ISO/TR 24813:2026

Technical
Report
ISO/TR 24813
First edition
Fibre reinforced plastics — Analysis
2026-07
of differences between circular-
section tubes and cambered
triangular thin-walled tubes in
three-point bending tests
Plastiques renforcés de fibres — Analyse des différences entre
les tubes à section circulaire et les tubes triangulaires cambrés à
paroi mince dans les essais de flexion en trois points
Reference number
© ISO 2026
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ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Comparison of existing three-point bending test methods . 3
4.1 Principle and existing standards .3
4.2 Specimen requirements .4
4.3 Test apparatus.4
4.4 Experimental conditions .4
4.5 Experimental procedure.5
4.6 Span-thickness ratio (L/h) and span (L) .5
4.7 Bending performance evaluation .6
5 Characteristics of cambered triangular thin-walled tubes . 7
6 Considerations for applying existing methods to cambered triangular thin-walled tubes . 7
Annex A (informative) Theoretical analysis of the cambered triangle thin-walled tubes . 9
Bibliography . 14

iii
Foreword
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iv
Introduction
This document focuses on the following issues and presents discussion and comparative analysis based on
existing three-point bending test methods.
a) It gives an overview of the three-point bending test methods applicable to circular-section tubes made
of fibre-reinforced plastic specified in current standards.
b) In view of the cross-sectional characteristics of cambered triangular thin-walled tubes, an analysis is
conducted on the limitations of the three-point bending test methods in current standards when applied
to cambered triangular thin-walled tubes.
c) Further explore the differences in test setup, apparatus, and evaluation criteria between circular-
section tubes and cambered triangular thin-walled tubes through calculation, analysis, and comparison.

v
Technical Report ISO/TR 24813:2026(en)
Fibre reinforced plastics — Analysis of differences between
circular-section tubes and cambered triangular thin-walled
tubes in three-point bending tests
1 Scope
This document explores and analyses the differences in the three-point bending test between circular-
section tubes and cambered triangular thin-walled tubes, both fabricated from fibre-reinforced plastic, in
view of the asymmetric characteristic of the cross-section of cambered triangular thin-walled tubes.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
cambered triangular
special type of triangle formed by three circular arcs
Note 1 to entry: It is also known as "reuleaux triangle".
Note 2 to entry: Construct circular arcs with the vertices of an equilateral triangle as centres and the length of its
sides as radii, as shown in Figure 1.

Key
r radii of three curved arcs/the side length of an equilateral triangle (mm)
Figure 1 — Schematic diagram of cambered triangular

3.2
cambered triangular thin-walled tube
thin-walled tube made from fibre-reinforced plastic with a cross-section of cambered triangular
Note 1 to entry: Its wall thickness t ranges from 1,0 mm to 2,0 mm and arc length r ranges from 20,0 mm to 60,0 mm.
3.3
loading speed
v
speed of relative movement between the supports and the loading member(s)
3.4
deflection
s
distance through which the top or bottom surface of the test specimen at mid-span has deflected during
flexure from its original position
3.5
support block
assembly of pair of rotatable disc-shaped blocks that support the ends of a specimen
Note 1 to entry: Its inner arc grooves arranged radially to match the outer contour of the specimen.
Note 2 to entry: An example is shown in Figure 2.

Figure 2 — Schematic diagram of support block
3.6
loading block
single rotatable disc-shaped block that applies a vertical load at the mid-span of a specimen
Note 1 to entry: Its inner arc groove arranged radially to match the outer contour of the specimen.
Note 2 to entry: An example is shown in Figure 3.

Figure 3 — Schematic diagram of loading block

4 Comparison of existing three-point bending test methods
4.1 Principle and existing standards
The principle of the three-point bending test involves applying a vertical load at the mid-span of the
specimen, deforming the specimen until fracture or a predetermined deformation value is reached, thereby
calculating the flexural strength and modulus.
The specimen is symmetrically placed on two supports, with the load applied at the mid-span of the
specimen, as illustrated in Figure 4. This configuration generates maximum bending moment and stress at
the centre of the specimen, making it suitable for testing short spans and simple structure.
Key
1 specimen
2 supports
F loading force
h mean specimen thickness
L span
Figure 4 — Schematic diagram of three-point bending test
The three-point bending test methods are specified in standards, such as ISO 14125, IEC 60855-1, IEC 61235,
and ASTM F711. These methods primarily focus on parameters such as flexural strength and flexural
modulus.
ISO 14125 primarily addresses the determination of flexural properties for fibre-reinforced plastic
composites (including laminates, layered materials and continuous fibre-reinforced materials). It specifies
both three-point bending test methods and four-point bending test methods. The three-point method is
more commonly used due to its operational simplicity.
IEC 60855-1 focuses on performance testing of insulating foam-filled tubes and solid rods, where the three-
point bending test is applied to evaluate the bending performance for tubes and rods of a circular cross-
section.
IEC 61235 applies to performance testing of live working insulating hollow tubes for electrical purposes.
The three-point bending test is used to assess their bending resistance.
ASTM F711 specifically targets performance testing of insulating rods and foam-filled tubes made from
fibreglass-reinforced plastic. Building on the three-point bending test method, it introduces requirements
for bending cycles and frequency to evaluate the mechanical ageing performance of specimens.

4.2 Specimen requirements
Specimen preparation strictly adhere to dimensional specifications, quantity requirements, and fabrication
protocols, with significant differences in specimen requirements across existing standards.
According to ISO 14125, test specimens are rectangular in cross-section without rounded edges. The
dimension is adjusted according to the material type, and the span/mean species thickness ratio L/h is 16/1,
20/1 or 40/1, respectively. For example, for discontinuous-fibre-reinforced thermoplastic, the specimen
length is (80 + 10) mm, the outer span is (64 ± 1) mm, the width is (10 ± 0,5) mm, and the thickness is
(4 ± 0,2) mm.
IEC 60855-1 specifies a specimen length of 2 m for solid rods and 2,5 m for foam-filled tubes, with
3 specimens per group.
IEC 61235 classifies specimens based on tube diameter: tubes with a diameter of 19 mm and above are 2,5 m
in length, while tubes with a diameter below 19 mm are 2 m in length, with 3 specimens per group.
ASTM F711 specifies a specimen length of 1,2 m for rods and 2,4 m for tubes, with 3 specimens per group.
4.3 Test apparatus
The test apparatus includes testing machines, measuring instruments, and supporting devices. These
existing standards all specify explicit requirements for the accuracy and functionality of apparatus.
ISO 14125 employs a central loading member with a radius of (5 ± 0,2) mm. When the specimen thickness is
3 mm or less, the support radius is (2 ± 0,2) mm. For specimens with thickness exceeding 3 mm, the support
radius is (5 ± 0,2) mm.
IEC 60855-1, IEC 61235, and ASTM F711 all employ a dual-support consisting of pulleys and apply the force F
through a 50 mm-wide leather or fabric strap. The dimensions of the pulleys are shown in Figure 5.
Dimensions in millimetres
Key
1 specimen
2 pulley
Figure 5 — Support with pulley
4.4 Experimental conditions
ISO 14125 does not specify exact temperature and humidity requirements, but requires conformance with
the atmospheric conditions defined in the relevant material standards.
IEC 60855-1 specifies the following environmental conditions:
— Temperature ranges from 15 °C to 35 °C.
— Relative humidity ranges from 25 % to 75 %.

— Atmospheric conditions conform with IEC 60212.
IEC 61235 further narrows the temperature range to 10 °C to 28 °C, with atmospheric conditions referring
to IEC 60212.
ASTM F711 does not specify temperature and humidity requirements.
4.5 Experimental procedure
The core of the test procedure lies in the loading method, data recording, and repeatability verification.
ISO 14125 requires the selection of an appropriate span-to-thickness ratio and loading speed, followed
by the application of load F at the mid-span of the specimen. Throughout the test, record both the loading
force and corresponding deflection. These data are then used to calculate the flexural strength and flexural
modulus through standardized formulas.
IEC 60855-1 adopts a phased force application methodology.
— A vertical force F is applied at the mid-span through a leather or fabric strap (50 mm ± 2,5 mm wide)
placed on the specimen.
— The force is increased progressively at a loading speed of (200 ± 5) N/s. The deflection is measured after
maintaining the load at 1/3F , 2/3F , and F for 30 s at each stage.
d d d
— The force is gradually reduced, and the residual deflection is measured 1 min after removing load.
— The specimen is rotated by 90°, 180°, and 270°, and the test is repeated at each orientation. The variation
in deflection difference "f " can’t exceed 15 % across all positions.
— The force is gradually increased to F and held for 30 s, during which no failure occurs.
r
— Loading continues until specimen failure, and the actual breaking load is recorded.
NOTE F is initial bending load. f is deflection difference. F is rated bending load.
d r
IEC 61235 follows a similar procedure to IEC 60855-1.
ASTM F711 requires cyclic loading of the specimen (1 000 cycles at 1 to 5 cycles per minute), followed by
inspection for surface degradation (Except for the areas in contact with the pulley bracket).
4.6 Span-thickness ratio (L/h) and span
...