Design of column strengthening with CF sheets - Strengthening of Concrete Structures with Adhesively Bonded Reinforcement - page 102

members, the researchers varied the slenderness, or rather the eccentricity of the axial
load, over a range roughly coinciding with the applicability of the DAfStb guideline
[1, 2]. The modification of Jiang's approach consisted of using the simplified
stress strain curve of Figure 7.6 for the design. Good agreement between model

and tests has been observed; the influence of the individual parameters was also
properly allowed for [56].

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7.5 Creep
Strengthening measures that increase the load-carrying capacity of compression mem-
bers by means of a wrapping of CF sheet do not increase the cross-section of the
member. This inevitably leads to higher stresses in the concrete as a result of the larger
actions. The work of Rüsch [138] over 50 years ago, likewise the later speci c
investigations of Stöckl [139] and other researchers, revealed a disproportionate increase
in strain in connection with higher long-term loads exceeding about 40% of the uniaxial
mean short-term compressive strength of the concrete. A linear relationship between the
elastic deformation and the limit value for creep deformation ε cc ( is

generally assumed for lower creep-inducing stresses, which is expressed by the final
creep coef cient φ (

∞

, t 0 ) at time t = ∞

∞

, t 0 ).

? σ c
E c

ε cc

∞ ; t 0

φ ∞ ; t 0 (7.25)

where:
σ c creep-inducing longitudinal compressive stress
E c modulus of elasticity of concrete subjected to compression, which according to
DIN EN 1992-1-1 [20, 21] is to be used as a tangent modulus.
With a view to avoiding disproportionate creep deformations, DIN EN 1992-1-1
[20, 21] specifies the following limit for concrete compressive stresses at the service-
ability limit state:
σ c 0 : 45 ? f ck (7.26)

The disproportionate non-linear creep as a result of creep-inducing compressive stresses
beyond this limit stress is described in DIN EN 1992-1-1 numerically using the
following equation, which can be used to determine a modi ed final creep coef cient
φ nl (

∞

, t 0 ):

? e α σ ?

k σ 0 : 45

φ nl

∞ ; t 0

φ ∞ ; t 0 (7.27)

where:
φ ( , t 0 ) final creep coefficient for linear creep

α σ stress intensity factor
k σ stress-strength ratio of concrete: k σ = σ c / f ck ( t 0 )
f ck ( t 0 ) characteristic concrete compressive stress at the time of loading.
DIN EN 1992-1-1 [20, 21] specifies a value of 1.5 for the stress intensity factor

∞

α σ .