Fyfe Co. LLC - Power Mesh · Fyfe Co. LLC TYFO® Fibrwrap® Design Manual (Rev. 6) Property of Fyfe Co. LLC assumed for the design and how much tension force is being transferred

Fyfe Co. LLC TYFO® Fibrwrap® Design Manual (Rev. 6) Property of Fyfe Co. LLC

FYFE CO. LLC

DESIGN MANUAL

FOR THE

TYFO® FIBRWRAP® SYSTEMS

January, 2005 (Rev. 6)

Fyfe Co. LLC

Nancy Ridge Technology Center 6310 Nancy Ridge Drive, Suite #103

San Diego, CA 92121 Tel: 858-642-0694 Fax: 858-642-0947

Email: [email protected] Web: http://www.fyfeco.com

© Copyright 2001 Fyfe Co. LLC. 7-01 Reproduction by written permission from Fyfe Co. LLC only. All rights reserved Tyfo® and Fibrwrap® are registered trademarks for the products of Fyfe Co. LLC


Table of Contents Introduction 2

Definition of Terms 3

General Design Considerations 5

Material Selection 7 Strain Limitations 10 Column Design Equations

Column Shear Enhancement 11

Column Axial Load Enhancement 12

Column Ductility Enhancement 13

Column Lap Splice Enhancement 14

Beam and Slab Design Equations

Beam Shear Enhancement 15

Beam Flexural Enhancement 16

Slab Flexural Enhancement 17

Wall Design Equations

In-Plane Wall Shear Enhancement 18

Out-of-Plane Wall Flexural Enhancement 19 Mechanical Anchorage 20

Literature References and Test Reports 21

Design Examples Appendix A

Typical Details Appendix B

Improved Detailing Using the Tyfo® SCH & SEH Composite Anchors Appendix C

Disclaimer

The contents of this design manual express the opinions of the manufacturer. Design recommendations and equations are based on structural engineering principles and data gathered through extensive structural testing. Examples and sample designs are for information only and should not be applied to a specific project. Each project must be evaluated individually with the optimal composite system chosen and designed based on identified structural requirements. Project engineers shall bear the responsibility to analyze each structure independently and work with the composite manufacturer to design the composite system best suited to satisfy identified design goals.

© Copyright 2001 Fyfe Co. LLC. 7-01 Reproduction by written permission from Fyfe Co. LLC only. All rights reserved 1Tyfo® and Fibrwrap® are registered trademarks for the products of Fyfe Co. LLC


Introduction

The design equations provided in this manual are based on extensive testing and research of our Tyfo® Fibrwrap® Composite Systems. The designs use the “Strength Design” method. Strength reduction factors shall apply to all nominal design strengths. It is the project engineer’s responsibility to identify existing structural capacities and new demands. This document solely provides equations for designing a composite system to satisfy the additional demands on that system. The following design equations and examples are based on using a Tyfo® Fibrwrap® System as an additional tension member. There are some design exceptions where composites can resist compressive forces, however, these applications are unique and are beyond the scope of this document. Each of the various Tyfo® Fibrwrap® Composite Systems has different material characteristics. The most important properties with respect to design are the material modulus and the cross-sectional area of the chosen composite. All Tyfo® Fibrwrap® Systems are essentially linear elastic, as are all advanced composite systems. The design of Tyfo® Fibrwrap® Systems for use in civil/structural applications is therefore based on strain compatibility and corresponding design stresses at the chosen strain levels. This design manual is to be considered a general guideline in the design of the Tyfo® Fibrwrap®

Composite Systems. Fyfe Co. LLC engineers are available to provide preliminary designs or design assistance for any project at no obligation.



Definition of Terms -SYMBOLS- ∆ = displacement (inches) ε = allowable design strain of composite εc = concrete strain εcu = ultimate confined concrete strain εs = steel strain εu = ultimate composite strain Φ = appropriate strength reduction factor for ultimate design methods per ACI 318 φu = ultimate curvature of section (1/in) φy = ideal yield curvature of section (1/in) µ∆ = desired design displacement ductility for the existing column µφ = required curvature ductility ρsj = volumetric confining ratio of the jacket -A- a = compression zone depth (inches) A = w⋅t = area of composite (in2) Ab = area of one longitudinal bar (in2) Ag = gross area of column (in2) As = area of steel reinforcement (in2) -B- b = section width of rectangular column (inches) bw = effective beam width (inches) -C- c = neutral axis depth (inches) CE = environmental durability reduction factor -D- d = depth of beam (inches) db = diameter of longitudinal bars (inches) dc = depth of cover concrete (inches) D = diameter of circular column (inches) D’ = confined core diameter of column (inches) -E- E = typical test value of composite tensile modulus (ksi) EG = guaranteed design value of composite tensile modulus (ksi) -F- f = guaranteed design stress of the composite (ksi) f′c = concrete compressive strength (ksi) f′cc = confined concrete compressive strength (ksi)f′l = 0.26 ρsj f = effective confining stress of the jacket (ksi) f’m = masonry compressive strength (ksi) fs = longitudinal steel stress required to be transferred (ksi) fu = guaranteed ultimate composite stress (ksi)



fy = yield strength of steel reinforcement (ksi) -H- h = section depth of rectangular column (inches) H = wall height (inches) -J- jd = distance from centroid of composite to centroid of compression zone (inches) -K- k = efficiency factor = 2.0 when jacket is bonded to both sides and carried around a wall end = 1.0 when jacket is bonded to one side and carried around wall ends = 0.75 when only bonded to one face of wall -L- l = column length (inches) le = effective column length (inches) lp = column plastic hinge length (inches) ls = length of lap splice (inches) lw = length of wall section parallel to the applied lateral force (inches) -M- M = moment capacity provided by composite (kip-inches) Mu = ultimate moment capacity of the existing section (kip-inches) -N- n = number of uniformly distributed reinforcing bars -P- p = perimeter of the crack surface forming before splice failure (inches)P = applied axial loading (kips) -T- t = composite thickness (inches) ts = slab thickness (inches) tw = wall thickness (inches) -V- V = shear strength provided by composite (kips) -W- w = width of composite (inches)



General Design Considerations Bond-Critical versus Contact-Critical Advanced composite applications to civil structures will typically fall into one of two groups, “bond-critical” or “contact-critical.” A “bond-critical” application is one that requires a bond between the composite and the substrate to transfer loads (e.g. slabs, walls & beams). A “contact-critical” application is one that requires intimate contact with the substrate but no special adhesion requirements in order to perform (e.g. columns). Generally speaking, if you can’t wrap all the way around an element then it must be a “bond-critical” application. The designer must verify which type of application exists in order to specify the proper surface preparation and quality control procedures. The required field quality control testing for “contact-critical” applications is the ASTM D3039, “Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials.” For “bond-critical” applications we suggest both the ASTM D3039 and the ASTM D4541, “Standard Test Method for Pull-off Strength of Coatings Using Portable Adhesion Testers.” These tests can help ensure a proper design and proper installation. Active and Passive Structural Members Fiber-reinforced composite retrofit designs also fall into two general categories, active structural members and passive structural members. Most of the advanced composites used for strengthening applications will be for passive structural members. For these members, the composites are designed to take tension during a specific event (e.g. seismic or blast loading). These applications experience no strain during the majority of their service life. Passive structural members will typically not need any special fire protection. Some applications will use the advanced composites for active structural members (e.g. flexural strengthening for an additional, sustained load). These types of applications need special consideration. The allowable strains should be kept low to account for potential stress rupture, or “creep” effects. Ultimate limit states and failure modes also need to be considered. For flexural applications, the failure mode should be yielding of the reinforcing steel followed by crushing of the concrete. Active structural members will typically require some type of fire protection. Fire resistant finishes are available for the Tyfo® Systems (e.g. Tyfo® FC/F System), however local code and general design limitations need to be considered. Designers should establish the type of structural member that needs strengthening before determining acceptable design strains. Detailing The detailing of the composite system is critical to the proper design and performance of these systems. As with any tension member, required development lengths, overlaps and end details will affect their performance. The development lengths for “bond-critical” applications are typically calculated by considering the total tension force taken by the composite and the bonded area of the composite to the substrate. Special details and mechanical anchors are often used. The available in-plane bond stress can be approximated by multiplying the direct tension bond strength (as determined by the ASTM D4541 testing) by 2 . For concrete, it is generally assumed that 200 psi (1.4 MPa) is an acceptable, conservative value for the available in-plane bond shear stress. The required overlaps in the materials will be determined somewhat by which material is



assumed for the design and how much tension force is being transferred. In general, we suggest a minimum overlap of six inches (152.4 mm) in the primary fiber direction when splicing the materials. End details will often be determined by the geometry of the structural member and adjacent obstacles. How the composite is terminated can have a substantial effect on the performance of the system. This is true of all applications but specifically relevant for wall and beam shear applications. See pages 14 & 17 for additional design information and Appendix B & C for some typical details. Shear and Flexural Enhancement of Sections When increasing the flexural capacity of a section (e.g. beams and slabs) the designer must note the corresponding increase in shear demand. The section capacity must be checked to ensure that there will not be a premature failure in shear. Similarly, when increasing the shear capacity of certain sections (e.g. walls), the designer must check the flexural capacity of the section to ensure that the new shear strength can be developed prior to a flexural failure. In general, it is suggested to limit the amount of additional moment capacity provided to approximately 1.5 – 2 times the members existing capacity. This restriction is essentially due to potential failure modes. The desirable mode of failure would be a yielding of the existing reinforcing steel followed by a concrete crushing failure. A tension failure in the composite can be catastrophic. Using a force balance equation, the strengthened section should be checked for both operating service strains and ultimate strains. Figure 1 shows a typical force balance diagram for a strengthened section.

e

c aC

TT

cu

Neutral Axis

o

f

f = (e - e )E

y

j j

jet

t

Figure 1: Force Balance Diagram of a Strengthened Section



Material Selection Advanced composite materials are all essentially linear elastic and may be described by Hooke’s Law (f = Eε), where “E” is the tensile modulus, “ε” is the strain, and “f” is the corresponding material tensile stress. Figure 2 shows the stress-strain behavior of grade 60 steel along with three, typical wet lay-up Tyfo® Fibrwrap® Systems.

Figure 2: Stress-strain behavior of composites versus steel

The material properties of any advanced composite material may be categorized as “Typical Test Values,” and “Guaranteed Design Values.” The “Typical Test Values” are those received from ASTM D3039 test results performed on the cured composite in ideal conditions. The “Guaranteed Design Values” are those that have considered exposure to the environment for the life of the repaired structure. These “Guaranteed Design Values” can be determined by multiplying the “Typical Test Values” by an environmental durability reduction factor, CE. The following factors are relevant for most exposure conditions (extreme exposure conditions may require additional design considerations):



Composite System Reduction Factor, CEGlass, wet lay-up 0.8

Carbon, wet lay-up 0.85 Pull-formed, pre-cured laminate 0.9

These environmental reduction factors should be considered when using the materials elastic modulus and/or ultimate tensile strength in a design. When the design is governed by strain limitations, as is often the case, the property most relevant is the tensile modulus. Once the design allowable strains are known (e.g. 0.004 for shear strengthening), simply multiply the guaranteed design modulus by the allowable strain to get the allowable design stress. Table 1 describes some of the various Tyfo® Systems and their properties. Each of the Tyfo® Fibrwrap® Systems is designed to provide the optimum performance at the lowest possible cost. The best way to know which advanced composite system to use for a particular type of project is to accumulate design, installation and estimating experience. The design engineers at Fyfe Co. LLC will provide technical support at no obligation.



Table 1: Material Selection Chart

Typical Test Values Guaranteed Design Values

System Name* Description Ultimate Tensile

Strength, f Tensile Modulus,

E Ultimate Tensile

Strength, f 1Tensile Modulus,

EG

Composite Thickness

Tyfo® SEH 51 Primary glass fiber, 0° with aramid fiber 90°

83,400 psi (575 MPa)

3.79 x 106 psi (26.1 GPa)

66,720 psi (460 MPa)

3.03 x 106 psi (20.9 GPa)

0.05 in. (1.3 mm)

Tyfo® SEH 51A Primary glass fiber, 0° with glass fiber 90°

83,400 psi (575 MPa)

3.79 x 106 psi (26.1 GPa)

66,720 psi (460 MPa)

3.03 x 106 psi (20.9 GPa)

0.05 in. (1.3 mm)

Tyfo® SCH 41 Primary carbon fiber, 0° with glass fiber 90°

143,000 psi (986 MPa)

13.9 x 106 psi (95.8 GPa)

121,000 psi (834 MPa)

11.9 x 106 psi (82 GPa)

0.04 in. (1.0 mm)

Tyfo® SCH 41S Primary carbon fiber, 0° with aramid fiber 90°

127,000 psi (876 MPa)

10.5 x 106 psi (72.4 GPa)

107,950 psi (745 MPa)

8.9 x 106 psi (61.5 GPa)

0.04 in. (1.0 mm)

Tyfo® WEB Primary glass fiber, 0°/90°

44,800 psi (309 MPa)

2.80 x 106 psi (19.3 GPa)

35,840 psi (247 MPa)

2.24 x 106 psi (15.4 GPa)

0.01 in. (0.25 mm)

Tyfo® BC Primary glass fiber, ±45°

40,500 psi (279 MPa)

2.70 x 106 psi (19.0 GPa)

32,400 psi (223 MPa)

2.16 x 106 psi (15.2 GPa)

0.034 in. (0.864 mm)

Tyfo® BCC Primary carbon fiber, ±45°

104,000 psi (717 MPa)

10.8 x 106 psi (74.5 GPa)

88,400 psi (609 MPa)

9.18 x 106 psi (63.3 GPa)

0.034 in. (0.864 mm)

Tyfo® UC Strips Unidirectional pull-formed carbon/epoxy composite

405,000 psi (2.79 GPa)

22.5 x 106 psi (115.1 GPa)

364,500 psi (2.51 GPa)

20.3 x 106 psi (103.6 GPa) varies

Tyfo® UG Strips Unidirectional pull-formed glass/epoxy composite

130,000 psi (896.3 MPa)

6.0 x 106 psi (41.4 GPa)

117,000 psi (806.7 MPa)

5.4 x 106 psi (37.3 GPa) varies

1 Guaranteed Design Strength, f, is at the ultimate strength of the material. Most designs are governed by strain limitations. See page 7, “Material Selection” * Additional Tyfo® Products are available for custom designs (e.g. prefabricated sections, underwater systems, etc.) Please contact Fyfe Co. LLC for assistance.



Strain Limitations It is important to limit the maximum design strains to acceptable limits so as to avoid the limit state that may occur if the composites are loaded until they rupture. In many applications, the design strain limits may also be limited by the spalling of the concrete or masonry, or by the need to minimize the dilation of cracks to achieve acceptable structural performance.

Table 1.1 provides recommended strain limits for the Tyfo® FibrWrap® system when used in various applications. As can be seen from the table, the performance of the composites can be improved by confining the structural element with composite that has the main fibers aligned perpendicular to the longitudinal axis of the element. This is because the confinement provided by the composite eliminates the possibility of concrete spalling and enables the composite to remain attached to the concrete surface at larger strains.

Table 1.1 Limiting Strains of Tyfo® Fibrwrap® Composite Materials

Considered Loads

Element completely confined using composite with main fibers

aligned perpendicular to longitudinal axis or mechanically

anchored

Sustained Live Loads

or

Live Loads ≥ 100 psf

Intermittent Live Loads

(< 100 psf)

Temporary Loads

(Earthquake or Wind)

Yes 0.002 0.004 0.006Flexural Enhancement No 0.002 0.004 0.004

Yes, or FibrAnchors® used 0.004 0.004 0.004 Shear Enhancement No 0.0015 0.0015 0.0015

Yes 0.002 0.004 0.006Axial Load Enhancement No - - -

Yes (Circular columns) 0.0015 0.0015 0.0015 Lap Splice Enhancement No - - -

Yes N/A N/A As CalculatedDuctility Enhancement No - - -



Column Shear Enhancement

Nominal shear strength of circular and rectangular sections can be enhanced by fiber-reinforced composite materials with fibers oriented perpendicular to the members’ axis, acting at an allowable design strain of 0.004. For rectangular sections, corners must be rounded to a radius not less than ¾ inch (19mm) before placement of the fiber. The required number of layers required for shear strengthening shall be carried up the full height of the column, or as required based on sectional demands and capacities. Nominal shear strength enhancement provided by the composite (kips), V:

Rectangular Sections Circular Sections

ΦV = Φ2.86 f t h ΦV = Φ2.25 f t D Composite Properties:

EG = guaranteed design modulus (ksi), see page 9 ε = 0.004 (max. allowable design strain for shear per ICC AC125) f = EGε = corresponding guaranteed design stress of the composite (ksi) t = composite thickness (inches)

Member Properties:

D = diameter of circular column (inches) h = section depth parallel to the applied lateral force for rectangular

column (inches) Φ = 0.85 for shear applications per ACI 318



Column Axial Load Enhancement

Fiber-reinforced composite material may be applied to external surfaces of concrete members to enhance axial load capacity. Depending on the section shape, axial load capacity enhancement may be provided by longitudinal and/or transverse orientation of the fiber for tensile and compressive enhancement, respectfully. All sections with a rectangular aspect ratio not greater than 1.5 may have axial compression capacity enhanced by the confining effect of fiber-reinforced composite material placed with fibers oriented perpendicular to the members’ axis. To determine the enhancement of the column axial load capacity, calculate the confined concrete compressive strength, f’cc (psi): Circular Sections

⎟⎟⎠

⎞⎜⎜⎝

⎛−−+= 25.1

'f'f2

'f'f94.7125.2'f'f

c

l

c

lccc

where: f′l = 0.26 ρsj f = effective confining stress of the jacket (ksi) ρsj = 4 t / D = volumetric confining ratio of the jacket

Composite Properties:

f = guaranteed design stress of the composite (ksi) t = composite thickness (inches)

Member Properties:

D = diameter of circular column (inches) f’c = concrete compressive strength (ksi)

Rectangular Sections

⎟⎟⎠

⎞⎜⎜⎝

⎛ ρ+=

c

sjccc 'f

f64.11'f'f

where: ρsj = 2 t (b+h) / bh = volumetric confining ratio of the jacket


ε = 0.002 (max. allowable design strain for rectangular sections) f = guaranteed design stress of the composite (ksi) t = composite thickness (inches)

Member Properties:

b = section width (inches) h = section depth (inches) f’c = concrete compressive strength (ksi)



Column Ductility Enhancement

Fiber-reinforced composite material oriented transversely to the members’ axis may be used to enhance flexural ductility capacity of both circular and rectangular sections where the aspect ratio does not exceed 1.5. The enhancement is provided by increasing the effective ultimate compression strain capacity of the concrete. For rectangular sections, section corners must be rounded to a radius not less than ¾ inch (19mm) before placement of the fiber. The number of layers required for plastic hinge confinement shall extend a minimum length of 0.25 le, the effective column length, but is not required to extend beyond a length of the greater of b or h (D for circular sections). The extent of this confining jacket shall be from the point of fixity; from the footing for single bending or from the footing and deck for double bending cases. Ultimate concrete compressive strain with the addition of composite strengthening, εcu: Circular Sections

cc

uusjcu 'f

f5.2004.0

ερ+=ε

where: ρsj = 4 t / D = volumetric confining ratio of the jacket f′cc = confined concrete compressive strength ≅ 1.5f’c (ksi)

Composite Properties: fu = ultimate guaranteed composite stress (ksi) εu = ultimate composite strain t = composite thickness (inches)

Member Properties:

D = diameter of circular column (inches) f’c = concrete compressive strength (ksi)

Rectangular Sections

cc

uusjcu 'f

f25.1004.0

ερ+=ε

where: ρsj = 2 t (b+h) / bh = volumetric confining ratio of the jacket f′cc = confined concrete compressive strength ≅ 1.5f’c (ksi)


fu = ultimate guaranteed composite stress (ksi) εu = ultimate composite strain t = composite thickness (inches)

Member Properties:

b = section width (inches) h = section depth (inches) f’c = concrete compressive strength (ksi)



Column Lap Splice Enhancement

Composite jackets can prevent bond failure in lap splices of circular columns by confining the section. Rectangular columns can be effectively confined to prevent bond failure but may require changing the column to a circular or elliptical cross section. The volumetric confining ratio of the column with composite strengthening, ρsj:

fplfA4.1

s

sbsj =ρ

where: p = perimeter of the crack surface forming before splice failure (inches)

Use the lesser of the following values:

)dd(2n2

'Dp cb1 ++⎟⎠⎞

⎜⎝⎛ π

= or )dd(22p cb2 +=


EG = guaranteed design modulus (ksi), see page 9 ε = 0.0015 (max. allowable design lateral dilation strain) f = EGε = corresponding guaranteed design stress of the composite (ksi) t = composite thickness (inches)

Member Properties:

Ab = area of one longitudinal bar (in2) fs = longitudinal steel stress required to be transferred (ksi) ls = length of the lap splice (inches) D′ = confined core diameter of column (inches) n = number of uniformly distributed reinforcing bars db = diameter of longitudinal bars (inches) dc = depth of cover concrete (inches)

Note that the lap splice length, ls must be greater than or equal to the quantity = (0.025dbfy)/√f’c The required composite thickness to achieve this volumetric confining ratio is:

Rectangular Sections Circular Sections

⎥⎦⎤

⎢⎣⎡

+ρ=

hbbh5.0t sj

4D

t sjρ=

Member Properties:

D = diameter of circular column (inches) b = section width of rectangular column (inches) h = section depth of rectangular column (inches)



Beam Shear Enhancement Shear strength of rectangular sections can be enhanced by fiber-reinforced composite materials with fibers oriented perpendicular to the members’ axis, acting at an allowable design strain of 0.004. Where the performance of the composite material depends on bond, the bond strength of the fiber-reinforced composite material to the substrate shall be a minimum of 200 psi (1.4 MPa). If the bond strength is lower, special design considerations must be taken. Bond stress shall be calculated based on the tension forces in the composite that are to be developed over the bond area. The following equations are limited for bw/d ratios less than or equal to 0.75. Special design considerations must be taken for beams dimensions that exceed this ratio. This equation applies to sectional shear strength and is not applicable to shear capacity between perpendicular end sections. These provisions do not apply to shear strength enhancement for flanged sections requiring placement of fiber around re-entrant corners. In these cases an effective beam depth shall be used between re-entrant locations. The use of anchors to mechanically attach the fiber-reinforced composite material at the section edges is effective in transferring the design fiber stress as well as promoting thermal compatibility and long-term durability. (See page 19 for more information on mechanical anchorage.) Section edges must be rounded to a radius not less than ¾ inch (19mm) before placement of the fiber. Structural testing has shown that mechanical anchorage along the top edge may be required to fully develop a design strain of 0.004 in/in. Nominal shear strength enhancement provided by the composite (kips), V:

θ2sin2 HftV jfsj =

where,

tf = Nominal thickness of composite fj = Stress in composite, which is given by εjEj 0.75 fju

Ej = Modulus of composite (Guaranteed Design Value) εj = Effective strain in shear composite 0.004 H = Effective depth of shear composite θ = Inclination of composite to longitudinal axis of member = 90 degrees

Design Procedure: 1. Calculate Existing Shear Capacity of Beam without Composites 2. Calculate Allowable Hoop Stress in Composite Layer 3. Calculate the Required Number of Composite Layers



Beam Flexural Enhancement Fiber-reinforced composite material may be bonded to surfaces of beams to enhance the design flexural strength of sections by acting as additional tension reinforcement. In such cases, section analysis shall be based on force equilibrium and strain compatibility between the substrate, reinforcement and composite material. Where the performance of the composite material depends on bond, the bond strength of the fiber reinforced composite material to the concrete or masonry shall be a minimum of 200psi (1.4 MPa). If the bond strength is lower, special design considerations must be taken. Bond stress shall be calculated based on the tension forces in the composite that are to be developed over the bond area. It is suggested that anchors or transverse fibers be utilized at termination points of longitudinal fiber to ensure the development of the design strain and to enhance the long-term durability of the bonded application. It is also suggested that the enhanced design strength of the section does not exceed 1.5 – 2 times the existing strength of the section and that serviceability requirements are checked. Nominal flexural strength enhancement provided by the composite (k-in), M:

ΦM = ΦA f (jd) Composite Properties:

f = guaranteed design stress of the composite (ksi) A = w⋅t = area of composite (in2) w = width of composite (inches) t = composite thickness (inches)

Member Properties:

jd = d – a/2 = distance from centroid of composite to centroid of compression zone (inches)

d = beam depth (inches) a = compression zone depth (inches) Φ = 0.9 for flexural applications per ACI 318

Design Procedure: 1. Calculate Existing Capacity 2. Calculate Strains Under Existing Loads 3. Estimate Required Number of Composite Layers 4. Check Moment Capacity of Strengthened beam

a) At Limit State for Ultimate Compressive Concrete Strain (Concrete Crushing at 0.003)

b) At Limit State for Maximum Allowable Composite Tensile Strain (see Table 1.1)



Slab Flexural Enhancement Fiber-reinforced composite material may be bonded to surfaces of concrete slabs to enhance the design flexural strength of sections by acting as additional tension reinforcement. In such cases, section analysis shall be based on force equilibrium and strain compatibility between the concrete, reinforcement and composite material. The bond strength of the fiber reinforced composite material to the concrete or masonry shall be a minimum of 200psi (1.4 MPa). If the bond strength is lower, special design considerations must be taken. Bond stress shall be calculated based on the tension forces in the composite that are to be developed over the bond area. It is suggested that anchors be utilized at termination points of longitudinal fiber to ensure the development of the design strain and to enhance the long-term durability of the bonded application. It is also suggested that the enhanced design strength of the section does not exceed 1.5 – 2 times the existing strength of the section and that serviceability requirements are checked. Allowances need to be made for vapor transmission from walls, slabs and other elements where the pressure potential will be in excess of 3 psi. This pressure can be measured in the field with simple equipment. If the pressure is in excess of 3 psi, allow 30% of the surface area to be clear for vapor transmission. The area climatic conditions and field conditions should also be considered. Nominal flexural strength enhancement provided by the composite (k-in), M:



Member Properties:

jd = ts – a/2 = distance from centroid of composite to centroid of compression zone (inches)

ts = slab thickness (inches) a = compression zone depth (inches) Φ = 0.9 for flexural applications per ACI 318

Design Procedure: 5. Calculate Existing Capacity 6. Calculate Strains Under Existing Loads 7. Estimate Required Number of Composite Layers 8. Check Moment Capacity of Strengthened Slab


b) At Limit State for Maximum Allowable Composite Tensile Strain (see Table 1.1)



In-Plane Wall Shear Enhancement In-plane shear strength can be enhanced by fiber-reinforced composite bonded to surfaces of walls with fibers oriented parallel to the applied shear force. Where the performance of the composite material depends on bond, the bond strength of the fiber reinforced composite material to the concrete or masonry shall be a minimum of 200psi (1.4 MPa). If the bond strength is lower, special design considerations must be taken. Bond stress shall be calculated based on the tension forces in the composite that are to be developed over the bond area. It is suggested that anchors be utilized at termination points of longitudinal fiber at wall ends to ensure the development of the design strain and to enhance the long-term durability of the bonded application. Allowances need to be made for vapor transmission from walls, slabs and other elements where the pressure potential will be in excess of 3 psi. This pressure can be measured in the field with simple equipment. If the pressure is in excess of 3 psi, allow 30% of the surface area to be clear for vapor transmission. The area climatic conditions and field conditions should also be considered. An efficiency factor, k, is used in the design of in-plane wall shear to account for the optimum placement of the composite to the wall surface. The most efficient design is to carry the composite around the wall ends and completely bond the material to both sides of the wall. This case will allow an efficiency factor of k = 2.0. If the composite can be carried around the wall ends, but only bonded to one side of the wall, the efficiency factor is k = 1.0. The least efficient option is to bond the composite to only one face of the wall, resulting in k = 0.75. Typical details are provided in Appendix B. Nominal shear strength enhancement provided by the composite (kips), V:

ΦV = Φk f t lw Composite Properties:

EG = guaranteed design modulus (ksi), see page 9 ε = 0.004 (max. allowable design strain for shear per ICC AC125) f = EGε = corresponding guaranteed design stress of the composite (ksi) k = efficiency factor (see above) t = composite thickness (inches)

Member Properties:

lw = length of wall section parallel to the applied lateral force (inches) Φ = 0.85 for shear applications per ACI 318



Out-of-Plane Wall Flexural Enhancement

Fiber-reinforced composite material may be bonded to surfaces of walls to enhance the design flexural strength of sections by acting as additional tension reinforcement. In such cases, section analysis shall be based on force equilibrium and strain compatibility between the substrate, reinforcement and composite material. The bond strength of the fiber reinforced composite material to the concrete or masonry shall be a minimum of 200 psi (1.4 MPa). If the bond strength is lower, special design considerations must be taken. Bond stress shall be calculated based on the tension forces in the composite that are to be developed over the bond area. It is suggested that anchors be utilized at termination points of longitudinal fiber at strip ends to ensure the development of the design strain and to enhance the long-term durability of the bonded application. It is also suggested that the enhanced design strength does not exceed 1.5 – 2 times the original strength of the section and that serviceability requirements are checked. Allowances need to be made for vapor transmission from walls, slabs and other elements where the pressure potential will be in excess of 3 psi. This pressure can be measured in the field with simple equipment. If the pressure is in excess of 3 psi, allow 30% of the surface area to be clear for vapor transmission. The area climatic conditions and field conditions should also be considered. Nominal flexural enhancement provided by the composite (k-in), M:



Member Properties:

jd = tw – a/2 = distance from centroid of composite to centroid of compression zone (inches)

tw = wall thickness (inches) a = compression zone depth (inches) Φ = 0.9 for flexural applications per ACI 318



Mechanical Anchorage Tyfo® SCH & SEH Composite Anchors are an exclusive development from Fyfe Co. LLC that can transfer tensile forces and improve the overall efficiency of many different types of strengthening systems. FibrAnchors® are suggested for use in “bond-critical” applications such as beams, slabs and walls. Tyfo® SCH & SEH Composite Anchors are applied by first drilling holes at designated locations during the surface preparation stage. The holes are cleaned along with the prepared surface prior to anchor installation. The fully hand-saturated anchors are installed and the hole is filled with Tyfo® WS or TC epoxy. The free fibers are splayed out and troweled with additional Tyfo® WS or TC epoxy. The required layers of the Tyfo® Fibrwrap® System is then applied as per the specifications. See Appendix C for a typical anchor details. FibrAnchors® are designed and installed as per each individual project requirement. In addition to the Tyfo® SCH & SEH Composite Anchors, conventional mechanical anchorage systems may be used to achieve similar design goals. Consult with Fyfe Co. LLC design engineers if any questions arise concerning the use of Tyfo® FibrAnchors® or conventional anchorage in conjunction with the Tyfo® Fibrwrap® Systems.



Literature 1. ICC Interim Criteria for Concrete and Reinforced and Unreinforced Masonry

Strengthening Using Fiber-Reinforced Polymer (FRP) Composite Systems, AC125, June, 2003.

2. Priestley, M.J.N., Seible, F., Calvi, G.M., Seismic Design and Retrofit of Bridges, John

Wiley & Sons, Inc., New York, 1996. 3. Paulay, T., and Priestley, M.J.N., Seismic Design of Reinforced Concrete and Masonry

Buildings, John Wiley & Sons, Inc., New York, 1990. 4. Priestley, M.J.N., Seible, F., Column Seismic Retrofit Using Fiberglass/Epoxy Jackets,

Department of Applied Mechanics and Engineering Sciences, University of California San Diego, 1994.

5. Priestley, M.J. Nigel, Seible, F., UCSD. Seismic Assessment & Retrofit of Bridges, July

1991. 6. ACI 440.2R-02, Guide for the Design and Construction of Externally Bonded FRP

Systems for Strengthening Concrete Structures, October, 2002. 7. Construction Productivity Advancement Research (CPAR) Program, US Army Corps of

Engineers, Construction Engineering Research Laboratories, Fiber-Reinforced Polymer Composite Materials Systems to Enhance Reinforced Concrete Structures, February 1998.

Test Reports Column Shear Enhancement: 1. SEQAD Consulting Engineers. Rectangular Shear Column Test. Mar. 1992. 2. SEQAD Consulting Engineers. Repair of Shear Columns Using Fiberglass/Epoxy

Jackets. 1993. 3. SEQAD Consulting Engineers. Shear Column Test No.1. May 1991. 4. SEQAD Consulting Engineers. Shear Column Test No. 2. July 1991. 5. Priestley, Assessment & Retrofit of Concrete Columns for Seismic Performance. UCSD,

July 1993. 6. SEQAD Consulting Engineers. Repair of Shear Column Using Fiberglass Epoxy Jacket.

July 1993. 7. Ohtaki, Benzoni/ UCSD. Seismic Performance of a Full Scale Bridge Column. Nov.

1996. © Copyright 2001 Fyfe Co. LLC. 7-01 Reproduction by written permission from Fyfe Co. LLC only. All rights reserved 21

Tyfo® and Fibrwrap® are registered trademarks for the products of Fyfe Co. LLC


8. SEQAD Consulting Engineers. High Strength Fiber Rectangular Column Shear & No

Lap-Splice Flexural Test. March 1992. 9. University of Canterbury, New Zealand. Retrofitting of Reinforced Concrete Members

Using Advanced Composite Materials.1999. 10. University of California at Irvine, Structural Qualification Testing of Composite Jacket

Circular and Rectangular Columns. Oct. 1999. Column Axial Load Enhancement: 1. SEQAD Consulting Engineers. Axial Load Characteristics of Rectangular Columns

Wrapped with TYFO® S Jackets. Feb. 1996. 2. K.W. Neale, INC. Axial Load Capacity of Wall Type Concrete Columns. April 1997. 3. USC. Full Scale Testing of a Typical Parking Structure Column. Oct.1995. 4. Texas D.O.T. Compression Test of Failed Concrete Cylinders Wrapped with TYFO®

Fibrwrap System. Oct.1995. 5. Kachlakev et. al, Oregon D.O.T., FHWA, Behavior of Concrete Specimens Reinforced

with Composite Materials – Laboratory Study, SPR-387., Feb. 2000. 6. University of California at Irvine, Structural Qualification Testing of Composite Jacket

Circular and Rectangular Columns. Oct. 1999. Column Ductility Enhancement: 1. Pennsylvania D.O.T. Fiber Column Wrap-Seismic retrofit System. Nov. 1998. 2. Priestley, Seible. Design of Seismic Retrofit Measures for Concrete & Masonry. Mar.

1995. 3. USC. Full Scale Testing of a Typical Parking Structure Column. Oct.1995. 4. SEQAD Consulting Engineers. Repair of Shear Column Using Fiberglass Epoxy Jacket.

July 1993. 5. SEQAD Consulting Engineers. Repair of Shear Column Using Fiberglass Epoxy Jacket.

July 1993. 6. Priestley / UCSD. Seismic Assessment & Retrofit of Bridge Columns. 7. Ohtaki, Benzoni/ UCSD. Seismic Performance of a Full Scale Bridge Column. Nov.

1996. 8. University of Toronto. Repair & Strengthening of Columns with Fiber. Mar 1998.



9. University of Canterbury, New Zealand. Retrofitting of Reinforced Concrete Members Using Advanced Composite Materials.1999.

10. University of California at Irvine, Structural Qualification Testing of Composite Jacket

Circular and Rectangular Columns. Oct. 1999. Column Lap Splice Enhancement: 1. SEQAD Consulting Engineers. High Strength Fiber Circular Column Lap Splice

Flexural Test Project. May 1991. 2. SEQAD Consulting Engineers. Seismic Retrofit of Bridge Columns Using High Strength

Fiberglass/ Epoxy Jackets. Aug. 1993. 3. USC. Full Scale Testing of a Typical Parking Structure Column. Oct.1995. Beam Shear Enhancement: 1. Kheled R. Saleh / Lawrence Technical University. Strengthening of Two- Span

Continuous Girders Using Fyfe FRP Sheets. 1997. 2. ISIS / University of Manitoba. Shear Strengthening of the Maryland Bridge Using CFRP

Sheets SCH-41. July 1997. 3. University of Alberta. Shear Rehabilitation of Type G Girders Using ACM. 4. A & M Texas University. Tests of Concrete Beams with Externally Bonded Glass Fiber

Fabric Web Reinforcement. 1999. 5. University of Canterbury, New Zealand. Recent Development in the Use of Advanced

Composite Materials for Seismic Retrofitting. 1999. 6. University of Canterbury, New Zealand. Retrofitting of Reinforced Concrete Members

Using Advanced Composite Materials.1999. 7. University of Canterbury, New Zealand. Increase of Load Carrying Capacity of Beams

by Means of Advanced Composite Material Plates. 1999. 8. Kachlakev and McCurry, Oregon D.O.T., FHWA, Behavior of Concrete Specimens

Reinforced with Composite Materials – Laboratory Study, SPR-387. Feb. 2000. Beam/Slab Flexural Enhancement: 1. Kheled R. Sleh. / Lawrence Technical University. Strengthening of Two-Span

Continuous Girders Using Fyfe FRP Sheets.1997. 2. Georgia D.O.T. Flexural Test of Concrete Beams Wrapped with TYFO® S Fibrwrap.

Feb. 1994. © Copyright 2001 Fyfe Co. LLC. 7-01 Reproduction by written permission from Fyfe Co. LLC only. All rights reserved 23



3. University of Pennsylvania. FRP Jacketed Concrete Under Flexure & Combined

Flexure. Feb. 1995. 4. Grace, Sayad, Saleh. Strengthening Reinforced Concrete Beams Using Fiber Reinforced

Polymer (FRP) Laminates. Oct. 1999. 5. A&M Texas University. Tests of Concrete Beams with Externally Bonded Glass Fiber

Fabric WEB Reinforcements. 6. University of Canterbury, New Zealand. Retrofitting of Reinforced Concrete Members

Using Advanced Composite Materials. 7. University of Canterbury, New Zealand. Increase of Load Carrying Capacity of Beams

by Means of Advanced Composite Material Plates. 8. Mc Maser University. Repair of Beam Column Joints Using GFRP Sheets. Oct. 1999. 9. Kachlakev and McCurry, Oregon D.O.T., FHWA, Behavior of Concrete Specimens

Reinforced with Composite Materials – Laboratory Study, SPR-387. Feb. 2000. 10. Naval Facilities Engineering Service Center, Navy Advanced Composite Technology in

Waterfront Infrastructure, SP-2046-SHR. December 1998. 11. Naval Facilities Engineering Service Center, Waterfront Repair and Upgrade, Advanced

Technology Demonstration Site No. 2, Pier 12 Naval Station, San Diego, SSR-2419-SHR. November 1998.

In-Plane Wall Shear Enhancement: 1. UCSD. Seismic Repair & Retrofit of a Full-Scale Five Story Masonry Building. Oct.

1993. 2. UCSD. Seismic Repair & Retrofit of Masonry Walls with Carbon Overlays. 1995. 3. PMR Enterprises/UC Irvine. TYFO® JT System Full Scale Structural Test Program.

Nov. 1996. 4. US Army Corps of Engineers. Upgrade & Monitoring of Unreinforced Masonry. Nov.

1997. 5. US Army Corps of Engineers. Masonry Bearing & Shear Walls Retrofitted with Overlay

Composite Material . Dynamic Test. Jun. 1998. 6. State University of New York, Buffalo. Evaluation of TYFO® W Fibrwrap System for In-

Plane Strengthening of Masonry Walls. March 1995.

© Copyright 2001 Fyfe Co. LLC. 7-01 Reproduction by written permission from Fyfe Co. LLC only. All rights reserved 24Out-of Plane Wall Flexural Enhancement:



1. Portland State University. Full Scale Tests of Retrofitted Hollow Clay Tile Walls. Jun.

1998. 2. US Army Corps of Engineers. Upgrade & Monitoring of Unreinforced Masonry. Nov.

1997. 3. US Army Corps of Engineers. Masonry Bearing & Shear Walls Retrofitted with Overlay

Composite Material. Dynamic Test. June 1998. 4. State University of New York, Buffalo. Evaluation of TYFO® W Fibrwrap System for

Out-of-Plane Strengthening of Masonry Walls. March 1995. 5. See, “Beam/Slab Flexural Enhancement” for additional supporting reports. Mechanical Anchorage: 1. University of Canterbury, Christchurch, New Zealand. Retrofit of Reinforced Concrete

Using Advanced Composite Materials. 1999. 2. University of Canterbury, New Zealand. Increase of Load Capacity of Beams by Means

of Advanced Composite Plates. 1999. 3. J. Neuner & R. Falabella. Composite Anchor System – Flatwise Tensile & Shear Testing.

June 1996. 4. Accu-Test Engineering Laboratories. Results of Flatwise Tension, Shear and Torque

Tests on Concrete Specimens bonded with Carbon Fiber Composite. 2000.



APPENDIX A

DESIGN EXAMPLES



Column Shear Design Example

Design Goal: Supplement original transverse reinforcement to provide increased shear strength

and improve earthquake performance of the structure. The target additional shear strength is 120 kips.

1) Existing Column Properties:

h = b = 24” (column width and depth) l = 19.33’ (column length) f’c = 3000 psi (concrete compressive strength) fy = 60 ksi (yield strength of reinforcement) Transverse reinforcement: #3 bars @ 8” o.c.

2) Properties of Tyfo® SEH 51 Glass Composite System:

ε = 0.004 (allowable design strain for shear) E = 3790 ksi (typical test value for tensile modulus) CE = 0.8 (environmental reduction factor) EG = CEE = (0.8)(3790 ksi) = 3032 ksi (guaranteed design modulus) f = ε EG = (0.004)(3032 ksi) = 12.1 ksi (guaranteed design stress) t = 0.05” (composite thickness)

3) Shear enhancement with one layer of composite:

ΦV = Φ2.86 f t h where: Φ = 0.85 (reduction factor for shear)

ΦV = (0.85)(2.86)(12.1 ksi)(0.05”)(24”) = 35.3 k

Shear enhancement provided by one layer of the Tyfo® SEH System. 4) Calculate required number of layers of composite: The required additional shear force the columns must carry is, Vreq = 120 kips.

Therefore, the number of layers required is: Vreq / V = 120 k / 35.3 k per layer = 3.4 ≈ 4 layers 5) Conclusions: Providing 4 layers of the Tyfo® SEH 51 System will enhance the shear capacity of the

column to carry the additional shear force of 120 kips. See Appendix B for typical details.



Column Axial Load Design Example Design Goal: Use Tyfo® SCH composite to provide 300 kips of additional ultimate axial

capacity to existing columns. The additional capacity is required during a seismic event and is not considered to be a sustained load.

1) Existing Column Properties:

diameter = 13” (column diameter) f’c = 3000 psi (concrete compressive strength)

2) Properties of Tyfo® SCH 41 Carbon Composite System:

ε = 0.002 (allowable design strain) E = 13900 ksi (typical test value for tensile modulus) CE = 0.85 (environmental reduction factor) EG = CEE = (0.85)(13900) = 11900 ksi (guaranteed design modulus) f = ε EG = (0.002)(11900) = 23.8 ksi (guaranteed design stress) t = 0.04” (composite thickness)

3) Calculate confined concrete compressive strength:

⎟⎟⎠

⎞⎜⎜⎝

⎛−−+= 25.1

'f'f2

'f'f94.7125.2'f'f

c

l

c

lccc

where: f′l = 0.26 ρsj f = effective confining stress of the jacket (ksi) ρsj = 4 t / D = volumetric confining ratio of the jacket

Assume two layers of SCH 41 carbon composite:

ρsj = 4 t / D = 0.0246 f′l = 0.26 ρsj f = 0.152 ksi

f’cc = 3941 ksi

4) Calculate additional axial load capacity:

Assume that the steel does not provide significant additional axial capacity to the column at levels in excess of the original design.

The original axial capacity of the column was:

ΦP0 = Φ f’c Ag



where: Φ = 0.85 (reduction factor for axial load) Ag = 132.6 in2 (gross area of column) ΦP0 = (0.85)(3.0 ksi)(132.6 in2) = 338.13 kips

The new axial capacity with two layers of the Tyfo® SCH Composite System is:

ΦPcomp = Φ f’cc Ag = (0.85)(3.941 ksi)(132.6 in2) = 444 kips This corresponds to an increased axial load of: 444 k – 338 k = 106 kips 5) Conclusions:

Two layers of the Tyfo® SCH 41 Composite System provide an additional 106 kips of axial capacity to the existing column.

The two-layer Tyfo® SCH 41 System must extend over the column’s full clear height. See Appendix B for typical details. Note that axial load enhancement of rectangular sections requires changing the cross-sectional shape to a circle or ellipse. This can be accomplished with pre-cast bolsters or by forming and pouring.



Column Ductility Design Example Design goal: Provide a composite system for the existing circular column that allows a

displacement ductility of six times the yield displacement of the section. 1) Existing Column Properties:

P = 212 kips (applied axial loading) f'c = 5000 psi (concrete compressive strength) D = 24” (diameter of column) l = 12’ = 144” (column height) fy = 60 ksi (yield strength of steel reinforcement) db = 0.75” (diameter of longitudinal bars) Longitudinal reinforcement: 6-#6 bars Transverse reinforcement: #3 hoops at 14” on center

Assume a fixed-fixed boundary condition, so le = (0.5) l = (0.5)(144”) = 72”

2) Results from Moment-Curvature Analysis of the existing section:

Fyfe Co. LLC engineers can provide a complete moment-curvature analysis for engineers use if given the information listed in the “Existing Column Properties” section of this example.

Mu = 4437.8 kip-in (moment capacity of the existing section) c = 6.1” (neutral axis depth at ultimate moment) φy = 0.000184 1/in (ideal yield curvature)

3) Properties of Tyfo® SEH 51 Glass Composite System:

εu = 0.022 (ultimate composite strain) E = 3790 ksi (typical test value for tensile modulus) CE = 0.8 (environmental reduction factor) EG = CEE = (0.8)(3790 ksi) = 3032 ksi (guaranteed tensile modulus) fu = εu EG = (0.022)(3032 ksi) = 66.7 ksi (guaranteed ultimate composite stress) t = 0.05” (composite thickness)

4) Ductility Calculations:

Determine the plastic hinge length, lp:

"5.12)"75.0)(ksi60)(15.0()"72)(08.0(df)15.0(l)08.0(l byep =+=+=

The required curvature ductility, µφ is:

© Copyright 2001 Fyfe Co. LLC. 7-01 Reproduction by written permission from Fyfe Co. LLC only. All rights reserved



⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−µ

+=µ ∆φ

ll5.0

1ll

3

11pp

where the target design ductility, µ∆ = 6.

5.11

"72)"5.12)(5.0(1

"72"5.123

161 =

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎟⎠⎞

⎜⎝⎛ −⎟

⎠⎞

⎜⎝⎛

−+=µφ

Therefore, the ultimate curvature, φu is: φu = µφφy = (11.5)(0.000184) = 0.00212

and the ultimate confined concrete strain to reach this ultimate curvature, εcu:

εcu = φu c = (0.00212)(6.1”) = 0.0129 5) Determine thickness of composite required:

First, the volumetric confining ratio of the composite jacket, ρsj is:

uu

cccusj f

)'f)(004.0(8.0ε

−ε=ρ

where:

f’cc ≅ 1.5 f’c = (1.5)(5 ksi) = 7.5 ksi

0364.0)022.0)(ksi7.66(

)ksi5.7)(004.00129.0(8.0sj =

−=ρ

The required composite thickness to achieve this confinement is:

ρsj = 4 t / D ∴ t = ρsj D / 4 = (0.0362)(24”)/4 = 0.2172”

# of layers = 0.2172”/0.05” per layer = 4.3 ≈ 5 layers



6) Conclusions:

Five layers of the Tyfo® SEH 51 System are needed to enhance the displacement ductility of the column to six times the yield displacement of the longitudinal steel. For axial load ratios of P/f’c Ag < 0.3 the composite thickness, t, must extend from the critical section a length of 25% of the effective column height, le, or the column diameter, D, whichever is greater.

Corresponding shear forces at the calculated ultimate levels for ductility should be checked to ensure that the column is not prone to shear failure. The ductility requirements for columns can also be stated in required drift, ultimate displacements, plastic rotation or curvature ductility. These values can be transformed into individual multiples of the displacement ductility described in this example in the “Ductility Calculations” section. If you require any assistance, please contact the Fyfe Co. LLC engineers.



Column Lap Splice Design Example Design Goal: Provide sufficient clamping force to existing inadequate lap splice length to

allow continuous column performance. 1) Existing Column Properties:

D = 30” (diameter of column) dc = 2” (depth of cover concrete) f’c = 4000 psi (concrete compressive strength) fs = fy = 40 ksi (steel stress required to be transferred) Longitudinal reinforcement: 12-#9 bars db = 1.128” (diameter of longitudinal bars) n = 12 (number of longitudinal bars) Ab = 1.0 in2 (area of longitudinal bars) D’ = 30” – (2)(2”) – .375” = 25.6” (confined core diameter of column) ls = 16” (length of lap splice)

Note that ls = 16” ≥ (0.025dbfy)/√f’c = 15.8” OK 2) Properties of Tyfo® SCH 41S Carbon Composite System:

ε = 0.0015 (allowable design strain for lap splices) E = 10500 ksi (typical test value for tensile modulus) CE = 0.85 (environmental reduction factor) EG = CEE = (0.85)(10500) = 8925 ksi (guaranteed design modulus) f = ε EG = (0.0015)(8925) = 13.39 ksi (guaranteed design stress) t = 0.04” (composite thickness)

3) Calculate the volumetric confining ratio of the composite:

fplfA4.1

s

sbsj =ρ

where: p = perimeter of the crack surface forming before splice failure (inches).

Use the lesser of the following values:

)dd(2n2

'Dp cb1 ++⎟⎠⎞

⎜⎝⎛ π

= or )dd(22p cb2 +=

)"2"128.1(2)12(2

)"6.25(p1 ++⎟⎟⎠

⎞⎜⎜⎝

⎛ π= = 9.61” or )"2"128.1(22p2 += = 8.85”

∴p = 8.85” Therefore,



)ksi39.13)("16)("85.8()ksi40)(in0.1(4.1 2

sj =ρ = 0.0295

4) Calculate required number of layers of composite: The required thickness of composite to achieve this confinement is:

t = ρsj D / 4 = (0.0295)(30”)/4 = 0.221” # of layers = 0.221”/0.04” per layer = 5.5 ≈ 6 layers

5) Conclusions:

Use 6 layers of the Tyfo® SCH 41S carbon composite to effectively clamp the existing insufficient lap splice. At a minimum, the composite jacket should be extended the full length of the existing lap splice. Note that rectangular sections with insufficient lap-splice detailing will often require changing the cross-sectional shape to circular or elliptical prior to wrapping. This can be accomplished using pre-cast bolsters or by forming and pouring.



Beam Shear Design Example

Beam Shear Strength Enhancement Using Tyfo® Fibrwrap® Fiber-Reinforced Composite System

Due to rehabilitation of an existing building, the beam shown in Figure E2-1 is required to resist a factored dead and live load shear of 175 kips. The effective depth of the reinforcement is 35 inches. The existing slab is 8 inches deep and so the clear depth of beam face is 30”. Use fiber-reinforced composites to provide additional shear capacity.

20”

38”

8”

d = 35”

#4 @ 16” o.c.

Figure E2-1. Beam Shear Reinforcement Layout Beam and Stirrup Properties: Concrete compressive strength, f ‘c = 3000 psi Effective depth of beam, d = 35 inches Specified steel yield stress of stirrups, fy = 40 ksi Elastic modulus of steel, Es= 29000 ksi Stirrup spacing, s = 16 inches Steel area in shear for each stirrup, Av = (2 legs) 0.2 =0.4 in2 Material Properties of Fiber-Reinforced Composite: Use TYFO® Fibrwrap® System, SEH-51

Ultimate tensile strength fuj = CEfG = 0.8(83.4) = 66.7 ksi Elastic modulus Ej = CEEG = 0.8(3790) = 3030 ksi Allowable strain for shear in composite, εj = 0.004 (per ICC report AC125) Thickness per layer, tj = 0.05 inches Angle of primary fiber orientation, θ = 90 degrees

Design Procedure: © Copyright 2001 Fyfe Co. LLC. 7-01 Reproduction by written permission from Fyfe Co. LLC only. All rights reserved



4. Calculate Existing Shear Capacity of Beam without Composites 5. Calculate Allowable Hoop Stress in Composite Layer 6. Calculate the Required Number of Composite Layers

1. Calculate Existing Shear Capacity of Beam without Composites: Calculate shear capacity of beam using following equation:

sdfA

dbfV yvwcn += '2

( )( )( ) 112

16354040.0

1000)35)(20(30002

=+=nV kips < 175 kips (Target Capacity)

The existing beam does not have adequate capacity to resist the anticipated shear.

2. Calculate Allowable Hoop Stress in Composite Layer: From ICC report AC125 allowable shear stress in the composite layer is determined using following equation, which is based on an effective strain of 0.004 in the shear-enhancing composite:

ujjj fEf 75.0004.0 ≤=

507.6675.01.123030004.0 =×<=×= ksi ksi

fj =12.1 ksi Note that the effective strain of 0.004 can only be attained if the shear enhancing composites are bonded effectively to the beam. This can be achieved by wrapping the composites around the entire cross-section. If the presence of a slab prevents the composites from being wrapped around the entire section, anchors should be used at the edges of the composite to ensure effective bond between the composite and the beam web. See the “Appendix C” for typical anchor details.

3. Calculate Required Thickness of Composite Layer: The enhancement of shear strength by composites applied to a beam is given by:



θ2sin2 HftV jfsj =

where,

tf = Nominal thickness of composite = 2×0.05 = 0.10 inches for two layers fj = Stress in composite, which is given by εjEj 0.75 fju

Ej = Modulus of composite (Guaranteed Design Value) = 3030 ksi εj = Effective strain in shear composite 0.004 H = Effective depth of shear composite = 30 inches θ = Inclination of composite to longitudinal axis of member = 90 degrees

The nominal thickness of composite required is therefore given by:

( )( )( ) 129.013012211285.0/175

sin2/

2, =−

=−

=θ

φHf

VVtj

nurequiredj ”

and the number of layers required is given by:

3~58.205.0

129.0, ===j

requiredj

tt

n

Use 3 layers of TYFO® Fibrwrap® System, SEH-51 (Anchors are required to ensure the design strain can be developed)



Slab Flexural Design Example

Slab Flexural Strength Enhancement Using the Tyfo® FibrWrap® Fiber-Reinforced Composite System

Due to rehabilitation of an existing building, the slab shown in Figure E1-1 is required to resist a factored dead and live load moment of 240 kip-in due to additional intermittent live load. Using fiber-reinforced composites, provide additional moment capacity. Assume 50% of the bottom face of the slab will be covered with composite layers (For example, 12-inch strips as a 12-inch spacing). The existing dead load moment in the slab is 84 kip-in.

12”

11.5”d = 9.3”

#5 @ 12” o.c.

Figure E1-1. Slab Section

Slab Dimensions: Assumed effective slab width, b = 12 inches Slab depth, h = 11.5 inches Effective depth of Slab, d = 9.3 inches Reinforcing Steel, As = 0.31 in2/ft (#5 @ 12” o.c.)

Material Properties of Slab: Specified concrete strength, f ’c = 3000 psi

Elastic modulus of concrete, 3122300057'57 === cc fE ksi

Specified steel yield stress, fy = 60 ksi Elastic modulus of steel, Es= 29000 ksi



Material Properties of Fiber-Reinforced Composite: To account for the effect of exposure to the environment during the life of the structure, the “Typical Test Values” for the composites are modified by the Environmental Durability Factor CE to obtain the “Guaranteed Design Values” that are used in design. If we use carbon TYFO® SCH-41S Fibrwrap® System, the Environmental Durability Factor is equal to 0.85. For TYFO® SCH-41S:

Ultimate tensile strength, fuj = fGCE = 127(0.85) = 108 ksi Elastic modulus, Ej = EGCE = 10500(0.85) = 8900 ksi Ultimate strain, εuj = 108/8900 = 0.012 (Per ICC report AC125 maximum strain in

composite layer shall not exceed 0.75εuj = 0.009. In addition, since there is no confinement of the concrete at the bottom of the slab, we can limit the tensile strain to 0.004)

Nominal thickness per layer, tj = 0.04 inches Nominal cross Sectional Area per Layer = (0.5) (0.04) (12) = 0.24 in2/Layer

Design Procedure: 9. Calculate Existing Capacity 10. Calculate Strains Under Existing Loads 11. Estimate Required Number of Composite Layers 12. Check Moment Capacity of Strengthen Slab


b) At Limit State for Maximum Allowable Tensile Strain (0.004)

1. Calculate Moment Capacity of Existing Slab Section without Composites: Figure E1-2 illustrates the force diagram in slab section at the ultimate state.

d

a0.85f ’abc

As yf

Figure E1-2. Equilibrium in the Slab at Ultimate State (Without Composite Layer) The moment capacity is calculated using following equation:

( )2/adfAM ysn −=



where: a = depth of concrete compressive stress block

( )( )

( )( ) inches608.012385.06031.0

'85.0===

bffA

c

ys

Thus:

3.167)2/608.03.9)(60)(31.0( =−=nM kip-in < 240 kips-in The existing slab does not have adequate capacity to resist the anticipated moment.

2. Calculate Strains Under Existing Loads The composite material will be applied to the slab while it is still subjected to the existing dead loads. Thus, the strain at the bottom of the slab due to the existing loads needs to be calculated. This existing strain will be subtracted from the strain at the bottom of the slab at ultimate loads to obtain the effective strain in the composite material. The existing moment of 84 kip-in is much less than the capacity of the slab. Therefore, we can assume that the concrete stresses are low and a cracked section with triangular stress block will develop as shown in Figure E1-3.

b

kd

εc

εs

εt

0.5f ’bkdc

fc

nAs

A fs y

Strain

Figure E1-3. Equilibrium in the Slab Under Existing Load (Without Composite Layer) The depth of uncracked concrete (neutral axis depth) is given by:

( ) nnnk ρρρ −+= 22 where:

© Copyright 2001 Fyfe Co. LLC. 7-01 Reproduction by written permission from Fyfe Co. LLC only. All rights reserved k = ratio of the depth of cracked portion to the effective depth, d



( )( ) 00278.03.912

31.0===

bdAsρ

289.93122

29000===

c

s

EEn

( ) ( ) ( ) ( ) ( ) 203.0289.900278.0289.900278.0289.900278.02 2 =−×+=k

Therefore the depth of the neutral axis is:

89.13.9203.0 =×=kd ” Tensile stress in reinforcing steel:

( ) ( )( )( ) 25.313/203.013.931.0

843/1

=−

=−

=kdA

Mfs

s ksi

Compressive stress in concrete:

( ) ( ) ( ) ( ) 86.03/89.13.93.9203.0

)84(23/

2=

−=

−=

kddkdMfc ksi

Maximum strain in reinforcing steel:

00108.029000

25.31===

s

ss E

fε

and by similar triangles from Figure E1-3, the existing stain in the concrete at the bottom at the bottom fiber is given by:

( ) 0014.000108.089.13.989.15.11

=−−

=−−

= si kddkdh εε

3. Estimate Required Number of Composite Layers We can assume a moment arm of 0.75h to calculate the additional moment contributed by the composite layers as shown in Figure E1-4. This is an approximation of the moment arm in a typical reinforced concrete beam.



~0.75h

Tj

C’ = Tc j

Figure E1-4. Assumed Moment Arm in Slab Section The target moment (Mu) in the section is then expressed as follows:

jeu hTMM 75.0+=

hMMT nu

j 75.0−

=

jjjjj fxbtfAT == = 0.5(12)(0.004-0.0014)8900tj = 139tj

where

Mn= Moment capacity of the unit width of the slab (167.3 kips-in)

x = Percentage of the bottom face of the slab being covered with composite layers. Rearranging the equations yields the following expression for the thickness of composite layer:

( ) ( )( ) inches061.01395.1175.0

3.16724075.0

=−

=−

=j

nuj fbxh

MMt

Try two layers of TYFO® SCH-41S (Thickness = 0.080 inches).

4. Check Moment Capacity of Strengthened Beam To calculate the moment capacity of slab section we need to check that the maximum strains at the ultimate capacity do not exceed the limiting strains in concrete, steel or the fiber composites. Figure E-1-5 shows the strain and stress diagram at various stages of loading for the cross-section.



b

(a) (b) (d)

kd

εc

ε = t ε + εi jεj

fc

Ts Ts

Cc

Cc

Tj Tj

a

0.85f ’c

Figure E1-5 (a) Slab Section with Composite Layer, (b) Strain Diagram, (c) Stress Diagram in

Linear Range, (d) Stress Diagram at Ultimate State For equilibrium of the cross section:

∑ =−−= 0jscx TTCF where:

bafC cc'85.0= (Compressive force in concrete when εc> 0.002, rectangular stress

block)

bcEC ccc ε21

= (Compressive force in concrete when εc< 0.002, triangular stress

block)

ysssss fAEAT ≤= ε (Tensile force in steel)

( itjjj EAT )εε −= (Tensile force in composite layer) where εi is the strain in the bottom fibers due to the existing moment in the slab and εi is the maximum tensile strain at the bottom of the slab at the ultimate moment. a). At Limit State for Ultimate Concrete Compressive Strain (Concrete Crushing) Assume neutral axis distance from top of slab section:

c = 1.5”

( ) 275.15.185.085.0 === ca ” Compressive strain in concrete (ultimate state):



003.0=cε Tensile strain at the bottom of the section:

( ) 020.0003.05.1

5.15.11=

−=

−= ct c

ch εε

Strain in reinforcing steel:

( ) 0156.002.05.15.115.13.9

=−−

=−−

= ts chcd εε

Compressive force in concrete:

( ) ( )( ) 02.3912275.1385.0 ==cC kips Tensile force in steel:

( )( )( ) ( )( ) 60.186031.0kips24.1400156.02900031.0 ==>== yss fAT kips Tensile force in composite layer:

( )( )( ) 5.79890024.020014.0020.0 =×−=jT kips Check equilibrium in section:

jscx TTCF −−⇒=∑ 0 = 39.02 –18.6 – 79.5 = 59.09 kips N.G. Modify Neutral axis location to achieve equilibrium:

Try c = 2.4 inches

a =0.85c = 2.04 in Compressive strain in concrete (ultimate state):

003.0=cε Compressive force in concrete:

( )( )( ) 4.621204.2385.085.0 ' === bafC cc kips Strain in composite layer:

( ) 0114.0003.04.2

4.25.11=

−=

−= cj c

ch εε



Tensile force in composite layer:

( ) ( )( )( ) 7.42890024.020014.00114.0 =×−=−= jitjj EAT εε kips Strain in reinforcing steel:

( ) 0086.00114.04.25.114.23.9

=−−

=−−

= js chcd εε

Tensile force in steel:

( )( )( ) ( )( ) 6.186031.0kips3.770086.02900031.0 ==>=== ysssss fAEAT ε kips Check equilibrium in section:

00 =−−⇒=∑ jscx TTCF

62.4 – 18.6 - 42.7 = 1.1 kips ~ 0 kips O.K. Calculate the moment capacity by summing the moments about the bottom of the beam:

( )dhTchCM sc −−⎟⎠⎞

⎜⎝⎛ −=

285.0

( ) 6133.95.1160.182

4.285.05.114.62 =−−⎟⎠⎞

⎜⎝⎛ ×

−= kip-in

Note that from the calculations, we can already tell that the concrete crushing does not govern because the maximum tensile strain at the bottom of the beam is larger than the allowable strain of 0.004. The calculations were shown to illustrate the procedure. b). At Limit State for Maximum Allowable Composite Tensile Strain (0.004) Assume a neutral axis distance from top of slab section:

c = 1.95” Strain in composite layer with existing concrete strain subtracted:

0026.00014.0004.0 =−=−= itj εεε Tensile force in composite layer

( ) ( )( )( ) 1.11890024.020026.0 =×=−= jitjj EAT εε kips Strain in reinforcing steel:



( ) 0031.0004.095.15.1195.13.9

=−−

=−−

= ts chcd εε

Tensile force in steel:

( )( )( ) ( )( ) 6.186031.0kips9.270031.02900031.0 ==>=== ysssss fAEAT ε kips Note that the steel reinforcement yields, ensuring a ductile behavior. The concrete compressive strain at the top of the slab is given by:

( ) 002.00008.0004.095.15.11

95.1<=

−=

−= tc ch

c εε

Concrete is in linear range and so a triangular stress block should be used. The compressive force in concrete is therefore:

( )( )( ) ( ) 2.291295.131220008.021

21

=== bcEC ccc ε kips

Check equilibrium in section:

jscx TTCF −−⇒=∑ 0 = 29.2 –18.8 – 11.1 = -0.5 kips ~ 0 kips O.K. Calculate the moment capacity:

( ) ( dhTchCM sc −−−= 3/ )

( ) 2763.95.116.18395.15.112.29 =−−⎟

⎠⎞

⎜⎝⎛ −= kip-in

The moment capacity of section for the case that strain in composite fibers reaches the maximum limit is less than previous case where concrete is at ultimate compressive strains. Therefore, the moment capacity of the slab section is governed by the strain in composites. Using a capacity reduction factor of φ = 0.9:

φMn= 0.9(276) =248.4 kip-in > Mu = 240 kip-in OK Use two layers of TYFO® Fibrwrap® System, SCH-41S with 50% of the bottom face of the slab covered with composite layers.



In-Plane Wall Shear Design Example Design Goal: Provide additional shear strength capacity to the existing reinforced concrete

walls. 1) Existing Wall Properties: lw = 12” (one ft unit wall length used for calculations)

tw = 8” (wall thickness) 2) Properties of Tyfo® SEH 51 Glass Composite System:

ε = 0.004 (allowable design strain for shear) E = 3790 ksi (typical test value for tensile modulus) CE = 0.8 (environmental reduction factor) EG = CEE = (0.8)(3790 ksi) = 3032 ksi (guaranteed design modulus) f = ε EG = (0.004)(3032 ksi) = 12.12 ksi (guaranteed design stress) t = 0.05” (composite thickness)

3) Calculate shear contribution from two layers of the composite: ΦV = Φk f t lw cot45° where: Φ = 0.85 (reduction factor for shear) k = 0.75 (efficiency factor for one-sided bonding to a wall)

ΦV = (0.85)(0.75)(12.12 ksi)(0.05”)(2 layers)(12”)(1) = 9.3 k per ft of wall Shear enhancement provided by two layers of the Tyfo® SEH System.

4) Conclusions:

The application of two layers of the Tyfo® SEH 51 System to the existing concrete walls will provide an additional shear capacity of approximately 9.3 kips per foot of wall length. This design does not take into account any openings in the walls or out-of-plane requirements. When increasing the shear capacity of a structural member, potential failure modes such as sliding shear, flexural failure or compression failure also should be considered to ensure that the additional shear can be developed. Connections to adjacent elements (e.g. diaphragms and foundations) should be analyzed by the engineer. The Tyfo® JT System can be designed to transfer these forces between adjacent elements. Contact Fyfe Co. LLC engineers for more information.

The Tyfo® SEH 51 System should be carried around any wall ends or into window/door jams whenever possible. Tyfo® FibrAnchors® should be provided at edges with an approximate maximum spacing of 24” on center. See Appendix B for typical details.



Out-of-Plane Wall Flexural Design Example Design Goal: Provide additional out-of-plane strengthening to the existing URM wall in order

to limit deflections to three-inches and provide an additional moment capacity of Mu=10 kip-in/ft.

1) Existing Wall Properties: H = 18’ = 216” (wall height) tw = 8” (wall thickness) f’m = 1,700 psi (masonry compressive strength) 2) Properties of Tyfo® SEH 51A Glass Composite System:

E = 3790 ksi (typical test value for tensile modulus) CE = 0.8 (environmental reduction factor) EG = CEE = (0.8)(3790 ksi) = 3032 ksi (guaranteed design modulus) t = 0.05” (composite thickness)

3) Calculate allowable stress based on deflection limits: Calculate the wall curvature at a design displacement (∆) of three inches at mid-height: ∆ = φu (H/2)2 / 3 = 3”

∴φu = (3)(3”)/(108”)2 = 0.00077 Calculate allowable strain at the design curvature, assuming neutral axis depth, c = 0.75”: ε = φu (d-c) = (0.00077)(8” – 0.75”) = 0.00559 Therefore, the guaranteed design stress of the composite, f, based on the allowable strain

and guaranteed design modulus above: f = ε EG = (0.00559)(3032 ksi) = 16.96 ksi 4) Determine thickness of composite required:

ΦM = Φ A f (jd) where: ΦM = 10 k-in/ft (required design moment) Φ = 0.9 (reduction factor for flexure) jd ≈ 0.9tw = (0.9)(8”) = 7.2” (assumed moment lever arm)

Solving for the composite area per ft width of wall: © Copyright 2001 Fyfe Co. LLC. 7-01 Reproduction by written permission from Fyfe Co. LLC only. All rights reserved



A = ΦM / Φ f (jd) = (10 k-in/ft)/(0.9)(16.96 ksi)(7.2”) = 0.091 in2/ft

Required thickness of composite assuming a 12” unit width: treq = A / 12” = (0.091 in2/ft)/(12” per ft) = 0.0076”

Using the thickness of one layer of the Tyfo® SEH 51A system of 0.05”, a percent coverage of composite can be determined: 0.0076” per ft/0.05” per layer = .15 = 15% coverage Use a minimum of 20% coverage. This corresponds 12” wide strips of composite, one layer thick, at 5’ on center.

5) Calculate neutral axis for checks: By equilibrium:

T = C A f = 0.85(f’c)(a)(b)

Solve for a: (12”)(0.05”)(20%)(16.96 ksi) = (0.85)(1.7 ksi)(a)(12”)

a = 0.12” (compression zone depth) c = a/β = 0.12”/0.85 = 0.14” (neutral axis depth)

6) Check calculations with a new neutral axis: Determine strain based on calculated neutral axis: ε = φu (d-c) = (0.00077)(8” – 0.14”) = 0.006

Calculate new guaranteed design stress for the composite based on the new strain value and the guaranteed design modulus:

f = ε EG = (0.006)(3032 ksi) = 18.2 ksi

Calculate new required area of the composite per ft of wall:

A = ΦM / Φ f (jd)

where: jd = tw – a/2 = 8” – (0.12”/2) = 7.94” (revised moment lever arm)

A = (10 k-in/ft)/(0.9)(18.2 ksi)(7.94”) = 0.077 in2/ft

Required thickness of composite assuming a 12” unit width: treq = A / 12” = (0.077 in2/ft)/(12” per ft) = 0.0064”



Find the percent coverage with a 0.05” thickness per layer, as above: 0.0064” per ft/0.05” per layer = .13 = 13% coverage Use a minimum of 20% coverage, as above.

7) Conclusions:

Use 12” wide bands of the Tyfo® SEH 51A System at 5’ on center. For fully reversible loading the system must be applied to both sides of the wall. This corresponds to 20% coverage of the wall. This design is purely for out-of-plane loads. In-plane shear has not been considered.

In addition to this, the wall should have some horizontal strengthening (“bond beam bands”) to tie the masonry together and provide transverse bending between the vertical bands. This is particularly important at the corners where the cracking would be more severe. We also suggest an additional bond beam immediately above any door openings.

See Appendix B for typical details.





APPENDIX B

TYPICAL DETAILS



APPENDIX C

IMPROVED DETAILING USING THE TYFO® SCH & SEH COMPOSITE ANCHORS

Structural test results have shown that the following detail examples will perform more efficiently than standard designs. The increase in performance must be compared to the increase in the cost of the installation. Projects must be reviewed based on their individual requirements. Fyfe Co. LLC provides technical guidance at no obligation.


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