ACI 355.1R.pdf

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ACI

355.1R-91

STATE-OF-THE-ART REPORT ON

(Reapproved 1997)

ANCHORAGE TO CONCRETE

Reported by ACI Committee 355

Patrick J. Creegan Harry A. Chambers

Chairman Secretary Edwin A. Burdette Robert W. Cannon Peter J. Carrato Peter D. Courtois Rolf Eligehausen Raymond R. Funk C. Raymond Hays Paul R. Hollenbach Gerard B. Hassehvander Harry B. Lancelot III*

Douglas D. Lee Alexander Makitka, Jr. Donald F. Meinheit Richard S. Orr Moorman L Scott George A. Senkiw Harry Wiewel Jim L Williams Richard E. Wollmershauser

*Committee Chairman during the formative years of this report.

For the first time concrete anchoring knowledge based on worldwide test programs is presented in a state-of-the-art document. Performance of different anchor types, including cast-in-place, grouted, expansion, torque-controlled, chemical (adhesive), and undercut anchors is presented in both uncracked and cracked concrete. Failure modes in tension and shear, spacing and edge distance, group performance, and load displacements are offered. The effect of loading conditions for structural supports, column bases, and pipe supports as well as base plate flexibility, how load is transferred to anchors, and ductility are discussed. Design criteria and existing code requirements, both domestic and foreign, are presented.

KEYWORDS: Adhesive anchors; anchorages; anchors; anchor groups; base plates; bolts; cast-in-place anchors; chemical anchors; code

requirements; combined loads; compression zone; concrete; cracked concrete; creep; deformation; design criteria; drilling; ductility; dynamic loads; edge distance; embedment; expansion anchors; failure modes; fatigue loads; fasteners; flexible base plates; grouting; loads; load transfer; load-displacement; post-installed anchors; preload; pullout; seismic loads; shear loads; slip; spacing; spalling; static loads; stiffness; studs; structural design; tensile strength; tension loads; tension zone; temperature; torque; torque-controlled anchors; ultimate strength; undercut anchor, yield strength.

FORWARD

This state-of-the-art report on anchorage to concrete is the first of a two-volume project being undertaken by ACI Committee 355. The second volume, currently being developed, is a design manual. This first volume includes no design aids or procedures, per se, but with emphasis on behavior will serve as the guide for preparation of the second volume.

Committee 355 is working with Committees 349 and 318 toward the objective of including the subject of anchorage to concrete in ACI 318-95.

ACI Committee Reports, Guides, Standard Practices, and Commentaries are intended for guidance in designing, planning, executing, or inspecting construction, and in preparing specifications. Reference to these documents shall not be made in the Project Documents. If items found in these documents are desired to be a part of the Project Documents, they should be phrased in mandatory language and incorporated into the Project Documents.

ACI 355.1R-91 became effective JuIy 1, 1991. Copyright 0 1991, American Concrete Institute.

All rights reserved including rights of reproduction and use in any form or by any means, including the making of copies by any photo process, or by any electronic or mechanical device, printed or written or oral, or recording for sound or visual reproduction or for use in any knowledge or retrieval system or device, unless permission in writing is obtained from the copyright proprietors.

355.1 R-l

Copyright American Concrete Institute

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TABLE OF CONTENTS

Chapter 1-Introduction, p 355.1R-2 1.1 Purpose

1.2 Significance of the subject 1.3 Scope

Chapter 2-Types of anchoring devices, p 355.1R-2 2.1 Introduction 2.2 Scope 2.3 Anchor systems 2.4 Cast-in-place systems 2.5 Post-installed systems

Chapter 3-Behavior of anchors, p 355.1R-9 3.1 Introduction

3.2 Behavior of anchors in uncracked concrete 3.3 Behavior of anchors in cracked concrete 3.4 Behavior of cast-in-place anchor bolts in

uncracked concrete piers 3.5 References

Chapter 4-Design considerations, p 355.1R-53 4.1 Introduction 4.2 Functional requirements 4.3 Materials 4.4 Design basis 4.5 Construction practices 4.6 References

Chapter 5-Construction considerations, p 355.1R-60 5.1 Introduction 5.2 Shop drawings/submittals 5.3 Tolerances 5.4 Installation of anchors 5.5 Inspection 5.6 Grouting 5.7 Field problems

Chapter 6-Requirements in existing codes and specifications, p 355.1R-66

6.1 Introduction

6.2 Existing codes and specifications 6.3 Application and development of codes 6.4 References

Appendix A-Conversion factors, p 355.1R-71 Appendix B-Notations, p 355.1R-71

CHAPTER 1 -INTRODUCTION

1.1-Purpose

The purpose of this document is to summarize the current state of the art in anchorage to concrete.

1.2-Significance of the subject

To date, anchorage to concrete has received little attention in structural codes. Emphasis has been primarily on the tensile and shear capacities of anchorage devices. As designs became more sophisticated and analyses more exacting, more emphasis was placed on the transfer of loads through single anchors and anchor systems. It was recognized that performance of anchors controlled these load transfers, and that generally, failure modes at ultimate anchor capacities were important. There were no definitive design codes or anchorage performance criteria on which designers and installers could rely. Subsequently, a myriad of approaches were developed.

1.3-Scope

This state-of-the-art report summarizes anchor types and provides an overview of anchor per-formance and failure modes under various loading conditions in both uncracked and cracked con-crete. It covers design and construction considerations and summarizes existing require-ments in codes and specifications. References are given for further review.

CHAPTER 2 -TYPES OF ANCHORING DEVICES

2.1-Introduction

There are many types of devices used for anchoring structures or structural members to concrete. The design of anchorages, involving the selection and positioning of these devices has been based on the Engineer’s experience and judgment, private test data, manufacturers’ data, and existing (sometimes obsolete) code requirements. It is proposed to promote a design of anchorages that more consistently reflects the performance potential of each type of anchor.

2.2-Scope

This report relates to the most widely used types of anchor, in sizes ranging from 1/4 in. (6.35 mm) to 2 l/2 in. (63.5 mm) in diameter. Included for consideration are only those devices which can generally be considered bolt and insert-type

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anchors. Excluded from consideration are shear lugs, structural shapes, powder actuated fasteners, light plastic or lead inserts, hammer driven concrete nails, screw driven systems, and cables. These are excluded because there is a paucity of test data regarding their performance. The anchors included in this report are either commercially available or may be fabricated. 2.3-Anchor Systems

According to present practice, there are two

2.4-Cast-in-place systems

2 . 4 . 1 Embedded Anchors, Non

-Adjustable - These anchors may have an end attachment, such as a coil loop, head, nut, or plate, which will enhance anchorage properties and develop full potential strength by means of bond, and/or bearing, or both. Typical examples of these anchors are:

Common bolts - structural steel bolts placed with the head into the concrete. (Fig. 2.1) broad groups of anchoring systems: cast-in-place

systems (anchors installed before the concrete is cast) and post-installed systems (anchors installed in holes drilled after the concrete has been cast and cured). Table 2.1 identifies these two groups of anchors.

Table 2.1 -Types of anchors in concrete

Hooked "J" or "L" bolts

Threaded rod

Cast-in-place systems _{Reinforcing steel} Embedded, nonadjustable

Threaded inserts Common bolts

Hooked "J" & "L" bolts Threaded rod Reinforcing steel Threaded inserts Stud-welded plates Bolted connections Adjustable anchors Fig. 2.1 Fig. 2.2 Fig. 2.3 Fig. 2.4 Fig. 2.5 Fig. 2.6 Fig. 2.7 Fig. 2.8 Post-installed systems Bonded anchors Grouted anchors

Headed bolts or anchor Fig. 2.9

Chemical anchors With threaded rod With reinforcing steel

Fig. 2.10 Fig. 2.11

Stud welded plates - steel plates which have smooth bent hooked bars, deformed bars, or headed stud anchors. (Fig. 2.6)

Expansion anchors Torque-controlled

Heavy-duty sleeve anchor Fig. 2.12

Sleeve anchor Fig. 2.13

Shell expansion anchor Fig. 2.14

Wedge anchor Fig. 2.15

Rock/concrete expansion

anchor Fig. 2.16

2.4.2 Bolted connections-These anchors consist of headed bolts, as embedded or through-connectors. (Fig. 2.7). Deformation controlled Drop-in anchor Self-drilling anchor Stud anchor Fig. 2.17 Fig. 2.18 Fig. 2.19 Undercut

With predrilled under-cut

hole Fig. 2.20

Self undercutting Fig. 2.20

L

Steel plate

Fig. 2.7-Bolted connections

-bent, smooth or deformed threaded bars. Have been known to straighten out in pull-out tests. (Fig. 2.2) - straight threaded rod,

usually with coarse threads. (Fig. 2.3) - Stock or trade-name

rein-forcing bar (Fig. 2.4) - wire form or internally

threaded ferrule inserts, or coils, usually manu-factured with internal or external threads, with wire loop struts. Headed anchors made from smooth or reinforcing steel bar also fall into this category. (Fig. 2.5)

Plastic

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W a s h e r t a c k w e l d e d

Fig. 2.1- Common bolts

.

b

v *

Fig. 2.3 - Threaded rod

. -D

P

N o t e : E i t h e r ' J ' o r ' L ' ’ b o I ts c a n b e m a d e f r o m p l a i n o r t h r e a d e d r o d

Fig. 2.2-J- and L-bolts (not recommended)

Fig. 2.4 -Reinforcing steel

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a *

.

‘X

_{. .}

v *

B

.

Fig. 2.5 - Threaded inserts

We I d

Fig. 2.6 - Stud- welded plates

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can be adjusted for lateral position or depth (Fig. 2.8). They are normally used for attaching large machines or equipment bases. On thin floor slabs, the anchor bolt often goes through the concrete to develop the required anchor capacity. When the floor slab or foundation is very thick, the anchor can develop full capacity and still be embedded in the concrete. After the equipment or machine base is installed and leveled, grout is used to fill the void around the anchor. The anchor then acts similar to a cast-in-place anchor.

.

P - 4

Fig. 2.8-Adjustable anchors 2.5-Post-installed s y s t e m s

These anchors are installed in a hole drilled in the cured concrete. There are two basic groups of post-installed systems: bonded and expansion.

2.5.1-Bonded anchors

2.5.1.1 Grouted anchors-Grouted anchors are headed or headless bolts or threaded rods. They are set in predrilled holes with portland cement and sand grout or other commercially available premixed grout. (Fig. 2.9)

2.5.1.2 Chemical anchors-Chemical anchors are usually threaded rods (Fig. 2.10) or deformed bars (Fig. 2.11) which are bonded in place with two-part chemical compounds of polyesters, vinylesters, or epoxies. The chemicals are available in four forms: glass capsules, plastic cartridges, tubes, or bulk.

Glass capsules are inserted into the drilled hole, and then broken by the anchor rod when it is ro-tated and hammered into place, thereby mixing two components to cause a chemical reaction.

The plastic cartridges are used with a dispenser and a mixing nozzle which mixes the two parts, initiating a chemical reaction while installing the compound into the drilled hole. The anchor rod is then inserted into the hole completing the installation. The setting time is dependent on temperature, varying from a few minutes at 90o F up to several hours at 30o F.

The tube or “sausage” type contains two components which are mixed by kneading the tube, placing the mixture into the hole, and finally, inserting the anchor rod into the hole.

The bulk systems predominantly use epoxies, which are either premixed in a pot and used immediately, or pumped through a mixer and injected into the hole. The anchor is installed immediately afterward. Epoxies can be form-ulated to set up quickly or slowly (up to 36 hr curing time).

i n o r

* .v _c_{hemical from capsule} Fig. 2.10-Chemical anchor with threaded rod

n

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2.5.2 Expansion anchors-Expansion anchors are designed to be inserted into predrilled holes and then expanded by either tightening the nut (torque controlled expansion anchor, Sections 2.5.2.1 to 2.5.2.5), hammering the anchor (deformation controlled expansion anchor,

Sections 2.5.2.6 to 2.5.2.8), or expanding into an undercut in the concrete (undercut anchors,

Section 2.5.2.9). These anchors transfer the tension load from the bolt to the concrete by expansion pressures or forces through friction and/or keying against the side of the drilled hole. They often are supplied with a bolt, nut, and washer. The following sections describe the various types of expansion anchors.

2.5.2.1 Heavy duty, torque controlled sleeve

anchor-This type of anchor consists of a bolt or

threaded rod with nut and washer on one end and a cone on the embedded end, (Fig. 2.12). Around the cone is a heavy expansion sleeve. Above the sleeve is a collapsible mechanism, sometimes made of plastic. A spacer sleeve extends to the surface of the drilled hole. The anchor is set by tight-ening the bolt head or nut which draws the cone up through the expansion sleeve, expanding it against the side of the drilled hole. The anchor develops its tensile capacity by means of a combi-nation of keying into the concrete and high friction between the sleeve and concrete. The spacer sleeve aids in increasing the shear capacity. Tensile capacity depends on the strength of the bolt and its depth of embedment.

BEFORE TORQUING AFTER TORQUING

Fig. 2.12 - Heavy-duty, torque-controlled sleeve anchor

2.5.2.2 Sleeve anchors- The sleeve anchor consists of a steel stud, an expansion sleeve usually made of sheet metal, and a nut and washer (Fig. 2.13). The bottom of the steel stud has a uniformly tapered mandrel which has the same diameter at the end as the expansion sleeve. The entire length of the bolt below the washer is enclosed in a section or sections of the steel tubing. The bottom of the expansion sleeve is slit longitudinally to provide for expansion. When the nut is tightened, the tapered mandrel moves into and expands the sleeve which in turn bears against the wall of the hole. This anchor is used for medium and light holding requirements.

. .

Fig. 2.13 - Sleeve anchor

2.5.2.3 Shell expansion anchors - The shell expansion anchor, (Fig. 2.14) is available in two types. One type consists of a two-piece shell held together by steel tabs with a tapered, internally threaded end plug. The second type consists of a two-piece shell section with two tapered steel cones, one at the top end and one at the bottom, which are held together by a steel spring at the center. The bottom cone is internally threaded to accept a bolt or stud. By torquing the fastener into the anchor, the steel cones expand the shell to bear against the wall of the hole.

S i n g l e - a c t i n g D o u b l e a c t i n g ( s h e l l e x p a n d e d ( s h e l

b y s i n g l e w e d g e n u t )

e x p a n d e d b y o p p o s i n g w e d g e )

Fig. 2.14 - Shell expansion anchor 2.5.2.4 Wedge anchors-The wedge anchor, (Fig. 2.15) consists of a steel stud bolt with a nut

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uniform tapered mandrel around which is posi-tioned an expandable steel clip or separate steel wedges with protrusions. When the nut is tightened, the clip or steel wedges ride up on the tapered mandrel, wedging between the mandrel and the wall of the hole.

BEFORE A F T E R TORQUING TORQUING

Fig. 2.15- Wedge anchor

2.5.2.5 Rock/concrete expansion anchor-The rock/concrete expansion anchor, (Fig. 2.16) con-sists of a stud bolt that is threaded on the top end for a hex nut. The bottom end consists of a large mechanical expansion anchor. To set the expan-sion anchor, the stud bolt is rotated in a clockwise direction. Grouting is optional down the center of the bolt to fill the annular space between the rod and the drilled hole for corrosion protection.

Grout hole Threaded rob Nut Air tube Plate Hollow bar Grout hole Thrust rl Mal leable shelle

Fig. 2. I6 - Rock/concrete expansion anchor (grouted)

2.5.2.6 Drop-in anchors-The drop-in anchor consists of a steel shell and an internal steel expander plug (Fig. 2.17). The anchor is internally threaded at the top end while the internal end is machined to a uniform taper, matching the shape of the steel plug inside the anchor. The lower portion of the shell is slit longitudinally into equal segments to allow the anchor to expand when the internal plug is hammered with a setting tool. By hammering the plug into the

portion of the shell expands to wall of the hole.

shell, the lower bear against the BEFORE AFTER

Fig. 2.17-Drop-in anchor

2.5.2.7 Self-drilling anchors-The self-drilling anchor, (Fig. 2.18) consists of a steel shell and a tapered steel end plug. The bottom of the shell has teeth for cutting its own hole in the concrete. The top of the shell is internally threaded to accept a bolt or stud. The bottom of the shell is expanded by hammer drilling the anchor over the steel plug. The plug expands the bottom of the shell which bears against the wall of the drilled hole.

BEFORE

b

0.

A F T E R

Fig. 2.18 -Self-drilling anchor Copyright American Concrete Institute

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2.5.2.8 Stud anchors -The stud anchor con-sists of a steel stud, threaded at the top end, and has a drilled hole with longitudinal slits at the bottom end, which accepts a tapered steel plug (Fig. 2.19). The top of the threaded section is raised to provide a surface for hammering. By hammering the top of the stud, the tapered plug expands the bottom end of the bolt causing it to bear against the wall of the hole.

BEFORE AFTER b 4 . . n . D Q * . . V .v v -. . 4 . . V ’ . t . I

v

-v

A .b

Q V’ .

Fig. 2.19 - Stud anchor

2.5.2.9 Undercut anchors-There are two primary designs of undercut anchors available (Fig. 2.20). They all operate by keying and bearing against an undercut in the concrete at the bottom of the drilled hole. They cause little or no expansion force in the concrete, but generate high tensile-loading capacities.

The first type requires a second drilling operation to create an undercut at the bottom of the first drilled hole. The anchor is installed with the bottom of the expansion sleeve at the under-cut. When the nut is tightened, the tapered expander plug expands the bottom of the steel expansion sleeve into the undercut.

The second type cuts its own undercut at the bottom of the drilled hole. A sleeve is hammered by a rotary hammer drill with a special setting tool. The bottom of the expansion sleeve is driven over a cone at the bottom of the hole. The bottom of the expansion sleeve has a sharp edge which, on expansion, cuts its own undercut into the wall of the hole. By tightening the nut, the

bolt and tapered cone are drawn up into the expansion sleeve, keeping the bottom of the expansion sleeve in the undercut.A

B E F O R E A F T E R

Fig. 2.20 - Undercut anchor

CHAPTER 3-BEHAVIOR OF ANCHORS 3.1 - Introduction

Understanding anchor behavior is necessary in specifying the appropriate anchorage for a given application. This includes an understanding of failure modes and strengths as well as load-displacement and relaxation characteristics of various anchor types. This chapter covers anchor behavior in uncracked concrete and in cracked

concrete.

Anchors are primarily loaded through attachments to the embedded anchor. The loading can be in tension and shear or combinations of tension and shear (Fig. 3.1). They may also be subjected to bending depending on the details of shear transfer through the attachment. The behavior of anchors in tension is of primary importance and will be discussed first.

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tension loading

combined tension

_{and shear loading}

[

shear loading

_bending

Fig. 3.1 -Possible loadings of anchors By far, most anchor testing to date has been

performed in uncracked concrete. While cracking occurs in almost all concrete, testing in uncracked concrete provides the basis for understanding anchor behavior.

3 . 2 - B e h a v i o r o f a n c h o r s i n uncracked concrete

3.2.1 Load-displacement behavior and failure

modes failure (a) (b) (c) (d) (e)

under tension loading- The five primary

modes of anchors in tension are (Fig. 3.2): Steel failure

Pull-out failure

Concrete splitting failure Concrete cone failure

Spacing and edge cone failure

The various types of anchors have different dis-placement characteristics depending on preload, load transfer mechanism, and failure mode. Fig. 3.3(a)-3.3(c) present three load-displacement graphs. Fig. 3.3(a) gives the characteristic curves for headed and undercut anchors while Fig. 3.3(b)

presents curves for torque-controlled, drop-in, and self-drilling expansion anchors. Fig. 3.3(c) gives load displacement curves for adhesive anchors. The displacements shown represent the displace-ment (slip) of the embedded anchor and the de-formation of the concrete as well as the defor-mation of the anchor.

When a preload is applied to an anchor, typically by tightening the nut to a prescribed moment torque, the displacement caused by an externally applied load is affected. The preloaded

a) steel failure b) pull-out failure c) concrete splitting failure

d) concrete cone failure e) spacing and edge cone failure

Fig. 3.2 - Typical failure modes of anchors loaded in tension Copyright American Concrete Institute

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I I

Iine anchor type bolt diameter anchorage depth

mm mm I

Fig. 3.3(a) - Typical load-displacement relationships Fig. 3.3(b) - Typical load-displacement relationships of headed and undercut anchors (from Rehm, of expansion anchors under tension loading (from Eligehausen, and Mallee 1988) Eligehausen and Pusill-Wachtsmuth 1982)

displacement [mm]

Fig. 3.3(c)- Typical load-displacement behavior of chemical anchors under tension and shear loading (from Eligehausen and Pusill- Wachtsmuth 1982)

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external loading until the preload in the anchor (and resulting clamping force on the concrete) is overcome. The preload has no effect on the ulti-mate static tensile capacity of the anchorage, but significantly reduces the anchor total displacement. In the case of steel failure (Fig. 3.3(a), Line 3) the ductility depends on the relationship between tensile strength and yield strength of the steel and the anchor length. Inelastic displacements of headed anchors due to concrete deformations under the head may be expected at relatively low loads unless preloaded. Increasing the bearing area under the head may reduce inelastic displace-ments but will have little influence on the failure

load [compare Lines 1 and 2 in Fig. 3.3(a)]. Headed anchors that fail due to fracture of the concrete will exhibit a brittle failure (Fig. 3.3(b), line 2).

The behavior of drop-in anchors is dependent on the magnitude of the expansion force created in setting the anchor. When expanded properly during installation, high expansion forces are induced and the load displacement curve may remain almost linear up to failure [Fig. 3.3(b), Line 2).

The expansion force, at installation, of torque-controlled expansion anchors is smaller than that of drop-in anchors and, therefore, the displace-ments are larger for equal loads. If the external load exceeds the preloading force in the bolt generated by the torquing during installation, the spreading cone is pulled further into the sleeve, leading to increased displacement. At failure the deformations are much larger than for comparable drop-in anchors [Fig. 3.3(b)].

Self-drilling anchors show larger displacements in the total load range than torque-controlled expansion and drop-in anchors [Fig. 3.3(b)]. This happens because load transfer is mainly by mechanical interlock which causes high pressure on the concrete and large concrete deformations. The displacement behavior of undercut anchors depends primarily on the bearing area (undercut area) and the installation torque. Therefore relatively large deformations may be expected with some undercut anchors while others exhibit elastic behavior well above service load [Fig. 3.3(a)].

Adhesive anchors exhibit elastic behavior up to nearly maximum load [Fig. 3.3(c)]. While the load-displacement curves of adhesive anchors exhibit relatively low coefficients of variation in

comparison to torque-controlled expansion and drop-in anchors, the bond strengths vary con-siderably depending on the adhesive component mix used and the installation procedure.

Under working loads all categories of anchors should behave elastically with little additional displacement after installation. However, at ultimate load a plastic behavior and in the case of cyclic loading only a limited strength degradation is desired. Fig. 3.3(a)-3.3(c) show that the actual load-displacement behavior of the currently available expansion, undercut, adhesive, and headed anchors differs somewhat from this plastic behavior.

Under sustained loads displacements will increase with time due to creep of concrete in the highly stressed load transfer area (bearing area in the case of headed or undercut anchors, contact area in the case of expansion anchors, bonded area in the case of adhesive or grouted anchors).

As an example, in Fig. 3.4 (see Seghezzi and Vollmer, 1982) the displacements of a torque-controlled expansion anchor loaded with a constant tensile force corresponding to approx-imately 70 percent of the static ultimate strength, are plotted as a function of load duration on a double logarithmic scale. It can be seen that the d i s p l a c e m e n t v e l o c i t y ( t a n g e n t t o t h e displacement-time curve) decreases with increasing time and, therefore, the displacements approach a limiting final value. The increase in displacements is smaller for lower sustained loads. If the load is increased after a sustained load test, the displace-ment curve is rather steep until it reaches the static envelope which is followed thereafter. Fail-ure load and displacement at maximum load are not negatively influenced by a previous sustained load smaller than about 70 to 80 percent of the static failure load.

10* 10 102

Duration [Days] Fig. 3.4 -Increase of displacement during sustained loading

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In principle, the same behavior is valid for cyclic loadings with up to 1 x lo6 load repetitions and an upper load (where the cyclic load ranges between an upper and lower value, both of which are tension) smaller than about 50 percent of the static failure load (provided no fatigue failure of the bolt occurs). For higher upper loads the dis-placements may increase significantly and a fatigue failure of the concrete might occur (Rehm, Eligehausen, and Mallee 1988).

Sustained and cyclic loadings in the working-load range have the same influence on dis-placements and ultimate loads of headed anchors as for expansion and undercut anchors.

3.2.2 Relaxation -If headed anchors are pre-loaded, the initial force induced in the anchor is reduced with time due to creep of the highly stressed concrete under the anchor head. The final value of the tension force in the anchor depends primarily on the value of bearing stresses under the head, the concrete deformation and the anchorage depth. In typical cases the value of that final force will approach 40 to 80 percent of the initial preload (40 percent for short anchors, 80 percent for long anchors).

Torque-controlled expansion anchors are usually preloaded by tightening the nut during installation. This preload is essential for the proper performance of such anchors. In a typical installation, locally high concrete stresses are created around the embedded anchor wedges or expansion devices as the anchor is preloaded. Creep of concrete under these high stresses results in a slight movement of the embedded anchor, and in turn, in a reduction in the load in the bolt.

Fig. 3.5 shows a typical load-relaxation test (Burdette, Perry, and Funk 1987). Preload is plotted as a function of time. The shape of the curve is essentially the same for all anchors (including headed anchors). There is an exponential drop-off of load immediately after the applied tension is released, followed by a continued gradual diminishing of the load over an indefinite period. It is estimated that the final preload will be about 40 to 60 percent of the initial value. This is confirmed by other test data (Seghezzi and Vollmer 1982, and Wagner-Grey 1976). After retorquing the anchors, the process of load relaxation starts again, however, the final value of the preload is increased (Fig. 3.6). Retorquing even a short time after anchor in-stallation can be effective (Wagner-Grey 1976).

0 I I I

I

0 10 20 30 40 50 60 70

Time [Days] Fig. 3.5 -Reduction of preload as a function of time

(after Burdette, Perry, and Funk 1987)

1 i

.I

I

Torque Controlled Expansion Anchor M12

I I

0

I

0 2,5 5,0 7,5 10 12,5

Time [h] Fig. 3.6 -Influence of retorquing on the final value of preload (from Seghezzi and Vollmer 1982)

Chemical anchors are usually preloaded by applying a predefined torque. Because of the high stresses in the adhesive bond, the preload force in the anchor declines faster and the final value is less than for torque-controlled expansion and headed anchors.

Long-term relaxation and creep has been investigated in several studies. Four Ml6 diameter polyester anchors tested at loads of 25, 30, 38, and 40 kN (6, 7, 8.5, and 9 kips), showed displacements still increasing after 5 years, but ranging from 0.090 to 0.140 mm (0.0036 to 0.056 in.)(Elfgren, Anneling, Eriksson, and Granlund 1988). Creep tests were also performed on 26 Ml6 anchors for 3 years at various loads and

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environmental conditions. At allowable working loads of 15 kN (3.4 kips), anchors tested indoors showed small creep, 0.10 to 0.40 mm (0.004 to 0.016in.). However, anchors tested outdoors exhibited continually increasing creep. Those tested indoors at 30- and 45- kN (7 and 10 kips), loads exhibited continually increasing creep. A 4 month test on epoxy anchors showed creep less than 0.009 in. (0.2 mm) (Wiewel 1989).

The U.S. Army Corps of Engineers performed creep tests on polyester and epoxy anchors, subjecting the anchors to 60 percent of the anchor steel yield strength for 6 months. Cement and epoxy grouted specimens exhibited low slippage, 0.0013 to 0.0008 in. (0.03 to 0.02 mm), while polyester anchors exhibited approximately 30 times as much movement, 0.008 to 0.024 in. (0.2 to 0.6 mm) (Best, Floyd, and McDonald 1989).

3.2.3 Ultimate strength in tension

3.2.3.1 Steel failure -The strength of anchor

steel controls failure when the embedment of the anchor is sufficient to preclude concrete failure and when the spreading forces are sufficiently high (expansion anchors) or the bearing area is suffi-ciently large (headed and undercut anchors) to preclude an anchor slip failure. The failure mode [Fig. 3.2(a)] is rupture of the anchor steel with ductility dependent on the type of anchor steel and embedment length. The ultimate strength can be determined from Eq. 3.1.

F_u = 4 x f,,, lb (3 .1) where

As = tensile stress area, in.*

f_ut = ultimate tensile strength of steel, psi For given material properties and anchor dimensions this case defines the upper limit for the tensile-load-carrying capacity.

Fig. 3.7 shows a comparison of the failure loads of headed anchors measured in tests to the values predicted by Eq. 3.1. Because the theoretical failure load was calculated with the nominal steel strength, the ratios of actual to predicted tensile capacity are larger than one.

number of specimens

10

-STEEL FAILURE

5

-Fig. 3.7-Ratio of actual to predicted tensile capacity according to Eq. (3.1) for steel failure (after Klingner and Mendonca 1982)

3.2.3.2 Concrete cone failure -When the embedment of an anchor or group of anchors is insufficient to develop the tensile strength of the anchor steel, a pullout cone failure of the concrete [see Fig. 3.2(d)] is the principal failure mode. When the spacing of anchors or location of an edge [Fig. 3.2(e)] interferes with the development of the full cone strength of an anchor, its capacity will be reduced.

The angle of the failure cone, measured from the axis of the anchor, varies along the failure surface and shows considerable scatter. In ACI 349, Appendix B, A C I Committee 349,1985) the angle of the failure cone of headed and expansion anchors is assumed as 45’. According to Cannon*, in the case of expansion anchors the angle varies from about 60’ for short embedments (Id ( 2 in) to 45O for 1, 2 6 in. According to Rehm, Eligehausen, and Mallee 1988, the angle varies between approximately 50° and 60”, (mean value 5S”) and tends to decrease with increasing anchorage depth.

The following formulas have been developed to describe behavior of headed studs, expansion, and undercut anchors.

*Cannon, Robert W., correspondence to ACI Committee 355, Nov. 1986.

Cannon, Robert W., correspondence to ACI Committee 355, Sept. 1988.

This correspondence is filed at ACIACI headquarters and is available at cost of reproduction and handling at time of request.

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--`,``,````,,,`,``,``,,,,,```,`-`-`,,`,,`,`,,`---ANCHORAGE TO CONCRETE 355.1R-1 5

ACI 349, Appendix B, limits the tensile capacity If an anchor is installed too close to an edge, the anchor will fail before developing the concrete cone strength. Therefore, for headed anchors, of the cone failure of an anchor, or wup of_.

anchors, to a uniform stress of 4 (psi) on+d$

the stress cone surface of the anchors. ACI 349 requires that the minimum edge distance

m to the center of the anchor be sufficient to

prevent a side cone failure. The following equation is suggested in the ACI 349 Commentary for determining this minimum value.

(3.2)

strength reduction factor 0.85 for uncracked concrete

m , in. _(3.3)

= 0.65 in zone of potential

cracking

A = the summation of the projected where areas (in.2_{) of individual stress}

cones minus the areas of over-lap and of any area, or areas, cut off by intersecting edges.

D = anchor diameter, in.

F = ultimate tensile strength of anchor, psi f '_c = compressive strength of concrete, psi Note: Other reductions are made based on

member thickness relative to embedment and the area of fabricated anchor heads (see Fig. 3.8).

ACI 349 has no requirements for minimum center-to-center spacing of single anchors or anchors belonging to a group.

Fig. 3.9 shows the frequency diagram of the

If this requirement cannot be satisfied, stirrup or tie reinforcement should be provided.

Cannon+_{found that for embedments less than} 6 in., ACI 349 becomes increasingly conservative with decreasing embedment. He has proposed a modification to Eq. (3.3) to provide a better fit to test data. For embedments less than 6 in., this modification would increase the angle of the failure cone, measured from the axis of the anchor.

ratio of actual to Predicted tensile capacity of headed anchors. Theoretical capacity was calculated according to Eq. (3.2). The tests were described by Klingner and Mendonca (1982a), and were evaluated by Cannon*. Tested were individual anchors with large and small edge distances and anchor groups. In all tests a concrete cone failure occurred.

For 1, c 3 in.: cy = 62 - 1.1 (l#, deg

For l_d 2 3 in. but < 6 in.: (Y = 45 + 0.79 (6-ld)(3 3,

deg (3 5).

With respect to the minimum edge distance he reported the results of tests which indicated a direct relationship between anchor load and side cone failure.** He suggested Eq. (3.6) instead of

Eq. (3.3) as a more correct lower bound for the edge distance for headed anchors:

-A Frequency [%] n = 45 tests 5i = 1,14 v = 26

O/o

20 10 m

F_ut= ASTM-specified tensile strength of the anchor bolt, kips

1,5 2,0 2,5

F /F

u,test u,pred *Cannon, private correspondence, 1988, previously cited (see footnote p 14).

+Cannon, private correspondence, 1986, previously cited (see footnote p 14).

**Cannon, Robert W., Letter to ACI 355, “Comparison of Testing Edge Conditions and Anchor Spacing with Predictions”, Dec. 1984.

Fig. 3.9 -Ratio of actual to predicted tensile capacity of headed anchors according to Eq. (3.2) (from Cannon, 1984 **)

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--`,``,````,,,`,``,``,,,,,```,`-`-`,,`,,`,`,,`---*EFFECTIVE STRESS AREA,

\L DEDUCT AREA OF ANCHOR HEADS

*REDUCE BY THE TOTAL BEARING AREA OF THE ANCHOR STEEL.

. A) Effective stress area for anchorage pullout

L d

*EFFECTIVE STRESS B

I41

AREA A t P L A N Pd t

L

EFFECTIVE STRESS AREA Pd t L J (a+2Ld-2h) EFFECTIVE STRESS

AREA . STRESS AREA REDUCTION FOR LIMITED DEPTH (Ar) Ar= (a+2Ld-2h)(b+2Ld-2h)

*REDUCE BY THE TOTAL BEARING AREA OF THE ANCHOR STEEL

B) Stress area reduction for I imited depth A

Fig. 3.8-ACI 349 method for determining effective stress areas Copyright American Concrete Institute

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--`,``,````,,,`,``,``,,,,,```,`-`-`,,`,,`,`,,`---ANCHORAGE TO CONCRETE 355.1R-17

The average failure load for a side cone (bursting) failure is given as:

where

F,

= 15m - kips (3.7)f

35cCo’ m = actual edge distance, in.

For expansion and undercut anchors, Eligehausen, Fuchs, and Mayer (1987 and 1988), derived Eq. (3.8a) from 287 test series with single anchors with large edge distances showing concrete cone failure.

(3.8a) where

Fu

= average ultimate load, N

‘d = embedment depth (see Fig. 3.10), mm f’, = average compressive strength of con-crete cylinders (6 by 12 in.) at time of testing, N/mm2

Fig. 3.10 -Illustration of embedment depth as used in Eq. (3.8a) and (3.86)

Results of an additional 196 tests on headed studs showed a similar relationship (from Rehm, Eligehausen, and Mallee 1988).

(3.8b) In the original equation the concrete strength was measured on cubes with a side length of 200 mm (8 in.). Eq. (3.8a) and (3.8b) assume f 'c

(cylinder) = 0.82 f 'cc (cube).

The tests with expansion, undercut and headed studs included anchorage depths from 40 to 525

mm (1 9/16 to 20 l/2 in.) and concrete strengths f’, = 20 to 50 N/mm2 (2900 psi to 7150 psi). Fig. 3.11 shows a histogram of the ratio of measured to predicted failure load.

The average failure loads given in Eq. (3.8) can only be obtained if the distances between anchors are large enough so that concrete cones do not overlap each other. Assuming an angle of the failure cone cy = 55o_{the critical distance is}

approximately three times the embedment depth. The failure load of a two-point fastening results in:

where

G = xcr x F,, (3.9)

F_{ul =}ultimate failure load, single anchor, from Eq. (3.8)

& = 1 +a/a,,it I 2 (3.10)

where

a = distance between center of anchors

acrit = critical distance between center

of anchors

= 31,, where 1d is the depth of

embedment.

Eq. (3.9) leads to the x-method for calculating the ultimate capacity of multiple anchor fasten-ings. For the calculation of the ultimate load of quadruple fastenings the xa factors can be derived separately for both directions and combined in product form as follows.

where

FIA4 = %a1 x Xd x Fur _(3.11)

xai = 1 + ai(acd 5 2 _(3.12)

a._{I =} spacing in direction i

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I

0.5 1.0 1.5 2.0

$,

test ’ %,pred

Fig. 3.11 (a) -Ratio of acutual to predicted tensile capacity for concrete cone failure of individual expansion and undercut anchors away from edges according to Eq. (3.8a). (from Rehm, Eligehausen, and Mallee 1988, and Eligehausen, Fuchs, and Mayer 1987 and 1988)

Fig. 3.12 shows the capacity of quadruple fastenings for headed studs, expansion and undercut anchors as a function of the ratio of anchor spacing to embedment depth as measured in tests and calculated according to Eq. (3.11).

Eq. (3.9) and (3.11) can also be extended for multiple anchorages with any number of anchors in any spacing by setting the value of ai as the distance atot between the outer anchors, and the x0- value is limited to xa I n with n = number of anchors in one direction. This is provided that the spacings between the individual anchors are smaller than acrit = 31, and the anchor plate is sufficiently stiff to assure an even distribution of tension forces to all anchors (see Rehm, Eligehausen, and Mallee 1988). The X-method can also be extended to take account of load eccentricities (Riemann 1985).

Fig. 3.13 shows the ratio of actual to predicted tensile capacity of groups of headed studs. In the tests the number of anchors was varied between 4

40 Frequency [%] n = 196 individual tests si= 1 0 0 v= 1 4 % 30 20 10 0.5 1.0 1.5

Fu,

test /Fu, pred

Fig. 3.11(b) -Ratio of actual to predicted tensile capacity for concrete cone failure of individual headed anchors away from edges according to Eq. (3.86). (from Rehm, Eligehausen, and Mallee 1988) and 36, the spacing of the outer anchors between 100 and 875 mm and the spacing of the individual anchors between 0.541, and 2.2&. The groups were loaded by a concentric tension load which was equally distributed to all anchors.

Eq. (3.13) covers the influence of edge dis-tances, a,, smaller than critical:

where Xa?n a_{m,crit =} = ‘= Fu = F_{u* =} a& * Fy (3.13) = 0.3 + 0.7 am/a,crit S 1 (3.14) critical distance from free edge 1.5 1d

actual embedment length

ultimate failure load, single anchor to be taken from Eq. (3.8)

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--`,``,````,,,`,``,``,,,,,```,`-`-`,,`,,`,`,,`---355.1R-19 0

5.0

4.0

3.0

2.0

1.0 I

I

FE according to eqn. ( 3.8 ) O

8 I

₀

Fig. 3.12-Ratio of actual failure load of a group of anchors to the predicted value for an individual anchor as a function of the ratio of anchor spacing to embedment depth (from Rehm, Eligehausen, and Mallee 1988)

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--`,``,````,,,`,``,``,,,,,```,`-`-`,,`,,`,`,,`---MANUAL OF CONCRETE PRACTICE

I L

,

l-

_.-Copyright American Concrete Institute

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--`,``,````,,,`,``,``,,,,,```,`-`-`,,`,,`,`,,`---ANCHORAGE TO CONCRETE 355.1R-21 Fig. 3.14 shows a comparison of test results with

the theoretical values according to Eq. (3.13). It should be noted, however, that minimum distances from the free edge are necessary for headed studs in order to allow proper concreting and avoid local spalling of concrete. Minimum edge distances for expansion and undercut anchors are necessary to avoid splitting of concrete during installation and expansion of the anchors.

If anchors are located in a corner [see Fig. 3.15(b,)], the factors xarn are calculated separately for each direction and then the two x-factors are multiplied.

Bode and Roik (1987), evaluated data of 106 tests with headed studs to arrive at Eq. (3.15).

F” = 12r,3/2(1 + d&,) 8, N (3.15) where F, = 1d = d, = f’, =

average failure load, N embedment length, mm head diameter, mm concrete cylinder strength

at time of testing, N/mm2

Fig. 3.16 compares the measured failure loads of headed studs with the values according to Eq.

Roik (1987), assume the critical spacing of neighboring headed

Fig. 3.15 - Typical failure modes of anchors Loaded in shear (from Rehm, Eligehausen, and Mallee 1988)

kN

TU’k

lN/mmz

I

acl+ = 41, (3.16) mean value

50 75 100 125 150

h

[mm]

Fig. 3.16 - Measured failure loads compared to Eq. 3.15 (where p, = concrete splitting strength) (from Bode and Roik 1987)

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.50

.00

.

o

Anchor

studs,

concrete

break-out

/

l

Headed studs,

0 local concrete

failure

L

( blow -out)

I

00 .50

1.00 _1.50

_1.75

Fig. 3.14-Ratio of actual failure load of an individual anchor close to the edge to the predicted value for an anchor with large edge distance (from Rehm, Eligehausen, and Mallee 1988)

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--`,``,````,,,`,``,``,,,,,```,`-`-`,,`,,`,`,,`---355.1R-23

With respect to the influence of free edges (see

Fig, 3.15) they consider the critical distance

beyond which there is no significant influence on load as being in the case of one free

ati1 IJ 1.21,

and in the case of two or more free edges:

acit.2 5 21,

For distances from center of headed stud to the free edge(s) which are smaller than the critical distance according to Eq. (3.17) and (3.18), they fou d that the assumption of a linear decrease of ulti

”

ate failure load in proportion to the ratio of act al distance/critical distance gives a lower bound of their test results, in much the same

ner as shown in Fig. 3.14.

raestrup, Nielson, Jense, and Bach (1976), give the predicted failure load as:

FM

= 0.21 x 2; (1 + d,ll&f$ N (3.19) Eq. (3.19) was deduced by applying the theory of plasticity to headed studs embedded in co rrete.

nI

The failure load is assumed to be pro ortional to the concrete compressive strength. 3.2.3.3 Pullout (slip) of the anchor- Slip failure occurs [Fig. 3.2(b)] with expansion anchors when the expansion force is too small to develop either the strength of the anchor steel or a shear cone failure of the concrete. This is a typical failure mode for wedge anchors at moderate to deep embedments in lower strength concrete where the crushing of the concrete at the wedges allows the bolt to “pull through”. The cause may also be due to an oversize hole. Slip failure may also occur in low strength concrete due to deformation of the wall of the hole.

The testing of wedge bolt expansion anchors by Hanks (1973), clearly demonstrated that the primary failure mode for individual anchor tests (uninhibited by edge conditions) was either cone failure of the concrete or anchor slip depending on the depth of anchor for a given size. Only 10 of 464 tension tests indicated any cracking associated with a cone failure. The line of demarcation between shear cone failure and slip

failure was approximately six bolt diameters. Under conditions of poor workmanship in the field (e.g., oversize holes) slip failure may occur at a much smaller embedment depth than ld = 6D.

Slip failure may also occur with bonded and adhesive anchors of insufficient embedment to develop the strength of the anchor steel or to cause a concrete cone failure.

Torque-controlled wedge anchors, which fail by slip, generally fail by slipping the expansion cone past the wedges. This failure mode may also occur with sleeve anchors. However, in some case anchors may fail by pulling the whole anchor (including expansion sleeve) out of the hole. Torque-controlled expansion anchors may also slip to a critical depth and fail the concrete. Deformation-controlled expansion anchors (e.g., drop-in anchors) have a fixed expansion and may slip to a critical depth and then fail the concrete. The slip failure load is dependent on the coefficient of friction between the sliding surfaces and on the spreading force at failure which is a function of the critical expansion force producing failure and the deformability of the concrete which varies with hole depth and concrete properties. All of these factors may vary with anchor type, manufacturer, and installation. The spreading force and thus the slip load of drop-in anchors decreases significantly with increasing diameter of the drilled hole with respect to the diameter of the anchor.

Theoretically the slip failure load F, could be calculated from Eq. (3.20).

Fit = ps (3.20) where

I, = coefficient of friction S = spreading force

The coefficient of friction depends mainly on the roughness and cleanliness of the drilled hole and of the surface of the expansion sleeve or wedge as well as on the spreading pressure. From Wagner-Grey (1976), the factor p for torque controlled expansion anchors is in the range of 0.2 to 0.3 and for drop-in anchors is approximately 0.35. The difficulty in using Eq. (3.20) lies in properly estimating the spreading force, since complex mechanics are involved. For this reason

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--`,``,````,,,`,``,``,,,,,```,`-`-`,,`,,`,`,,`---355.1R-24 MANUAL OF CONCRETE PRACTICE the profession relies on test data. However,

equations for estimating of the spreading force are given by Wagner-Grey (1976).

Because of the large variability of the spreading forces and the coefficient of friction, Eq. (3.20)

gives only an approximate estimate of the pullout load (see Eligehausen, and Pusill-Wachtsmuth 1982). Furthermore, in important applications it is advisable to test expansion anchors, which typically fail by slip at specified embedments, in design strength job concrete to confirm slip characteristics.

For pullout failures of a chemical anchor, the bond between the wall of the drilled hole and the mortar is critical (see Sell 1973). Assuming a uniform bond stress distribution along the anchorage length, the bond strength is in the order of 1300 psi (9 MPa) with a coefficient of variation of 10 to 15 percent for polyester and vinylester chemical anchors. This value is for a concrete compressive strength of 3000 psi (21 MPa) and an embedment of about nine anchor diameters. The bond strength increases approximately with the square root of the concrete strength.

The pullout capacity of chemical anchors increases with increasing embedment depth: however, after about nine anchor diameters the increase is not proportional to embedment. This is due to the high bonding effect resulting in high load transfer to the concrete at the top of the anchorage. The bond stress is no longer uniform, and if the tensile load is sufficiently high, the failure initiates with a concrete failure in the upper portion of the concrete and then the bond fails in the remainder of the embedment.

For headed anchors local failure in front of the head will occur when the pressure on the concrete is larger than about 12f’, to 15f’, (Rehm, Elige-hausen, and Mallee, 1988). This type of failure is somewhat similar to a pullout failure.

3.2.3.4 Splitting failure of concrete -This failure mode will occur only if the dimensions of the concrete are too small, the anchors are placed too close to an edge or too close to each other [Fig. 3.2(c)], or the expansion forces are too high. The failure load is usually smaller than for a concrete cone failure.

Torque-controlled expansion and deformation-controlled anchors (e.g., drop-in and self-drill anchors are the type anchor most likely to experience splitting failure due to the high lateral thrust required to resist sliding by friction on the

steel wedges. Deformation-controlled expansion anchors generate higher spreading forces and require larger edge distances than torque-controlled expansion and undercut anchors.

The capacity of expansion anchors which fail by splitting of the concrete has been evaluated by Pusill-Wachtsmuth (1982), using theoretical considerations. It was assumed that splitting occurs when the tensile stresses averaged over a critical area reach the concrete tensile strength. The size of this area was found by evaluating the results of tests with concentrated loads and of tests with thick concrete rings subjected to a constant inner pressure. According to this theory, the necessary side cover or spacing to preclude a splitting failure before reaching the concrete cone failure load must be about 1.751d or 3.51,,

respec-tively. For drop-in anchors a side cover m I 31d

was recommended. The validity of this evaluation was checked by relatively few test results.

With respect to the minimum edge distance Cannon* has proposed the following criteria to preclude a splitting failure occuring at a load lower than the capacity for concrete cone failure or pullout failure:

m = D(11.4 - 0.92& in. (3.21) where

:

= minimum edge distance = anchor bolt diameter, in.

ld = embedment depth to the bottom of the anchor, in

Eq. (3.21) is valid for anchor spacings s L 2 in. If side cover or spacings of anchors are too small, splitting cracks may occur during installation of anchors. This possibility is greater for drop-in anchors and for self-drilling anchors than for torque-controlled expansion anchors because of the higher initial spreading forces. The minimum edge distance and the minimum spacing to avoid splitting during installation, as recommended by Rehm, Eligehausen, and Mallee (1988), are based on many tests and are given in Table 3.1 for the different types of anchors.

*Cannon, Private correspondence previously cited Dec. 1984 (see footnote p 14).

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Table 3.1 -Minimum edge distance and minimum spacing to avoid splitting failure

Mihimum edge distance m / 1d to avoid splitting during installation

Minimum center-to-center spacing a / 1d to avoid splitting during installation

Undercut anchors 1.0 1.0

3.2.4 Load-displacement behavior and failure

modes in shear-For anchors with an applied

preload, the initial friction forces between the baseplate and the concrete have to be overcome by the shear load before there is initial anchor movement (Fig. 3.17). The baseplate slides and the anchor moves to the side of the hole in the second stage of behavior. The third stage of load-displacement behavior is a pressure loading against the top surface of the concrete and a surface spa1l of the concrete at the edge of the hole. Depending on edge distance and anchor embedment, the failure may be by shearing of the anchor (for deep embedments) with or without a concrete spa11 preceding the steel failure [Fig. 3.15(a)] or by shearing of the concrete (concrete failure) in the case of anchors loaded near an edge [Fig. 3.15(b1), (b2), (b3)].

Shear loading generally produces larger displacements than tension loading [see Fig. 3.3(c)]. This can be attributed to the bending of the anchor rod and the deformation of the concrete in the direction of loading. This is especially true if the anchor is not flush with the concrete at the hole opening (e.g., when the concrete is spalled during drilling). For cast-in-place anchors, the behavior will depend on the type of anchorage used, the embedment and the steel strength.

The distribution of shear from the attachment to anchors of a group depends on the details of the anchors to the attachment connection and on overcoming the frictional resistance of the attachment. The frictional resistance depends on surface conditions, the existing preload (if any) in the anchors and the compressive forces applied

Torque-controlled expansion anchors

I

Drop-in anchors with one cone (recent design)

2.0

I 3.0

1.0

through the attachment as a result of direct loads or applied moments. The connection details concern the treatment of connecting surfaces and the fit and manner of connecting the anchors to the attachment.

Onset of bearing crushing in the concrete

lip of loading plate into bearing on anchor stud

Load transfered by friction to embedment

. ~~~ r r -7

0 .50 10 1.5 0 20

Deformatlon

Fig. 3.17- Typical load-displacement curve for wedge anchor in shear from Meinheit and Heidbrink 1985)

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3.2.5 Ultimate strength in shear

3.2.5.1 Steel failure -Steel failure usually occurs after relatively large displacements and is most common for deep embedments, lower strength steels and large edge distances. The failure load

depends on the steel area and the steel strength x

and is given by Eq. (3.22).

F8l

= N A,f,, lb (3.22) where the factor N takes account of the steel “shear” strength and has the range 0.6 to 0.7 [Klingner and Mendonca, (1982b)], A, is the ten-sile stress area (as defined in Eq. (3.1)) and f,t is the ultimate tensile strength.

Eligehausen and Fuchs (1988), propose the value N = 0.6 on the basis of an evaluation of 230 tests.

3.2.5.2 Concrete failure -Concrete failures will exhibit two modes; (1) blow out cones due to edge proximity (Fig. 3.15) and (2) concrete spa11 followed by a possible anchor pullout or steel failure away from an edge.

3.2.5.2.1 Edge failure- For all types of anchors loaded in shear toward an adjacent, free edge and exhibiting a concrete failure (Fig. 3.15), the failure load is influenced by the concrete tensile strength, the edge distance m and the stiffness of the anchor. Another influencing factor is the embedment depth. The failure surface has a conical shape that may radiate from the em-bedded end of the anchor for shallow embedments or from the upper part of the anchorage for deep embedments.

In the following paragraphs, several formulas for calculating the failure load for an edge failure are reviewed.

ACI 349, Appendix B, Commentary gives a design shear strength of

vu = 24$$n2, lb (3.23) where

cb = 0.85

f’, = compressive strength of concrete m = distance from anchor to free edge

(see Fig. 3.15) number of specimens ” I 0,: 0.65-4 I RATIO OF ACTUAL TO F’FQICTED CAPACITY

Fig. 3.18 -Histogram of actual to predicted capacity ACI 349, Appendix B further recommends a minimum side cover or edge distance m required to preclude edge failures: be calculated by Eq. (3.24).

m = , in. (3.24)

where

D = anchor diameter, in. F t

fr”,

= anchor ultimate tensile load, lb = concrete compressive strength, psi Eligehausen and Fuchs (1988), have suggested, based on the evaluation of some 80 test results with headed and expansion anchors (anchorage depth ld > 4D), the average ultimate failure load of the concrete of a single fastener in shear be calculated by: F,, = 1.4@$n1.s~~, N (3.25) where D f’, m

shank diameter (mm) of headed studs or drill-hole diameter for anchors, D < 25mm

average concrete compressive strength (cylinders) at time of testing, N/mm2

distance from anchor to free edge, mm

Fig. 3.18, taken from Klingner and Mendonca (1982b) gives the ratio of actual to predicted shear capacities for this approach.

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h Xh =-sl_1.4m where

h = member thickness, mm

Eq. (3.25) is valid for 1,/D = 4 to 6.

Fig. 3.19 shows a comparison between failure loads according to Eq. (3.25) and test results. The thickness of the test specimens was h 1 1.4m. The tests were performed in concretes with different strengths and anchors ranging in diameter between 12 and 22 mm. The test results were normalized to a concrete strength f 'c =

20N/mm2 and D = 18 mm.

If an anchor group is loaded in shear toward an edge, a common failure cone may occur [see Fig. 3.15(b2)]. T he corresponding failure load may

also be calculated as described in Section 3.2.3.2

for tension loading [Eq. (3.9), (3.11), and (3.12)] according to the x-method. The x-values for shear loads, however, depend on the distance from the free edge measured in load direction.

The critical (minimum) distance between two or more anchors beyond which no intersection of failure cone will happen is given by Eligehausen and Fuchs (1988), as:

where

a_Wit= 3.5m (3.27) m = distance to free edge.

For a I a,,i, Eligehausen and Fuchs (1988), have proposed the calculation of the average failure load of a group of anchors (see Fig. 3.20) subjected to shear load by:

F_{I(, Group}= x,F, (3.28) where

& = 1 + a/a,,i, F, is from Eq. (3.25)

Fig. 3.20 (Eligehausen and Fuchs, 1988) shows the ratio of the failure load of a group loaded in shear towards the edge to the failure load of an individual anchor calculated according Eq. (3.25). The failure load ratio is plotted against the ratio of spacing to edge distance.

0 3.0 ' 3.5 4.0 a/a, [-]

Fig. 3.20-Ratio of actual shear failure load of anchor group to shear failure load of an individual anchor as a function of spacing between anchors

Similar expressions are proposed for calculating the failure load of single fastenings or anchor groups situated in a corner or in narrow members. The influence of load eccentricity on the failure load of an anchor group can also be taken into account by the x-method (Rehm, Eligehausen, and Mallee 1988). The method has been extended to anchor groups with an arbitrary number of anchors.

Klingner, Mendonca, and Malik (1982), recommend a critical (minimum) edge spacing of:

mkD -, in.

Fut

%@

(3.29)

where

#C = 0.90 and the other terms are as given for the ACI 349 [Eq. (3.24)].

For anchors with small embedment depth situated away from an edge and loaded in shear, the failure mode may be a tensile cone failure as the anchor bends under load and induces a tensile loading into the concrete. Because of ductility requirements and reversible load conditions associated with seismic design, ACI 349 does not distinguish between embedment requirements for shear and tension. This is very conservative if only shear is considered (see Shaikh and Yi, 1985).

(28)

--`,``,````,,,`,``,``,,,,,```,`-`-`,,`,,`,`,,`---MANUAL OF CONCRETE PRACTICE

ACI 355.1R.pdf

ACI

355.1R-91

STATE-OF-THE-ART REPORT ON

ANCHORAGE TO CONCRETE

Reported by ACI Committee 355

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