DANIEL P. JENNY RESEARCH FELLOWSHIP

Strengthening and Repair of aColumn Bracket Using aCarbon Fiber Reinforced Polymer(CFRP) Fabric

Robert W. CorryStructural EngineerCarl Walker Inc.Denver, ColoradoIFormer Graduate Research Assistantand Daniel P. Jenny Fellow,Department of Civil and ArchitecturalEngineering, University of Wyoming,Laramie,Wyoming] T

he focus of this paper is on thestrengthening and/or the repairof corbels and brackets using an

epoxy bonded Carbon Fiber Reinforced Polymer (CFRP) fabric wrap.Corbels and brackets are commonlyused in precast concrete construction.Brackets project from a column andcorbels from a wall; however, theseterms are often used interchangeably.The specimen used in this research is acolumn bracket.

Loads on brackets are generally vertical. However, unless precautions aretaken to alleviate horizontal forces,horizontal forces must be consideredin the design.1’2Horizontal forces canbe caused by bearings restrainingshrinkage, creep or temperaturechange. A general layout of a bracket

is shown in Fig. 1, where V, is the vertical shear force and N is the horizontal tensile force.

Brackets fail in one of three modes.First, if vertical and tensile forces arepresent, the bracket may fail in a combined tensile flexural failure causingthe main steel, A, to yield. Second,under high vertical load, the bracketmay shear off of the face of the column, shearing both the main steel andthe hoop steel, Ah. Finally, the mainsteel can yield in tension due to N.These failure modes are illustrated inFig. 2.

A premise of this research is thatshear-friction principles have beendeveloped for internal steel reinforcement based on small-scale testsamples.3’4Work on small-scale

This paper examines the repair or rehabilitation of column bracketsusing CFRP (Carbon Fiber Reinforced Polymer) bonded fabric. Acolumn bracket test specimen is designed, analyzed, precracked,repaired and tested The experimental program loaded the originalbracket to 75 percent of its nominal capacity The cracked bracketwas strengthened to increase the original capacity by 50 percent andretested. The repaired bracket exceeded the predicted strengthincrease. The CFRP fabric wrap was found to be an extremelyeffective form of column bracket repair. Surface preparation andCFRP installation procedures are discussed. Detailed designrecommendations and a design example are included.

Charles W. DolanProfessor and HeadDepartment of Civil and

Architectural EngineeringUniversity of WyomingLaramie,Wyoming

54 PCI JOURNAL

shear-friction tests using externallybonded CFRP reinforcement indicates a high variability in responsedue to bond failures.5

The externally bonded small-scaletests had two different failure modes.Tests with a single layer of fabricfailed by debonding or by ripping thefabric. Tests with laminates or multi-pie layers of fabric always failed inbond. Therefore, a single well-documented full-size test was deemed themost effective manner to demonstratethe CFRP repair and strengtheningconcepts providing that at least twolayers of fabric are used.

The differentiation between strengthening and repair is not always obvious.A bracket may be damaged due to anoverload or due to insufficient initialcapacity. In either case, cracking orother distress is evident. Whether this isa repair or a strengthening activity depends on the source of the damage. Ifthe bracket is undamaged and the structure live load is to be increased, thenthe application is only for strengtheningpurposes.

This research addresses strengthening and repair concurrently. By precracking the specimen, initial damageis created and the effectiveness of therepair without epoxy injection is evaluated. A rationale for strengtheninglimitations is provided.

DESIGN APPROACH

This project examines the effect ofwrapping a bracket with a CFRP fabric. The objective is to load the original bracket to 75 percent of the original theoretical ultimate capacity,thereby causing substantial damage.The bracket is then repaired with aCFRP fabric and loaded to failure.

As will be seen in the paper, the latter objective was not achieved. Thestrength of the repaired bracket exceeded the predictions and the capacity of the hydraulic loading jack. ASikaWrap Hex 1 03C fabric was usedto repair the corbel. The fabric is bidirectional and the material propertiesof the fabric are listed in Table 1.

Bracket DesignThe test specimen is an 18 in. deep

x 12 in. thick (450 x 300 mm) column

segment with a double bracket. Onebracket is a 30 in. (760 mm) long reaction block while the other end is a 12in. (300 mm) test bracket. Fig. 3shows the bracket design and theplacement of the reinforcing steel.

Fig. 1.Corbel diagram fromPCI DesignHandbook.

The specimen is built so that a 60-ton (54 t) hydraulic jack can be placedbetween the two brackets for testing.The larger bracket and column areheavily reinforced to ensure that onlythe test bracket fails. The bearing sur

mi tial position

__________

Finicsl position

Flexur-at Failure Shear’ Failure Tension Failure

Fig. 2. Bracket failure modes.

Table 1. Material properties of CFRP fabric (Ref. 8).

Cured unidirectional laminate properties

Tensile strength 139,000 psi 960 N/mm2

Modulus of elasticity 10.6 x 106 psi 73.1 GPa

Elongation at break 1.33 percent 1.33 percent

Thickness 0.040 in. 1 mm

Strength per inch of width 5560 lbs per layer 24.7 kN per layer

January-February 2001 55

Fig. 3. Bracket test specimen.

face is built at an angle of 5.7 degreesto produce a 10 percent “horizontal”tensile force component. This designallows both a horizontal and verticalforce to be applied simultaneously,thus more closely modeling actualbracket behavior.

The test bracket is designed so thebracket fails at a load between 40 and60 kips (180 and 270 kN). Two #3Grade 40 bars [Ah 0.44 sq in. (280mm2)] are used for the hoop steel andtwo #3 and one #4 Grade 40 bars [A =

0.42 sq in. (270 mm2)] are used for theflexural steel in the test bracket.

Because a prediction of actual strengthis desired rather than a design value, ayield strength of 55 and 70 ksi (380 and480 MPa) are used for Grade 40 andGrade 60 bars, respectively, based ontensile tests of similar reinforcement.

The capacity of the test bracket inflexure and tension combined is deter-

mined by using the normal flexuraldesign equations in the ACT BuildingCode Requirements for StructuralConcrete:6

A= Mf Øf(d — a12)

Affa=

0.85fb

= + N(h — d)

Af=AS — A (4)

A =-n

f = yield strength of steel, ksi(MPa)

d = distance from main steel tobottom of bracket, in. (mm)(see Fig. 1)

f’ = specified concrete strength, ksi(MPa)

b = width of bracket, in. (mm)V,, = shear component of F, kips

(N)a1 = distance from corner of

bracket to load point, in. (mm)(see Fig. 1)tensile component of F, kips(N)

h = distance from top to bottom ofbracket, in. (mm) (see Fig, 1)

A = area of steel required for flexure and direct tension, in. (mm)

A = area of steel required to resisttensile component of force, in.(mm)

(1) Eqs. (3), (4), (5), and (6) aresubstituted into Eq. (1).

0.101’(2) A—

(3) (ai) ± [0.10(h - d)]

bf,(d — a12)

A = 0.33 sq in. (210 mm2)(5

= 1 for direct comparison ofpredicted to experimental

(6) performance

f =70 ksi (480 MPa)a1 = 3.5 in. (89 mm)h = 15 in. (380 mm)d =l4in.(360mm)a =1/2in.(l3mm)

4-#9I—I I I

I I

I I— — _I_

I II I

— — —.I I i I I I I

I I I I II P I

II

I I I I III II I I II I II II I I I I I I II II I I I l I I

.

I I ji I I

— — , —

,8in. (200 mm)

18 in.(458 mm)

3-#3

#3@ 6 in-1

where

(7)

0.0fl’

whereAf = area of steel required for flex

ural reinforcementcapacity reduction factor

Fig. 4. Completed bracket test specimen. Fig. 5. Installed CFRP fabric strip.

56 PCI JOURNAL

The theoretical combined tensileand flexural capacity of the bracket isfound by solving Eq. (7) for V,. Thecapacity is V, 64.1 kips (284 kN),which corresponds to a load P, of 64.5kips (287 kN).

The shear capacity can be foundusing the two shear-friction equationsfrom ACT 318, Eq. (11-25):

where

V=Ajl5JLf

A=AS+Ah

A = 0.42 sq in. (270 mm2)A,, = 0.44 sq in. (280 mm2)

f = 55 ksi (380 MPa)= 1 for direct comparison of pre

dicted to experimental performance

= 1.4 (ACT 319, Section 11.7.4.3for uncracked concrete)

Substituting Eq. (9) into Eq. (8) andsolving for V, determines the theoretical shear capacity for the test bracket.The theoretical capacity is V = 66.2kips (294 kN), which corresponds to aload P, of 66.6 kips (296 kN). Theanalysis predicts that the test bracketwill fail in combined tension and flexure, and the theoretical capacity is64.5 kips (287 kN).

Normal ACT notation would use Vin Eq. (8). However, V, = V, and for

= 1.0, the two values are interchangeable. Note that V, is used whenthe full test capacity is being computed and V is used to predict the design capacity.

The reinforcement for the largerbracket and column is designed suchthat the strength exceeds the strengthof the test bracket. Three #9 Grade 60bars are used as the main steel andfour #4 Grade 40 bars are used as thehoop steel for the larger bracket.

The normal component of P. isacting toward the column for the largebracket and is, therefore, neglected.

(8) Using Eqs. (1) and (8) and substitutingin the corresponding values, the flexu

(9) ral capacity of the larger bracket is825 kips (3670 kN) and the shear capacity is 361 kips (1606 kN).

The column portion of the bracket isdesigned to resist 120 kips (534 kN),the maximum capacity of the hydraulic testing jack. The required reinforcement in the bracket side of thecolumn is four #9 bars with an Ac =

4.0 sq in. (2580 mm2). The development length for the #9 bars in the column is greater than the space available; therefore, they must have hooks.

The required steel in the bottom ofthe column is 0.204 sq in. (132 mm2).Three #3 bars with a steel area Ac =

0.33 sq in. (215 mm2) are selected.The basic layout of all the reinforcement is shown in Fig. 3.

Bracket Construction

A single-use form was built for theconstruction of the double bracketspecimen. The concrete had a 28-daystrength of 3400 psi (23.4 MPa). Theform was stripped two days after theconcrete was placed and the bracketwas allowed to cure for a minimum of

28 days before testing. Fig. 4 showsthe completed bracket before testing.

Bracket Loading and Repair

The bracket was loaded to 75 percent of the theoretical ultimatestrength and cracks appeared at the reentrant corner of the bracket. After initial testing, the bracket was repairedwith a CFRP fabric. Two separate6 in. (150 mm) wide strips of CFRPfabric were wrapped around the testbracket (see Fig. 5).

The only surface preparation performed was to round off the corners ofthe test bracket and clean the surfaceof dust. Simply using a hand-heldhammer was all that was necessary toknock off the corners of concrete sothat the corners would not rip the fabric during the test.

Actual field repairs should considerusing a grinding operation or a bushhammer and epoxy putty to smooththe corner in order to avoid stress concentrations. ACT Committee 440 draftdocuments recommend a minimum radius of 1/2 in. (12 mm) on repair corners. This ensures that there are nosharp angles or points of pressure totear the fabric.

The fabric was wrapped completelyaround the bracket, and the fabric wasoverlapped on the face of the bracket.The CFRP manufacturer recommendseither a high or low viscosity epoxyfor use with the fabric. The low viscosity epoxy was used to adhere thefabric to the concrete because it bettersaturates the fabric.

it

Fig. 6. Application of fabric application. Fig. 7. Bracket test setup.

January-February 2001 57

Immediately before the epoxy wasapplied, the bracket was cleaned withcompressed air to remove any dust orother loose sediment that may havebeen on the bracket surface. Theepoxy was applied with a paint rolleras shown in Fig. 6.

Epoxy was first applied to the concrete. Then, the fabric was placed onthe epoxy and a second coat of epoxywas rolled into the fabric. The secondstrip of fabric was then applied and athird coat of epoxy was rolled into thesecond strip of fabric. The fabricsplices were staggered by a minimumof 6 in. (200 mm). The epoxy was allowed to cure for at least 48 hours before testing.

The strength of the repaired bracketis computed using shear-friction equations. The following two equationsare used to determine the strengthenedcapacity:

Vn=Vbr+VfabNuc (10)

Vfab(FWfl)U (11)

whereV = nominal ultimate capacity of

repaired bracketVbr theoretical shear capacity of

unrepaired bracket, 63.8 kips(284 kN)

F = strength per inch width of fabric, 5.56 kips per in. (975kNIm) (see Table 1)

w = width of fabric, 6 in. (152 mm)n = number of fabric layers, four

(two per side)= shear-friction coefficient (0.7

— based on recommendations

in ACI 318 for a concrete castto concrete reflecting thecracked concrete)

Vfab theoretical increase in shearcapacity due to fabric repair,93.4 kips (415 kN)

= tension force O.l(Vbr + fab)’

15.7 kips(7OkN)

The design capacity for the strengthened connections is V. Note that afactor of 0.85 is recommended forshear connections.

By solving Eq. (10), the theoreticalcapacity is 141.5 kips (629 kN), andthe design capacity is 120.3 kips (535kN). This corresponds to a P, of 142.2kips (632 kN), and a çbP of 120.9 kips(538 kN).

Test Setup

The double bracket makes testingextremely simple. The hydraulic jackis centered horizontally and verticallybetween the two brackets and load isapplied (see Fig. 7). A dial gauge isused to measure the deflection of thetest bracket.

The theoretical ultimate capacity ofthe repaired bracket is above the capacity of the hydraulic jack and thedesign capacity of the repair equalsthe jack capacity. Further details aregiven below.

TEST RESULTS ANDDiSCUSSION

The test program loads the bracketto the jack design capacity to verifythe bracket performance. The CFRPfabric is then cut and the originalbracket retested to failure to validatethe fabric effectiveness. The performance of the unrepaired and repairedtest bracket is then reviewed.

Fig. 8. Load-deflection plot for unrepaired bracket.

—DRepair Loading #1

—— Repair Loading #2

140

120

— 100(a

600-J 40

20

0.00 0.02 0.04 0.06

Deflection (in)

0.08 0.10 0.12

Fig. 10. Load-deflection plot for repair tests 1 and 2.

58 PCI JOURNAL

The load-deflection curve of theunrepaired bracket test is presented inFig. 8. The maximum applied loadwas 48.4 kips (215 kN), which is 75percent of the theoretical capacity.The load-deflection plot suggests thebracket was entering the plasticrange. The damage caused by the initial loading can be seen in the re-entrant corner of the bracket (see Fig.9). It is apparent from the crackingthat the bracket was failing in flexure,which corresponds to the strengthpredictions.

Repaired Bracket Tests

Two loading sequences were conducted on the repaired corbel. Eachtest went to 124 kips (532 kN), thecapacity of the jack (see Fig. 10).The second load test was performed24 hours after the first test to verifythat no residual damage had beencaused by the first repaired brackettest.

The first repaired bracket test resulted in a permanent deflection of0.023 in. (0.58 mm). The second loadtest was softer than the first test andhad less total deflection. However, ifthe 0.023 in. (0.58 mm) permanentdeflection caused by the first test isadded to the final deflection of thesecond test, the total deflection ofboth tests are nearly identical. Thisimplies that the fabric repair has notlost capacity even though there is asmall stiffness reduction due to thecracking.

There was no apparent damage tothe fabric. The concrete cracked alongthe edge of the fabric as well as diago

nally beneath the fabric on the backside of the sample. The concrete crackcaused the fabric to debond on thebackside of the bracket (see Figs. 11and 12).

The area of debonding was determined by tapping the fabric with acoin. Areas where the fabric debondedhad a distinct hollow sound. The factthat the fabric debonded from the concrete and that the bracket still reacheda high strength supports the theory thatby fully wrapping the connection, thebond of the fabric to the concrete is notcritical for strength performance.

The bond of the fabric provides theinitial stiffness in the connection. Thedebonding occurred during the firstloading cycle. Therefore, the lowerstiffness in the second load test resultedfrom the longer effective gauge lengthof the fabric during the second loading.

The shear-friction capacity of theconnection is due to accumulatedstrain on the fabric. Complete debonding of the fabric and a small crackwidth could lead to a less than predicted strength gain.

After the second repaired bracketload test, the fabric was cut with a masonry blade along the face of the column (see Fig. 13). The bracket wasthen retested without the benefit of theCFRP repair. The load-deflectioncurve for this test is shown in Fig. 14.At a load of 45.8 kips (204 kN), a corner of the bracket failed on the sideopposite the dial gauge (see Fig. 15).

After the break, the jack was resetand bracket loading was continued.The bracket carried an additional 40kips (178 kN), for a total load of 85.8kips (382 kN). The failure includedsome twisting of the bracket and dialgauge readings were not indicative ofthe total movement. Consequently, theadditional applied load is not shown inFig. 14.

Bond Behavior

Although the CFRP bond on thewrapped bracket was not critical to thistest, bond tests were performed in accordance with the recommendations of

Fig. 13.Cut fabric.

Unrepaired Bracket Test

Fig. 12. Cracking of bracket.

Severed Fabric Bracket Test

January-February 2001 59

ACT Committee 5O3. This test was performed on the side of the bracket thatdid not delaminate. CFRP manufacturers generally specify that the epoxyused to adhere CFRP to the concreteshould have a bond strength greaterthan the tensile strength of the concrete.

Fig. 15.Failure of bracket

after fabric cut.

The tensile strength of the concreteused in the bracket was between 200and 300 psi (1.4 and 2.1 MPa). Thebond strength was 344 psi (2.4 MPa).Therefore, the ACI 503 bond recommendations are met and installationquality control was validated.

MAJOR FINDINGSBy comparing the load-deflection

curves, it was determined that the repair was very successful (see Fig. 16).The calculations predicted that therewould be a strength increase in excessof the jack after the repair, and that thestrength was realized. In addition,there was less deflection after the repair than there was before indicatingthat an increased stiffness accompanied the increased strength.

In most CFRP applications, surfacepreparation of the concrete is a criticalfactor and strongly influences the effectiveness and strength of the repair.Every effort should be made to ensurethat the concrete is sound and free ofany loose aggregate or dust. The success of this test is due in part to thewrapping of the entire bracket and column. Wrapping prevented localdebonding from causing a progressivefailure of the connection.

Field applications may not allowwrapping all the way around thebracket and column. If wrapping is notpossible, a mechanical anchoring device should be considered in order todevelop the tensile capacity of the fabric. Anchoring devices include a sawcut groove, a plug insert, or a studbolted through the concrete.

Experimental work with mechanicalfasteners suggests that the ability todevelop the full tensile capacity of theFRP is highly variable and a test program is recommended prior to specifying a mechanical anchorage system.Reinforcing corbels (projecting from awall rather than a column) presentsseveral anchorage problems and ismost likely quite difficult with CFRPfabrics.

CONCLUSIONS ANDRECOMMENDATIONS

When designing a bracket repairusing CFRP fabric, the followingguidelines are recommended:

First, a minimum of two layers offabric is recommended. This providessome protection against a sudden failure in a single layer of fabric thatcould occur if a crack propagatesacross the repair zone.

Second, the maximum strengtheningattributed to the CFRP should be such

504540 -

—. 35 - .

0 _.- —-___________

_________————

C.)

20 -- -W-— -- -

.__

10 — — --

5 — - — -

o• I

0.00 0.01 0.02 0.03 0.04 0.05

Deflection (in)

Fig. 14. Load-deflection curve for severed fabric test.

—•— Loading #1—D— Repair Loading #1—k—Repair Loading #2--I1 Loading #4 Severed Fabric

140

120

1000a

Cu0

40

20

0

0.00 0.02 0.04 0.06 0.08 0.10

Fig. 16. Load-deflection curves for all tests.

Deflection (in)

0.12

60 PCI JOURNAL

that the load factor on the originalstructure should be greater than one ifthe CFRP is lost. For example, assumethe original structure was designed fora load composed of 60 percent deadload, and 40 percent live load.

Using ACT load factors of 1 .4D and1.7L and a minimum load factor of1.1, the maximum allowed strengthening would be:

1.4(0.6) + 1.7(0.4)1.38

or a 38 percent increase in capacity.This criterion allows increases in

applied loads between 28 and 54 percent depending on the relative ratio ofdead load to live load. The philosophyensures that failure of the CFRP does

not result in a catastrophic failure ofthe structure. This philosophy additionally presumes that the fabric andadhesive would be lost in a fire. Provision of fire protection and supplemental fabric cover could argue for ahigher load increase.

The brittle behavior of the CFRP,stress concentrations on the corners,the effects of localized debonding, andthe possibility of fabric failure at acrack, suggests a lower factor beused for the CFRP repair. The designexample given in Appendix B uses =

0.75 for the CFRP component and =0.85 for the steel conthbution. The example illustrates a 50 percent increasein applied load, corresponding to anoriginal structure having a very high

live load to dead load distribution ofloadings.

ACKNOWLEDGMENTSThe Precast/Prestressed Concrete

Institute Daniel P. Jenny ResearchScholarship, the Department of Civiland Architectural Engineering at theUniversity of Wyoming, Sika Corp.,and Rocky Mountain Prestress supported this research. Their support isgratefully acknowledged.

Any opinions expressed in thispaper are those of the authors and notnecessarily those of the sponsors.

The authors acknowledge and thankthe PCI JOURNAL reviewers of thispaper for their timely and valuablecomments.

REFERENCES

1. PCI Design Handbook — Precast and Prestressed Concrete,Fifth Edition, PrecastfPrestressed Concrete Institute, Chicago,IL, 1999.

2. Nilson, Arthur H., Design of Concrete Structures, 12th Edition, McGraw-Hill, New York, NY, 1997, pp. 353-354.

3. Birkeland, P. W., and Birkeland, H. W., “Connections in Precast Concrete,” ACI Journal, Proceedings, V. 63, No. 3, March1966, pp. 34-368.

4. Mattock, A. H., and Hawkins, N. M., “Shear Transfer in Reinforced Concrete—Recent Research,” PCI JOURNAL, V. 17,No. 2, March-April 1972, pp. 55-75.

5. Dolan, B. E., Hamilton, H. R., and Dolan, C. W., “Strengthening with Bonded FRP Laminate,” Concrete International, V.120, No. 6, June 1998, pp. 5 1-55.

6. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318R),” American Concrete Institute,Farmington Hills, MI, 1999.

7. ACT Committee 503, “Use of Epoxy Compounds with Concrete,” American Concrete Institute, Farmington Hills, MI, 1998.

8. Sika/Hexcel, SikaWrap Hex 103C, Carbon Fiber Fabric forStructural Strengthening Data Sheet, Hexcel Corporation, Lyndhurst, NJ 07071, 1999.

APPENDIX A - NOTATIONa = depth of equivalent compression blocka1 = distance from corner of bracket to load pointAf area of steel required for flexural reinforcementA = area of steel required to resist tensile component of

forceA = area of steel required for flexure and direct tensionb = width of bracketd = distance from main steel to bottom of bracketF = strength per unit width of fabric

f’ = specified concrete strength

f = yield strength of steelh = distance from top to bottom of bracket

= length of bearing seat

n = number of fabric layers= tension force

P = applied load on bracket testVbr = theoretical shear capacity of unrepaired bracketV, = theoretical additional shear capacity due to fabric

repairV = nominal capacity of repaired bracketV1 = factored shear load before strengtheningV2 = factored shear load after strengtheningw = width of fabric

= capacity reduction factor= friction coefficient

1.1

January-February 2001 61

APPENDIX B — DESIGN EXAMPLE

Given: 12 x 12 in. (305 x 305 mm) column with a bracketBracket dimensions (see Fig. Bi)

a =4 in. (101 .6 mm)l=6 in. (152.4 mm)h=l3in.(330mm)d= 12 in. (305 mm)

Loads:V,1 = 50 kips (222 kN) factored load before CFRP

strengtheningV2 = 75 kips (333 kN) factored load after CFRP

strengthening= 20 percent of V,,

Fabric strength F = 5.56 kips per in. per layer (975kN per meter per layer) per manufacturer’s recommendations (see Table 1).8

f = 60 ksi (413 MPa)

f’ = 4000 psi (27.5 MPa)

Required: Design the steel and CFRP reinforcement.Solution: The bracket is designed in accordance with ACT

3 18-99.Calculate N1 and N2:

N1 = 0.2 V rz N1 = 10 kips (44.5 kN)

N2 = 0.2V2 N,.2 =15 kips (66.7 kN)

Check d for the maximum shear stress limits permitted byACI 318:

V,, = 0.2 (fC’bd) or equal to 800 bd forf = 4000 psi

Hence, both equations give the same results.b = 12 in.; therefore, V, = 9600 d.

V11 = 9600 d; therefore,d = 5.2 in. < 12 in. (132mm <304mm)d = 12 in. (304 mm) > 5.2 in. (132 mm) required, ok

Shear-friction steel, Af:

A = area of steel required for shear-frictionreinforcement

0 =0.85= 1.4 (ACI 11.7.4.3)

Substituting values in the above equation:

Af= 0.70 sq in. (450 mm2)

— Va1 + N(h — d)f—

0 =0.85a1 =4in. (102 mm)a = 1/2 in. (12 mm)

Substituting values in the above equation:Af= 0.350 sq in. (224 mm2)

Tensile steel, A:

A =

Calculate A:

A = Af +A A 0.546 sq in. (350 mm2)

or

= +A = A = 0.663 sq in. (427 mm2)

A = 0.663 sq in. (427 2)

Check A mm:

Asmin = O.04 bdAsmin =0.384 sq in. (248 mm2)

Fig. Bi. Design example bracket.

62

A5 >Asmjn, ok

0iLf

where

(ACT 11-25)

The flexural design equation is used to determine the required flexural steel, A!

where

12

Af = area of steel required for flexural reinforcement

L —VIA

=4

Nuc

(ACI 318, Section 11.9.3.4)

A,1= 0.196 sq in. (126 mm2)

h = 13

/45,

PCI JOURNAL

Fig. B2.CFRP design example.

Select main reinforcing steel: Use four # 4 bars, A = 0.78sq in. (503 mm2). For hoop steel, use two # 3 bars, Ak = 0.44sq in. (284 mm2).

Detailing and layout of the steel should be done in accordance with the PCI Design Handbook.

The next step is to design the CFRP reinforcement tocarry an additional 25 kips (111 kN) of load.

4) V,, = 75 kips (333 kN)

4) V,r 5Okip5 (222 1(N)

4) = 0.75= 15 kips (66.7 kN)

from which VIab = 53.3 kips (237 kN).By substituting this value into Eq. (11) and assuming that

n = 1, a required width w of 13.7 in. (348 mm) is obtained.The available CFRP width is the flat portion of the bracketminus 1 in. (25.4 mm) on either side, i.e., 7 in. — 2 in. = 5 in.(127 mm). Therefore, two layers of CFRP are required andare desirable to avoid a single layer solution.

(12) Select two 4 in. (102 mm) wide layers. The equivalentwidth is 4 in. x 2 layers x 2 sides = 16 in. (400 mm). The

(13) total required fabric is 70 in. x 4 in. (1800 x 100 mm), including a 10 in. (250 mm) overlap. The final bracket design

(11) is shown in Fig. B2.

Main steel As4—# 4s

Hoop steel Ah2—# 3s

Vu

Nuc

wide

whereCalculate Ak:

Ah = O.5Af =A =0.175 sqin. (113 mm2)

or

Ak =0.5Af = Ak = 0.233 sq in. (114 mm2)

Ah = 0.233 sq in. (427 mm2)Therefore:

4)VfabI’Iuc2Skips (ill kN)

V, = 4) V,,

4)V= øVbr+4)VfabNuc

Vfab = (Fwn)#

January-February 2001 63