Structural Engineering Report MUST-98-1

Strengthening Existing Reinforced ConcreteBeams for Flexure Using Bolted External

Structural Steel Channelsby

Christopher M. Foley and Evan R. Buckhouse

January 1998

Marquette UniversityCollege of EngineeringDepartment of Civil & Environmental EngineeringResearch Report

MUST-97-1: i

Table of Contents

1.0 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Research Significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Review of Existing Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Evaluation of Previous Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.0 Design Procedure for Concrete Control Specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.0 Design Procedure for Strengthened Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.0 Construction of Test Specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

5.0 Experimental Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.1 Strain Gage Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255.2 Loading Test Frame and Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.3 Testing of Control Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.4 Testing of Wedge Expansion Anchor Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.5 Testing of Epoxy-Anchor Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.6 Load Deformation Behavior of Specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.7 Strain Distribution Within the External Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

6.0 Evaluation of Proposed Design Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

7.0 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

8.0 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Appendix - A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

MUST-97-1: ii

Acknowledgments

This research report is based on the MS Thesis of Evan R. Buckhouse entitled: External FlexuralReinforcement of Existing Reinforced Concrete Beams Using Bolted Steel Channels. The authors wouldlike to thank the Graduate School at Marquette University for the financial support during the duration ofthis project. The support of the Department of Civil and Environmental Engineering of MarquetteUniversity’s College of Engineering is gratefully acknowledged.

The authors would also like to acknowledge the support of the Society of Iron and SteelFabricators of Wisconsin for the generous donation of the structural steel channels used in the research;Ace Iron and Steel Corp. (Mr. David Mathews) for fabrication of the channels; Zignego Redi-Mix, Inc. forthe concrete donated to the research effort; Powers Fastening, Inc. for the generous donation of fasteningmaterials, without which, this research project could not be undertaken.

MUST-97-1: 1

1.0 Introduction

Many existing buildings and bridges are in need of repair or upgrade. A crumbling infrastructure is a

reality that all communities are dealing with. Existing beam members that are deficient with respect to

flexural capacity are costly to demolish and reconstruct. An efficient, cost-effective means of

strengthening existing concrete beams is needed so an unsafe or unuseable structure can once again be

utilized.

The method of epoxy-bonding steel plates and fiberglass reinforced plastics to the tensile face of

reinforced concrete beams has been studied extensively as a method to strengthen existing reinforced

concrete structures. Experimental results have proven that these techniques can be an effective means of

increasing a beam’s flexural capacity and stiffness. However, a problem that has been encountered

during the testing of reinforced beams with epoxy-bonded plates is separation of the plate from the beam

at the plate termination prior to concrete compression failure. Furthermore, there is some question as to

the loss of the ductile failure mode usually associated with reinforced concrete failure when carbon fiber

sheets and plates are used for external reinforcement. The use of expansion anchors has been examined

as a method of eliminating epoxy-bonded plate tear off at termination.

Bonding of steel and fiber-reinforced plastics is the most popular means of reinforcing existing

concrete beams. However, applying epoxy can be a delicate process requiring near perfect working

conditions. The beam must be properly prepared for epoxy application (smooth, flat, sandblasted, dust-

free, clean surface), and the thickness of the epoxy layer must be uniform. Perfect conditions are not the

norm when one is working in the field. This procedure can be successful, but the quality control

measures can be extreme. A solution to this problem is to take advantage of the fact that bolts have been

successful in stopping plate tear-off, and go one step further and use anchor bolts as the main system of

anchoring supplemental external steel reinforcement to the beam. This method can be used under

frequently encountered field conditions since the work environment need not be ideal and prep work for

mounting the reinforcement is minimal (aside from drilling holes into the flexural member).

MUST-97-1: 2

The objective of the research outlined in this report was to investigate and evaluate the use of

bolted steel channels to existing R.C. beams as the primary means of additional flexural reinforcement.

First of all, a literature review was conducted to evaluate previous experimental and analytical

procedures, including similar research results. A design procedure is developed for the flexural

reinforcement of existing R.C. beams using structural steel channel shapes. An experimental program

involving nine concrete beams, 10"(w) x 18"(h) x 15'-6"(l), was conducted to test the design procedure

developed. Three beams served as control beams with no external reinforcement. The remaining beams

consisted of three utilizing Rawl-Stud wedge style expansion anchors and three using threaded anchor rod

with Rawl Foil-Fast® epoxy-adhesive for attachment of structural steel channel reinforcement. The beams

were designed for shear failure of the mounting anchors for reasons to be highlighted and discussed in the

report.

Testing was done to investigate the increase in flexural strength and stiffness of the externally

reinforced R.C. beams. Each of the nine beams were tested to failure using four point loading. During

testing, the applied load, vertical deflection of the beam centerline, strain in the internal reinforcing steel,

and strain in the web and flanges of the structural steel channel were recorded. The measured ultimate

loading was also recorded.

An analytical technique is developed for predicting the ultimate load; load deformation response;

and strains in the internal and external reinforcement. The theoretical values obtained using the design

procedure and analytical method are compared to the experimental results. Conclusions are drawn and

suggestions for further research are made.

1.1 Research Significance

This research report presents the experimental and analytical results of a practical method of

strengthening existing reinforced concrete beams using structural steel channel shapes bolted to the

exterior soffit. Common construction techniques and materials (structural steel channels, expansion

anchors and epoxy adhesive anchors) are used in the reinforcement scheme developed. Experimental

MUST-97-1: 3

testing is used to evaluate a design procedure developed based on first principles of reinforced concrete

design. The design procedure and experimental results are intended to form the basis for procedures

externally reinforce existing (or damaged) concrete members.

1.2 Review of Existing Literature

A very popular method for reinforcing existing concrete beams is to epoxy-bond steel plates or fiberglass

reinforced plastics (GFRP) to the tension face. Much testing and research has been done involving these

reinforcing schemes. The following is a literature review of relevant articles discussing the utilization of

various reinforcing techniques for increasing the flexural strength of reinforced concrete beams. All of

the experimental results discussed pertain to non-high strength concrete and common reinforcement

configurations and strengths.

Sharif, et al (1994)studied glass-fiber reinforced plastic (GFRP) plates bonded with epoxy-

adhesive to the beam soffit and sides as means of repairing structurally deteriorated reinforced concrete

beams. A total of ten beams 150 x 150 x 1250 mm (5.9 x 5.9 x 49.2 in) were used, with internal steel

designed to insure an under-reinforced section. Concrete was used with an average compressive strength

of 37.7 N/mm2 (5500 psi). The yield stress of the reinforcement was 450 MPa (65 ksi). Strain gages

were mounted to the tension steel and to the fiberglass plate at midspan. Deflection was measured at the

beam centerline. The beams were simply supported over a span of 1180 mm (46.4 in). The techniques

for repair included bonding of three different thicknesses of GFRP plates to the beam soffit. Anchoring

of the plate ends with steel bolts and the addition of 3 mm FRP plates bonded to the sides of the beam in

the shear zone were evaluated. Lastly, a special I-shaped jacket plate of 3 mm thickness was bonded to

the beam soffit and sides. Each beam was preloaded to a centerline deflection of 10 mm (.3/8 in);

unloaded; repaired using one of four techniques; and then reloaded to failure.

The test results reported show that as the plate thickness increased, premature failure by plate

separation began to occur. The use of steel bolts to anchor the plate to the beam eliminated plate

separation, but introduced a failure due to a diagonal tension crack between the support and the end of the

MUST-97-1: 4

plate. It was concluded that the development of flexural cracks in this region produced high localized

bond stress concentrations at the tension steel which magnified the shear stress causing steep diagonal

cracks. Stirrups in this region failed to bridge these cracks. The use of the added side plates in the region

where the diagonal flexural cracking occurred, resulted in fully developed flexural strength with failure

by crushing of the concrete in the constant moment region. Horizontal flexure cracking formed below the

side plates and developed into a vertical crack up the beam at the end of the side plate. The I-jacketed

beams also reached full flexural capacity.

Jones, et al (1988) attempted to quantify and measure the stresses formed at the plate ends in

simply supported reinforced concrete beams with epoxy-bonded plates on the tensile face. Seven

reinforced concrete beams, 155 x 255 x 2500 mm (6.1 x 10 x 98.4 in.), were tested simply supported over

a span of 2300 mm (90.5 in) with loading at third points. The strain in the plates and the centerline

deflection of the beam was measured. Three beams were reinforced with the varying plate arrangements.

Two used straight plates with the addition of epoxy-anchor bolts at the plate curtailment. The last two

beams had a plate bonded to the bottom and then had different size L-shaped anchor plates epoxy bonded

to the bottom plate which extended up the side of the beam.

The first three beams failed by tearing off of the plate at the end. The two beams with epoxy-

anchors experienced partial separation of the plates, with the beams eventually failing by crushing of the

concrete in the constant moment region. The L-shaped anchor plates were the most effective reinforcing

system, with each beam reinforced in this manner reaching full flexural capacity. All the anchorage

systems had similar stiffness, about 60% greater than a beam with no plating. The three beams with only

anchor plates had a sudden failure, but the addition of the anchor bolts resulted in a ductile failure for the

two beams reinforced this way.

Hussain et al (1995) repaired pre-loaded beams by bonding steel plates of varying thickness to the

tension face. Eight test beams 150 x 150 x 1250 mm (5.9 x 5.9 x 49.2 in) were discussed. The steel

reinforcing plates were 1100 mm (43.3 in) long, 100 mm (3.9 in) wide, and varied in thickness from 1 to

3 mm (. 1/32 to 1/8 in). The yield stress of the steel plate was 269 MPa (39 ksi). Strain gages were

MUST-97-1: 5

mounted to the main reinforcement, the concrete upper surface at midspan, and to the plate at 50 mm (2

in) intervals to monitor distribution along the plate. Deflection was monitored at midspan of the beam

and at the load points. The beams were supported over a span of 1200 mm (47.2 in) with loading applied

at third points. The beams were all preloaded to 85% of their ultimate load capacity, equivalent to a

centerline deflection of 10 mm (.3/8 in). They were then unloaded allowing the different reinforcing

methods to be applied. The repaired members were then reloaded to failure. The deflection rate during

loading, unloading, and reloading was 1 mm per min. The method of strengthening the beams included

epoxy-bonding steel plates of different thickness to the bottom of the beam. For each reinforcing scheme,

two identical beams were made with one of the beams having anchor bolts installed at the end of the plate

arrangement. Preparation for application of the epoxy was extensive including sandblasting the beam

soffits and then washing them to remove dust. Also, the steel plates were sandblasted to remove the oxide

layer and roughen the surface.

Experimental results showed that as the reinforcing plate thickens, the failures became brittle

(shear-type). This implies that the beams did not have adequate shear strength prior to application of

external reinforcement. The inclusion of end anchorage increased the ductility of the beams with the

thicker plates, but the percentage increase in ductility decreased as the plates got thicker. The prediction

of ultimate load strength for the beams with thin plates ( 1 mm, 1.5 mm) was successful. The beams with

thicker plates (2 mm, 3 mm) failed prematurely due to plate separation, never reaching ultimate capacity.

The addition of anchor bolts did not have any effect in improving ultimate load capacity, with these

beams also failing prematurely.

Swamy, et al (1989) studied strengthening previously damaged structural members with 1.5 mm

plates under sustained loading. Nine reinforced concrete beams 155 x 255 x 2500 mm (6.1 x 10 x 98.4

in) were tested. The beams were simply supported over 2300 mm (90.6 in) with loading applied at third

points. Performance was monitored via measurement of deflections, rotations, concrete strains, and strain

in the reinforcing bars and the plates. Two beams served as control beams with no external plating. The

control beams were tested to failure. One beam was tested to failure with a 1.5 mm plate bonded to the

MUST-97-1: 6

bottom. A set of three beams were preloaded to varying percentages of ultimate strength, unloaded, and

then 1.5 mm plates were epoxy-bonded to the beam soffits. After curing two weeks, they were tested to

failure. Another set of three beams were preloaded to varying percentages of ultimate strength. The

applied load was held constant while the 1.5 mm plates were bonded to the beams. The epoxy was

allowed to cure for a period of two weeks, whereupon the beams were loaded to failure. Preparation for

epoxy bonding of the plates was again extensive with sandblasting occurring prior to application of the

epoxy layer.

All the beams reached full flexural capacity with failure by crushing of the concrete in the constant

moment region and yielding of the reinforcing bars and the plate. The predicted values of ultimate

strength, centerline deflection, and beam rotation were close to the experimental values. Both sets of

beams that had plates applied after initial loading exhibited an increase in stiffness during the second

loading stage. All beams showed similar ductility to the control beams. The strain results show that the

plate strains are almost identical for the loaded/unloaded set of beams and the control plated beam,

showing the effectiveness of using epoxy-bonded plates on heavily cracked beams. The strain over the

depth of the beam showed linear distribution, proving that fully composite action occurred between the

beam and the plate. The conclusion of this testing is that plating severely damaged beams is structurally

efficient and can restore a member to stiffness and strength conditions better than the original undamaged

beam.

Chajes, et al (1994) tested reinforced concrete beams to determine the ability of externally bonded

composite fabrics to improve flexural capacity. Fourteen R.C. beams 76.2 x 127 x 1180 mm (3 x 5 x 46.5

in) were tested. The internal reinforcing steel was varied for the different reinforcing techniques so all

members remained under-reinforced. The beams were simply supported over a span of 1120 mm (44 in)

with loading applied at third points. During testing, deflection was measured at the end points, at the load

points, and at mid-span. Strain gages were mounted on the concrete through the depth of the beam and on

the external reinforcement at mid-span. Three test beams served as control beams with only internal

reinforcement. Three sets of three beams were made with the same reinforcement as the control beams

MUST-97-1: 7

plus externally applied Aramid, E-glass, and graphite fiber fabric reinforcement attached to the beam

soffit. In addition, two beams were made with twice as much internal reinforcement as the control beams.

The beams were designed so the tensile capacity of the external composite fabric reinforcement was close

to that of the yield strength of the additional internal reinforcement. This resulted in the use of one layer

of Aramid fabric, two layers of graphite fabric, and three layers of E-glass. Preparation of the specimens

was extensive including vacuum curing.

The general flexural behavior to failure of all the fabric reinforced beams was similar, with the

stiffness and failure mode varying depending on the fabric used. The E-glass and graphite fabrics did not

display as much ductility as the control beams, but some measure of ductility still existed prior to failure.

These beams failed by tensile failure of the fabric first followed by crushing of the concrete. The first

aramid-reinforced beam failed by tearing off of the fabric from the beam. After this occurred, the last two

beams had fabric wrapped around the beam along its sides at the end to prevent tear-off. This worked as

anticipated, with the last two beams failing by crushing of the concrete before reaching the tensile

strength of the fabric. The ductility behavior of these beams is similar to the other two reinforcing

methods. The fabric reinforced beams increased the flexural capacity by approximately 43%, while the

beams with additional internal reinforcement added 62.8% to the ultimate strength. The difference can be

attributed to the steel being approximately 20% higher strength than the fabric reinforcement, as tests

showed. The increase in stiffness of fabric-reinforced beams and the beams with additional internal

reinforcement were similar.

Ziraba, et al (1994) analyzed previous research to develop guidelines for the design of reinforced

concrete beams with external plates bonded with epoxy adhesive. Three steps were outlined as the main

design procedure. The first step is to design the beam and plate assembly for flexure assuming failure

will occur with the plate yielding and the concrete crushing using concepts of basic reinforced concrete

beam design. The second step is to check interface stresses to make sure they are within limits so plate

debonding does not occur. A maximum cutoff distance from the beam support based on an allowable

value coefficient of cohesion of the steel-glue-concrete interface is computed at this stage. Lastly, the

MUST-97-1: 8

shear capacity of the beam is checked using first principles of R.C. beam design. Several excursions into

finite element and experimental regression analysis are made to determine characteristic constants used in

the design procedure. Fifty beams 100 x 150 x 2250 mm (3.9 x 5.9 x 88.6 in) were designed using the

proposed procedure and were then tested to failure using four point loading. Experimental results show

that the design procedure accurately predicts ultimate capacity for beams where failure is governed by

yielding of the steel. Premature failure was found to occur as the thickness of the plates increased.

In addition to the flexural reinforcement of existing and damaged concrete beams using epoxy

bonded steel plates and GFRP, existing concrete columns have been retrofitted using externally bolted

structural steel shapes. Oey and Aldrete (1996) strengthened existing stocky and slender reinforced

concrete columns using epoxy anchored bolts to attach steel angles at the column corners. These

reinforced columns were part of a building that was being upgraded with the addition of three new floors.

The bolts were designed as shear connectors for a force assumed equal to 2% of the total compressive

force in the column. First principles of mechanics of materials was used to govern the design.

Arduini, et al(1997a) performed analytical and experimental studies to quantify the behavior of RC

beams strengthened and stiffened with FRP plates and sheets. A variety of failure mechanisms including

brittle and ductile failures were simulated and verified experimentally. The experimental results indicated

failure mechanisms very much in line with those found in the previous research discussed. The failure

mechanisms found were; FRP rupture, concrete shear at the end of the FRP reinforcement, and FRP

debonding. All of these failure mechanism can be classified as brittle. Arduini, et al(1997b) continued

the study in FRP reinforced RC beams to include a parametric study. The results of the parametric study

show that brittle failure mechanisms can develop at loads much lower than expected when considering

only flexural performance controlled by concrete crushing and FRP tensile rupture; Arduini, et

al(1997b). The results of the research indicate that FRP reinforced RC beams can achieve significant

increase in both strength and stiffness.

MUST-97-1: 9

1.3 Evaluation of Previous Research

The use of epoxy-bonded plates to strengthen existing or damaged reinforced concrete beams has

been extensively researched. It has been proven to be a useful and reliable method of increasing the

ultimate flexural capacity of both damaged and undamaged members. As long as the thickness of the

reinforcing plate is kept thin, the beams will fail in flexure as expected. Ziraba, et al (1994) recommend a

maximum thickness of plate to insure flexural failure. Furthermore, testing that has been done to date has

been on relatively small beams. The cross sections have ranged in size from 76.2 x 127 mm (3 x 5 in) to

155 x 255 mm (6.1 x 10 in), while the lengths have ranged from 1180 mm (46.5 in) to 2500 mm (98.4 in).

As the experimental motivation moves toward determining if a method of reinforcement can be applied

to upgrading and repairing existing structures, full-scale testing should be employed for real-life results.

The only way to truly know if a reinforcement technique is adequate structurally, efficient, and capable of

being implemented for bridge girders is to test the technique on a bridge girder.

Furthermore, the use of epoxy to bond steel plates and composite fabric to beams is a method that

requires much preparation prior to application of the adhesive. The contact surfaces must be sand

blasted, clean, and dry to insure good bonding. Some research discussed in the literature review has even

gone as far as to cure the epoxy in a vacuum to meet these conditions. When working in the field,

conditions like these are often difficult if not impossible to achieve and control. Also, the thickness of the

epoxy layer must be uniform and the plate needs to be clamped in place while curing. All these

drawbacks in the application procedure will result in an increase in final cost, which could in the worst

case scenario eliminate a method as an economical solution.

A common problem that occurred in the testing of the bonded plates was the sudden tearing off

(delaminating) of the plate near the support. It was discovered that high localized stresses develop at the

end of the plate. As the plate thickness increased so did the probability that premature failure would

occur. In some tests, the use of anchor bolts at the plate ends proved a successful means of eliminating

the plate separation. Lastly, the basic underlying philosophy of reinforced concrete design has been to

ensure a ductile failure of reinforced concrete members. Many of the previous (fabric reinforcement)

MUST-97-1: 10

techniques exhibited loss in ductile behavior at the ‘reinforced’ ultimate load. This is counter to the basic

code philosophy. Providing economical mild-steel shapes as reinforcement is a step in preserving

ductility in the reinforced member.

Taking into consideration all that has been stated above, it was decided to test a method of

retrofitting existing reinforced concrete beams (bridge, floor, etc.) to increase their flexural capacity. The

members could be bridge beams that are deficient and the only other option would be to tear down the

structure; or floor beams that need to carry additional load because of a change in use for a building. It

was decided to test 10"(w) x 18"(h) x 15'-6"(l) [254 mm x 457 mm x 4.724 m] reinforced concrete beams,

smaller than a typical bridge girder but large enough to use as a real-world comparison. Because of the

ability of anchor bolts to stop the occurrence of plate tear-off and the preparation conditions that are

needed for epoxy, it was decided to use anchor bolts as the means of mounting a steel member to the

tension face of the beam. For this analysis, structural steel channels were used as the reinforcing member

rather than a plate.

2.0 Design Procedure for Concrete Flexural Members

This section describes the design procedure used for the RC (control) beams tested. The flexure and shear

design of the control beams using first principles of reinforced concrete design is discussed. The different

reinforcing schemes that were studied are schematically outlined and discussed. Finally, a preliminary

design procedure for externally reinforcing a concrete beam by mounting a structural steel channel to the

bottom is presented. This includes the flexural design, the shear design and the design of the anchoring

bolts used for mounting the steel member.

Three control beams (no external reinforcement) are used for comparing the ultimate load of the

externally reinforced beams. The width and height of the beams were chosen as 10" x 18" [254 mm x

457 mm], respectively, while the length of the beam was set at 15'-6" [4.724 m]. These beam dimensions

were used to simulate an actual structural member and also because of physical limitations in laboratory

space and moving equipment. The control beams were analyzed and designed using first principles for

MUST-97-1: 11

D 'As

bd# 0.75Dbal (1)

Dbal '0.85 fc' $1

fy

8700087000 % fy

(2)

under-reinforced concrete beam sections. The design procedure is highlighted in this section to illustrate

the basic concepts carried over to the procedure used in the design of a retrofitted beam.

Internal equilibrium for a typical singly reinforced member is shown in Figure 2-1. Preliminary

calculations were done using an assumed 28-day concrete strength of 4000 psi [27.6 MPa] and a yield

strength of reinforcing steel of 60,000 psi [413.4 MPa]. The amount of reinforcing steel was chosen so

that ductile failure would occur. This was done by limiting the reinforcement ratio of the section, D, to,

The following assumptions are made in the design of the RC members:

1.) Plane sections before bending remain plane after bending (the variation in strain is

linear throughout the member).

2.) Concrete does not contribute any tensile strength.

3.) No slip exists between the steel bars and the surrounding concrete during the

development of tensile force in the bars.

4.) The Whitney equivalent rectangular stress block is used for concrete compressive

stress.

The first step in the design is to select an area of steel less than 0.75Dbal where,

in which:

fc! = compressive strength of concrete, (psi)

fy = yield strength of reinforcing steel, (psi)

$1 = 0.85 - 0.05(fc! - 4000) / 1000 # 0.85 ; $1 $ 0.65

Dbal is the reinforcement ratio when the concrete reaches its assumed ultimate strain just as the steel

reaches its yield strength. A value of D equal to one half of 0.75Dbal, or 0.375Dbal, is used to compute an

area of reinforcing steel using,

MUST-97-1: 12

As ' Dbd (3)

a 'As fy

0.85 fc' b(4)

Mn ' Mult ' As fy d &a2

(5)

P '3ML

L(6)

where:

As = area of reinforcing steel, (in.2)

b = width of compression face of beam, (in.)

d = distance from the extreme compression fiber to centroid of reinforcing steel,

(in.)

Based on this area of steel, the number and size of the bars is chosen and Dact is calculated. This must be

greater than Dmin = 200 / fy.

The next step is to calculate the depth of the approximate Whitney rectangular stress block, a,

using equation (4),

As a result of theoretical strength capacities being computed, the nominal moment capacity of the beam,

Mn, dead load moment due to the beam self-weight and superimposed live load are computed in

unreduced, non-factored forms. The nominal moment capacity of the beam can be found using,

The moment due to the dead weight of the beam is subtracted from Mult to give the moment capacity of

the beam due to superimposed live load. Assuming the simply supported beam loaded at third points, the

nominal load the beam can theoretically support is calculated as,

where:

ML = moment due to superimposed live load, (kip-ft)

L = simply supported length of beam, (ft)

P = each load for a two-point loading, (kips)

MUST-97-1: 13

Vc ' 2 fc! bd (7)

s 'd2

#Av fy

50b(8)

s 'Av fy d

P & Vc

#Av fy

50b(9)

Shear reinforcement is designed so the beam will not fail in diagonal tension. This is done in

accordance with ACI(1995). The nominal shear strength of the concrete, Vc , is found first, using,

If this value is greater than P, only minimum stirrup steel need be provided at a spacing,

where:

Av = area of both legs of stirrup, (in.2)

s = minimum spacing of stirrups, (in.)

If P > Vc , the spacing of the stirrups is,

which must be less than, d/4.

The procedure for design of the control beams resulted in a typical unreinforced (control) member

shown in Figure 2-2. It should be noted that the overall cross-sectional dimensions, internal

reinforcement, and material properties were kept constant for all control members. However, one

exception to the constant material properties was the 28-day compressive strength which varied for each

of the control beams.

3.0 Design Procedure for Strengthened Beams

Many different external reinforcing schemes were analyzed for applicability. The first was to

mount two structural steel channels to the sides of the beam at the bottom. This seemed the most practical

since in many cases height clearances are important and mounting structural steel shapes to the underside

of a beam may not be an option in an existing building that plans to use this retrofit technique. This also

would be a relatively simple method for attaching the reinforcement since holes could be drilled directly

into the sides of the beams and would have an excellent chance of not violating the integrity of the main

MUST-97-1: 14

flexural reinforcement. A problem with this method is that two steel sections add a large additional area

of steel to the beam. Using the smallest available steel channels would still result in a section that may be

slightly over-reinforced. An option would be to redesign the beams to get a larger cross-section, but

working with a member larger than the one already designed in the laboratory environment was not an

attractive solution.

A second method that was studied was to use steel angles or plates mounted to the sides of the

beam at the bottom. It would clearly be easier to achieve an under-reinforced section because smaller

members would result in a smaller additional area of steel. As with channels, it would be relatively easy

to drill directly into the sides of the member to mount either of these sections. Steel plates were not

considered as an option because they are more expensive than rolled structural steel shapes for the size

and lengths considered in this research.

A third method that was examined was to mount one structural steel channel to the bottom of the

beam. The main motivation behind this method is the obvious fact that this would require the purchase of

half as many steel sections as the previously mentioned methods. This method would also require drilling

half as many holes as the previously considered options. It would be easier to get an under-reinforced

section since half as much steel is being used to contribute to the reinforcement ratio. Care in placement

of holes so as to minimally disturb the main flexural reinforcement has to be taken in this scheme. This

retrofit technique would require more labor to drill the holes for the anchors since the beams would have

to be rolled over to safely get at the bottom, but this was an acceptable trade-off. In the field, overhead

drilling could be performed and therefore, the retrofit technique proposed is still feasible and economical

in field applications.

It was decided to use wedge style expansion anchors and threaded rod bonded into pre-drilled holes

with epoxy-adhesive as the mechanical connection between the the external channel and the existing

reinforced concrete beam. All anchors (and necessary equipment for installation) was generously donated

by the Rawl Plug Company of New Rochelle, New York. Three beams utilizing each of the two

mounting methods were tested and the two methods compared.

MUST-97-1: 15

D ' Drebar% Dchannel 'As ,rebar

bd%

As ,channel

bd(10)

All of the methods studied require the same basic design procedure for externally reinforcing an

existing concrete member. Ziraba, et al (1994) stated that “strain compatibility and a rectangular

compression stress block similar to the ACI method for RC beams in flexure” can be utilized for epoxy-

bonded steel plates as long as the thickness of the plates does not exceed a maximum value. The

externally reinforced beams were designed as regular reinforced concrete beams with additional steel area

which results in a second tensile force at the centroid of the attached steel section.

The design procedure is the same for both the epoxy-adhesive anchor beams and the wedge style

expansion anchor beams. The RC beams have the same internal reinforcing steel for flexure and shear.

The six retrofit beams are the same as the three control beams designed in Section 2.0 (10" x 18" x 15'-

6"). Concrete strength was initially assumed to be 4 ksi, rebar yield strength 60 ksi, and the yield strength

of the steel channels to be 36 ksi. As with the control beams, the retrofitted beams were designed to be

under-reinforced with the additional external reinforcement.

Internal equilibrium for a flexural member containing internal (rebar) and external reinforcement

can be schematically represented as shown in Figure 3-1. The internal tension force that usually consists

of a single component provided by the internal reinforcement, now has two components with

supplemental tension provided by the external reinforcement.

A structural steel channel section was chosen for the external reinforcement, which requires that a

modified reinforcement ratio be defined. The sum of the reinforcement ratios from the rebar and the

channel less than 0.75Dbal should insure ductile failure; with the implication that the steel channel would

yield as well as the internal reinforcing steel. The value of Dbal is calculated using a modification of

equation (1). The combined reinforcement ratio is now calculated using,

where:

As,rebar = area of reinforcing steel, (in.2)

As,channel = area of channel, (in.2)

MUST-97-1: 16

a '

(As fy )rebar

% (As fy )channel

0.85 fc' b(11)

Mn ' Mult ' { As fy }rebar

d1 &a2

% { As fy }channel

d2 &a2

(12)

The depth of the Whitney rectangular stress block is calculated with the following addition to equation

(4),

The nominal moment capacity of the reinforced beam is then calculated as,

where:

d1 = distance from extreme compression fiber to centroid of internal reinforcing steel,

(in.); see Figure 3-1.

d2 = distance from extreme compression fiber to centroid of channel section, (in.).

If one assumes that sufficient bolt strength is available such that the external channel yields at the

ultimate condition, the computation of the depth of the rectangular stress block is a simple procedure

involving direct application of equation (11). However, special procedures (iteration) must be employed

if the full yield strength of the channel cannot be developed through shear of the anchoring bolts. This

situation will tend to be the norm in practice, and the iteration is discussed in subsequent sections.

The design procedure for the externally reinforced beam using equations (10) through (12) results

in a beam the same size as a control beam with a C5 x 6.7 structural steel channel mounted to the bottom

as shown in Figure 3-2. The calculated ultimate capacity of the externally reinforced beam assuming full

channel yielding was a total of 62.2 kips (2 - 31.1 kip loads at third points on a simple span). Concern

was raised about applying a load of this magnitude in the testing laboratory. Properly constructed beams

using commercial materials, would most likely exceed this capacity. Another issue of concern was the

number of anchors that would be required to mount the channel and transfer a load large enough to insure

channel yielding. Practically speaking, with spacing and edge distance requirements, the number of

anchors required for channel yielding will probably not physically fit in the space available on the beam

member’s soffit.

MUST-97-1: 17

Mult ' { As fy }rebar

d1 &a2

% Tanchor d2 &a2

(13)

As a result, it was decided to design the beams to fail by shearing of the anchor bolts rather than

channel yielding. In this manner, a ‘comfortable’ failure load for the reinforced beams could be set and

the number of anchor bolts designed to achieve this strength. The design of the beam up to this point is

still utilized; but now instead of designing the anchor bolts for the full strength of the retrofitted beam, the

number of anchors is designed for a certain acceptable ultimate load (less than full capacity of the beam

based on channel yielding). This will translate very smoothly into a design procedure where a defined

ultimate load for the retrofitted beam is needed. Thus, the number of anchors can be tailored to match the

design load.

It was (rather arbitrarily) decided to use an applied failure load of twice the capacity of the control

beam, which is P =2(12.4)=24.8 kips. Rounding up, a target load of 25 kips was used to design the

anchors. The first step was to calculate the shear force in the anchors at the desired load of 25 kips.

The shear force in the anchors is the tensile force carried by the external reinforcement, Tanchor, shown in

Figure 3-1. It should be noted that Tanchor is assumed to be developed in the region outside the constant

moment region (central 1/3 portion). This is computed by solving equation (6) for the ultimate

superimposed live load moment that results from the two loads of 25 kips each applied at third points of

the beam. The moment due to the dead load of the beam is added to ML to get the nominal/ultimate

moment applied to the beam.

The next step involves an iterative solution of equation (12) for the tension force required to be

carried by the anchor. An iteration procedure is necessary because the depth of the compression area, a,

is unknown as well as the value of Tanchor. Equation (13) is equation (12) with Tanchor replacing (Asfy)channel,

The value of d2 is now assumed to be at the shear interface of the beam and channel. The depth of the

Whitney rectangular compression block, a, is assumed and equation (13) is then solved for the resulting

value of Tanchor . This value of Tanchor is substituted into equation (11) for a revised value of a,

MUST-97-1: 18

arevised '

{ As fy }rebar

% Tanchor

0.85 fc' b(14)

N 'Tanchor

Vult'(15)

Equation (13) is resolved with arevised for a new value of Tanchor. The above procedure is continued until

arevised converges for a value of Tanchor. This value of Tanchor becomes the shear force that the anchors must

be designed for. Equations (13) and (14) assume the internal reinforcing steel is at ultimate strength even

though for this procedure the design is for shear failure of the anchors with the channel reinforcement not

reaching yield.

The design procedure for the anchor bolts is the same for both Rawl-Stud wedge style expansion

anchors and the Rawl Foil-Fast® epoxy-adhesive anchors. The tables from Rawlplug(1994) are

referenced to obtain shear design values, minimum spacing and edge distance requirements of both types

of anchors. The anchors are designed so the required channel force is achieved within the end five feet of

the beam. These outer thirds of the reinforced beams were chosen as regions for “development” of the

channel forces required. Due to the location of the loads, there is constant shear and linearly decreasing

moment in these regions which makes them ideal for this purpose.

The first step in the anchor design procedure is to determine a size and length of anchor from the

shear load tables based on concrete strength and depth of embedment. The appropriate reductions are

then applied to the ultimate shear capacity based on spacing and edge distance requirements. The result is

a modified shear capacity, Vult!, for the anchor. The tension force at the location of the anchors, Tanchor

calculated from equation (13), divided by the modified shear capacity results in the number of anchors

needed, N,

The anchors are laid out within the end five foot section and the shear capacity must then be modified

again based on the spacing and edge distances that result from the anchor pattern layout. This cycle is

continued until the modified shear capacity converges for the number and layout of anchors used.

MUST-97-1: 19

A larger size bolt may need to be used if the section becomes too congested. The above process is

redone using the new value of ultimate shear capacity for the larger diameter bolt. Once the iterations

converge to a final number of anchors, the design of the externally reinforced beam is complete. The

appropriate design checks must be made for the block shear strength of the steel channel and the yield of

the bolt holes. An example calculation for the design of a beam using the Rawl-Stud wedge style

expansion anchors is included in an example design for an externally reinforced beam in Appendix-A.

The design of the shear reinforcement in the form of stirrups for the 25 k load at third points is

accomplished using the same procedure as was discussed in Section 2.0.

The result of the retrofit design procedure is the specimen given in Figure 3-2. All reinforcement

(rebars) were Grade 60. The stirrups were placed as shown in the figure. Cover to all steel (flexural and

stirrup) was 2 inches. The layout of the anchor bolts for the wedge type expansion anchors and epoxy

adhesive anchors are shown in Figure 3-3. It should be noted that the anchor layout is determined largely

based on edge distance and spacing requirements obtained from RawlPlug (1994). Also, the anchors

were intended to enter the space between the main internal reinforcing steel (3-bars)..

4.0 Construction of Test Specimens

Nine concrete beams were tested to failure for this research. Three were control beams to be used as a

comparison for the remaining six. The remaining beams were externally reinforced with structural steel

channels mounted to the bottom. Three beams used Rawl-Stud wedge style expansion anchors to attach

the channel to the beam. The last three beams to be tested used threaded anchor rods with Rawl Foil-

Fast® epoxy-adhesive to mount the channel. This section discusses the materials used to make the

specimens, as well as the procedures used for externally reinforcing the beams. The experimental testing

method is then described in detail.

Form-work was built of construction grade lumber in the Structural Testing laboratory of the

Haggerty Engineering building. Due to space restrictions and budget considerations, form-work for only

MUST-97-1: 20

three beams was built. As a result, three beams were poured at a time at the loading dock of the

laboratory.

Commercially obtained redi-mix concrete was used for construction of the beams. A basic, non-

air-entrained footing mix of 3000 psi strength was used. The concrete was poured into one end of the

form and then shoveled down the length until the forms were full. A concrete vibrator was used to

eliminate air pockets and insure the concrete flowed into all corners of the form-work and around all

reinforcing bars. Concrete finishing tools were used to smooth the top surface of the beam. The beams

were allowed to cure undisturbed for a period of one week, and then moved into the main lab.

The RC beam specimens were designated as follows. The C, W, and E indicate Control beam,

beam using Wedge style expansion anchors to mount the external channel, and beams using Epoxy-

adhesive anchors to mount the external channel, respectively. The numbers after the C, W, and E

designations correspond to the date of concrete pour for the beam. One, two, and three stand for the first,

second, and third concrete pours, respectively.

Three standard testing cylinders, with 6" diameter and 12" height, were made for each set of beams

to obtain an average 28-day compressive strength for the concrete. The cylinders were cured in the same

environment as the beams. Each cylinder was compression tested using a Forney QC-410-D/TA-0103

digital readout compression loading apparatus. The maximum values for the three cylinders were

averaged together to obtain an average concrete compressive strength for the three sets of beams. The

values of fc! for the three sets of beams are included in Table 4-1.

The internal flexural reinforcement for each beam consisted of 3-#5 bars. The shear reinforcement

for the beams was #3 bars bent in a U-shape and spaced at 7½". The cover to reinforcement was 2", with

plastic rebar chairs used to insure this was met. Grade 60 steel was purchased for both the main and

stirrup steel. Three representative samples were cut from the stock of bars for tension testing to obtain

estimates for the actual yield stress and modulus of elasticity of the steel. The material property results of

the tension testing of the rebar samples are included in Table 4-2.

MUST-97-1: 21

The preliminary design of the beams has been discussed in previous sections. Table 4-3 shows the

actual dimensions of the test beams that were measured at quarter points along the length. The

measurements were averaged for each beam and are included in the table. Grade 36 structural steel

channels were obtained. Shop drawings of the channels were provided to a local fabricator, who

performed the fabrication. The final layout of the channels, as a result of the preliminary design

procedure is shown in Figure 3-3 and the measured material properties for the channels is shown in Table

4-4. Two methods, as discussed previously were used to mount the structural steel channels to the RC

beams. The first method discussed is Rawl-Stud wedge style expansion anchors. Threaded anchor rod

utilizing Foil-Fast® epoxy-adhesive was the second attachment method used. Both are examined in the

following discussion.

Rawl-Stud wedge style expansion anchors made of carbon steel were used as one technique for

mounting the structural steel channels to the bottom of the R.C. beam. The anchors are designed with a

tapered expansion section on the working end. Interlocking wedges at this end are held on by tabs which

grip the anchor firmly to prevent spinning of the anchor during tightening. As the anchor is tightened, the

shaft is pulled upwards causing the tapered expansion section to compress the wedges outwards against

the wall of the anchor hole. Rawlplug(1994), was referenced for the performance data, installation

specifications, and the installation procedures for the anchors used. A ½" by 7" Carbon Steel Rawl-Stud

wedge style expansion anchor was used. The design values were based on an embedment into the

existing concrete beam of 4".

Rawl Foil-Fast® epoxy injection gel with threaded steel anchor rod was the second method used for

mounting the structural steel channels to the bottom of the R.C. beam. The gel is a two component

structural epoxy that comes in a dual-tube cartridge. One tube of the cartridge contains the base resin and

the other a hardener. A special ‘injection gun’ is used to dispense an equal amount of epoxy into a static

mixing nozzle. The mixing nozzle contains a series of mixing elements that progressively divide and

recombine the components, automatically mixing them as they are pumped through. Rawlplug(1994),

was referenced for the performance data, installation specifications, and the installation procedures of the

MUST-97-1: 22

anchors used. A ½" by 6 ½" Grade B7 carbon steel threaded anchor rod was used for this mounting

technique. The design values used were based on an embedment into the concrete of 2". A fast set gel

was used since the laboratory setting consists of ideal conditions.

Attaching the structural steel channels to the bottom of the beam created a problem as to the safest

way to drill the holes and mount the channel. It was decided to roll the beams 180E so the bottom was

facing upward. Once the beam was in the correct position, the anchor pattern was laid out using the

channel as a template. The holes were drilled using the appropriate size Rawl SDS-Plus Carbide drill bit

and a Black & Decker rotary hammer drill. A ½" diameter bit was used for the epoxy-adhesive anchor

holes, while a 9/16" diameter bit was used for the holes of the wedge style expansion anchor system, as

recommended in RawlPlug(1994).

While drilling some of the holes, pieces of steel were seen with the concrete dust. It was assumed

this was from the reinforcing steel, whether stirrup or flexural steel is unknown. The fact that this

occurred was noted, but nothing was changed in the analysis due to this decrease in the area of the bar

since it is not known how much material was removed or what bar it came from. This is an acceptable

risk when one blindly drills into a RC beam (a procedure conceivably done in field situations).

The drill had a depth gage mounted to it which could be set to the appropriate depth for the

different anchors. The actual embedment depths of the anchors were measured, and the average

calculated on a per beam basis. The results are summarized in Table 4-3. The wedge-anchors were

designed for an embedment of 4", while the epoxy-adhesive anchors were designed for an embedment of

2". The actual embedment of the wedge-anchors all came close to the required embedment, with those

for beam W2 exceeding 4". The reason that the actual embedment of the epoxy-adhesive anchor was 3½"

larger than the required embedment was because the threaded anchor rod delivered was longer that what

was ordered. The maximum design value for the epoxy-adhesive anchor based on shear only is for a 2"

embedment of the anchor into the concrete. A greater embedment depth may be used, but this has no

effect (increase or decrease) on the shear strength of the connection. Therefore, these anchors were used

with an embedment of 51/2" and no change was made to the design shear value.

MUST-97-1: 23

Installation of the wedge type expansion anchors followed the procedures established in

Rawlplug(1994). The anchors were first set loosely into the holes. The channel was then placed onto the

beam with the anchors directed through the appropriate holes. A 3 lb. hammer was used to drive the

anchors. Pounding was continued until the anchors ‘felt’ like they were all the way into the hole. This

was decided by a solid feeling in the hammer as the anchor was hit indicating it was against the bottom of

the hole. Once all the anchors were driven to their full embedment depth, they were tightened by hand

using a ratchet and socket. The wedge-anchors were first finger tightened and then tightened an

additional 3 to 4 turns of the nut as directed in RawlPlug(1994).

The installation of the epoxy adhesive anchors followed the procedures contained in

Rawlplug(1994). The initial step was to fill the holes approximately half way with epoxy. After a few

holes it was discovered that three and one-half pumps of the injection gun trigger would fill the hole with

enough epoxy. Upon insertion of the threaded rod to the appropriate embedment depth, epoxy would be

forced out of the hole indicating it was full. After insertion of the epoxy, the threaded rod was

immediately pushed into the hole turning it slightly (like one turns a screw) to insure positive distribution

of the epoxy. Once the anchor rods were in place, the channel was placed on the beam. This was not a

good method, because the anchors did not all line up exactly with the holes in the channel. Some

manipulation of the anchors was done to get them through the channel holes. This caused the anchor rods

to be pushed deeper into the holes, which caused excess epoxy to be emitted from the holes. Once all the

anchors were through, there was epoxy between the channel and the beam that could not be removed. It

was not anticipated that this would cause a problem in the testing, but this did cause an unsightly gap

between the channel and the beam. This method was only used for beam E1, with the following revised

procedure used for beams E2 and E3.

The first step of the second procedure was to place the channel onto the beam, lining up the holes.

The channels were then mechanically strapped to the beam eliminating a possible gap between the

channel and the beam that epoxy could seep into. The epoxy was inserted into the holes in the same

manner as used for beam E1. The threaded rod was then pushed into the holes to the appropriate depth,

MUST-97-1: 24

allowing the epoxy to flow out onto the channel where it could be wiped off. The epoxy was then

allowed to cure. This method worked much better. A guide torque was not provided for the epoxy-

anchors, so the nuts were turned as much as could be done by hand with a ratchet and socket. The

tightening of the epoxy-anchors was done after a 24 hour cure period.

5.0 Experimental Program

An experimental program was undertaken to verify the proposed design procedure and to calibrate future

analytical studies. The nine full-scale specimens described in the previous section were instrumented for

deflection, strain, and load measurements. Each specimen was tested to failure in the Marquette

University Structural Testing Laboratory. This section gives an overview of the experimental program

including details of the instrumentation and data acquisition.

5.1 Strain Gage Instrumentation

General purpose strain gages were used to measure strain on the channel and internal reinforcing steel.

The gages had a fully encapsulated grid and exposed copper solder tabs. The preparation and application

of the gages was completed as directed in the instruction bulletins supplied by Measurements Group, Inc.

A bondable terminal was used to insure that tension in the wiring was not applied directly to the strain

gage. A small length of wire was connected between the gage and the bondable terminal. Each main

wire from the data acquisition system was then soldered into the same solder joint on the bondable

terminal as the wire from the gage to complete the circuit. This is illustrated in Figure 5-1.

Before the concrete was poured for the six channel-mounted beams, a strain gage was mounted to

the center reinforcing bar of the group. This was done by grinding and sanding a 4 inch smooth section

over one-half the diameter of the bar at approximately the center. The surface was then cleaned with the

necessary solutions and the gage applied to the bar using epoxy-adhesive. Pressure was applied to the

gage during curing to insure proper bond. After curing 24 hours, wires were soldered to the gage and a

MUST-97-1: 25

protective gel was put over it. This gel covered the entire gage, and once set up, would protect it from the

concrete and the moisture.

The concrete was placed in the formwork taking care not to vibrate in the area of the strain gage.

The wires were allowed to move freely in the concrete, trying not to introduce tension into them which

may pull on the gage. The wires were brought up through the top of the beam to the data acquisition

computer. After the beams were poured, the strain gages were checked with a digital multi-meter to

verify the installed gage resistance. Several of the strain gages mounted to the internal reinforcing steel

were damaged during concrete placement. Ramifications of this will be discussed in later sections.

While the beams were rolled over for mounting of the channels, strain gages were also mounted to

the channels. Two gages were located on the channel flanges (near mid-flange height), while a single

gage was located on the channel web (refer to Figure 5-1). This was done by first grinding and sanding a

4 inch smooth section of the channel. These areas were cleaned with the necessary solutions. Gages were

then mounted to the web of the channel and to each flange at approximately mid-span. Pressure was

applied to the gages during curing to insure proper bond. No special procedure was employed to ensure

the flange gages were located at nearly the same distance from the flange tips.

The mounting of the gages was performed with the intent to determine the distribution of strain

within the external reinforcing channel. A uniform (average) distribution of strain and stress in the

external channel is assumed in the design procedure proposed. Experimental results will shed additional

light on the validity of this assumption. Furthermore, the mounting of strain gages on the internal

reinforcing steel will allow the determination as to whether or not the internal steel has yielded prior to

any yielding of the external channel. This is an additional assumption made in the design procedure

proposed. Lastly, a check of the composite action of the member (fully- or partially-) can be made with

information pertaining to the strain in the internal reinforcing steel and the external channel..

MUST-97-1: 26

.2 Loading Test Frame and Data Acquisition

A loading frame made of structural steel tube-columns and W-section cross-beams was used to load the

beams. The columns were anchored to the floor, with each having a tensile capacity at the floor

connection of 50 kips. A picture of the loading frame is shown in Figure 5-2. As can be seen in the

figure, there are two hydraulic loading rams attached to the W-section cross-member. These rams are

hooked up to an Enerpac hydraulic pump with the ability of producing a load of 50 kips each. Specimens

C1, W1 and E1 were set up with centerline to centerline support distances equal to 15'-0" with loading at

one-third points. The remaining six specimens were set up on a 14'-6" centerline to centerline support

spacing with 4'-6" separating the two loading rams. An explanation of why this was done will be

discussed later in the report.

The Marquette University Department of Civil and Environmental Engineering Daytronic data

acquisition system was used to record loading, beam deflection at the midpoint, strain in internal

reinforcement, and strain in the web and flanges of the external channel. Two 50 kip capacity load cells

were placed under each loading ram, as shown in Figure 5-3. The load cells were hooked up to the

computer to record the amount of applied load.

Two LVDTs, pictured in Figure 5-4, were used to measure vertical displacement of the beam at

mid-span. The LVDTs were placed on two metal tabs that were epoxied to each side of the beam

approximately 5 inches below the top surface. One tab was 3 inches to the left of centerline and the other

was 3 inches to the right of centerline. This was done in case the concrete compression failure occurred

directly at the center of the span. An average of the two deflections was used in the data analysis.

5.3 Testing of Control Beams

Three control beams were constructed as part of the experimental program. Each control beam was white

washed for better detection of cracks. As cracks formed in the concrete member, they were highlighted

with a heavy black marker to make the cracks more visible to the naked eye. This section will highlight

MUST-97-1: 27

observations made during the testing and also enumerate pertinent data collected during the testing of the

control beams.

Each of the three control beams was tested with monotonic load application. The load was applied

at a rate of approximately 400 lbs/min until 'failure' of the member occurred. Failure was defined in the

context of these experiments to be a compression failure in the concrete within the constant moment

region following sustained increase in vertical deformation after cracking. Beam C1 was tested with a

centerline to centerline support spacing of 15'-0" and a distance between loading rams of 5'-0" (placed

symmetrically about the beam centerline). Beams C2 and C3 had a centerline to centerline span of 14'-6"

with loading rams spaced at 4'-6" (placed symmetrically about the beam centerline).

The experimental results are contained in the description that follows. The monotonic loading was

applied to the member after which hairline cracks began to form in the constant moment region. As the

loading was increased further, the cracks extended vertically up the cross section as shown in Figure 5-5.

Cracks then formed in the constant shear zone (the member length between load and support) as a result

of redistribution of flexural stress. These cracks extended up the member approximately (3/4)h,

whereupon they began to extend diagonally toward the load points exhibiting classic diagonal tension

behavior. The diagonal cracks formed throughout the shear zone, but never encroached upon the final

15" before the support.

All control beams failed in classic flexural mode with significant yielding followed by crushing of

the concrete between the load points. Figure 5-6 illustrates the cracking and crushing of the concrete at

the extreme compression fiber. The two loading rams applying load were not exactly of equal magnitude

for each of the tests, and as a result, the crushing location was slightly off the member centerline. Table

5-1 summarizes important highlights from the testing of the control beams. Full load deformation data

was acquired for the beam testing and this data will be discussed in later sections. Upon examination of

Table 5-1, it can be seen that the average load at first visible crack was approximately 4000-4500 lbs.

First cracking was observed in beam C3 at approximately 3300 lbs. The differences in these results are a

result of experimental error as the cracks were detected and recorded visually and also a result of

MUST-97-1: 28

differences in concrete strengths for the three members. The ultimate loads recorded at failure for all

three members are very close to one another. However, differences are due to the variation in 28 day

ultimate concrete compression strengths for the members. The deformation at the ultimate load condition

typical of the lightly reinforced control beams is shown in Figure 5-7.

It is prudent to discuss several difficulties that were encountered with the experimental setup

during the testing procedure. As can be seen in Table 5-1, the centerline deflection at ultimate is

excessive ( ). This resulted in the load cell and roller beneath it to be loaded in a severely3.28 '' . L /57

eccentric condition. This eccentricity caused the load cell and roller support to slide out from under the

loading ram in the tests of beams C2 and C3. In each of these tests, however, evidence of compression

failure was observed in the top of the concrete (cracks and spalling), so it was assumed that failure for the

member had been achieved.

5.4 Testing of Wedge Expansion Anchor Beams

This section describes the experiments conducted and results obtained for the members externally

reinforced using structural steel channels mounted to the beam soffit using wedge type expansion

anchors. As done previously in the case of the control beams, each of the members were white washed

for crack detection. Furthermore, the structural steel channels were also painted with white-wash

compound to detect yielding within the structural steel channel if and when it occurred. Beam W1 was

placed within the testing frame with support rollers placed at 15'-0" on center and the loading rams placed

symmetrically about the beam centerline at 5'-0" apart. Figure 5-8 illustrates the typical setup for the

wedge anchor beams. Beam W3 were placed within the loading frame with centerline to centerline

support spacing equal to 14'-6" and the loading rams placed symmetrically about the beam centerline with

spacing of 4'-6". This was done as a result of an unexpected failure of beam W2 to be discussed. The

applied moment within the zero shear region of the member remained the same for all three wedge anchor

specimens. The steel channel area surrounding the anchors were white-washed to make signs of yielding

within the channel more visible to the naked eye as shown in Figure 5-9.

MUST-97-1: 29

All beams were subjected to monotonic loading until failure occurred. Failure in the retrofitted

beams was characterized by the member’s inability to support further increases in loading. Failure was

defined to be the result of shear failure of the bolts, crushing at the extreme compression fiber, or both.

The failure of beams W1 and W3 were characterized by shearing of the anchors followed by a very

subtle (almost imperceptible) compression failure of the concrete in the constant moment region. Prior to

failure of the member there was significant cracking of the concrete throughout the constant moment

region and constant shear zone. The anchors failed in progression beginning with the anchors near the

supports and ending with the several anchors moving inwards toward the loading points. Pertinent

information related to the testing of the wedge anchor specimens can be found in Table 5-1. Furthermore,

Figure 5-10 illustrates the significant reduction in deformation at the ultimate load condition for the

wedge anchor specimens. Overall cracking of the members were very similar to that of the control

beams. The cracking patterns for these beams had a similar pattern as the control members which can be

shown in Figures 5-11, 5-12 and 5-13. The spacing of the cracks corresponded closely with the locations

of the anchors. The channel members did not exhibit any sign of yielding, although a forensic analysis of

the channels after removal from the beam showed that there was very slight deformation (elongation) of

the bolt holes in the channel. The elongation was more pronounced in the anchor holes near the supports

as expected. ‘Creaking’ of the channels could be heard approximately midway through the test indicating

possible “seating action” of the anchors within the channel holes. Upon further inspection of the beams at

the conclusion of testing, evidence of a slight compression failure in the concrete was evident. It is

unknown whether this compression failure occurred after failure of the bolts or not as it was not

witnessed.

The failure of the anchors in beams W1 and W3 warrants further discussion as it will enlighten the

reader as to behavior exhibited on the load deformation plots shown later in this section. The anchor near

the support (as mentioned previously) was the first anchor to fail. At this point, the beam(s) unloaded and

began taking slightly decreasing load until four additional anchors failed in the case of beam W1 and a

complete unloading occurred in the case of beam W3. The multiple anchors that failed in specimen W3

MUST-97-1: 30

failed more or less simultaneously and hence the beam unloaded suddenly. Beam W1 exhibited a slight

ability to carry a decreased load in a ductile manner. Both specimens W1 and W3 exhibited channel

‘delaminating’ near the support(s). Figures 5-14 and 5-15 depict the typical delaminating that occurred.

It should be noted that this ‘peeling’ of the channel occurred subsequent to anchor failure and virtually

coincident with the ultimate load achieved for the specimen.

Specimen W2 gave undesirable test results. This member suffered from a sudden and complete

diagonal tension failure near the support. The failure is shown in Figure 5-16. Upon inspection of the

failure, it was determined that the main reason this occurred was poor craftsmanship during casting of the

member. After reviewing the failure and the method used to cast the concrete beam, it was concluded that

the main internal reinforcement had shifted within the formwork during the concrete pour. The stirrups

were tied to the flexural reinforcement to create a “cage”. As the concrete was cast, it was manually

shoveled down the length of the formwork. During this process, the reinforcing cage shifted to one end.

The diagonal tension failure was then a result of a combination of the main flexural steel not extending

into the support region at all and the lack of stirrup steel at the support. These justifications can be clearly

seen in the failure exhibited in Figures 5-16 and 5-17. The ultimate load and deflection at ultimate

attained by this specimen indicates that the shear failure was nearly identical to the ultimate flexural

failure for the member. Furthermore, upon examination of the load deformation response for the member,

it can be seen that it exhibited very similar behavior as beams W1 and W3 and therefore, the experimental

results can be used in further discussion.

The failure of beam W2 by diagonal tension prompted a re-evaluation of the testing procedure. It

was decided to move the beam supports inward 6" (3" from each end) and add an additional 5/8" steel

plate in between the support roller and beam to distribute reaction force to a larger length at the end of the

beam. The spacing of the two loading cylinders was also reduced by 6” to give the same applied bending

moment to the member as previously applied. This plate can be clearly seen in the subsequent figures

used in the discussion of the epoxy adhesive anchored beams. As evidenced by the testing results of

MUST-97-1: 31

specimens E2, C3, W3 and E3 the modification of the test procedure and setup succeeded in solving the

likely problem of rebar cage shifting.

5.5 Testing of Epoxy-Anchor Beams

As in the previously discussed tests, the epoxy anchor specimens were white-washed for crack detection

as well as the channel reinforcement. Beam E1 was placed within the test frame with 15'-0" centerline to

centerline support spacing with 5'-0" load separation, while beams E2 and E3 were set up with 14'-6"

support spacing with 4'-6" load separation. The reason for this change in setup was discussed in the

previous section. The typical setup for the epoxy-adhesive specimens is shown in Figure 5-18. Also, the

exposed length of threaded rod beyond the channel was much less in the case of epoxy-adhesive anchors.

The differences can be seen in Figure 5-19. This difference had no effects on the results. All specimens

were tested until failure characterized in a similar manner as for the wedge anchor beams using

monotonic loading.

Failure of the epoxy anchor specimens were all characterized by shearing of the anchors followed

by a very subtle compression failure of the concrete in the constant moment region of the member. Prior

to failure, there was significant cracking of the concrete in the constant shear zone and the constant

moment region of the member. Pertinent data related to the tests are given in Table 5-1. As one can see,

the deflections at ultimate are very similar to those measured in the wedge anchor specimens.

Furthermore, the average failure load for the specimens are very similar. The differences in the average

load at first crack are significant, however, resulting from experimental error and/or inaccuracy in visually

detecting cracking from one specimen to another. Cracking patterns and deformations at ultimate for a

typical failure of an epoxy anchored member are given in Figures 5-20 through 5-23. The epoxy-

adhesive specimens exhibited similar ‘delaminating’ of the reinforcing channel to that of the wedge

anchor specimens. The delaminating of the channel can be seen in Figure 5-24. This separation of the

channel occurred simultaneously with the failure of the bolts and the ultimate load condition. Figure 5.25

MUST-97-1: 32

is a close up of the underside of the channel in the bolt failure region. As one can see, no distress of the

channel is exhibited.

Table 5-1 illustrates the very encouraging consistency in the results between epoxy-adhesive and

wedge-type expansion anchor specimens. All channel reinforced members (neglecting W2) failed with

very comparable ultimate loads and deflections. This is to be expected since the both anchor types were

capable of supporting nearly the same shear force. There is, however, a rather wide variation in the

average load to first visible crack. This could have been a result of visual error in detecting the cracking

as a result of the small vertical deflection of the beam. That is to say, the beam simply was not deflecting

as much as in the case of the control members, and therefore, cracks were difficult to catch at the instant

of there formation.

5.6 Load Deformation Behavior of Specimens

The load deformation response of the specimens are also useful to an understanding of the externally

reinforced member’s behavior. Table 5-2 contains information related to the deformations of all tested

specimens at the ultimate load condition. Also, the percentage decrease in deflection at ultimate load is

given. From the data it can certainly be said that the externally reinforced members are much stiffer than

their control counterparts. This is to be expected since the transformed moment of inertia for the new

cross-section in the case of the channel reinforced member has increased.

In addition to single deformation values of deformation at ultimate load, the load-deformation

response of the members throughout the loading history is important. Figures 5-26 through 5-28 illustrate

the load-deformation response of all specimens tested. The externally reinforced members (using both

wedge and epoxy anchors) exhibit very consistent load deformation response. Externally reinforced

specimens, E1 and W1, exhibit some redistribution of force and sustained deformation after the ultimate

load is achieved. However, the load level for this sustained deformation is significantly lower for

specimen E1. Specimens, E2, E3, W2 and W3 do not exhibit any sustained deformation after the ultimate

load condition. Therefore, one can consider the failure of the externally reinforced member as brittle and

MUST-97-1: 33

outside the philosophy of reinforced concrete design. (The general philosophy of design in reinforced

concrete is to provide member ductility at the ultimate load condition.) The externally reinforced

members do not reflect ductility normally associated with reinforced concrete members.

The lack of ductility in the failure mode can be directly attributable to the sudden shear failure of

the anchors. Recalling the design procedure used for the externally reinforced members; the shear

strength of the connector was the governing failure mode in assigning an ultimate superimposed load to

the member. This failure mode was achieved in the specimens, so that although the failure was non-

ductile, it was expected. If space is available on the existing reinforced concrete member to provide

enough anchors to ensure the failure mode of the externally reinforced member is governed by tensile

failure of the channel, it is believed the ductility requirements can be met. Also, there is the opportunity

for providing fuses at the anchor holes in the external reinforcing member to shift the failure mode into

the channel (from the anchor) to return the ductility to the externally reinforced member.

The increase in stiffness of the externally reinforced members can also be seen in Figures 5-26

through 5-28. A service load level reduction relative to the ultimate load for each member (externally

reinforced and control) can be approximated by,

(16)

SLR 'Resistance Factor

Load Factor

'N(

'0.851.7

' 0.5

One can consider a service level of loading to be approximately 7,500 lbs for the control (un-reinforced)

members. At this load level, the increase in stiffness (decrease in deflection) of the externally reinforced

members is apparent. Furthermore, this increase is consistent for all externally reinforced specimens,

without preference for one type of anchor over another.

Overall, the externally reinforced specimens displayed consistent expected behavior relative to

ultimate load and load-deformation response. The load-deformation behavior is consistent for both

wedge type and epoxy adhesive type anchors.

MUST-97-1: 34

5.7 Strain Distribution Within the External Channel

Both the wedge type and epoxy adhesive anchor specimens were fitted with strain gages on the surface of

the external channel reinforcement. It should be noted that specimens W1 and E2 had questionable strain

readings within the web as a result of possibly damaged gages. Therefore, these specimens are not

present in the discussion.

Strain within the channel for the wedge type expansion anchor specimens are contained in Figures

5-29(a) and 5-29(b). The average strain in the flanges of the channel and the strain in the web are

presented in the figures as a function of the average applied load. The average flange strain was used as

the gages were not mounted in the same position (vertically). As one can see from the data, the flange

strain and web strain start out virtually identical for the first 5000 lbs of applied (average) load. At this

point, one could say that the distribution of strain (and therefore, the tensile force) within the channel is

essentially uniform. However, once the load level equal to 5000 lbs. is exceeded, the strain tends to

deviate significantly from one another. This separation widens as loading is increased on the beam

member. There is an obvious gradient of strain through the depth of the channel. The strain in the

internal reinforcing steel is also shown in the figures. Based on the vertical locations of the internal

reinforcement relative to the external channel, the strain in the re-bar is much less than that in both the

average flange and web strain in the channel at load levels below approximately 8000 lbs. At

approximately 8,000 lbs, the strain in the internal reinforcement begins to exhibit significant nonlinear

behavior. Furthermore, the strain in the reinforcing steel increases significantly beyond that in the

channel. If perfectly composite action was occurring within the member, the strain in the channel should

be significantly above that in the re-bar at any given load level. However, as a result of slip at the

interface of the channel and concrete member, linear strain distribution is lost. Therefore, the member

behaves in a partially composite manner beyond about 8,000 pounds of average applied load (and at

ultimate).

Similar strain behavior is exhibited for the epoxy adhesive anchor bolted members. The average

flange strain and the web strain in the external channel reinforcement are given in Figures 5-30(a) and 5-

MUST-97-1: 35

30(b). Unfortunately, the strain gage on the internal reinforcement was non-functional for these

members. However, the overall similarity in strain behavior within the channel between the wedge type

expansion anchor and the epoxy adhesive anchor specimens can be seen. The maximum strain achieved

at the ultimate load for all anchor specimens are comparable. As a result of the data obtained for the

epoxy adhesive anchor, it is believed that similar behavior for the internal reinforcement would have been

obtained with ‘good’ gages and therefore, the discussion of the wedge type anchor specimen behavior is

applicable in this case.

It is interesting to see how the strains in the web of the external channels vary with the type of

anchor bolt used. The strain at the web is useful, since the vertical distance from beam neutral axis to

extreme channel web face is nearly the same for all specimens. The same can not be said about the gages

mounted on the flanges of the channel. Figure 5-31 illustrates the variation of microstrain in the channel

webs for the various anchor types as the average applied load is increased. It can be seen that all

specimens had virtually identical strain behavior and therefore, the wedge and epoxy anchors performed

in nearly identical fashion. Thus, in this application the anchor types makes essentially no difference to

strain behavior and transfer of force from the channel to the concrete member.

6.0 Evaluation of Proposed Design Methodology

The design procedure outline in Section 3.0 for the design of external reinforcement for existing

reinforced concrete members can now be evaluated and discussed in the light of the experimental results.

Table 6-1 illustrates the theoretical ultimate load predicted using the procedure from Section 3.0 and the

measured ultimate loads obtained via experiment. The load deformation response for the specimen

groups are given in Figures 6-1 through 6-3.

All specimens, with the exception of W1 and W2 attained the theoretical ultimate load. Specimen

W2 suffered the premature diagonal tension (shear-type) member failure discussed in previous sections.

Member W1 is a wedge type expansion anchor specimen. In this case, it is believed that the natural

variability in the construction technique resulted in a slightly inadequate torque being provided to this

MUST-97-1: 36

anchor set. However, the deficiency with respect the theoretical is small. Specimen W3 is consistent

with specimens E1, E2, and E3 with respect to attained theoretical ultimate load levels.

Overall, the design methodology proposed is adequate in predicting the ultimate load behavior of

the externally reinforced concrete members using structural steel channels with wedge and epoxy

adhesive anchors. It is difficult to assess the reliability of the method with the results of only nine

specimens. However, in the case of the epoxy adhesive anchors, the reliability of the technique and

design procedure appears high. The reason for this is that the epoxy anchors are not as sensitive to the

installation torque during construction to set the anchor. The wedge type expansion anchors are more

sensitive to the installation procedure. It should be noted that the procedures outlined in RawlPlug(1994)

were followed rigorously during the installation of the epoxy adhesive anchors. The benefits of this

adherence are apparent in the experimental results. However, in the case of the wedge type expansion

anchors, there was no defined torque recommended by RawlPlug(1994) for installation. A three-to-four

turns after contact is an extremely variable definition of application torque. This variability displayed

itself in the experimental results for the wedge type expansion anchor specimens.

7.0 Conclusions

An experimental investigation to determine the feasibility of using externally attached structural steel

channels to the tension face of reinforced concrete beams as additional external reinforcement has been

presented. The experimental program consisted of fabrication of nine test specimens: three control

beams without external reinforcement, three externally reinforced members with wedge type expansion

anchors, and three specimens with epoxy adhesive anchors. All externally reinforced members utilized a

C5x6.7 structural steel channel as reinforcement.

A design procedure was presented for determining the strength of the externally reinforced

member. The procedure suggested is based on a strength of materials approach and basic mechanics of

reinforced concrete design. Design values pertaining to anchor strength are taken from corporate

literature; RawlPlug(1994). The specimens designed in the present study assumed that anchor shearing is

MUST-97-1: 37

the controlling mode of failure for the member. The reason for this is the space limitations on the tension

face of the RC beam and the edge distance and spacing requirements for the anchors. If a smaller channel

were used in the design, perhaps the controlling mode of failure would be yielding of the external

reinforcement rather than anchor shearing. Ductile failures may then be expected. Furthermore, steel

plates could be bolted to the sides of the existing RC member. Mounting steel elements to the sides of the

member could minimize interference with the main flexural steel in the RC member. Also, these plates

could have small additional cross-sectional areas and therefore, could lead to ductile failures.

The nine test specimens were loaded to failure in four point bending. Variability in ultimate loads

for control specimens was small. The variability in the ultimate loads for the externally reinforced

members was smaller than the control members since the failure was due to anchor shear failure. The

shear failure of the anchors (both epoxy adhesive and wedge) were very reliable and predicted. The six

externally reinforced members all achieved nearly the desired ultimate loading predicted using the design

procedure. It should be noted that no reliability or workmanship factors were employed in the analysis

for strength prediction. Therefore, the ultimate load values should only be used as a schematic reference.

More testing could be done to establish reliability factors for design purposes. The measurements of

strain within the specimens indicate that the internal reinforcement in the control members has undergone

nonlinear behavior and therefore yielding of the internal steel can be assumed for design purposes. The

strain in the external reinforcement, although greater than the internal reinforcement at lower load levels,

is less than that in the internal reinforcement at higher levels indicating partially composite behavior. The

strain measured in the webs of the various externally reinforced specimens indicated that the variability

due to anchor type in providing the partially composite behavior was minimal. Lastly, the strain

measured in the flanges and web of the external reinforcement indicated a gradient of stress through the

channel. Therefore, a uniform distribution of stress could be considered, but this stress would be an

‘average’ over the channel depth.

Overall, the design methodology proposed for the external reinforcement of existing RC beams is

adequate. Both strength of the member and stiffness are improved. One deficiency of the reinforced

MUST-97-1: 38

member is the lack of ductility at failure. This non-ductile behavior arises from anchor shear being the

controlling failure mechanism. If yielding of the channel could be guaranteed, this non-ductile failure

could be avoided. Therefore, the proposed external reinforcing method has the opportunity to preserve

the RC design philosophy of ductile failure lacking in proposed methodologies using GRFP and FRP

fabrics.

8.0 References

1.) ACI (1995), Building Code Requirements for Structural Concrete (ACI 318-95). American

Concrete Institute. Detroit, MI.

2.) Arduini, A., Di Tommaso, Nanni, A. (1997a) “Brittle Failure in FRP Plate and Sheet Bonded

Beams”, ACI Structural Journal, Vol. 94, No. 4, pp. 363-370.

3.) Arduini, A., Di Tommaso, Nanni, A. (1997b) “Parametric Study of Beams with Externally Bonded

FRP Reinforcement”, ACI Structural Journal, Vol. 94, No. 5, pp. 493-501.

4.) Chajes, Michael J.; Thomson, Theodore A. Jr.; Januszka, Ted F.; and Finch, William W. Jr. (1994),

“Flexural Strengthening of Concrete Beams Using Externally Bonded Composite Materials,”

Construction and Building Materials, V.8, No.3, pp191-201.

5.) Hussain, M.; Sharif, Alfarabi; Basunbul, I.A.; Baluch, M.H.; and Al-Sulaimani, G.J. (1995),

“Flexural Behavior of Precracked Reinforced Concrete Beams Strengthened Externally by Steel

Plates,” ACI Structural Journal, V.92, No.1, Jan.-Feb., pp14-22.

6.) Jones, R.; Swamy, R.N.; and Charif, A. (1988), “Plate Separation and Anchorage of Reinforced

Concrete Beams Strengthened by Epoxy-Bonded Steel Plates,” Structural Engineer, V.66, No.5,

March, pp85-94.

7.) Oey, Hong Sioe and Aldrete, Carlos J. (1996), “Simple Method for Upgrading an Existing

Reinforced Concrete Structure,” Practice Periodical on Structural Design and Construction, V.1,

No.1, Feb., pp47-50.

MUST-97-1: 39

8.) Rawlplug (1994), The Rawlplug Company Inc., Drilling & Anchoring Systems Design Manual,

New Rochelle, NY.

9.) Sharif, Alfarabi; Al-Sulaimani, G.J.; Basunbul, I.A.; Baluch, M.H.; and Ghaleb, B.N. (1994),

“Strengthening of Initially Loaded Reinforced Concrete Beams Using FRP Plates,” ACI Structural

Journal, V.91, No.2, March-April, pp160-168.

10.) Swamy, R.N.; Jones, R.; and Charif, A. (1989), “The Effect of External Plate Reinforcement on the

Strengthening of Structurally Damaged R.C. Beams,” Structural Engineer, V.67, No.3, Feb., pp45-

54.

11.) Wang, Chu-Kia and Salmon, Charles G., (1992). Reinforced Concrete Design. Harper Collins

Publishers Inc.

12.) Ziraba, Y.N.; Baluch, M.H.; Basunbul, I.A.; Sharif, A.M.; Azad, A.K.; and Al-Sulaimani, G.J.

(1994), “Guidelines Toward the Design of Reinforced Concrete Beams with External Plates,” ACI

Structural Journal, V.91, No.6, Nov.-Dec., pp 639-646.

MUST-97-1: 40

- This page intentionally left blank -

MUST-97-1: 41

- This Page Intentionally Left Blank -

MUST-97-1: 42

Table 4-1: 28-Day Compressive Strengths for Concrete Batches Used in Beam Specimen Construction.

BeamSet

Cylinder No. orAverage

Applied CompressiveLoad (lbs.)

28-Day CompressiveStrength (psi)

C1E1W1

1 131248 4645

2 137123 4850

3 135916 4807

Average 134796 4767

C2E2W2

1 123000 4350

2 111177 3932

3 117446 4154

Average 117208 4145

C3E3W3

1 138349 4893

2 134453 4755

3 137637 4868

Average 136813 4839

MUST-97-1: 43

Table 4-2: Sectional and Material Properties for Reinforcing Steel (Re-Bars) for Test Specimens

Bar

SampleNumberor Avg.

YieldStress(ksi)

UltimateStress(ksi)

ElasticModulus

(ksi)

#3 Bars(Batch 1)

1 77.15 102.7 38576

2 60.95 103.3 30473

3 70.50 - 35250

Average 69.53 103.0 34766

#3 Bars(Batch 2)

1 67.57 109.0 33787

2 70.49 111.1 35244

3 56.63 106.1 28317

Average 64.90 108.7 32447

#5 Bars

1 66.72 - 33359

2 68.99 109.1 34494

3 70.20 109.2 35103

Average 68.64 109.1 34318

Table 4-3: Average dimensions for concrete beam specimens: h = height (in.), b = width (in.) andaverage embedment depths in inches for anchors.

Dimension C1 C2 C3 W1 W2 W3 E1 E2 E3

h 18.26 18.21 18.14 18.17 18.21 18.15 18.24 18.18 18.24

b 10.14 10.03 10.05 10.05 10.05 10.09 10.19 10.03 10.05

Embedment - - - 3.94 4.35 4.02 5.57 5.57 5.43

MUST-97-1: 44

Table 4-4: Section and Material Properties for Structural Steel Channels Used as External FlexuralReinforcement.

SpecimenDesignation

Yield Stress(psi)

Elastic Modulus(psi)

#1 48417 28015800

#2 47272 36954500

#3 48300 22105100

Average 47996 29053727

Table 5-1: Pertinent Data Related to the Testing of the Nine Beam Specimens.

SpecimenDesignation

Avg. Load atFirst Crack

(lbs.)

Avg. FailureLoad (lbs.)

Avg. CenterlineDeflection atFailure (in.)

Failure Mode

C1 4500 16310 3.65compression failure

of concrete

C2 4000 17780 3.27compression failure

of concrete

C3 3300 16280 3.28compression failure

of concrete

E1 7000 28660 1.21shear failureof anchors

E2 6000 28050 1.10diagonal tensionfailure at support

E3 6250 30315 1.08shear failureof anchors

W1 9000 29310 1.04shear failureof anchors

W2 6000 30400 1.48shear failureof anchors

W3 7600 31070 1.44shear failureof anchors

MUST-97-1: 45

Table 5-2: Comparison of Average Centerline Deflection at Ultimate Load.

SpecimenDesignation

Deflection at UltimateLoad (in.)

Percentage Decrease inDeflection Over Control Beam

C1 3.65 n.a.

C2 3.27 n.a.

C3 3.28 n.a.

E1 1.04 351

E2 1.48 221

E3 1.44 228

W1 1.21 300

W2* 1.10 297

W3 1.08 304

* - Indicates specimen that suffered from unexpected shear failure at the support.

Table 6.1: Comparison of Theoretical Versus Measured Ultimate Loads Using Design Procedure.

SpecimenDesignation

Theoretical UltimateLoad (lbs.)

Measured UltimateLoad (lbs.)

PercentageDifference

C1 14600 16310 +11.7

C2 14400 17780 +23.5

C3 14500 16280 +12.3

E1 28500 29310 +2.8

E2 27900 30400 +9.0

E3 29600 30320 +2.4

W1 29600 28700 -2.8

W2* 29200 28010 -4.1

W3 29600 30320 +2.4

* - Indicates specimen that suffered from unexpected shear failure at support.

MUST-97-1: 46

Figure 2-1: Internal equilibrium for the typical control beam.

Figure 2-2: Typical internal reinforcement layout for the control beams.

Figure 3-1: Internal equilibrium for externally reinforced member.

MUST-97-1: 47

Figure 3-2: Reinforcement layout for typical externally reinforced member.

Figure 3-3: External channel configurations with anchor layout and spacing: (a) wedge-typeexpansion anchor specimens, (b) epoxy adhesive anchor specimens.

MUST-97-1: 48

Figure 5-1: Mounting of General Purpose Strain Gages to the Reinforceing Channel on a TypicalRetrofitted Beam.

MUST-97-1: 49

(a)

(b)

Figure 5-2: Structural Testing Setup: (a) Illustration of Testing Frame, Loading Cylinder, Specimen, andSupport Mechanism; (b) LVDT Mounting, Data Acquisition System and Hydraulic Pump.

MUST-97-1: 50

Figure 5-3: Load Cells and Roller Supports Located at Points of Load Application on the BeamSpecimen(s).

MUST-97-1: 51

Figure 5-4: LVDT and LVDT ‘Tab’ for Measuring Vertical Deformation of the Beam Specimen(s).

MUST-97-1: 52

(a)

(b)

Figure 5-5: Specimen C1 at Failure Load Condition: (a) Central Region of Flexural Cracking, (b) Zoneof Cracking Near Support(s).

MUST-97-1: 53

Figure 5-6: Zone of Crushing Exhibited in All Control Beam Specimens Located Within the Length ofBeam Bounded by Loading Cylinders.

Figure 5-7: Typical Deflected Shape of Control Beam at Failure Prior to Final Load Removal.

MUST-97-1: 54

Figure 5-8: Typical Wedge Type Anchor Specimen (W1 shown here)in Test Apparatus.

Figure 5-9: Close Up Illustrating Position and Orientation of Wedge Type Expansion AnchorsPrior to Testing for Typical Specimen.

MUST-97-1: 55

Figure 5-10: Permanent Deformation Typical of Wedge Type Expansion Anchor SpecimenSubsequent to Load Removal.

Figure 5-11: Cracking in Central Region of Member Typical of Wedge Type Expansion AnchorSpecimens.

MUST-97-1: 56

Figure 5-12: Cracking at Support where Bolt Failure Occurred Typical of Wedge Type ExpansionAnchor Specimens.

Figure 5-13: Cracking at Opposite Support from Bolt Failure Side Typical of Wedge Type ExpansionAnchor Specimens.

MUST-97-1: 57

Figure 5-14: Reinforcing Channel ‘Delamination’ Typcial of Wedge Type Expansion AnchorSpecimens.

Figure 5-15: Close Up View of Expansion Anchors After Load Removal in Region of Anchor FailureTypical of Wedge Type Expansion Anchor Specimens.

MUST-97-1: 58

Figure 5-16: Wedge Type Expansion Anchor Specimen W2 Displaying Unexpected Shear Failure Near theSupport.

Figure 5-17: Close Up of Shear Failure Near Support Roller for Wedge Type Expansion Anchor SpecimenW2.

MUST-97-1: 59

Figure 5-18: Typical Epoxy Adhesive Specimen in Testing Appratus.

Figure 5-19: Epoxy Adhesive Specimen and Wedge Type Specimen in ‘Rolled Over’ ConfigurationIllustrating the Differences in Bolt Shank Extensions.

MUST-97-1: 60

Figure 5-20: Deformed Shape of Epoxy Adhesive Specimen E2 Typical of all Epoxy Adhesive SpecimensPrior to Load Removal at Failure Condition.

Figure 5-21: Crack Pattern at Support Opposite Bolt Failure Side Typical of Epoxy Adhesive Specimens.

MUST-97-1: 61

Figure 5-22: Cracking Pattern in Central Region of Beam (Between Loading Cylinders) Typical of EpoxyAdhesive Specimens.

Figure 5-23: Cracking Pattern In Region of Bolt Failure Typical of Epoxy Adhesive Specimens.

MUST-97-1: 62

Figure 5-24: Delamination of External Reinforcing Channel Typical of Epoxy Adhesive Specimens.

Figure 5-25: Close Up View of Beam Soffit Showing Failed Bolts Near Support Typical of Epoxy AdhesiveSpecimens.

MUST-97-1: 63

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

5000

10000

15000

20000

25000

30000

35000

Figure 5-26: Load Deformation Response for Beams Specimens in Group 1.

MUST-97-1: 64

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

5000

10000

15000

20000

25000

30000

35000

Figure 5-27: Load Deformation Response for Beams Specimens in Group 2.

MUST-97-1: 65

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

5000

10000

15000

20000

25000

30000

35000

Figure 5-28: Load Deformation Response for Beams Specimens in Group 3.

MUST-97-1: 66

0 200 400 600 800 1000 1200 14000

5000

10000

15000

20000

25000

30000

0 200 400 600 800 1000 1200

0

4000

8000

12000

16000

20000

24000

28000

32000

(a)

(b)

Figure 5-29: Load vs. Microstrain in Wedge type Expansion Anchor Specimens: (a) Specimen W2, (b)Specimen W3.

MUST-97-1: 67

0 100 200 300 400 500 6000

4000

8000

12000

16000

20000

24000

28000

32000

0 100 200 300 400 500 600 7000

5000

10000

15000

20000

25000

30000

35000

(a)

(b)Figure 5-30: Load vs. Microstrain in Epoxy Adhesive Type Expansion Anchor Specimens: (a) Specimen E1,

(b) Specimen E3.

MUST-97-1: 68

0 100 200 300 400 5000

4000

8000

12000

16000

20000

24000

28000

32000

Figure 5-31: Average Load vs. Micro-Strain in External Channel Reinforcement Web as a Function of AnchorType.

MUST-97-1: 69

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

5000

10000

15000

20000

25000

30000

35000

Figure 6-1: Load Deformation Response for Beam Specimens in Group 1.

MUST-97-1: 70

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

5000

10000

15000

20000

25000

30000

35000

Figure 6-2: Load Deformation Response for Beam Specimens in Group 2.

MUST-97-1: 71

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

5000

10000

15000

20000

25000

30000

35000

Figure 6-3: Load Deformation Response for Beam Specimens in Group 3.

MUST-97-1: 72

$1 ' 0.85& 0.05fc'& 4000

1000' 0.85& 0.05 4000& 4000

1000' 0.85

Dbal '0.85 fc' $1

fy

8700087000% fy

'0.85(4000)(0.85)

6000087000

87000% 60000' 0.0285

Dact' Drebar% Dchannel 'As,rebar

bd1

%As,channel

bd2

'3(0.31 in.2 )10'' (15.31'' )

%1.97 in.2

10'' (18.48'' )' 0.0167

0.75Dbal ' 0.75(.0285) ' 0.0214 > Dact ' 0.0167 U ok

Appendix - A: Design Example for Externally Reinforced Beam

This example illustrates the steps necessary for the preliminary design of an externally reinforced

concrete beam used for testing. The design procedure is the same for both types of anchoring systems

used. The concrete and rebar strengths and beam dimensions were assumed, with corrections made in the

final design for the actual values of these variables to get theoretical ultimate strengths. The beams are

the same as the control beams with the addition of a structural steel channel mounted to the bottom.

Data:

b = 10" h = 18" L = 15'-0"

fc! = 4000 psi fy,rebar = 60000 psi fy,stirrup = 60000 psi

cover = 2" d1 = 15.31" (see Figure 3-1) d2 = 18.48" (see Figure 3-1)

As,rebar = 3-#5 bars

Solution:

Part 1

The following is the design procedure to calculate the capacity of the externally reinforced concrete

beams. The first step is to choose a channel section. Try a C5 x 6.7 structural steel channel. To insure an

under-reinforced section, Dact must be less than 0.75Dbal,

Calculate the nominal moment capacity and moment due to superimposed live load,

MUST-97-1: 73

a '

(As fy )rebar

% (As fy )channel

0.85 fc' b

'(0.93 in.2)(60000 psi) % (1.97 in.2)(36000 psi)

0.85(4000 psi)(10'')' 3.73 in.

Mn ' Mult ' (As fy )rebar

d1&a2

% (As fy )channel

d2&a2

'

(0.93 in.2 )(60 ksi ) 15.31''& 3.73''2

12

%

(1.97 in.2 )(36 ksi ) 18.48''& 3.73''2

12' 160.7 k @ft

P '3ML

L'

3(155.4 k @ft )15'

' 31.1 kips

Vc ' 2 fc'bd '2 4000 psi (10'' )(15.31'' )

1000' 19.4 kips

s 'Av fy d

P& Vc

'2(0.11 in.2 )(60 ksi)(15.31'' )

(31.1 k& 19.4 k)' 17.3 in.

Vs' P & Vc ' 31.1&19.4 ' 11.7 kips

4 fc' bd ' 2Vc ' 38.8 kips

The superimposed live load, P, the beam can carry with loads applied at third points is,

The stirrups are designed by first calculating the shear strength of the concrete section,

Since this is less than P, shear reinforcement must be provided. Spacing for #3 stirrups is,

With,

and Vs < , s must be less than,4 fc' bd

MUST-97-1: 74

s 'd2'

15.31''2

' 7.66 in <Av fy

50b'

2(0.11 in.2 )(60000 psi)50(10'')

' 26.4 in. U ok

ML '13

(P)(L) ' 13

(25 kips)(15' ) ' 125.0 kip @ft

Mn ' Mult ' ML% MD

' 125.0 %(0.150 kcf )(10'')(18'')(15' )2

8(144)' 130.3 kip @ft

Tanchor '

Mult& (As fy )rebar

d1&a2

d2&a2

'

12(130.3 k@ft)& (0.93 in.2)(60 ksi) 15.31''& 4''2

18''& 4''2

' 51.3 kips

Thus, a spacing of d/2 controls. Use 7½ in. for a distance of 5 ft. from each support, with the first stirrup

at 3 in. from the end. The center 5 ft. of the beam is not experiencing any shear due to superimposed

loading, but it was decided to put stirrups in this area at 12 in. to have vertical steel in this region to resist

shear from the beam self-weight.

Part 2

In this part, shear failure of the anchors is the controlling mode on which the reinforced strength is based.

It was decided to design the beams to fail by shearing of the bolts at a load corresponding to P = 25 kips.

A concrete strength of 4000 psi and steel yield strength of 60000 psi for reinforcement was assumed for

the preliminary calculations and is used in the following design procedure for the anchor bolts. Note that

the value for d2 is now the distance to the shear interface of the anchors and the beam.

The first step is to calculate the superimposed live load moment due to the point loads using the

equation given below,

The dead weight of the beam is added to this to get the nominal moment capacity of the beam,

Tanchor is computed based on an assumed value of ‘a’ and the assumption that the internal reinforcing steel

is at yield. Try a = 4",

Calculate arevised based on this value of Tanchor using,

MUST-97-1: 75

arevised '

(As fy )rebar

% Tanchor

0.85 fc' b'

(0.93 in.2 )(60 ksi)% 51.3 kips0.85(4 ksi)(10'' )

' 3.15 in.

Tanchor '

Mult& (As fy )rebar

d1&a2

d2&a2

'

12(130.3 k@ft )& (0.93 in.2 )(60 ksi) 15.31''& 3.15''2

18''& 3.15''2

' 48.5 kips

arevised '

(As fy )rebar

% Tanchor

0.85 fc' b'

(0.93 in.2 )(60.0 ksi )% 48.5 kips0.85(4 ksi)(10'')

' 3.07 in.

Calculate a new value of Tanchor and recalculate arevised ,

Continuing the above iterations, the answer converges at Tanchor = 48.3 kips and arevised = 3.06 in..

The anchors will now be designed for a shear of 48.3 kips. Rawlplug (1994), is used to obtain the

design values and spacing requirements for the anchors. A carbon steel Rawl-Stud wedge style expansion

anchor is used. For a ½" diameter anchor, a depth of embedment assumed to be 4 inches, and a concrete

strength of 4000 psi; an ultimate (pure) shear load capacity of 7535 lbs. is obtained from Table A-1

below; taken from the Rawlplug (1994).

Table A-1: Ultimate Shear Capacity for Rawl-Stud Anchors

Anchor

Size (in.)

Embedment

Depth (in.)

Guide

Torque (ft.-lbs)

2000 psi

Concrete (lbs)

4000 psi

Concrete (lbs)

6000 psi

Concrete (lbs)

1/2 2 - 1/4 60 7025 7150 7150

1/2 3 60 7200 7190 7295

1/2 4 60 7280 7535 7710

1/2 6 60 7280 7535 7710

Assuming that spacing and edge distance requirements are adequate, the number of anchors needed, N is,

MUST-97-1: 76

N 'Tanchor

Vult

'48.3 kips7.535 kips

' 6.4 anchors

Figure A-1:: Preliminary Layout for Wedge Style Expansion Anchors

Vult' ' Re Vult ' 0.75(7535 lbs.) ' 5651 lbs.

The anchors are placed within the end five feet of the beam, or in the constant shear zone. One should

round up to 7 or 8, but for a first iteration try 6 anchors within the end 5 feet of the beam on each side. A

preliminary anchor layout gives the following,

To obtain the maximum load in shear, a spacing of 10 anchor diameters (5") between anchors in all

directions should be used. An examination of the layout in Figure A-1 shows that all anchor spacing,

including the diagonal spacing between anchors, is greater than 10d. Therefore no reduction is needed for

spacing requirements.

An edge distance, E, of 12 anchor diameters (6") should also be used to obtain the maximum shear

load. The current layout includes an edge distance of 4¼" (8.5d), which is greater than the minimum

allowed of 5d. The load reduction factor, Re, for E = 8.5d is interpolated from the following table taken

from Rawlplug (1994).

Table A-2: Edge Distance Reductions for 1/2” diam. Rawl-Stud Anchors (shear only)

Edge Distance /

Reduction Factor

Edge Distances - shear only

12d 11d 10d 9d 8d 7d 6d 5d

Edge Distance 6 5 - 1/2 5 4 - 1/2 4 3 - 1/2 3 2 - 1/2

Re 1.00 0.93 0.86 0.79 0.71 0.64 0.57 0.50

A reduction of 0.75 is applied to the ultimate shear load capacity of 7535 lbs. to get,

The number of anchors now needed is,

MUST-97-1: 77

N 'Tanchor

Vult''

48.3 kips5.651 kips

' 8.5 anchors

Figure A-2: Final Layout for Wedge Style Expansion Anchors

Round up to ten anchors and try the layout shown in Figure A-2.

The spacing requirements of 10d is still met in all directions. The edge distance is still 4¼" which gives a

reduction of 0.75, the same reduction that was used the previous calculation. The answer has converged,

therefore use the layout shown in Figure A-2. The final step in the design is to check the channel strength

for block shear, bolt bearing, and yield of the anchor holes. The channel is okay for all of these checks.