chapter 1 augest 2009

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1Chapter OneIntroduction

The subject of this thesis is the end anchorage of the main bars of reinforced concrete

beams and slabs. The main emphasis is on anchorages at simple supports but part of the

work is relevant to anchorages in uncracked regions around sections of contraflexure.

End anchorages can be critical in design, particularly where the presence of shear cracks

produces the need for significant bar forces to be developed in short lengths.

The use of truss or strut and tie modelling helps in the evaluation of the forces to be

anchored, but the assessment of resistance remains a problem and the objective of the

work reported here was to improve the means of calculating resistances.

The research treats the commonest types of anchorages at simple supports, i.e. straight

bars and bars with 90 and 180 bends in vertical planes. It does not treat anchorages

with welded cross bars, horizontal loops, forged heads or welded bearing plates. It treats

only deformed reinforcement and all test data used are bottom-cast bars. The approach

developed in the subsequent chapters is essentially empirical.

The BS8110(1) treatment of bond and end anchorage ignores many factors known to

influence resistance. The Eurocode EC2-2004(2) takes account of more parameters, but

there appears to be no publication in which its expressions have been verified by

comparisons with test results and its approach to end anchorages using hooks or bends

seems confused and not really usable for standard hooks and bends with test results.

Thus the two sets of design rules likely to be of interest in the UK leave much to be

desired, and most theoretical work on bond does not deal with end anchorage. The

present research is therefore aimed at the development of an approach with a rational

basis, accounting for the major influential factors and yet simple enough for practical

use.

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Chapter two is a literature review. Following an introduction, section 2.2 considers and

compares code of practice recommendations relevant to end anchorage. This is followed

by four sections on research publications.

Section 2.3 on straight anchorages without transverse pressure is a relatively brief

review of works on bond in general including some papers giving expressions which

could be used to predict bond strengths of anchorages without transverse pressure, e.g.

anchorages in regions of contraflexure.

Section 2.4 is a more comprehensive review of research on bond with transverse

pressure. One reason for its length is that it tries to show what data are available from

tests of specimens representing beam ends and other situations. It also presents theupper bound plastic theory approach to end anchorage.

Section 2.5 is commentary on the state of knowledge on bond/anchorage of straight bars

with and without transverse pressure.

The final section of chapter 2 reviews work on anchorage by bends and hooks. As only

one publication has been found dealing directly with the strength of bent anchorages at

simple supports this section also considers wider research on bent anchorages. These

include anchorages of the top bars of beams in external columns, anchorages a concrete

webs and blocks etc

Chapter 3 uses test results from the literature to make comparisons between

experimental and calculated bond strengths of straight anchorages without and with

transverse pressure. BS8110 and EC2 are included in both comparisons along with two

relevant research-based approaches in each case. Considering both the mean ratios of

experimental to calculated strengths and the coefficients of variation, it is concluded

that an equation by Darwin et al. is a promising basis for treating anchorages without

transverse pressure although it requires improvements. The picture for anchorages with

transverse pressure is less clear. Nielsens plastic theory is fairly reliable, if a little on

the unsafe side, but it is complicated to use. EC2 is also quite successful.

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No parallel comparisons were made for anchorages with bends or hooks due to the

almost complete lack of relevant test data.

Chapter 4 describes the experimental work undertaken in this research. Tests were made

on sixty five simply supported rectangular beams subjected to central concentrated

loads. The main bars were exposed in one of he shear spans so that the forces acting at

the support could be easily determined.

The anchorages in thirty seven of the beams were straight bars and the main variables

were the covers, the anchorage lengths and the ratios between the transverse pressure

and the bond stress. In most cases the transverse pressures were relatively low as this

condition is not well represented in the published data.

Of the remaining tests, fifteen were of anchorages with 90 bends and thirteen were of

anchorages with 180 hooks. The main variables here were the diameters of the bends

and the side covers. In some tests the bars were debonded up to the centre lines of the

supports, where the bends started.

Most of the tests resulted in anchorage failures characterized by splitting of the concretealong the bars or by bursting/splitting within bends.

Chapter 5 is devoted to the analysis of the results of the present tests together with those

from the literature and the development of equations for predicting anchorage

capacities.

The first step is a modification of Darwins expression for the bond strength of straight

bars without transverse pressure to obtain more rational treatments of the influence of

the ratios of the bond length to the bar size and of the effect of covers and bar spacings.

This is followed by a numerical investigation of the strengths of straight anchorages

with transverse pressure resulting in a bi-linear relationship between the ultimate bond

stress and the transverse pressure. With the pressure equal to zero this gives a bond

strength equal to the modified Darwin value. The gradient of bond stress/transverse

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The final chapter summarises the main conclusions from the work and makes proposals

for future research.

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chapter 1 augest 2009

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