.

31


3000 2 – 20M bars 1 – 15M bar 0 0 4

40 mm cover to reinforcement

BEAM #1 25

* all dimensions in millimeters 200 100 2 – 20M bars 1 – 15M bar 10M stirrups

0 0 4

30 mm cover to stirrups

BEAM #2

25

* all dimensions in millimeters 200

Etc.. 100100 25

150

150

4 – 25M bars 10M stirrups 30 mm cover to stirrups

0 0 4

35 mm vertical spacing between bars

BEAM #3

25

* all dim. in mm 200

Etc.. 100

25

150

150

2 – 25 mm ∅ glass FRP bars 10M stirrups

0 0 4


BEAM #4

25


Etc.. 100

25

150

150

2 – 10 mm ∅ glass FRP bars 10M stirrups

0 0 4


BEAM #5

25


Etc.. 100

25

150

150

32


1 – Load cell 2 – Concrete compression strain gauge 3 – Reinforcement strain gauge 4 – Displacement transducer

1

2 3 4

1000 mm

900 mm

1000 mm

CALCULATIONS AND ANALYSIS

RESULTS AND DISCUSSION

The calculation and analysis section of your report should include calculations of the following parameters according to traditional reinforced concrete theory, as presented in class. Each group should should perform the calculations for for their specific beam and then forward their results to all other groups: 1. Issues related to flexural strength : a. The bending moment at first cracking of the concrete in tension (cracking moment, M moment, M cr cr ). b. The bending moment at an extreme fibre concrete compressive stress of 0.4 f’ c. c. The nominal (predicted) moment capacity of the section. d. The design (ultimate) moment capacity of the beam according to CSA A23.3-94 for steel-reinforced beams and according to ISIS Design Manual No. 3 for FRP-reinforced concrete beams. 2. Issues related to strain and deformation : a. The strain in the reinforcement and in the concrete compression fibre at first cracking of the concrete in tension. b. The strain in the reinforcement and concrete at an extreme fibre concrete compressive stress of 0.4 f’ c. c. The strain in the reinforcement and concrete compression fibre at ultimate. 3. Issues related to curvature and deflection : a. The midspan curvature and deflection at first cracking of the concrete in tension. b. The midspan curvature and deflection at twice the cracking moment, 2⋅ M cr cr . c. The midspan curvature and deflection at a concrete compressive stress of 0.4 f’ c. d. The midspan curvature at ultimate.

In addition to presenting, through the use of graphs and tables, a summary of experimental data obtained for all five beams, the results and discussion section of each report should contain, for all five beams, discussions on the following topics: 1. A comparison of the theoretical calculations versus the results obtained during testing and a discussion of discrepancies between theory and observation. 2. Plots showing: a. Load versus deflection for all 5 beams. b. Midspan bending moment versus deflection for all 5 beams. c. Midspan moment versus strain in the reinforcement for all 5 beams. d. Midspan moment versus concrete extreme compression fibre strain. Each plot should include points showing: the cracking moment, steel yielding (where applicable), a compressive fibre concrete stress of 0.4 f’ c, a compressive fibre concrete strain of 0.0035, and the maximum load/moment. A bar chart should should also be included showing a comparison of the five beams based on selected important criteria (left to the discretion of the student). Each plot should should be followed by a brief commentary and discussion. 3. A comparison should be made between the calculated design ultimate load, the calculated nominal load capacity, and the observed load capacity for all beams. What does this imply for the design of actual reinforced concrete beams in practice? Students are expected to provide clear and concise discussions of the above-listed topics and to add additional commentary and calculations as they see see fit. The reports will be graded in part on the quality of independent thought and discussion brought to bear on the various concepts demonstrated in this laboratory, and on the students’ explicit recognition of the greater significance of the results obtained.

33


34

Isis Ec Module 3 - Notes (PDF)

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