Table Of ContentTHE INSTITUTION OF CIVIL ENGINEERS
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FIBRE REINFORCED MATERIALS =
design & engineering applications
FIBRE REINFORCED
MATERIALS: design &
engineering applications
Proceedings of the conference held in London,
23-2k March 1977
INSTITUTION OF CIVIL ENGINEERS, LONDON, 1977
Conference sponsored by the Joint British Committee for Stress Analysis and organized by
the Institution of Civil Engineers
ORGANIZING COMMITTEE
Professor K. C. Rockey (Chairman)
Mr H. L. Cox
Professor B. P. Hughes
Mr R. E. Beckett
Mr H. Lackenby
PRODUCTION EDITOR
Joyce S. Davis
ISBN: O 7077 0051 O
@ The Institution of Civil Engineers, 1977
All rights, including translation, reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted in any form or by any means
electronic, mechanical, photocopying, recording or otherwise, without the prior written
permission of the Institution of Civil Engineers
^The Institution of Civil Engineers as a body is not responsible for the statements made
or for the opinions expressed in the following pages
Published for the Institution of Civil Engineers by Thomas Telford Ltd at the Institution
of Civil Engineers, 26-34 Old Street, London EC1V 9AD
Contents
SESSION I
1. Optimum design of fibre reinforced annular discs surrounding a circular
hole in a flat plate. E • H. Mansfield
2. The general principles governing the stress analysis of composites.
H. L. Cox
3. Fibres in pneumatic tyre design. M. A. Young
4. Simple methods of stress analysis for highly anisotropic materials.
A. J. M. Spencer
Discussion
SESSION II
5. A theoretical and experimental analysis of a tensile member of anisotropic
material under static and fluctuating loads. G. Hedley and B. S. Owen
6. Stress analysis of lap joints in fibre reinforced composite materials.
R. D. Adams and N. A. Peppiatt
7. The effect of fibre diameter on the strength and stiffness of glass fibre
reinforced polymeric resins. W. F. Thomas
8. Design data for stiffness in short fibre reinforced thermoplastics.
M. W. Darlington and G. R. Smith
Discussion
SESSION III
9. The detection of matrix cracks in fibre reinforced plastics and their
effect on shear strength, R. D. Adams and J. E. Flitcroft
10. Toughness and ductility of fibre reinforced concrete composites in
flexure. R. N. Swamy and C. V. S. K. Rao
11. Environmental fracture toughness testing of plain and reinforced plastics
and other materials, D. G. Ashwell and M. G. Hancock
Discussion
SESSION IV
12. Fibre reinforced cement composite concrete construction employing asbestos
cement as surface reinforcement. N. J. Dave and J. D. Pennington 109
13. The tensile stress/strain curve of brittle matrices reinforced with glass
fibre. V. Laws and M. A. Ali 115
14. Glass fibre reinforced cement and its commercial exploitation.
J. W. Heavens 125
15. Economic fibrous concrete. J. Edgington 129
16. Fibre reinforced concrete in direct tension. B. P. Hughes and
N. I. Fattuhi 141
17. Chopped steel fibres as shear reinforcement in concrete beams.
N. A. Muhidin and P. E. Pegan 149
18. Ultimate strength of reinforced steel fibrous concrete beams.
C. H. Henager 165
Discussion 175
SESSION V
19. Design and testing of some reinforced plastic components. P. Tetlow 185
20. Elastic and creep performance of TEo millimetric glass reinforced
x
plastic waveguide for use on main trunk routes in telecommunication
systems. J. Bradbury, D. J. Greene and A. J. Moore 203
21. Carbon fibre reinforcement of experimental military bridge structures.
F. J. H. Tutt 211
22. Structural evaluation of GRP ship designs. C. S. Smith, M. Anderson
and M. A. Clarke 221
Discussion 241
CLOSING REMARKS. Professor A. M. Neville 245
Paper 1. Optimum design of fibre reinforced annular discs
surrounding a circular hole in a flat plate
EH MANSFIELD, FRS, Royal Aircraft Establishment
A theoretical study is made of the title problem when the plate is subjected to a remote uniform
radial tension and the annular discs are symmetrically disposed about the mid-plane of the plate.
The three-dimensional treatment brings into consideration the shear lag effects normal to the plane
of the plate. Detailed numerical results, including maximum stresses, are presented for discs of
carbon fibre reinforced plastic bonded to plates of aluminium alloy. By considering families of
discs of constant weight it is possible to optimise the disc geometry for any given ratio of plate
thickness/hole diameter.
INTRODUCTION for example, is some 4-5 times that of aluminium
1. In many structures, particularly those in alloys.
the aerospace field, the saving of weight is of
paramount importance. Aircraft structures, for 3. Here we consider an infinite isotropic
example, are generally of stressed skin con elastic plate subjected to a remote uniform
struction in which loads are carried primarily radial tension; the plate contains a circular
by membrane stresses in flat or curved plates. hole whose boundary is reinforced with cylindri-
When such a plate contains a hole there is a cally wound fibre composite annular discs sym
redistribution of stress in the vicinity of the metrically disposed about the mid-plane of the
hole and a consequent weakening of the plate. plate. Such a reinforcement is primarily under
To counteract this the designer reinforces the hoop tension, although the transfer of load from
plate and a considerable body of research lite the plate necessarily introduces shear and
rature is devoted to this problem. There are, transverse stresses and therefore brings into
needless to say, conflicting requirements. play the relatively poor transverse properties
Thus, confining attention to the flat plate, of the composite. The stresses are accordingly
the optimum reinforcement is symmetrically analysed in a three-dimensional manner although,
disposed about the mid-plane so as to avoid the because of the complexities of a rigorous
introduction of bending stresses, but this is analysis, an approximate theory is invoked which
not practicable if the plate forms part of the takes into account the essential features while
aerodynamic surface; similarly, according to omitting the relatively unimportant role of the
classical two-dimensional theory the optimum direct stresses normal to the plane of the plate.
reinforcement generally consists of a compact Of course, because of rotational symmetry in the
member following the (curved) boundary of the applied loading the analysis is mathematically
hole and carrying direct rather than bending only two-dimensional but it is hoped that the
loads, but this compactness can lead to diffi present solution will show the way for solving
culties in transferring the load from the plate the more complex case of an applied shear, for
and, indeed, in transferring load to those parts example, thus yielding by superposition the
of the reinforcement furthermost from the plane solution for more general loadings. The
of the plate; finally, for a given basic stress (structurally) two-dimensional analysis of these
field in an uncut plate it is theoretically and other related problems has been given by
possible by appropriate choice of the hole s h a pe McKenzie and Webber (ref.l).
as well as the degree of edge reinforcement to
design a n e u t r al hole in which the stress field 4. Symbols
is unaffected by the hole, but a different shape Ep Young's modulus in plate
may be prescribed for engineering or,aesthetic Ej, E2, E3 Young's moduli in reinforcement, Ej
considerations. in fibre direction
Gi2> G23 shear moduli in reinforcement
2. There is now renewed interest in this prob h half total thickness of
lem because of the introduction of fibre compo reinforcement
sites, particularly those based on carbon n defined in equation (14)
(CFRP). Such composites show up to maximum r, 8, z cylindrical coordinates, see Fig. 1
advantage when they carry purely tensile or rj, r2 inner and outer radii of
compressive loads for these require a unidirec reinforcement
tional array of fibres. In these applications t thickness of plate
the potential gains are considerable because u radial displacement
the specific strength of unidirectional CFRP, w weight or volume of reinforcement
Fibre reinforced materials. Institution of Civil Enqineers, London, 1977 I
SESSION I
ri/t
"21 12
parameter defined in equation (14) (2)
shear strain
parameter defined in equation (14)
direct strain For practical purposes it is adequate to take
r/r, E* » E,, E* « E, v* * v , etc., but the
2 2 2 J2
vp> v12 Poisson's ratios in plate and
asterisks will be retained as a reminder of the
reinforcement
underlying assumption. Alternatively the
a, T direct and shear stress
ensuing theory can be regarded as rigorous for
£1 weight parameter defined by equations
a material in which E3 = » . •
(21), (22)
* signifies the assumption of zero dis
8. Similarly for the plate, which is treated
placement normal to plate
in the customary two-dimensional manner
Suffix p refers to plate.
e. = [a, - v*a WE* ,
THE STRUCTURE AND MATERIAL PROPERTIES 0
1 \ 1,P P 2,p// p
5. A flat plate of thickness t is subjected (3)
to a uniform radial stress at infinity. The e = /a - v*a, HE* ,
0 0
plate contains a circular hole of radius r\ 2 ^ 2,p p i,y/ p
P
and is reinforced over an annulus from rj to
where, for practical purposes, we may take
T2 by cylindrically wound fibre composite
E* « E , v* « v .
annular discs of thickness h symmetrically P P P P
disposed about the centre line of the plate.
9. Now in the present problem the 1-2-3 axes
are identified with the coordinates 0, r, z
6. The fibre reinforced composite, see Fig.l,
respectively. Furthermore, in terms of the
possesses cylindrical orthotropy with Young's
radial displacement u ,
moduli E], E2, E3 . The corresponding
Poisson's ratios are v\2> v21 > etc. and the
shear moduli are G12 etc. but, because of the u
rotational symmetry in the structure and load
ing, the only relevant shear modulus is G23 . au
e = (4)
In contrast, the plate, which is isotropic with r 3r 9
Young's modulus Ep and Poisson's ratio Vp ,
9u
is treated in the customary two-dimensional
r23 3z
manner which embodies the assumption of an
infinite value for the transverse shear modulus
The stresses in the reinforcement are accord
G23,p- ingly given by
7. Stress-strain relations. In describing the
stress-strain relations for the fibre-reinforced Jl
composite we adopt the standard convention shown ^ T ^r V21 3rj
1 2
in Fig.1 in which the 1-axis is aligned to the
fibre direction while the mutually orthogonal
E2 /au . * u\
axes 2, 3 are respectively in and normal to the , > (5)
plane of the plate. Now because of the geometry (1 - v^v*,) \dv + V12 rj
of the structure and the planar nature of the
9u
applied loading, stresses normal to the plane = G
of the plate do not play a significant role. rz 23 3z
This feature can be turned to some advantage in
while in the plate,
the subsequent analysis by making the common
engineering assumption that £3 is zero or,
u 3u \
preferably, some constant chosen to minimise
t-Z ) ,
any deviation from a rigorous three-dimensional JE. + v*
solution. The stress-strain relations under r p 3r J 9
such conditions can be expressed in the form > (6)
1
E* u \
°1 °2 P rj
el = v5i E* y
EQUILIBRIUM CONDITIONS
°2 °1
(i) 10. In the fibre-reinforced composite the equa
e2 -
tion of equilibrium is
T23
Y23 (7)
G23 -> 87 (wr»
where, from the Reciprocal Theorem, which can be expressed in terms of the radial
displacement u as
2
