SAMPE Journal - January/February 2021 - 27

The loading and unloading load/elongation lines
matched before and after the 11.3 million load cycles for the CFRP hangers A and B well. The fatigue
tests had only a very minor influence on the stiffness
behavior of the CFRP hangers.
ULTIMATE LOAD AND SAFETY FACTORS OF
CFRP HANGERS
Finally, the MPA University of Stuttgart estimated
the ultimate load of all three hangers (A, B and C).
Table 1 represents the results of these experiments.
The results show, even with this small number of
experiments, quite clear the influence of fretting fatigue due to the " 100 years of train operation " . However, this was after previous research on large series
of small samples not surprising12,13.
Carbo-Link determined the ultimate load of not
pre-damaged CFRP hangers based on FEM calculation with 1800 kN.
The following Schürmann-equitation allows calculating the ultimate load analytically14:

CFRP hanger

Loading history and pre-damage status

Ultimate load
[kN]

A

816,000 + 11,600,000 load cycles and
severe thermal damage

1250

B

11,300,000 load cycles with 20 mrad
misalignment and thermal damage

1330

C

none

1795

Table 1. Ultimate loads of the CFRP hangers A, B and C.

To prove the durability of CFRP was after more than
a quarter century of such applications3 for strengthening tasks in bridge engineering relatively easy. Also all
materials connecting the CFRP hangers with the steel
arch and with the post-tensioned concrete deck must
be sufficiently corrosion-resistant under the atmospheric conditions that exist on the bridge. The influence due to galvanic corrosion can be classified as very
low in the present material pairings, so that no acceleration in corrosion has to be expected.

fE(Fb)= stress exposure value for fibre failure.

E|| [N/mm2]

180'000

Table 2 gives the input data for the Schürmannequation and Table 3 shows the results of the iterative
process to estimate the stress exposure value fE(FB)
and therefore the ultimate load of 1600 kN.
The low number of experiments to estimate
the experimental value of the ultimate load may be
criticised. However, it must be considered that Carbo-Link produced within the last two decades thousands of similar tendons for mechanical and marine
engineering applications. This helped a lot to build
up the needed confidence.
A partial safety factor of 1.5*1.15 = 1.72 on the resistance side compared to the lower limit of the 95%
quantile value of the ultimate load of a hanger without cyclic preloading in relation to the design load
in the ultimate limit state (ULS) and a partial safety factor of 1.5 on the resistance side compared to
the residual strength of a hanger in relation to the
design load of the hangers in the ULS after cyclic
loading were applied. Comprehensive statistic
data in15 was the source to derive the 95% quantile
value of the ultimate load.

E^ [N/mm ]

9'650

2

Table 2. Input data.

n||^ [−]

0.28

n^|| [−]

0.015

n^^ [−]

0.42

F [kN]

fE (Fb)

rinside [mm]

88.5

1300

0.81

routside [mm]

97.0

1400

0.87

width b [mm]

49.8

1500

0.93

msf

1.1

1600

0.99

Ef|| [N/mm2]

294'000

1700

1.05

nf^|| [-]

0.1

1800

1.12

2'130

1900

1.18

R|| [N/mm ]
2

Table 3.
Estimation of fE(Fb).

FURTHER REQUIREMENTS FOR THE
SINGLE CASE APPROVAL
There was a long list of requirements for the single
case approval. In the following section, some will
be discussed.

w w w. s a m p e . o r g

J A N UA R Y/ F E B R UA R Y 2 0 2 1

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SAMPE JOURNAL

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SAMPE Journal - January/February 2021

Table of Contents for the Digital Edition of SAMPE Journal - January/February 2021
